FUNDAMENTAL ASPECTS OF PHOTOSENSITIZATION. INTERCOMBINATIONS IN MOLECULES

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP81-01043R000200200012-0
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 134
• Document Creation Date: December 22, 2016
• Document Release Date: August 9, 2010
• Sequence Number: 12
• Publication Date: September 15, 1956
• Content Type: REPORT

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Technical Report No. 1
to the Chemistry Division U. S. Air Force Office of Scientific Researc'
Contract No. AF 18(600)-.678
Project No. AFOSR Chem 20-4
FUNDAMENTAL ASPECTS OF PHOT OSENS IT IZAT ION.
INTERC OMBINATIONS IN MOLECULES
Department of Chemistry, Florida State University
Tallahassee, Florida
September 15, 1956
Project Supervis or
M. Kasha
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Technical Report No. 1, to the U. S. Air Force Office of
Scientific Research, Air Research and Development Command.
Contract No. AF l8(600)-678 September 15, 1956
FUNDAMENTAL ASPECTS OF PHOT OSENS IT IZAT I ON. INTERC OMBINAT I ONS
IN MOLECULES.
Department of Chemistry, Florida State University, Tallahassee
Table of Contents
1. Molecular Electronic Spectroscopy. Spin Intercombinations
in Molecules, M. Kasha and S. P. McGlynn.
2. Interpretation of the Lowest Frequency Electronic Absorption
Bands of Inorganic Molecules of Type XOZ ) as Y a n-,fl'
Transitions, S. P. McGlynn and M. Kasha.
3. On the Application of the Molecular Orbital Method to the
Spectra of Substituted Aromatic Hydrocarbons, L. Goodman,
I. G. Ross and H. Shull.
4. Theory of Solvent Effects on Molecular Electronic Spectra.
Frequency Shifts, E. G. McRae.
Distribution List.
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Prepared for Annual Review of Physical Chemistry,
Vol. 7, 1956
MOLECULAR ELECTRONIC SPECTROSCOPY.
SPIN INTERC OMBINATIONS IN MOLECULES(1,2)
By M. Kasha and S. P. McGlynn
Department of Chemistry, Florida State University
Tallahassee, Florida
This review covers selected topics of research published
in molecular electronic spectroscopy in 1955? The topics
in this general category which are undergoing rapid develop-
ment at present are (a) spectra of molecular complexes,
(b) spectroscopy of molecules in crystals, including polariza-
tions and assignments, (c) study of spin-intercombinations
in molecules, (d) study of transitions of n,17' type, (e)
intermolecular energy transfer; and, extending the general
category, (f) spectra of transition metal ions in various
environments.
From this broad range of topics this review will ab-
stract but one: we shall review the topic S pin-Intercombina-
Lions in Molecules.
(1) The survey of the literature pertaining to this review was
concluded in December 1955.
(2) The writing of this review was done as part of the work
related to a research program supported by the Office of
Scientific Research, U. S. AIR FORCE, under a contract with
the Florida State University.
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Our method will be the setting of a perspective by a
coverage of key papers on this topic from past literature.
Integrated with this treatment will be all pertinent papers
published in 1955. This presentation should have the ad-
vantage of a certain unity, although at the same time failing
to catalog the many papers published in unrelated fields.
The yearly service performed by the Annual Reports, of the
Chemical Society (London) cannot be overlooked, however, and
rnrri~rwrr~r ~.~~ ~rr,rr~r~
makes up for the latter deficiency. As the present method
of review is extended, most important papers will have been
surveyed in a brief cycle of years.
The topic we have selected is greatly in need of review.
In the literature of about ten years ago, very little if any
mention was made of the subject of spin-orbital interaction
in molecules. The number of papers on this and related
topics has increased rapidly in recent years, to the point
where they now number well over one hundred. It thus appears
worthwhile to organize and examine what has been done thus
far in these subjects, and to cast the research of the past
year against this background.
GENERAL BACKGROUND
The full development of this field of research came late
in the history of molecular spectroscopy, and in some respects
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in an unexpected way. The theory of spin-orbital coupling
and its application to the electronic spectra of atoms and
diatomic molecules had been known since the early years of
the development of quantum mechanics. It seemed natural to
suppose with Sponer and Teller (1):
tAs in the case of atoms we have, in first approx-
imation9 the selection rule that only states of the
same multiplicity combine with each other. Inter-
combinations occur with appreciable intensity only
if the molecule contains some heavier atoms.t
Developments since 1944 have shown that, although high-'Z
atoms have their expected effect, frequently spin-intercom-
binations occur with great intensity even in molecules
composed of atoms of atomic number 8 or less. Thus, a type
of transition which usually is neglected in atomic spectroscopy
except in heavy atom cases, assumes great importance in
molecular spectroscopy, and dominating importance in the light
emission properties of most molecules. As we shall see, this
extraordinary result is due ePtirely to the important role
played by radiationless transitions in complex molecule
spectroscopy. As a consequence of these, the lowest triplet
states of most molecules are readily populated upon light
absorption which excites the allowed singlet states (ground
singlet states assumed thruout) . On the other hand, the
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radiative intercornbinatlonal transition probabilities are
extremely small in (light atom) complex molecules, just as in
atomic and diatomic cases. The transition probability for
emission of light is measured by the decay constant
(reciprocal mean lifetime), so that a high intensity (quantum
efficiency) of emission need not be incompatible with a
highly forbidden transition.
The fact that complex molecules emit phosphorescence at
low temperatures was known since the pre-twentieth-century
observations of Wiedemann (2) on solid solutions and Dewar (3)
on crystals. The apparent general requirement of a solid
state medium was puzzling, if not distasteful to the spec-
troscopist nurtured on unperturbed gaseous molecule spectra.
There were numerous attempts to interpret the spectra on the
basis of complicated solid state interactions, Although
Lewis, Lipkin, and Magel (4) and Terenin (5) speculated on
the possibility that the phosphorescence emission might be
triplet -~ singlet in nature, alternative hypotheses were
considered equally suitable. Finally, the general identifi-
cation of the phosphorescence emission of polyatomic or
cc)mplex molecules as a triplet -- singlet emission was made
in 1911+ by Lewis and Kasha (6). At the time of publication
of this paper the theoretical justification for the identifi-
cation was not very secure, nor was the apparent incompati-
bility with the behavior of atomic and diatomic systems fully
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recognized. Nevertheless, the paper catalyzed almost
feverish research activity in this field, and it is appro-
priate to acknowledge a debt of gratitude owed by spec-
troscopists to G. N. Lewis for his contribution to this
general advance in spectral accessibility. Before 1944 the
interest in intercombinational transitions in molecules was
severely limited by the lack of experimental information.
Subsequently, much work has been published relating to
spin-intercombinations: on the triplet .-' singlet emissions
of numerous molecules, the very weak singlet - triplet
absorption spectra, the transient triplet --~ triplet absorp-
tion spectra, the study of spin-orbital perturbations --
intramolecular and intermolecular -- introduced by high-.Z
and paramagnetic atoms. These researches have enhanced con-
siderably the understanding of the nature of radiationless
transitions in complex molecules, and of the application of
spin-orbital coupling theory to molecular cases. Applications
are following close on the heels of this spectroscopic work.
These include the interpretation of fluorescence quenching,
photochemical reactions, photochr omism and thermochromism,
and perhaps most important of all, the theory of chemical
reactivity.
Previous reviews touching on this general topic have
been rather fragmentary, but are useful sources: Kasha (7),
Forster (8), Kasha (9), and Craig (10).
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THEORETICAL COMMENTARY
EJ.ectric dipole and magnetic dipole transitions between
pure singlet and pure triplet states are forbidden rigorously
on account of the orthogonality of the spin wave-functions.
The intervention of spin-orbital coupling brings about a
mixing of singlet and triplet states, destroying their purity
9
and permitting intercombinations between nominal singlet and
triplet states to be observed. Great interest attaches
therefore, to the form of the spin-orbital Hamiltonian, since
only by a thorough knowledge of its form and action can the
spectroscopist realize fully his opportunities for observa-
tion of intercombinations.
The spin-orbital interaction operator in its generalized
form is given by Dirac (11) : cf. Mott and Sneddon (12). The
spin-orbital interaction part of the total Hamiltonian is
introduced as a relativistic correction. The strongest con-
tribution to spin-orbital interaction occurs when the electron
comes closest the nucleus, and is travelling with relati-
vistic velocities. Consequently, insofar as spin-orbital
interaction influences chemical behavior (cf. below) it may
a Y
be said that in those cases there is evidenced a relativistic
chemical effect.
How the symmetry of the spin-orbital interaction
operator may be deduced for any symmetry of the nuclear
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potential, V, has been shown by Weissman (13) and Mizushima
and Koide (14). However, the simplest discussion is obtained
by allowing V to have spherical symmetry, whereupon the
properties of the operator become evident immediately. This
case is applicable strictly only to atoms (see Kramers (15)),
but it has been applied to molecules as an approximation by
McClure (16) (vide infra). It is found that the spin-orbital
interaction operator may be separated into sums containing
orbital and spin factors which are separately symmetric or
antisymmetric under electron interchange. The antisymmetric
spin factors lead to mixing of singlet and triplet states,
and the symmetric spin factors lead to multiplet splitting.
The orbital factors determine the orbital types of the states
which may mix (16)(17). The validity of the separation of the
orbital and spin parts of the Hamiltonian has been discussed
by Weissman (13) and Ross (18).
The spin-orbital interaction operator involves the
gradient of the potential. This will be largest in the
proximity of the nuclei of the atoms on which the (molecular)
orbitals are centered, and particularly large close to the
nucleus of highest atomic number (Z) in the molecule. In
the special case of one high-Z atom in a molecule otherwise
composed of low-'Z atoms, e.g., thiophene, bromobenzene, etc.,
where most of the contribution to spin-orbital coupling in
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a molecular electronic orbital is derived from a single atom,
the assumption of a spherical potential as made by McClure
(16) is not an unreasonable one. Furthermore, since most of
the contribution to the spin-orbital interaction derives
from the electron's orbital motion nearest the nucleus, the
form of the orbital wavefunction in this vicinity will be of
unusual importance. In ordinary valence and spectroscopic
calculations the form of the orbital wavefunction near the
nucleus is comparatively less important, Consequently9 the
use of Slater-type orbital wavefunctions in calculations of
spin-orbital interaction may be open to question. Both of
the published calculations (14)(17) use Slater orbitals,
For a hydrogenic atom, the transition probability for
spin-intercombinations has an 8th power dependence (the matrix
elements of the spin-orbital interaction depending on the
4th power) on Z, the atomic number (see Condon and Shortley
(19))? A strong Z dependence is found also in molecular
spin-intercombinations, as shown in numerous experimental
results to be cited below.
In the application of the theory of spin-orbital inter-
action to the case of benzene, the result is obtained that
the observed mean lifetimes for the triplet ~-~ singlet
emission are up to 1000 times greater than those calculated
from the atomic spin-orbital coupling factors (McClure (20)).
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McClure (17) has shown that this may arise from a fortuitous
cancellation, on symmetry grounds, of the matrix elements for
spin-orbital interaction in the planar molecule. On the
other hand, Mizushima and Koide (14) have shown that D"- T+
interaction would be sufficient to account for the observed
long intercombinational lifetime in benzene. In order to
decide which of the theories is applicable to benzene,
polarization studies of the phosphorescence emission would be
necessary. Thus far, such a study has not been made.
PHOT OMAGNET ISM STUDIES
Before proceeding to spectroscopic observations, it is
worthwhile to review the experimental work on the paramagnetic
susceptibility of the phosphorescent, or lowest triplet,
state of complex molecules, At the time that the phospho-
rescence emission was interpreted as a triplet - singlet
emission, such measurements seemed an important and necessary
proof of the interpretation. Moreover, here was a delicious
opportunity, since near-saturation of the excited state could
be obtained under certain conditions (see (~+) for example).
Subsequent spectroscopic studies, based on the nature of spin-
orbital interactions, have made direct measurements of para-
magnetic susceptibility unnecessary for assignment of state
multiplicity. Nevertheless, it i5 an interesting chapter in
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the development of the field, and new work on this phase has
appeared very recently.
Lewis and Calvin (21) carried out exploratory experiments
on the paramagnetism of a dyestuff excited to its phospho-
rescent state. This work was followed by a thorough quanti-
tative study by Lewis, Calvin, and Kasha (22). For acid
fluorescein dye a satisfactory measurement of the paramagnetic
susceptibility was obtained, confirming the triplet assign-
ment for the phosphorescent state.
It is interesting to note that empirical photomagnetic
experiments were carried out earlier by Frohlich, S zalay,
and Szor (23). These authors investigated the behavior of
dyestuffs in solid solutions, in the form of plates, suspended
in a magnetic field. A photomagnetic effect was noted.
Yamamoto (24) also carried out a series of magnetic dichroism
researches on solid solutions of dyestuffs, upon illumination.
His results confirm the photomagnetism results of Lewis,
Calvin, and Kasha (22).
Porter (25) has commented on the need for further para.-
magnetism studies of the phosphorescent state; he was unaware
of the researches described immediately above.
Direct measurements of paramagnetic susceptibility have
been extended by Evans (26) recently to include fluorescein
dye, 1-hydroxy-2-naphthoic acid, and triphenylene. Using an
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apparatus different from the Theorell balance used by Lewis,
Calvin, and Kasha (22), Evans not only observed positive
results in each case, but also was able to follow the decay
of paramagnetic susceptibility with time upon extinction of
the exciting light. The time constants for this decay, which
was observed to be exponential, coincided with the decay
constants for the phosphorescence emission. This provides
proof that the paramagnetism arises from excited triplet states
which decay spontaneously, and not, e.g., from radicals dis-
appearing by a bimolecular recombination process,
RADIATIONLESS TRANSITIONS: INTERSYSTEM CROSSING
In molecular electronic spectroscopy internal conversion
may be defined as the rapid radiationless combination of
electronic states of like multiplicity. Experience indicates
that, in general, internal conversion takes place between
excited levels, but not between the lowest excited level and
the ground level This evidence is summarized in the rule (9):
The emitting level of a given multiplicity is the lowest
excited level of that multiplicity. This behavior depends on
the relative spacing of the electronic levels, and on the
necessity for removal of the excess vibrational energy by
intermolecular collisions. In solid solution experiments at
77?K only the behavior of na hthacene (2
p 7) and azulene (28)
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have provided anomalies, both of these also having exceptional
energy spacings. Theoretical studies relating to the general
problem of rad iationless transitions in molecules have been
carried out by Teller (29), Duschinsky (30), and Davydov (31).
Recently, crystal spectroscopic studies at 20? and
have provided many further examples of the breakdown of normal
internal conversion. These examples are particularly interest-
ing since they involve molecules which behave normally at
77?K in solid solution emission studies. Evidently, at very
low temperatures, the intermolecular collision process is
inhibited to the point where vibrational energy cannot be
carried off effectively. Hence, essentially "resonance"
emission may occur. This technique is rich in possibilities
for resolution of superposed electronic transitions in mole-
cules. Such observations have been reported recently in a
series of exploratory researches on molecular crystals by
Pesteil et al (32,33,34,35,36,37,38,39) Of particular
interest is their report of two triplet - singlet emissions
in benzene: one at 30574 cm , which they assign as
B
1 -+ lA y and one at 38724 cm, which they assign as
u is
Eu -- ~ A1g. The lowest triplet of benzene is well known from
earlier work (6,1+0,)+l,5)+,55). The second triplet has been
predicted by theory (see Roothaan and Mulliken (42)) and it
has been reported by Pesteil to be evident in absorption in
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the spectrum of crystalline benzene at 83?K (43,44) ( see
footnote on p. 230, rev. (10), however). The observations of
Ham (45), which were described as evidence for the second
triplet in benzene, have been criticized by Bayliss and Hulme
(46). Further examples of the apparent breakdown of internal
conversion have been found recently by Sidman and McClure (47)
in their very thorough study of the absorption and emission
spectra of solid crystal solutions biacetyl and biacetyl-d-6
at 20?K and 1+?K.
A further anomaly of low temperature crystal spectroscopy
was noted by Pesteil et al (see above), in which apparently
at the lowest temperatures, the electronic transition is dis-
placed to lower frequencies by a vibrational quantum, compared
with higher temperature spectra. We shall not elaborate on
this since it has no direct bearing on internal conversion.
Intersystemcrossing has been defined as the spin-
orbital coupling dependent internal conversion in molecules
(9). The intensity of the phosphorescence emission (in terms
of quantum efficiency, i.e., number of T -. S quanta emitted
per number of S' ~- S quanta absorbed) does not measure the
probability of T --~ S emission, but is determined by the ratio
of the transition probabilities for the (radiationless)
intersystem crossing (S' - T) and the spontaneous fluorescence
(S' - S). (It is assumed here that S' is an excited singlet
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state lying above the lowest triplet state T, and that most
of the triplet excitation occurs by intersystem crossing from
this singlet). The intersystem crossing ratio x =
therefore measures this transition probability ratio (Kasha (9);
see McClure (20), especially Table vi), and states the relative
quantum efficiency for phosphorescence and fluorescence. If
the transition probability for fluorescence becomes too small,
the lowest triplet state may become the only emitting state
in the molecule. This situation is especially common where the
lowest singlet-singlet transition is of n,11 type (9).
Since intersystem crossing is spin-orbital coupling
dependent, perturbation effects involving the electric field
of high-Z nuclei or the magnetic field of paramagnetic atoms
should be observable, Kasha (9) has observed a strong Z
dependence of the r /r ratio in halogenated aromatic
molecules (cf. Yuster and Weissman (48)). In certain organo-
metallic chelates involving rare earth ions, Yuster and
Weissman (48) have found the same effect, and in a case where
the ion was paramagnetic, an especially strong perturbation
was noted. In all such studies the main effect observed is a
great increase in the p/ ratio, while the total quantum
efficiency remains essentially constant.
Recently Becker and Kasha (49, 50) have made use of spin-
orbital perturbation effects to establish the lowest triplet
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state of the chlorophyll molecule. A porphyrin molecule,
phthallocyanine, and several chlorophyll species were studied
each without a metallic atom, and containing both heavy and
paramagnetic atoms. The effects observed were exactly parallel
to the predictions of spin-orbital coupling theory. The lowest
triplet levels of the chlorophylls and the porphyrin studied
were thus established with certainty.
Porter and Windsor (51) (see also Porter (25)) have
applied the synchronized flash (flash photolysis) spectro-
scope c method to the study of triplet states in fluid solutions.
Their kinetic analysis has given important new information con-
cerning the intersystem crossings involved. However, at the
same time, further problems of interpretation have arisen,
causing these authors to emphasize the need for a critical
examination of the triplet state interpretation of the phos-
phorescent state. At this juncture, there seems to be no doubt
concerning the validity of the triplet state interpretation.
However9 the flash technique undoubtedly offers a valuable
method of study of triplet state excitations, depopulations,
and reactions.
TRIPLET STATES : TRIPLET -~- SINGLET EMISSION STUDIES
Lewis and Kasha (6) gave spectroscopic data on the phos-
phorescence emission spectra of 89 molecules, We have already
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discussed their interpretation of these as lowest triplet -
singlet emissions (see General Background section, above).
of the molecules studied, only the results given for stilbene
and ethylene and its halogen derivatives are now known to be
wrong (see Potts, in section on Singlet -p Triplet Absorption
Spectra); for the remaining cases the emissions are authentic,
Kasha (7) presented a discussion of the function of the rigid
glass solution, and elaborated on the mechanism of excitation
of the lowest triplet state; further triplet - singlet
emission data were reported (e.g., hexachlorobenzene and
phenanthrene). One general conclusion drawn from this earlier
work is that the viscous or rigid medium used as a solvent
serves mainly to inhibit diffusion controlled quenching of
the triplet state. On the other hand, Lewis and Kasha (52)
stressed the fact that if the lowest triplet state intrinsic
mean lifetime were short enough, triplet -~ singlet emission
would be observable even in the liquid and gaseous state.
Porter and Windsor (Si) in the papers already referred to
have made studies recently on the lowest triplet state in
liquid solutions (see Radiationless Transition section above,
and section on Triplet - Triplet Absorption Spectra, below),
although under their conditions triplet .- singlet emissions
could not be observed directly, The studies of luminescence
spectra of vapors, by Robinson (53), involve triplet - singlet
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emissions. The case of biacetyl vapor luminescence is
another well known example (52; see also 47) of a strong
triplet .-4 singlet emission of a complex molecule in the vapor
state. In such cases, the inherent short lifetime allows
emission to occur without complete quenching. In other cases,
where the triplet -- singlet lifetime is relatively long
(see below), only singlet .~- singlet emission is observed in
the vapor luminescence spectrum.
More detailed studies of triplet -' singlet emission
spectra have been made subsequent to the research of Lewis
and Kasha. Thus, the triplet -- singlet emission spectrum
of benzene was carefully re-studied and a vibrational analysis
carried out by Shull (}+0); parallel studies on benzene have
been made by Dikun and Sveshnikov (1+1, 51+, 55). Pesteil
et al (33, 39) have recently studied the triplet -)' singlet
emission in crystalline benzene, and also crystalline hexa-
chlorobenzene (37, 3$), at very low temperatures. Some of
their results already have been mentioned in the section on
Radiationless Transitions. The naphthalene triplet -
singlet emission was restudied by Ferguson, Iredale, and
Taylor (56), who gave vibrational analyses for naphthalene,
and monosubstituted and disubstituted naphthalenes. In the
case of anthracene, Reid (57) presented indirect evidence
against the lowest triplet level reported by Lewis and
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Kasha (6). Padhye, McGlynn, and Kasha (58) have restudied
the lowest triplet level in anthracene and have confirmed the
level reported by Lewis and Kasha. Triplet - singlet
emission spectra of anthracene and several substituted anthra-
cenes, singlet -.. triplet absorption spectra, and solvent-
perturbation experiments (see below) were used to confirm the
assignment. McGlynn, Padhye, and Kasha (59) presented a
correlation diagram for the lowest triplet levels for the
first four linear polyacenes. Craig (10) has discussed the
symmetry assignment of electronic levels in this series.
Besides the polyacene hydrocarbons described above,
phosphorescence spectra were reported for various pyrene
hydrocarbons by Ilina and Shpolskii (60) and for coronene and
1,2-benzoperylene by Bowen and Brocklehurst (61). McClure (20)
had previously reported frequency data on triplet -~ singlet
transitions of pyrene, coronene, and other hydrocarbons not
studied by Lewis and Kasha. Neporent and Inyushin (62)
reported phosphorescence and fluorescence spectra of phthalliM
mide and eleven derivatives.
Becker and Kasha (50) published spectroscopic data on
the lowest triplet -) singlet transitions in several chloro-
phylls and porphyrins. Their observations are complemented
by the studies of Livingston (63), who has used the synchronized
flash technique to study the lowest triplet state of the
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chlorophylls. The observations using this technique yield
triplet ..) triplet absorption spectra, and also lifetimes of
the triplet state under the experimental conditions used.
The research of Witt (64) parallels that of Livingston.
The transition probability for triplet -) singlet emission
rr.n.~rrrrr .~~
is measured by the decay constant, or the reciprocal of the
intrinsic mean lifetime. Numerous studies of the mean life-
time of the lowest triplet state of molecules are now pub-
lished. Some discretion must be exercised in using the
published data directly, since only the intrinsic mean life-
time in the absence of quenching is a true measure of the
transition probability. Probably, lifetimes determined for
dilute solutions of a molecule in rigid glass solvents
approach the intrinsic lifetimes, according to quantum
efficiency measurements (see below). McClure (20) published
the first detailed study of triplet -- singlet lifetimes in
complex molecules. His measurements provided proof of the
intercombinational character of the emission, thru his demon-
stration of the Z.-effect on the emission lifetime in haloge-
nated hydrocarbons. His correlation of the mean lifetimes
with spin-orbital coupling factors for the substituting atoms
gave semi-quantitative agreement. Similar observations were
made by Yuster and Weissman (48) on the dibenz oylmethane
derivatives of trivalent metal ions, including some rare earth
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Ions. Kaskan and Duncan (65) made a study of the triplet 4
singlet emission lifetimes of ketones in the gaseous state.
An empirical study of phosphorescence lifetimes was made by
Sveshnikov and Petrov (66), who studied the influence of the
medium on the lifetimes. A comprehensive empirical study of
phosphorescence lifetimes was published by Dikun, Petrov, and
Sveshnikov (67) , with data on numerous mono, di, and tri-
substituted hydrocarbons. Similar empirical phosphorescence
lifetime studies were made by Pyatnitskii (68). The study
of triplet 4 triplet absorption spectra (see pertinent
section, below) affords independent information on lowest
triplet state lifetimes, although in fluid solvents the
quenching effect markedly shortens the observed lifetime.
Thus, Craig and Ross (69), Porter and Windsor (51),
Livingston (63) and Porter and Wright (70) have determined
lifetimes by following the decay of triplet -. triplet
absorption. Apparatus for phosphorescence lifetime determina-
a
tion has been described recently by Skarsvag (71) and van
Roggen and Vroom (72).
Studies of quenching of phosphorescence of organic mole-
cules have been published recently by Kato and Koizumi (73)
and Kato, Kimura, and Koizumi (7+), Measurements of absolute
yield of phosphorescence were reported earlier by Gilmore,
Gibson, and McClure (75).
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In this paragraph we shall itemize theoretical papers
having special reference to intercombinations and triplet
states in molecules; papers on calculation of electronic
levels in which triplet states are incidental will not be
covered. In the section Theoretical Commentary reference has
already been made to the paper on selection rules for inter-
combinations by McClure (16) and the paper on the vector
model for spin-orbital interaction by Weissman (13). The
papers on calculation of matrix elements for spin-orbital
coupling in benzene by McClure (17) and Mizushima and Koide
(l)+) also were alluded to briefly. Transition probability
calculations for spin-orbital interaction in atoms had been
published by King and Van Vleck ( 76) . Barne s , Bray , and
Harrick (77) reported briefly on spin-orbital and spin-spin
interaction parameters for molecular hydrogen, as derived
from radiofrequency spectroscopic measurements. Herman (78)
considered symmetry selection rules involved in molecular
intercombinations. This paper seems to suffer from in-
accurate translation and is otherwise difficult to evaluate.
Kovner and Sverdlov (79) have described a simple method for
calculation of triplet states by the Valence Bond method
(Ruiner diagrams). Longuet -Higgins and Pople (80) have
studied excited states of odd alternant hydrocarbon radicals
and ions, and relate the singlet-triplet separation of the
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ion to the separation of the two low-lying doublets of the
radical (cf. Longuet-Higgins and Murrell (81)). Merrifield
(82) has compared matrix elements for excitons of singlet and
triplet multiplicity.
SINGLET .-~ TRIPLET ABSORPTION SPECTRA
Radiative spin-intercombinations are highly forbidden
in complex molecules just as in the case of atoms. Conse-
quently, singlet ,-~ triplet absorption intensities are ex-
tremely low, and triplet -. singlet emission lifetimes
correspondingly long. A factor of about lob relates the
corresponding singlet ..- singlet transition probabilities.
Because of the very low transition probabilities for
the spin-intercombination absorption case, considerable
difficulty is experienced in observing singlet .. triplet
electronic absorption bands, and distinguishing them from
bands due to vibrational harmonics and impurities. This will
be evident in the examples which f ollowe
Lewis and Kasha (52) carried out the first systematic
search for singlet -- triplet absorption bands in molecules.
They made use of the classical relation between absorption
and emission probabilities (cf. reference in Kasha (9)) as a
guide to amenable cases. Their work suffered from their
failure to realize the importance of the Z-effect on
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intercombinational transition probabil ities. C onsequently,
only the singlet -y~ triplet absorption band reported for
benzene is authentic; the absorption bands for the remaining
molecules investigated by them have been shown subsequently
to be singlet - singlet in nature. McClure, Blake, and
Hanst (83) made use of the Z-effect in intercombinations in
their study of singlet .- triplet absorption bands of haloge-
nated benzenes and naphthalenes.
The case of benzene deserves special mention as the
singlet '4 triplet absorption band has been investigated by
numerous researchers. Sklar (84) first reported observing
this band, although the absorption curve was not published.
Lewis and Kasha (52) reported a detailed spectrum observed
for 10 cm, of liquid benzene. The correspondence with the
previously observed triplet ..~- singlet emission was used as
a criterion of authenticity. Also they demonstrated that the
vibrational overtones, although observable even in the visible
region, could not account for the observed ultraviolet bands
owing to the rapid diminution of the intensity of overtones
with frequency. Pitts (85) reinvestigated the same band.
McClure, Blake, and Hanst (83) gave additional proof of its
intercombinati.onal character by demonstrating its intensifi-
cation with increasing Z of substituent atoms, Shibata,
Kushida, and Mori (86), on the other hand, reported weak
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absorption bands for benzene in the visible region. They
designated these as singlet - triplet, whereas they were
identified previously by Lewis and Kasha (52) as merely
vibrational harmonics. (See reference (10), footnote on p. 230;
and reference (59), footnote 12), Cheshko (87) believed the
bands reported for benzene by Lewis and Kasha C52) to be due
to impurities; however, the data he published on his research
merely indicates that his benzene was never pure enough to
observe the bands.
In the case of pyridine, Reid (88) reported in detail
on two weak transitions in the ultraviolet region. Recently
Brealey (89) has shown that both of these bands are due to
a very small impurity of pyrazine in pyridine.
In the ethylene molecule Snow and Allsopp (90) made an
early report on a weak absorption band near 2100 A, which
they assigned as singlet .- triplet. Moffitt (91) supported
their assignment with theoretical calculations. Thus, this
assignment of Snow and Allsopp is evidently the first
authenticated singlet - triplet observation in complex mole-
cules. These bands were studied further by Carr and Stucklen
(92), Picket, Muntz, and McPherson (93), and recently by
Potts (94). Lewis and Kasha (6) had reported phosphorescence
emission in halogenated ethylenes near 4000 A. Potts searched
for phosphorescence in tetramethylethylene and found none.
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..~5_
From the energy and the lifetime point of view, the phospho-
rescences reported by Lewis and Kasha for ethylenes do not
appear to be authentic.
Sidman and McClure (i-7) have recently observed weak
absorption bands in biacet,yl at low temperature, which they
assign as the lowest singlet .* triplet absorption. Padhye
and Desai (l0Lf) have reported on the lowest singlet .. triplet
absorption band in th_ iophene.
The difficulties which occur in the discrimination of
very weak absorption bands due to impurities and vibrational
harmonics, from those due to authentic spin`-intercombinations
can be overcome in applicable cases by the use of the solvent.
perturbation technique (Kasha (95) ; see section on Inter-
molecular Spin-Orbital Perturbations).
TRIPLET -+ TRIPLET ABSORPTION SPECTRA
Triplet .-- triplet absorption bands are of course not
intercombinational in nature, but are discussed here because
of their dependence on triplet excitation. The bands are
inherently medium strong to intense, since the only selection
rule would involve orbital symmetry. Where favorable popula-
tion of the lowest triplet is attainable, the transient
absorption originating in this metastable state is readily
observed.
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w ~ 6 r
Early in the research conducted by Lewis on the phospho-
rescence state of molecules, observations on transient
absorption spectra were recorded and identified as "absorption
spectra of the phosphorescent state." Today these are
recognized as triplet -- triplet absorption spectra, and are
essential for the location of upper triplet levels in
molecules.
Lewis, Lipkin, and Magel (~+) published data on a triplet
.-. triplet absorption band of the acid fluorescein dye, and
Lewis and Lipkin (96) observed a triplet -~ triplet absorp-
tion band in diphenylamine. Clar (97) reported observations
on a triplet -' triplet absorption band in triphenylene.
Sveshnikov and D:ikun (98) reported difficulty in reproducing
Lewis, Lipkin, and Magel's result on acid fluorescein.
McClure (99) made a general study of triplet --triplet
absorption spectra in complex molecules. Spectra and
frequencies were reported for ten molecules, mainly aromatic
hydrocarbons and simple derivatives. Craig and Ross (69)
extended triplet -- triplet absorption studies still farther,
giving data on various aromatic hydrocarbons and multiple
ring nitrogen heterocyclics. Their determination of lowest
triplet state lifetimes have been referred to previously.
Craig and Ross also noted photodecomposition effects, which
constitute an interference in the physical absorption work.
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All of the above observations have been made in rigid
glass solutions at low temperature. The development of the
synchronized flash spectroscopic method has made it possible
to study triplet -4 triplet absorption spectra in fluid so-
lutions at room temperature. Thus Porter and Windsor ( 51),
Porter and Wright (70), Livingston (63), and Witt (0+) have
carried out such studies in papers already referred to.
McClure and Hanst (100) have recently used the synchronized
flash technique to study triplet .4 triplet absorption in
aromatic ketones,
Ross (101) has made a theoretical study of the optimal
optical conditions for triplet -t triplet absorption studies.
There are two difficulties which exist in this field at
present. First, phot odecomposition may constitute a serious
interference especially in the flash method, owing to the high
light intensities used. Second, there is a gap at present,
due to experimental inaccessibility, between the lowest
triplet observed in phosphorescence, and upper triplets
observed in triplet `3 triplet absorption. Thus, in benzene,
no triplet -~ triplet absorptions have been observed as yet,
possibly because they exist in the near infra-red region.
The observations of thermochromism are related to the
subject of triplet - triplet absorption spectroscopy. These
are discussed in the last section of this review.
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INTERMOLECULAR SPIN-ORBITAL PERTURBATIONS
Even if only intermolecular spin-orbital effects could
be observed, intercombinations in molecules would have an im-
portant bearing on chemical problems. The discovery of inter-
molecular spin-orbital perturbations serves to make ideas on
intercombinations in molecules of direct applicability to
the development of chemical reaction mechanisms. Such a
possibility is just becoming apparent to chemists and has been
almost entirely neglected up until now. In this section we
shall be concerned with physical intermolecular effects.
Chemical effects will be listed in the next section.
Kasha (95) made use of the Z-effect on intercombination
absorption intensity, extending previous work in an inter-
molecular spin-orbital perturbation experiment. Ethyl iodide
was used as a solvent to bring about an enhancement of the
singlet -~ triplet absorption intensity in a naphthalene
derivative. Ham (45) made similar observations on benzene,
in which he observed enhancement of absorption bands in
between the individual singlet -~ singlet near-ultraviolet
absorption bands of benzene. Bayliss and Hulme (46) have
questioned Ham's assignment of the observed bands as
singlet - triplet; admittedly his observed intensities are
very high for intercombinations, and the possibility of
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confusion with the singlet - singlet absorptions in this
case is rather great.
McGlynn and Kasha (102) have made a comprehensive ex-
tension of the earlier observations of Kasha (95). Many
new examples were found of singlet -- triplet band enhance-
ment, and the dependence on Z was fully delineated. Up to
100-fold enhancements were observed with alkyl iodide solvents.
of particular interest is their demonstration that vibrational
harmonics and impurity absorption bands (which are necessarily
singlet s4 singlet) are unaffected by solvents containing
high-Z atoms. This, as mentioned earlier, offers a criterion
of authenticity for singlet -' triplet absorption work, in
those cases where the solvent-perturbation method can be used.
In some cases, a reaction of the solute with the high-Z atom
solvent makes the method inapplicable. Dyck and McClure (103)
have recently used the solvent-perturbation method to induce
the singlet -- triplet absorption band in trans-stilbene.
This band could not be detected in the absence of an external
perturbation, and the converse emission also was not
observable.
The solvent-perturbation experiments of Kasha (95) were
undertaken because of the known Z-dependence of inter-
molecular fluorescence quenching. Since the spin-orbital
Hamiltonian has a high Z-dependence, it was expected that
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the mechanism of "heavy atom" fluorescence quenching could be
due to an intermolecular spin-orbital perturbation. The
demonstration of singlet -* triplet absorption band enhance-
ment offered direct proof of this interpretation of fluores-
cence quenching. This paved the way to other intermolecular
or chemical applications.
The Russian researchers have thought along rather different
lines from those described in this review. The work of
Terenin, Karyakin et al indicate that they have not recognized
the mode of excitation of triplet states, and the dependence
of spin-orbital interaction on atomic number. Thus,
Ermolaev and Terenin (l0 5) do not believe that triplet states
can be excited directly by light absorption and dispute the
Lewis and Kasha (6) interpretation of phosphorescence. They
believe that intermolecular energy transfer may be required
for excitation of triplet -' singlet emission. Terenin (5)
in his first writings on the subject acknowledged Lewis,
Lipkin, and Magel's ()+) tentative discussion on the possibility
of the triplet - singlet interpretation of phosphorescence.
On the other hand, in this and later papers he and his co-
workers laid emphasis on the need for "paramagnetic quenching"
as a mechanism of excitation of the lowest triplet state.
In a long series of researches Terenin and Karyakin studied
the intermolecular paramagnetic quenching by 02 molecules (106
,
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107, 108, 109, 110) and NO molecules (111). Mainly anthra-
quinone derivatives were studied, both in the gaseous and in
the adsorbed state. Karyakin and Kalenichenko (112) continued
their efforts to induce triplet -.' singlet emission by inter-
molecular magnetic perturbation effects by adsorption of
aminoanthraquinones on silica gel surfaces impregnated with
paramagnetic ions, Cu. They observed an infrared lumines-
cence which they believed to represent the triplet 4 singlet
emission of the adsorbed molecule. Probably they had observed
an intramolecular energy transfer between the T-electron
levels of the aminoanthraquinones and the d -levels of the
Cup" ion; the reported emission was at 8800 A which
~ corresponds
to the wavelength of the cupric absorption band. Such intra-
molecular energy transfers are known since the work of
Weissman (113) on rare earth chelates; in the experiments of
Karyakin and Kalenichenko adsorption probably is accompanied
by chelations of the metal by the organic molecule adsorbed.
Bowen and co-workers also have carried out intermolecular
quenching experiments, investigating fluorescence quenching
in the gaseous state by both high-Z atom containing molecules
and paramagnetic molecules. Bowen and Metcalf (114) and
Metcalf (115) reported preliminary studies of this sort
following earlier work by Bowen et al. Recently Stevens (116)
has adduced a spin-orbital perturbation mechanism to explain
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high-Z and paramagnetic atom quenching. Bowen et al (117,
118) have reported further work on fluorescence quenching,
with intercombinational interpretation.
Reid et al (57, 119,120) have investigated the light
emission properties of both trinitrobenzene-aromatic hydro-
carbon molecular complexes, as well as hydrocarbon-hydrocarbon
complexes. The trinitrobenzene-aromatic hydrocarbon com-
plexes yielded emission spectra close7.y resembling the
triplet ..~ singlet emission spectra of the parent aromatic
hydrocarbon. Reid has proposed a mechanism to account for
this behavior based on the idea that in the molecular com-
plex the plane of symmetry of the hydrocarbons is destroyed,
resulting in non-vanishing matrix elements for spin-orbital
interaction as compared with the parent hydrocarbon.
Orgel (121) and Sponer (122) have discussed some aspects of
this work. The results of Reid et al are especially interest-
ing since they illustrate that in aromatic hydrocarbons the
intercombinational transition probability is sensitive to
other effects than those due to field of high-Z and para-
magnetic atoms.
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INTERCOMBINATIONS IN PHOTOCHEMICAL AND CHEMICAL
REACTION MECHANISMS
As an empirical science, photochemistry has been a field
of active investigation paralleling the earliest investigations
of spectroscopy. The application of spectroscopic theory to
photochemistry has been fragmentary. Probably, the neglect of
intersystem crossing information in photochemical researches
has resulted in a delay in spectroscopic interpretation.
Typifying some of the more recent photochemical investigations
has been an emphasis on the role of triplet states and inter-
combinations in photochemical processes. In an earlier paper
Calvin and Dorough (123) discussed a photooxidation reaction
with a possible triplet state intermediate. Recently, Seely
and Calvin (124) have studied in detail a photoreduction re-
action involving a triplet state intermediate. These re-
searches deal with porphyrin-like molecules. Ashkinazi and
Karpitskaya (125) have described photochemical investigations
on Zn and Cu analogs of chlorophyll. Becker and Kasha (49, 5O)
have discussed the role of triplet states in the photosynthetic
system. Beacom (126) has investigated photochemical reactions
of transition metal complexes.
Bowen and Tanner (127) have published recent results on
the photochemistry of anthracene. Livingston (12$) has
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reviewed the primary act in photochemical reactions sensitized
by polyatomic molecules. Fujimori (129) has described a com-
prehensive photochemical investigation which reviews general
interpretations in various systems of biological importance
including photosynthesis. Norrish and Porter (130) discussed
the production of triplet state molecules by photolytic tech-
niques. Callear and Robb (131) described work on the mercury
photosensitized decomposition of ethylene, in which the lowest
triplet state of ethylene is described as an intermediate in
its decomposition to acetylene and hydrogen. A valuable dis-
cussion of this process was conducted by Bauer, Kistiakowsky
Callear, Robb, Patrick, Ogg, Walsh, and Porter (132),
In chemical reaction theory, triplet states usually are
not involved directly in thermally induced reactions, although
there are some cases in which a particularly low energy
barrier makes this possible. A situation of this sort prevails
in the recent researches on relative methyl affinity
(relative rate of addition of methyl radicals) by Szwarc et
al
(133,13+,135,136,137), This work indicates that there is a
linear relationship between the log of the methyl affinity
and
the energy of the lowest triplet state of the aromatic mole-
cule, for some 14 aromatic hydrocarbons investigated. The
transition state is taken to lie at the position of crossing
of the two energy curves which apply to the interaction of
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the radical with the singlet ground state and the lowest
triplet state. The experimental methyl affinity values of
Szwarc et al have been corroborated by Hey and Williams (138),
and Coulson (139) shows how theoretical values may be deduced.
Levy, Newman, and Szwarc (137) have referred to unpublished
work of Coulson and of Matsen which indicates that the corre-
lation proposed by Szwarc et al may not be unique.
Isomerization reactions involving triplet state mechanisms
have been studied quite extensively in the past, e.g., in the
work of Magee, Shand, and Eyring (140). Recently Davies and
Evans (1)-i-1) have extended this field of research.
Magnetic catalysis of chemical reactions have been con-
sidered in many early researches, and we include a brief
review here for its relation to the present problem. A
theoretical study of the mode of interaction involved has been
published by Wigner (142). An early research in this topic
was published by Harman and Eyring (148), who considered the
effect of paramagnetic substances on chemical reactions.
Gelles and Pitzer (14)+, 145, 146) have studied the effect, of
diamagnetic and paramagnetic ions of the same size and charge,
on decarboxylation rates of malonic type acids. The para-
magnetic ion Dy yielded a 10% increase in rate of the
reaction at the conditions used. A cis-trans Isomerization is
involved in the proposed reaction mechanism. McConnell (147)
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has proposed an alternative interpretation to the magnetic
interaction ideas favored by earlier workers.
THERMOCHROMISM AND PHOTOCHROMISM
Recent researches on thermochromic and photochromic
phenomena, i.e., the reversible production of colored sub-
stances upon heating and light excitation, have indicated
some interesting relationships to the spectroscopic work
reviewed above. On the other hand, the additional complexity
of these topics has left their interpretation in a rather
uncongealed state for the present.
Schonberg and Schutz (l+8) in an early paper reported
on the thermochromism of bixanthylene. Recent researches by
Schonberg et al (l+9, 150) and Mustafa and Sobhy (151) have
resulted in the conclusion that substituents which hinder
coplanarity of the two main parts of the molecule lead to an
interference with thermochromic behavior. Grubb and
Kistiakowsky (152) studied the thermochromism of bianthrones.
Their interpretation indicates that the origin of color is
due essentially to a triplet .-> triplet absorption, in which
the lowest triplet is populated by thermal excitation from
the ground singlet. Matlow (153) carried out an LCAO-MO
calculation on bixanthylene and bianthrone, giving values of
the energy differences between the singlet planar ground
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state molecule and the lowest triplet state perpendicular
molecule; these results are in accord with the experimentally
observed values. Nilsen and Fraenkel (154) carried out para-
magnetic resonance absorption experiments on bianthrone, which
serve to confirm the existence of paramagnetic molecules in
solution, whose concentration is temperature dependent. At
room temperatures it was found that the paramagnetic molecules
were absent. In the solution experiments, the paramagnetic
resonance absorption was reversible with temperature. In the
crystalline state, an irreversible high temperature para-
magnetic resonance absorption was noted,
Photochromic behavior has been reported by Hirshberg (l55)
in compounds related to bianthrone. The color is induced by
ultraviolet illumination at low temperatures, and is spon-
taneously reversible in the dark at a rate depending on the
temperature. Presumably, the colored species is not a
product of photofragmentation, but is some electronic state or
geometrical modification of the original molecule. The re-
lation of this modification to that produced in thermochromism
studies has become a topic of some controversy. Careful
spectroscopic investigation should eventually decide the issue.
In this section we omit all discussion of photochr omism in
which definite evidence of photofragmentation has been found,
as in the work of Lewis and Lipkin (96) and other well known
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papers by Lewis. Hergmann and Fischer (156) and Hirshberg
and Fischer (157) reported on thermochromism and photochromism
of bianthrone compounds, and Hirshberg and Fischer (158)
reported similar results in spiran compounds. Kortum,
Theilacker et al (159, 160) have taken issue with the interprets
tation made by Hirshberg and Fischer regarding the relation
between the photochr omic and thermochromic phenomena.
Unfortunately, a somewhat mediaeval polemic has marred the
discussion of this subject (161, 162).
The study of photochromism and thermochromism should be
of exceptional interest to the spectroscopist because of the
possibilities it offers for the study of low-lying electronic
states of complex molecules. Extrapolating the paramagnetic
resonance absorption results of Nilsen and Fraenkel (15+)
indicates these could be exceptionally low-lying triplet
states. The results reported also indicate a pronounced
effect of the solid medium on the potential function of rather
cumbersome molecules, apparently hindering the free excitation
of electronic states of contrasting geometry. It is quite
possible that the full understanding of thermochromic and
photochromic phenomena in appropriate complex molecules could
serve as the shortest bridge between molecular spectroscopy
and molecular chemistry.
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LITERATURE CITED(3)
(1) Sponer, H. and Teller, E., Revs. Modern Phys., fl, 75
(1941).
(2) Wiedemann, E., Ann. Physik, 3, 446 (1888),
(3) Dewar, J., Roy. Inst. Proc. l2, 557 (1888)? 14, 665
(1895). Proc. Roy. Soc. (London), 68, 3~O T1901).
()+) Lewis, G. N., Lipkin, D., and Magel, T. T., J. Am. Chem.
S oc . , ~, 3005 (1941) .
(5) Terenin, A., Acta Physicochimica U.R.S.S., 18, 210 (1943)
(In English).
(6) Lewis, G. N., and Kasha, M., J. Am. Chem. Soc., 66, 2100
(19)+)+).
(7) Kasha, M., Chem. Revs., 41, 401 (1947).
(8) Forster, Th., Naturwissenschaften, j, 240 (1949)?
(9) Kasha, M., Faraday Soc. Discussion No. 9, 14 (1950).
(10) Craig, D. P., Revs. Pure and Applied Chem. (Roy.
Australian Chem. Inst.) 3, 207 (1953)?
(11) Dirac, P. A. M., "Quantum Mechanics," Clarendon Press,
Oxford, England, 1947, 3rd ed., p. 252.274.
(12) Mott, N. F., and Sneddon, I. N., "Wave Mechanics and
Its Applications", Clarendon Press, Oxford, England,
1948, p. 296-350.
(13) Weissman, S. I., J. Chem. Phys., 18, 232 (1950).
(14) Mizushima, M., and Koide, S., J. Chem. Phys., 20, 765
(1952).
(15) Kramers, H. A., "Die Grundlagen der Quantentheorie,"
Akademische Verlagsgesellschaft M. B. H., Lepizig,
1938, p. 239 ff.
(3) In a few cases the original paper was not available, and
only Chemical Abstracts was consulted. In these cases,
the Chemical Abstracts reference is added.
I
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Interpretation of the Lowest Frequency Electronic Absorption
w
Bands of Inorganic Molecules of Type XOz( as n iT
Y -'t
Transitions)
Sean P. McGlynn and Michael Kasha
Department of Chemistry, Florida State University
Tallahassee, Florida
The lowest electronic transitions of simple molecules of
type XOz() were studied theoretically. In the formula, 0 is
Y
an oxygen, or a sulfur atom; X is generally a non-metallic, or
a transition metal atom; y : 1, 2, 3, +; z : 0, 1, 2, 3.
The procedure was: (a) Group orbitals for the 0-atoms
were formulated as LCAO's appropriate to the molecular point
group. (b) The total MO's were constructed from the 0 group-
orbitals and the central atom A.O' a e In doing this, use was
'~ 43
9
made of the criterion of maximum x~.lrlum overlapping of wavefunctions2
and the non-crossing rule9 4 and by consideration of the
rouA -orbitals.5,6 Simultaneously,
"energies of the isolated group-orbitals 5,6
the total MO's were graded in energy. (c) Finally, the si~nglle_
configuration approximation to the state functions was used.
From this, symmetries and relative energies of the various
molecular states were derived.
The following table summarizes the results. Column five
gives the selection rule (A, allowed; F, forbidden) for the
lowest frequency transition. The last column gives the ex-
perimeiital absorption intensity (S, strong, molar absorption
coefficient 1000; W, weak, molar absorption coefficient ( 50).
9
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-2-
There is agreement between the predicted selection rules
and the observed intensities, in spite of the approximations
used. In most cases the transition is of n -*T type (this
nomenclature here refers to the AO origins of the MO's, and is
merely a convenient codification, having its usual significance
only in planar molecules). This r esult is physically reason-
able. Those MO's which are mainly non-bonding (n) are
relatively unaffected in energy during the process of formation
from the AO's. Consequently, the highest filled orbitals in
the molecule are more likely to be of (n) type than bonding
( II , ?) type. The lowest energy transition will be expected
to be from a "non-bonding" orbital to a pi-antibonding orbital.
In all the cases labelled n 4 I(* in Table I, the n-orbitals
are the non-bonding MO's which are appropriate linear combi-
nations of 2p11 oxygen (or sometimes, sulfur) AO's.
To a first approximation, the n-orbital energy should be
independent of the central atom. Conversely, the energy of
the antibonding (11) MO will be a function of the electro-
negativity of the central atom. Thus, the order of the electro-
negativities (Mulliken scale7) of the central atom should be
the reverse order of the frequencies for the lowest n .~Tf*
transitions. The theoretical basis for this simple correlation
is found in the semi-empirical treatment of n ',TI * transi-
tions by Goodman and Shull.8 The predicted order of
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-3-
transition frequency (D3h group) is, e.g.,
NO3 < N03 Z So3 < 30` < SiO3 , which is the same as the
3
experimental order.
Our study is being extended to the CoC and D~ h group,
including Va~~, U02~", and related molecules. Preliminary
considerations for U02' indicate that the lowest frequency
molecular transition is n -.]f (~ - 'Lau ) and is
symmetry forbidden (weak absorption band observed). The par-
ticipation of f-electrons in this case is being investigated.
In our full report to follow shortly, we shall present
the details of our study and a correlation with the volumi-
nous and largely uninterpreted literature which exists on
the spectra of these molecules. Although our treatment is a
fundamentally primitive one, we believe it offers some
systematization of a field which is at present largely
neglected. It is our hope that this preliminary study will
draw additional attention of theoretical and experimental
spectroscopists to this group of simple molecules.
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?4-
(1) This research was done under a contract between the
Office of Scientific Research, ARDC, and the Florida State
University.
(2) L. Pauling, J. Am. Chem. Soc., a..~, 1365, 3225 (1931).
(3) J. C. Slater, Phys. Rev., , 1109 (1931),
(4) Cf., e.g., C. A. Coulson, "Valence", Clarendon Press,
Oxford, 1951, pp. 61-65.
(5) R. S. Mulliken, Rev. Modern Phys., l4, 204 (1942).
(6) A. D. Walsh, J. Chem, Soc. (London), 1953, 2260-2329.
(7) R. S. Mulliken, J. Chem. Phys., 2, 782 (193+); ibid., ,,,
573 (1935).
(8) L. Goodman and H. Shull, J. Chem. Phys., 229 1138 (1954).
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 Table 1
Summary of Results on Lowest Frequency Electronic Transitions in Simple
Inorganic Molecules
Symmetry
Group
Td
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Molecules
AsO~,CrO",MnO,(MoO4),
4
~ 4 4
von, wog
0s04,Re0 ,RuO ,U0',
_ 4 4 4
Number of
Valence Selection Observed
Electrons Transition" Rule Intensitya
24b
Ac S
Td
CSC
22
I! --~ n, n .Ti*
3T c,d
A
S
1 2
Td
Ru0
25
n 411*
--f*
A
S
4
,
2T -~ 2A
c,d
2 1
Td
RuO~
26
n 4 II *, *
fl *
A
S
3A - 3T
c,d
1 2
D
NO ~Co ),CS~, (Si0 ),SO
24
e'f
n -~ T
~-
F
W
h
3
3 3 3 3 3
1A' ~ lAn
1 1
D
N0
2
g
71*
3h
3
3
n >
2A r 2Af
A
S
2~ 2
C3v
Ir0, IO,SeO,S0
26
n --~7( #
w
33 3 3
1
'
A
F> A
1
2
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Symmetry
Group
Molecules
Number of
Valence
Electrons
Transition
Selection Observed a
Rule Intensity
c 2v
2v
2
1$h'i
n ---} 'f #
F
W
1 1
A
A
l
2
C
C10
19~ ~k~ 1
n ---~ #
A
S
2v
2
2A
,.-128
1
2
C
C10
20
n ?1T*
A
S
2v
2
lA
4 1B
l
1
(a) In the case of uncertain data, e.g., where the absorption band
appears as a shoulder on a stronger band,the molecular species is enclosed in
parentheses.
(b) M. Wolfsberg and L. Helmholtz, J. Chem, Phys., 20, $37 (1952), gave a
w
semi-empirical calculation of the MO energies for MnO~ and Cr01 (also C10).
Our assignment coincides with theirs. See footnote (c).
(c) In the single configuration approximation (also assumed by Wolf sberg
and Helmholtz) all states arising from the same configuration are, of course,
energy degenerate. In the 24 valence electron Td case, the allowed component
of the configurational transition is taken to determine the selection rule.
(d) This is one of the allowed components of the configurational
transition.
(e) H. McConnell, J. Chem, Phys., 20, 700 (1952) suggested that the
lowest frequency absorption bands in NOT, C03,CS3 might be n 411* transitions.
(f) Walsh (cf. Reference 6) has treated NOw,CO3 , and SO With results
3 3
which coincide with ours.
(g) Walsh (of. Reference 6) has treated NO giving the (multiplicity
3
mis-labelled) transition 1A2 i - > E' (allowed).
(1) W. G. Trawick and W. H. Eberhardt, J. Chem. Phys., 22, 1462 (1954)
concluded from polarization studies of single crystals of sodium nitrite
that the lowest frequency transition was of n ' type, with the n-orbital
identified as a nitrogen atom A0.
cute SO2 giving ~A1 ..j B1 (allowed) as the lowest frequency transition.
(h) Walsh (cf. Reference 6) has treated the 1$ valence electron C2v mole-
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(j) Walsh (cf. Reference 6) has treated C102 giving the lowest
frequency transition as 2B1 + 2A2 (allowed).
(k) Our assignment agrees with the requirements set by the detailed
spectroscopic studies on the 21,016 cm"1 band of C102 made by J. B. Coon,
J, Chem. Phys., , 665 (1946).
(1) R. S. Mulliken (cf. Reference 5) has treated the triatomic mole-
cules in detail; however, although his results apply to the ionic species,
he did not consider them explicitly.
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 Sanitized Copy Approved for Release 2010108109: CIA-RDP81-01043R000200200012-0
ON THE APPLICATION OF THE MOLECULAR ORBITAL METHOD TO THE
SPECTRA OF SUBSTITUTED AROMATIC HYDROCARBONS}
Lionel Goodman*
Department of Chemistry, Florida State University,
Tallahassee, Florida
Ian G. Ross
Department of Physical Chemistry, University of Sydney,
New South Wales, Australia
and
Harrison Shull*
Department of Chemistry and Institute for Atomic Research,
Iowa State College, Ames, Iowa
Supported in part by the Ames Laboratory of the Atomic Energy
Commission and by a contract between the Office of Scientific
Research, Air Research and Development Command and the Florida
State University.
Present addresses: L. G., The Pennsylvania State University,
State College, Pennsylvania; H. S., The University of Indiana,
Bloomington, Indiana.
(Abstract) The MO theory of the spectra of substituted hydro-
carbons is presented in rather general terms, with careful
emphasis on the precautions to be observed in introducing the
inevitable approximations. Previous treatments of the problem,
notably by Sklar, Herzfeld, and Matsen, are then examined.
Satisfactory calculations of energy-level shifts are con-
sidered to require closer attention to the definition and
dissection of the perturbed Hamiltonian. The most interesting
intensity effects concern the enhancement of weak transitions:
here earlier treatments do riot satisfy the requirements of
orthonormality of the perturbed MOs, and unjustifiably
neglect interactions with intense transitions. The conse-
quences of neglecting overlap in these calculations are
discussed in an appendix.
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INTRODUCTION
In the course of independent work192, the present
(1) L. Goodman and H. Shull, J. Chem. Phys. , 33 (1955)
(2) I. G. Ross, Thesis, London (1952).
authors have had occasion to examine in detail the papers of
Sklar3'4
on the intensities of substituted benzenes and of
(3) A. L. Sklar, J. Chem. Phys. 7, 986 (1939).
(4) A. L. Sklar, J. Chem. Phys, lO, 135 (1942).
Herzfeld5 on the corresponding energy shifts. The results
(5) K. F. Herzfeld, Chem. Rev. 41, 233 (1947).
of these interesting papers have been widely quoted and used
(see e.g., the recent papers of Nagakura and Baba6 and of
(6) S. Nagakura and H. Baba, J. Am. Chem. Soc. , 5693 (1952).
Ramamurty7). In this paper we propose to examine the same
(7) S. Ramamurty, Indian J. Phys. 289 325 (1954).
problem from more straightforward procedures and to compare
critically the results thus obtained with those of the
previous authors.
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Hydrocarbon Tr-electron Energies
Consider a parent hydrocarbon of N carbon atoms, with
each of which is associated a-11-type atomic orbital (AO),
substituted by a single substituent, -X, which has a II AO
interacting with the 'r-electron system of the hydrocarbon.
If H represents the effective i one-electron Hamiltonian of
the substituted compound, x the substituent IFAO and
j
the unperturbed MO eigenfunctions of the parent hydrocarbon,
then the orbital energies C- appropriate to the substituted
compound can be derived by generalized perturbation theory;
in the approximation analogous to second-order perturbation
theory8 these are
(8) See, for example, Pauling and Wilson, 'Introduction to
Quantum Mechanics', McGraw-Hill, Pa 195.
Nr
)2
(H
)2
S
H
(H
E. -
-
j1
jj
jx
jx-
(1
)
a
3.1
1_l
(H3.3.-Hii
(xx_Hj j )
6
H
N
Z
(Hxi-SxiHxx) 2
x =
xx
(lb)
i~l
(Hxx-Hii)
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in which Hxx o HQxdv? H
- x o~H~idv; o dxdv;
H x = / o H? dv and the prime on the summation indicates
j x
omission of the term with zero denominator. It is convenient
to introduce the Sklar-Herzfeld migration coefficient, i,
defined by
r i = (Hxi-Sxi Xx)/( Xx-Hii), (2)
which is a measure of the extent of interaction between the
ring and substituent. We shall also approximate by neglecting
the matrix elements Hsi, which implies neglect of the in-
ductive effect of the substituent upon the parent hydrocarbon9.
(9) Expansion of the integral H11 in terms of AO's yields:
N
Hi ' c uc iu ,. ~uH' dud v + ?:?? ' ' .' c. ' v
u-1 uw Ju ciw u Hwd
The first type of integral represents the increment in the
Coulomb integral of the uth carbon atom9 whereas the second is
the analogous increment in the bond exchange integral between
atoms u and w due to the field of the substituent. These are
just the terms that are conventionally attributed to the
inductive effect' of the substituent. We have shown else-
where (ref. 1) that Sklar's argument for neglect of the
inductive effect (ref. 3) based on the similarity of the
observed spectrum for anilinium ion with that of benzene is
fallacious and leads to considerable errors when applied to
substituents which both resonate with and exert an inductive
effect upon the ring simultaneously. In this paper, we are
not concerned with quantitative details and consequently
ignore the inductive effect for brevity and convenience,
Eqs. (la) and (lb) are then written very simply;
H..-(,\.*S.)2(H__ -H )
JJ J Jx x Jj
r
i(Hxx-Hii)?
(3a)
(3b)
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We obtain the energy of the ground state in which ~; and
~x
each of the occupied contain two electrons by simple
summation over tie orbital energies:
E 2 )~? T 2 ~x 2 20 H 'r 2H - 2 r'?6.
N
2
* 2 A
( -H.) (4)
i Hxx ii
In these and subsequent equations, a superscript ? on the
summation indicates summation only over occupied orbitals,
v summation over vacant orbitals.
Eqs? (3) are generalizations of Matsen's10 eqs. (4) and
(10) F. A. Matsen, J. Am. Chem. Soc. , 5243 (1950).
(5), and eq. (4) is a generalization of the expression for the
energy obtainable by Herzfeld's5 approach and assumptions
namely:
E ; 2
? H.+ 2H
jJ xx
Nv 2
+ a. CH
i~l
xx
(5)
Eq. (4) reduces to eq. (5) if one omits S. If one can bring
~x
oneself to accept (;) the validity of all these assumptions,
then evaluation of the migration coefficients, Ai, and the
unperturbed energy differences, H - Hii, determines the energy
xx
shift of the spectrum of any hydrocarbon as a result of charge
migration from the substituent. The Sklar-Herzfeld procedure
now divides the total Hamiltonian, H, of the substituted com-
pound into a sum of two terms, H? fi Hx, So chosen that H? has
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u.5w
as its eigenfunctions the of the unperturbed parent hydro..
carbon. H is then interpreted as perturbation due
to the
substituent and is replaced by the potential of the neutral
substituent atom less that of a missing 7-electron. By
utilizing this operator, it is then possible to calculate
Hii and HiX in a straightforward manner. H is evaluated
xx
experimentally as the negative of the ionization potential of
cH3X.
We have shown elsewhere', however, that a very important
part of the perturbation of the parent hydrocarbon by the sub-
stituent arises from the change in the electron repulsion
integrals over the parent hydrocarbon orbitals as a result of
the change in the latter. It is a consequence of the sensi
tivity of these integrals to the perturbed charge distribution
that this effect must be included either in H? or in HZ if the
Hamiltonian is to be divided in this fashion. Thus, if H is
chosen as above, then HZ bears no necessary direct relation-
ship to the ionization potential of -X. One could equally
well have chosen HZ to agree with the ionization potential of
-X, but then the integrals over H? would, in general, bear no
simple relation to corresponding integrals over the unperturbed
hydrocarbon wave-functions and the unperturbed Hamiltonian.
A further criticism of the procedure of theoretically calcu
lating transition energy shifts by formulas which just involve
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simple differences of orbital energies is that a tacit
assumption is made about the Hamiltonian. Namely, that such
a procedure corresponds to a median Hamiltonianl,ll, -- (Ti r F)
(11) R. G. Parr, J. Chem. Phys. , 799 (1951)0
where F is the Hartree-Foch one electron Hamiltonian operator
and Ti is a core part, containing the kinetic energy and nuclear
framework operators. For certain excited states a major error
can be incurred by theoretical calculation with the incorrect
operator12. This is especially true for calculation and
(12) L. Goodman and H. Shull, paper presented at The Symposium
for Molecular Structure and Spectroscopy, at The Ohio State
University, Columbus, Ohio, June 195+.
comparison of energies of excited states with different nodal
properties. It is possible to evaluate Hix and H~ - H11
with more validity either by an empirical procedure, or by
one involving a self-consistent-field approach. For further
work along more rigorous lines, the reader is referred to
ref. 1.
Intensities in the electron S ectra of Substituted Benzenes
In turning now to a consideration of spectral intensities,
we particularize the treatment to the specific case of benzene,
leaving a discussion of some aspects of the wider problem to
the appendix. Moreover, we shall concentrate especially on
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transitions stemming from the forbidden Btu-Alg band (occurring
at 2600 ~)?of the parent molecule.
This transition in a monosubstituted benzene, C6H5X,
acquires the symmetry designation B1-A1 of group C2v, and is
now formally allowed. The forbiddenness of the parent transi-
tion, and the direction of polarization, namely, at right angles
to the C-X bond, are special features of this particular
problem, for they conspire to make the final intensity especially
weak, which in turn should favor the validity of a straight-
forward perturbation treatment. Experimental support for the
latter expectation is afforded by the factl3 that in poly-
(13) J. R, Platt , J. Chem. Phys. , 263 (1951).
substituted compounds the transition moment is very closely
the vector sum of the transition moments of the appropriate
monosubstituted benzenes, for a large class of substituents.
The special features of this particular problem are most
easily understood in terms of the valence bond theory, to which
we turn for a moment , In the VB theory, only polar bond-
structures can give rise to contributions to a transition
moment. Hence we need consider only the following types of
structure here;
Q
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?8w
State wave-functions will each contain contributions from
structures of these and kindred higher-energy kinds, and the
weights of structures like P,Q, ... in which the substituent
does not formally participate, will differ from the weights of
the corresponding structures in benzene itself. This last of
course is simply the formal expression of that part of the
inductive effect due to the -electron system. If overlap is
neglected, the transition moment integral emerges as a weighted
sum of the dipole moments of structures P,Q,...,U,V,...
individually. It is at once seen that the components of
these dipole moments are predominantly larger than the corre-
sponding x-components, and indeed that the latter vanish in a
number of important structures, such as Q and V.
Now in benzene the intensity of a forbidden transition can
be regarded as having been stolen from allowed transitions, and
for transitions whose lower level is the ground state, the
major source of intensity will be the known Elu-Aig transition
0
(1850 A) . Consequently, in the expanded expression for the
0
transition moment of the 2600 A absorption in C6H5X, those
terms involving structures P,Q,... can be attributed directly
to stealing from the intensities of allowed transitions in
benzene itself, especially the transition noted above.
Terms involving structures U,V,... are peculiar to a
perturbation by an interacting substituent. Now, when the
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transition is polarized In the x-direction, only structures
like U contribute to the intensity, whereas both U and V have
to be reckoned with for y-polarized transitions. Having regard
to the general pattern of the magnitudes of the dipole moment
components, noted above, it is seen that the intensity of a
transition which becomes -polarized (such as B -A ?
lu lg) well be
more enhanced by substitution than the intensity of one which
becomes x-polarized.
The algebra of the MO method does not allow the same clean
dissection of the final transition moment into two parts with
such clear physical meanings. However, there is a formal
similarity. Namely, the transition moment comes out as a sum
of (a) terms allowing for the interaction of the individual
benzene MOs with the appropriate AO of the substituent
("migration moment"), and (b) a term which takes account of the
mixture of the perturbed B2 state with the proper component of
u
the perturbed Elu state, the degeneracy of which has of course
already been removedo An intuitive understanding of the terms
(a) is not aided by the fact that they only creep in via the
normalizing coefficients of certain perturbed MO wave-functions
in the Btu-Alg case.
Since a significant part of the total intensity can be
ascribed to stealing from the 1850 A transition in benzene,
it is next noted that the results of a numerical calculation
of the perturbed Intensity are likely to be high as far as
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this term is concerned, since a calculation based on single-
configuration wave-functions of the intensity of the allowed
band predicts an oscillator strength (f . 2.64) over two times
too large (observed f : 0.6 - 1.214' 15) .
_ That is, this part
(1)+) L. Wo Pickett, M. Muntz and E. M. McPherson, J. Am. Chem.
Soc. , 4862 (195].).
(15) W. J. Potts, J. Chem. Phys. ' 73 (1955) .
of the transition moment is likely to be nearly twice as large
as it should be. The inclusion of configuration interaction,
which with benzene cuts the intensity down to a reasonable
figure (f - 0,816) is quite impracticable here
._ .
(16) C,W.L. Bean and D. P. Craig, Trans. Faraday Soc.,,
564 (1951).
We now develop the required theory, on the basis of single-
configuration MO wavefunctions in general terms. We do not
start immediai,ely with the wave-functions pre'riously used in
discussing transition energies since these are not necessarily
the most suitable for calculating the corresponding intensities.
Perturbed MO wave-functions are written down as before,
taking for the of the benzene MOs, in their real form, as
defined by Sklar 'E '
,~ s q. (7)3, The substituent is attached to
position 19 along they axis (axes as in figure above) To
simplify the notation, we adopt henceforth the following
convention.
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11-Subscripts i, j run over 0, 1, 2, 3; p, g, run over -'.1,
-2; and k, 1 are unrestricted
We then have the following (Eq. (6b) has such a simple
form because the orbitals ~p are antisymmetric under reflection
in the rz-plane, the remaining orbitals being symmetric with
respect to this operation):
9'i = r; ai . -- . * aix .x (6a)
~ J J
L- - (6b)
p apq '"q
q
IJx = ti aX3 . ? axx x
(6c)
The akl are coefficients, the best possible values for which
would be obtained by solving the secular equations derived
from the seven primitive wavefunctions fib. In the approxima-
tion in which Eqs. (la) and (lb) give the perturbed energies,
we would have
aix/aii = -(Ai i.. Six) , axi/ate : i
(7)
akl/akk c Hkl/(Hkk-H11) .
However, we can separate out the question of how refined the
calculation of these coefficients must be by supposing for the
time being that they are 'exact'.
Having in mind Eqs. (7), we shall assume that the pertur-
bation is weak enough for the following to apply:
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a11, app, axx are approximately unity
aix, as., Six are of order
aid' apq
are of order
iaixsix ~
The final expression for the transition moment will be obtained
as a sum of terms of order ~.2. Consequently we may only 9 Y Y omit
from the algebra terms smaller than these. The MOs (6) must
be orthonormal. Normalization leads to the following relations
between the coefficients:
2
a.. 1 - 2a. - S. a
a.x ix ix
app =1
a:
1 - -- -
plus terms of order
(8)
(9)
To the same approximation, the
orthogonality relations are;
ai+aj.ita.axiaS
J ix
J ix ix r aJ,xsix - o
apq aqp - 0 (10)
axi t aix + Six . 0
While Eqs, (10) are not used specifically in what follows
compliance with them is mandatory; for if, with a 9 particular
set of coefficients ak , the residue after evaluating the
1
left-hand side of any of the. Eqs. (10) is of order .k 9 there
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will be spurious contributions to the transition moment of the
same order of magnitude.
Wave-functions g and ~a are now written down for the
ground and excited states. For the present purpose we can
omit the spin wave-functions, and antisymmetrization also,
since all the orbitals are orthogonal and the transition moment
is a sum of one-electron operators. For convenience, we also
leave out the serial numbers of the eight electrons. Then17
(17) There is a misprinted sign in Eq. (9') of Sklar3, which
is the appropriate equation in that paper with which to com-
pare the present Eq. (lib).
y,;g
o *o l t/1
1
t o o l -2 1 l x `fix S
(lib)
The quantity ,'\ in Eq. (lib) is a parameter concerning
which we may say either: that the degeneracy which in benzene
obtains between the orbitals .~1 and between no longer
holds -- the /1 belong to different representations, A and
B2 of group C2v
-- so that the two configurations in (lib)
are of unequal energy and therefore do not mix equally any
more; or; that A. measures the mixing of wave-functions
analogousl$ to the lowest energy B2 gy 2u and E1u wave-functions of
. (18) By 'analogous' is meant that benzene wave-functions are
obtained from (11) by writing f for ), and omitting the two
/1X factors.
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unsubstituted benzene. The latter interpretation can be con-
firmed by setting /1 = 0 in (lib); then (lib) is the analogue
of the Btu wave-function of benzene itself, while if the sign
of the second term is changed, there results the appropriate
component (i.e. of B1 symmetry) of the pair of Elu-like wave-
functions.
The moment M of the transition between the two states is
then readily evaluated in terms of one-electron moments
-
Mkl =
~k (e x) 1 dv:
J
i' i e xi e dv : cos (=- - A) M-12 * sin( - A) M' .
and this in turn can be expanded solely in terms of benzene
transition moments M? : / k (e) dv9 the direction of
kl 1
the transition precluding the direct participation of terms in
.. x. If overlap is neglected, the non-zero moments are
N? 2 1.2 R x' -M?
pti,.l 0 _~3 9
1 --,
z R x0
where R is the C-C bond distance in benzene,
vector in the x direction. Then, using Eqs.
0
- Ml-2
and xo is a unit
(8) and (9)19
(19) Sin n is normally positive, and a13, a will normally
have opposite signs; nevertheless, there is~ill extensive
cancellation among the terms of (1'+) which leads one to recall
with misgivings the host of neglected terms of order .1 3.
M = - R (a2xS2x - alxSlx + 2 a2x - 2 alx2)
2 (a13 - a20 )
* 2 sin A x' (15)
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~o
In the Btu-Alg transition of benzene, the moments Ml
and M?12 are equal and opposite, and in the total transition
moment have equal coefficients, thus cancelling each other
precisely. In a monosubstituted molecule, both equalities, of
magnitude and weight, are destroyed, giving, as Eqs. (13) and
(15) show, two distinguishable sources of intensity.
Comment on previous treatments of this problem centers on
two aspects of our derivation of Eq. (15) conformity of the
perturbed wave-functions with the requirements of ortho-
normality to the accuracy prescribed by (8), and inclusion or
omission of the mixing coefficient of Eq. Cub). We must
also consider the adequacy of the methods used to calculate
the coefficients akl~
Sklar commenced by approximating ' -'i of Eq. (6a) by i,
and Y-'X of (6c) by .'X -- that is, the interaction
i i
was supposed to take the form of leakage of electrons from
the substituent into orbitals unoccupied by an electron of
like spin. There appears to be no justification for dropping
the terms in `;Ux involving occupied orbitals -- in fact,
these seem to be just the most important ones. These wave-
functions are now no longer orthogonal, and, more seriously,
were not properly normalized. Antisymmetrized product wave-
functions based on these non-orthogonal orbitals were then set
up, and the moment integral was calculated taking due account
of the non-orthogonality. This calculation can fairly be
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described as arduous. Inspection of Eq. (15), however9 the
first terms of which are simply the difference between the
normalizing coefficients all and a , reveals that neglect of
22
such coefficients is quite inadmissible. Sklar's final formula
(Eq. (13) of ref. 3) is thus quite incorrect; and indeed, if
due account is taken of the requirements of normalization, a
new expression for the transition moment results the terms of
which roughly cancel each other out, and which thus hardly pre-
dicts any significant increase in intensity at all; These
criticisms, to which others are added below suggest that
9 the
formulae of Sklar's papers on intensities3l be used only with
the utmost caution.
We next examine the validity of a transition moment cal-
culation based on the wave-functions of second-order pertur-
bation theory. The terms in Eq. (11+) are all of order A 2
and in particular explicitly include coefficients
of the type
aid. According to second-order perturbation theory, these are
quoting from Eqs. (7) 9
l
..:H.~/(H..-H )
_ 11 JJ
(omitting the normalizing factor a.. which is close to
unity).
Neglect of the inductive effect by setting H , equal to zero
iJ
means that these terms are simply omitted, which is the pro-
cedure adopted by Sklar3 and Matsenla. This is seen to be an
arbitrary approximation, but one which could conceivably be
reasonable were the matrix elements H ij . especially small.
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..17..
However, if the perturbation expansion is carried one step
further still, , acquires some extra terms one of
~ , which is
not negligible under any conditions; i.e. we now have
(omitting overlap for simplicity);
-----1 .... 4.H1xHx j
(Hii_H~) (Hii'H . )
jJ
(16)
Comparison with Eqs. (2) shows that the new term is of
order
A 2, and the necessity of
including it follows at once.
We must also point out that certain pairs of these per-
turbation-theory wave-functions are Insufficiently orthogonal:
thus, when Eqs. (7) and (16) are substituted into the first of
the Eqs. (10), there is a residue of order A 2. In the light
of the comments made regarding Eqs. (10), it is necessary to
take heed of this non-orthogonality -- most conveniently by
20
orthogonalizing the perturbed wave-functions before
pro-
(20) P 0. Lowdin, J. Chem. Phys. 18 365 (1950).
ceeding further.
We come finally to the mixing coefficient first intr0-
duced in Eq. (11). We note that Matsen10 in an appendix, drew
attention to the possible importance of this quantity,
but
did not consider it in his calculations. To calculate
sin A
it is necessary to evaluate the matrix element of the total
hamiltonian between the El ..like and B -like wave-.f
u 2u unctions
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of C6H5X. Attempts to do this by the regular ASMO method
break down because sin J\ emerges as a small difference be-
tween sums of very many large terms. Semi-empirical pro-
cedures, however, can be used to estimate the likely importance
of this mixing coefficient. The result of calculations of
intensities using a more definitive calculational scheme,
shortly to be published21, show that for small interactions
(21) L. Goodman and H. Shull, to be published in J. Chem. Phys.
Independent calculations relating to purely inductive sub-
stituents will be published by D. P. Craig and I. G. Ross in
J. Chem. Soc. (London).
whether of an inductive or resonance kind, the change in the
mixing coefficient A. is the dominant influence on the
intensity. The relative importance of '1. decreases as the
substituent-ring resonance interaction becomes larger, but
it is clear that any treatment which wholly ignores the mixing
coefficient is grossly inadequate.
Nor can it be assumed that the occurrence of a term like
our ",, is a peculiarity of the benzene problem alone, where it
arises particularly imperatively because the MOs happen to be
degenerate in the parent hydrocarbon. It is too early in our
present state of understanding of molecular spectra to say
whether intrinsically weak bands frequently steal large
amounts of intensity from stronger bands, by vibrational
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perturbations, but this begins to look likely (as, for example
in the weak 3200 A transition of naphthalene22, the interpre-
(22) See e.g., D. S. McClure, J. Chem. Phys. 22, 1668 (195+)
and references therein.
tation of which is hindered by just this phenomenon). Attach-
ment of a substituent would seem to be no less drastic a
perturbation than the excitation of a particular active
vibration, and one can foresee, with some regret, the necessity
of exploring the interaction of other molecular levels with
the levels of direct interest if the intensity effects of
substitution are to be accounted for in hydrocarbons generally23,
(23) Indeed, we might well have included in the present treat-
ment of benzene a further parameter to take into account
interaction of the ground state with the excited E like
states; this was omitted because the term thus int2rgduced into
the final expression for the transition moment, Eq. (15), is
likely to be distinctly smaller than 2s.; i
The change in the mixing coefficient A also affects the
transition energy shifts, Thus, besides the substituent
perturbation on the orbital energies, the variation of the
mixing coefficient between the configurational wave functions
and the change in the electron repulsion integrals over the
orbitals involved in the excitation process (J , J
1-2 -129
K1-2' K_12 in usual notation), must be taken into account.
Success in attributing changes in transition energies to
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orbital energy perturbation alone hinges on the magnitude
of the second factor and the variation of the ?r,
electron repulsion integrals with the perturbation. Expansion
of these integrals over the perturbed orbitals shows that for
small perturbations they vary as A2,21, which is indeed
identical to the variation of the orbital energies in Eq. (3).
By correct choice of empirical parameters, then, these
integrals need not be evaluated explicitly; however, calcula-
tions which neglect such effects are likely to give only
qualitatively useful results.
fiend ix
We wish to investigate the magnitudes of the effects
introduced by the neglect of overlap integrals in the frame-
work of the simplest molecular orbital approach to substi-
tution problems, In particular, the calculation of
transition probability integrals will be discussed, with
benzene providing a specific example.
In alternant hydrocarbons, the overlap effects are
especially simple and will be reviewed briefly. The lowest
energy transition for a 2n n-electron alternant hydrocarbon
takes place between corresponding bonding and antibondi
levels, a and , The MO's corresponding to these levels
may be writ ten24
(2~+) H. C. Longue t?Higgins, J. Chem, Phys. , 18 265 (1950);
C ? A. Coulson and G. S. Rushbrooke Proc . C ' ~ ambridge Phil,
Soc. , 193 (19Li0); and B. H. Chirgwin and C. A. Coulson
Proc. Royal Soc. (London) 201A, 96 (1950). '
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b
a
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1 2n - -
Cauu = ' M(lt ' aS) .
N
~
a
1 u_1
U
w aw w .J
(17)
- 1
U - -a au 'U aw ' j
a
where M, the normalization constant with overlap neglected, is
of the order of 2n; and S, the nearest neighbor overlap integral,
?;a defines the energy of the orbitals a and a, which,
relative to the lr -electron coulomb integral of sp2 carbon,
are ? .,a (` . The starred terms refer to one alternating set
of atomic orbitals, the "o" terms referring to the other set,
w. The transition moment formulae may then be written
2 2 _1
(1- 0,faS) 2* 2 .
'
0 2 > -
1
M - f ' C
- ) C h I (18)
as - M ? au u t, aw w
.
provided that the cross terms between non-adjacent atomic
centers can be regarded as negligible, since those involving
adjacent centers, f F" dv, just cancel out. It is
u u+l
clear then that for transitions between corresponding bond-
ing and antibonding levels, the effect of overlap is mainly
felt through the normalization factor. Since S and, for
the lowest energy transition, ' .;a a ' its neglect intro-
duces an error of perhaps 5f in the transition moment integral.
However, if the transition does not take place between corre-
sponding levels, the nearest neighbor cross terms no longer
cancel out and the normalization factor becomes considerably
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-22..
more overlap dependent -- specifically, )]. r ';a S
' t a + ; ~) S I z. Since the nearest neighbor cross terms are
of the order S, a considerable error is possible, especially
for weak transitions whose total moment integral may be small
due to cancellation of many large overlap dependent atomic
moments.
In general, as far as we need to consider, for the calcu-
lation of transition moments upon purely conjugative substi-
tution, two effects are important: (1) Corresponding alternant
levels in the hydrocarbon are no longer so; (2) New atomic
moment integrals appear involving ,? The relative influence
of these effects will of course depend upon the hydrocarbon
and the orientation of the substituent, The second effect
plays no role in the benzene long wavelength transition, upon
monosubstitution. We need only to consider the degree of
"nonalternantness" of the substituted levels. It is convenient
to consider at first the benzyl radical, which may be con-
sidered the limiting case of a substituent, having the same
electronegatj.vity and thus the same coulomb integral as the
sp2 carbons about the ring. Although the levels are still
alternant, the transition no longer takes place between
corresponding bonding and antibonding levels, as was the case
in benzene. Consider the transition moment Nf, The MO's
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2t
are
:1/n
The overlap dependence of the product of the normalization
r
factors is (1 - S) by virtue of the fact that is a zero
1
energy MO and is overlap independent. The transition moment
is (N N )-2(3)k(S/2-1 R. Eve
1 -2 ) n though both the cross terms
and the normalization factor are overlap sensitive, the moment
is virtually independent. Thus, in this limiting case where
the substituent has electronegativity equal to that of the
hydrocarbon carbon atoms, inclusion of overlap has little
effect (a similar result holds for M12) on the transition
-
moments.
Turning to the situation where the substituent has arbi-
trary electronegativity, greater than sp2 carbon, examination
of E q. (1) shows that the orbital energies depend on overlap
in two ways: (1) through the difference (Hii - H); (2)
xx
through the substituent - hydrocarbon overlap term, H..S,.
ii lx
The first factor is dependent only upon the hydrocarbon
overlap integrals through the relation H1? - H1 (1 S)
11 - ~i ~a
(primed quantities indicating neglect of overlap), showing
that the calculated perturbation is increased for bonding
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orbitals through neglect of overlap. The converse is true
for antibonding orbitals. But it is clear that as long as the
difference (Hii - Ham) is large, i.e., the perturbations are
small, this factor will not be important. The second factor
involves Hii. This quantity governs the dependence of the
orbital, on the substituent-hydrocarbon overlap integral, which
is strong when Ei is large; it clearly vanishes for a zero
energy M0. Because of this term, bonding orbitals will be
more overlap-sensitive when the substituent perturbation is
weak (electronegativity high). The antibonding orbitals
generally are little perturbed, so as to remain nearly con-
stantly sensitive to overlap for all values of Ham. The
conclusion is that the hydrocarbon overlap integrals are more
important in the case of large perturbations; the substituent -
hydrocarbon overlap, with small ones, -- as is illustrated for
the bonding ethylene orbital in Fig. 1.
(2') Exact solutions of the 3 x 3 secular equation were ob-
tained as a function of Ham, assuming the substituent -
nearest - carbon exchange integral constant for all Ham, and
equal to ( ., c-c' Also assumed was neglect of non-nearest-
neighbor exchange and overlap integrals. All carbon atoms
were assigned the coulomb integral 4\ .
The solutions all converge when H , since El is then a
zero energy MO; but the perturbations (Ei - Hii) diverge as
H is lowered in accord with the first factor.
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It is clear then that through neglect of overlap the
greatest percentage discrepancy in the orbitals will be in-
curred at high substituent electronegativities, and in general
this will be the case for the transition moment antegrals.
This same general conclusion applies to the calculation of
transition energy and ionization potential shifts by the
simplest MO procedure.
Finally, a remark may be made on the empirical evaluation
of H. This parameter is frequently estimated from shifts
in the transition energy or ionization potential10. Inversion
of Eq. (1) for Ham, in terms of the first ionization potential
shift -
H~ . Haa
( Hxa - Sax Haa )
~.
( n' I)obs
2
(19)
which shows that the value of H will depend upon both hydro-
carbon and substituent - hydrocarbon overlap integrals. Here
too, inspection of Fig. 1 reveals that neglect of overlap
causes the most discrepancy f or highly electronegative
substituents.
Al - (Ea - Haa) gives
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t
W
0.0
~4 *+ w }a.,..y q~r" arty ~ " y~7 r"+ ~ r .~~ ~^ >t~ A to ., r.
G J. U l Ui L( r )r.C r:i 1 v' t r 11 u~] ) 1 _.._. ~..
o, ie c ?1n~,.~ i, i l' I'c ti
i.,r Ia1. enery L. u-e in urii - Cs ' '
I .inns C : U: Lb., 1 L1. I. in ~-~ values o. a:; v&n.1} j i
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THEORY OF SOLVENT EFFECTS ON MOLECULAR ELECTRONIC SPECTRA.
FREQUEPICY. SHIFTSI
(1) This work was carried out under a contract between the
U0 S. Air Force, Office of Scientific Research, ARDC, and the
Florida State University.
by E. Ga McRae
Department of Chemistry, Florida State University
Tallahassee, Florida
(Abstract)
The effects of electric dipole interactions on electronic
band frequencies in solution spectra are analyzed theoretically.
A general expression for the frequency shift is derived by per-
turbation theory. The frequency shift is the sum of contribu-
tions from dispersive and static dipole interactions. The
dispersive contribution represents the general red shift, which
is present in all solution spectra; it depends in part on the
weighted mean wavelength characteristic of the solvent. In the
electrostatic contribution the role of the quadratic Stark
effect is emphasized. The introduction of a simple electro-
static model permits the derivation of formulae relating
frequency shifts in both emission and absorption spectra to the
refractive index and static dielectric constant of the solvent.
Illustrative numerical applications are described.
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I. INTRODUCTION
In several recent discussions of solvent effects in
electronic spectra, solvent-induced frequency shifts have been
interpreted in terms of electric dipole interactions. The
well-known red shift2 in the spectra of non-polar solutes has
(2) Shifts to lower frequencies relative to the vapor frequency
are called red shifts, and shifts to higher frequency, blue
shifts. In algebraic expressions, red shifts will be designated
by a negative sign, blue shifts by a positive sign.
been related by Bayliss3 to the solvation energy of the
(3) N. S. Bayliss, J. Chem. Phvs., 18, 292 (1950).
transition dipole, while the work of Ooshika4 indicates that
(4) Y. Ooshika, J. Phys..Soc. Jap, 9, 594 (l95+).
the red shift is caused by dispersive interactions. Several
authors~'4~596 have discussed frequency shifts in the spectra
(5) L. G. S. Brooker, Experientia Supplementum II, (XIVth
International Congress of Pure and Applied Chemistry), 229
(1955).
(6) N. S. Bayliss and E. G. McRae, THIS JOURNAL, 58, 1002 (1954).
of polar solutes in terms of the relative solvation energies of
the permanent dipoles appropriate either to the combining
states of the solute, or to the resonance structures contribut-
ing to those states. As has been stressed by Bayliss and
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McRae6, it is necessary in general to consider the frequency
shifts arising from interactions involving the solute permanent
dipoles as superposed on a general d shift?, which is present
(7) Bayliss and McRae6 used the term olarization red shift.
in all solution spectra.
In this paper we present a further discussion of frequency
shifts caused by dipole interactions. The most important con-
tribution of this study is the derivation, by perturbation
theory, of a general expression for the frequency shift. It is
hoped that this formulation will serve to correlate previous
interpretations, and provide the basis for a more precise and
complete qualitative interpretation. A second contribution of
the present work is the derivation, from the general expression,
of formulas linking the frequency shift to the solvent re-
fractive index and static dielectric constant. The formulas
presented here are more widely applicable than those previously
put forward
II. THORTICAL
The method of treatment consists of the application of
second order perturbation theory to the calculation of the
electronic state energies of a solution containing N identical
solvent molecules and one solute molecule. We suppose in the
beginning that the molecules have fixed positions and
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orientations. In view of the comparative rapidity of electronic
transitions, the same positions and orientations are appropriate
to the ground and excited states of the solute.
In the zeroth order of approximation, we consider the
molecules not to interact. The zeroth-order electronic state
functions of the solution are then made up of products of state
functions for the unperturbed component moleculeso Neglecting
the non-orthogonality of the latter, we shall employ simple
product functions, f or which we introduce notations such as
gy(p) b(9) ,J
?- c2('p)c
0 '9 (4
r , , o J
114 , . a , , ,
v-( i) v~l f 1 zt(9) , ;(/A/)
o 07 and
0 0a
where for example u (p) b(q)J denotes the zeroth-order
function representing the state of the solution in which the
solute molecule is in its jth excited electronic state
~1 9
and the jb th and 9 th solvent molecules are in their a th and
bth excited states O '&9 zL4') respectively8.
b
(8)(a) It should be noticed that the subscripts for unexcited
solvent molecules are omitted, but the subscript for the
unexcited solute molecule is retained.
(b) The above notations embrace all of the required zeroth-
order functions, for in the approximations of the present
treatment, matrix elements involving zeroth-order functions
corresponding to the simultaneous excitation of more than
two solvent molecules are zero.
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Throughout this paper the notations u and 'v(p) will refer
to the solute and the j'th solvent molecules, and the subscript
zero will indicate the ground electronic state of a single
molecule.
The zeroth-order electronic state energies are sums of the
electronic state energies of the unperturbed component mole-
cules; e, g. the energy corresponding to is given by
UU (N-i) wr + W+ sv7 , where W denotes the elec-
t
tronic state energy of an unperturbed molecule. Energy
differences will be expressed in cm~l, and denoted by V ;
thus, for example, the energy difference between the nth and
jth states of the solute will be expressed by
vat;: = ( LJ - w ) h c , where h and C have the
usual meaningso
We represent, the energy of interaction of the molecules in
solution by the classical energy of dipole interaction, which
is given in the poir+t-dipole approximation by
N _
N
= - z e jf v-vp.) - (/2) Z ?'Lf (p) tiY9~ W'99 (1)
where Ail denotes the instantaneous magnitude of the dipole
moment of a molecule and ) is a geometrical factor dependent
on the mutual orientation and separation of two dipolesa
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The energy of the stated , corresponding in the zeroth
order of approximation to '7 , is governed principally by the
matrix elements H; = W ?S,G + ? ? d t ( 5j. Is
the Kronecker delta), Ha(p)j,. fat J ? ~,( ~; and
Ha(p h(9, - j -a(p)b(q. Here and in
what follows, the state functions are for simplicity taken to
be real. In view of (1), the matrix elements may be written
,~s~ ~ dJ~ ~~ oo M M' O,'2) Cio as (7vi)2 SJG ,
p-1 p^r y=i
_ u 'U-(P} u It _, ~ ~~) ~'
___ ,(M1)2 /
3hc Q#o~)
where the primes indicate summation over terms correspond-
ing to known transitions in the absorption spectrum of the
solvent in question.
As long as the frequency and intensity of at least
one strong transition is known, the limits are sufficiently
close that their arithmetic mean is a good estimate of L0.
For example, we have for the solvent benzene, utilizing the
known polarizability, the formula relating the oscillator
strength to the transition dipole moment and the information
in Table I:
0 0
185o > L0 > 650 (Angstrom units) yielding L U 1250 A.
This value is quite insensitive to refinements such as
taking into account some Rydberg transitions. It is appro-
priate to many benzene derivatives as well as to benzene
itself.
Unfortunately the ultraviolet absorption spectra of
most other common solvents are not sufficiently well known
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for the above method to be useful. However we discuss a
few typical solvents as follows :
Cyclohexane: from the absorption spectrum16 we have
(16) L. W. Pickett, M. Muntz and E. M. McPherson,
J. Am. Chem. Soc., 73, 4862 (1951).
0 o
L0 < 11+50 A, and guess (~a ti 1000 A. This value
should be equally applicable to most saturated hydrocarbon
solvents .
Dioxane: from the absorption spectrum l7 we have
(17) L. W. Pickett, N. J. Hceflich and Tien-Chuan Liu,
J. Am. Chem. Soc., 73, 1+865 (1951).
L0< 1800 A. Since the oscillator strength of the
0
first band (0.11) is less than that of the ,\1800 A
band of benzene, the value of L a for dioxane probably
lies between those for bonze. e and cyclohexane.
Water: from the absorption spectrum 8 we have
(18) K. Watanabe and M. 7elIkc f, J; Opt._Soc. Amer.,
439 753 (1953). r
0
La < 1350 A, suggesting a value of La approximately
equal to or less than that for cyclohexane.
It should be noticed that the values of L0 tend to
increase in the same order as the solvent refractive
index.
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Comparison with _Previous Work. -- In the first term in (14),
the general red shift is related to the solvent refractive
index. This expression may be compared in an interesting way
with that previously derived by Bayliss3. To facilitate the
comparison, we write the result of the present treatment in
the form
1.07 x 10-1
L.Li0fw h%d"
cz3 2 r~~ -t-~
a, z
d
_ i
i? rI
- I
f
P?
'
J
)
:
j
j.
'::L
)
_ _ a3 Z n+/ ~ l-j~J a3 Z n ,+! fj (16)
L~0
h
whereas the Bayliss expression is -1.07 x 10 l4 / ? - _
7 V a3 2 ri
L (!
The first term in (16) differs from the Bayliss expression
in that it contains 2 LL in place of I/ Zia . Terms
such as those under summation in (16) appear also in the
treatment due to Ooshika. However, the result of the present
treatment is not identical with that obtained by Ooshika. In
particular, the weighted mean wavelength appears, in the
present work, in place of the wavelength of onset of solvent
absorption in Ooshika's expression. This modification is con-
sidered to be quite important, because the two wavelengths do
not in general vary in the same way from solvent to solvent.
Application to Benzene.-- The terms under summation in
(16) make a dominant contribution to the red shift in weak
transitions, since' is then small. This point may be
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illustrated by a numerical application of (16) to the shifts
0
Induced by the solvent cyclohexane in the A 2500 A and
0
A 2000 A absorption bands of benzene. We assume that the
shifts are caused by the transitions indicated in the first
column of Table 119, the notations and assignments being those
(19) Transitions to still higher energy states must unfortunately
be omitted, for practical reasons. However, the contributions
of such transitions probably tend strongly to cancel.
of Pariser20. Since the intensities of the transitions between
(20) R. Pariser, J. Chem. Phys., 24, 250 (1956).
excited states are unknown, we prefer to apply (16) in an
indirect way, by calculating the intensities that these
transitions must have in order to account for the observed
shifts. Possible contributions from forbidden transitions be-
tween excited states will be neglected. For the radius of the
benzene molecule, we adopt a : 3.0 A. Since the first absorp-
tion band of cyclohexane lies at a considerably higher
frequency than any of the benzene transitions indicated in the
Table, the weighted mean wavelength may be considered approxi-
mately as a constant. We adopt the value indicated above,
0
viz. L a 4 1000 A. With the transition intensities, transition
frequencies and solvent refractive indices, fl , indicated in
the Table, we require in order to fit the observed shift of
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TABLE 1
D
FREQUENCY SHIFTS IN THE BENZENE SPECTRUM
Transitions
V(cm)
h
Contribution to LS~ cm1)
~_
A 2500A band
A 2000A?
band
-+
Bz
0.002b
x+0,000
1.49f
-3
2
A
--p
B
12c
0
50
000
1.56g
112
-238
,
9
.
,
~-
+
c
g
Aug
-''
E+u
1.2
55,000
1.58
951
951
B
-4
E
(0.72)d
309000e
1.)5f
(-1368)d
0
B
-4
E~ 1
(050)d
19000e
9
1.43 f
0
(-1785)d
Observed shift -308b
-1070b
(a) Notations and assignments of Pariser20.
(b) Reference 21.
(c) Reference 16.
(d) Values required to fit observed shifts. 20
(e) Differences of energies calculated by Pariser
(f) Land olt-Bornstein "Physikalisch-chemisch Tabellen", Springer,
Berlin, 1935, Part 3 (II), p. 1683,
(g) Extrapolated from literature values,
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0 21
308 cm 1 in the A 2500 A band that the oscillator strength
(21) N. S. Bayliss and L. Hulme, Australian J. Chem., 6, 257
,
(1953).
of the 82,E * Ez transition be 0.7. This value is in
accord with the fact that the transition is allowed. The
fifth column in the Table shows the contribution of each
transition to the shift. The A,q -~ transition itself
is seen to contribute only one per cent of the total. A similar
calculation shows that in order to fit the observed shift of
1070 cm 1 in the A 2000 A band21, the oscillator strength of
the B -.,~ Ely transition must be 0.5, again an appropriate
value for an allowed transition. The last column of the Table
shows that the A,9 -. B, transition itself contributes
about one-quarter of the total shift.
The above example indicates that the frequency shifts
are caused predominantly by strong transitions. The inten-
sities of these transitions are probably not greatly altered
upon the introduction of substituents into the benzene ring.
Consequently, we are able to explain Fer uson's22 observation
(22) J. Ferguson, J, C hem. Phys., 249 1263 (1956).
that in the A 2500 A bands of weakly polar substituted ben-
zenes, the frequency shifts are all about the same, and in
0
particular are independent of the A 2500 A band intensities.
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Effect of the Weighted Mean Wavelet. -- The influence of
the weighted mean wavelength is manifest in the relative mag-
nitudes of the general red shift induced by different solvents.
The general red shift is observed directly only when both the
solvent and solute are non-polar. In such cases, it is known
that the frequency shift is approximately proportional to
n'-/ / 2,' + / , where h denotes the solvent refractive
index at some particular visible or near-ultraviolet
3921923
frequency . (The linearity is also observed in certain
(23) (a) N. D. Coggeshall and A. Pozefsky, JC_he_rn. P_ hys.9 19,
980, (1951);
(b) G. M. Badger and R. S. Pearce, Spectrochim. A tag 4,
280 (1951) ;
(c) J. Ham, J. Am. Chem. Soc., 76, 3875 (19 54) .
WV
other cases, which will be discussed later). From the
relatively few studies in which frequency shifts have been
referred to the vapor frequency3921~2259 it appears that the
(2+)(a) S. Samburaky and G. Wolfsohn, Trans. Faraday Soc., 369
427 (19+O);
,,,
( b) G. Kortum and B. F inckh, Z~ hysilcal. Chem. 9 B529
263 (1942) "Iv
This work has been summarized and discussed by Forster25.
(25) Th. Forster, "Fluoreszenz Organischer Verbindungen,t'
Vandenhoeck and Ruprecht, Gottingen, 1951, p, 135.
plots of dy vs. r~? /2,i-/ do not in general extrapolate
to the origin, as they should according to Bayliss' theory, but
tend to cut the frequency axis beyond the origin. This behavior
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led Bayliss3 to suggest that the frequency shift is caused in
part by interactions other than those accounted for by his
theory. Actually, the discrepancy may arise from the slightly
incorrect form of the Bayliss expression, According to the
present theory, the frequency shift is approximately pro-
portional to (A L0-& ~) (i'-f/2l7-t/) which is a form of
(16) obtained by replacing refractive indices and weighted mean
wavelengths at all frequencies by ri and L0 respectively. A
and B denote constants characteristic of the solute. Since
the weighted mean wavelength tends to be shorter for solvents
of lower refractive index, the plot of y vs.
C AL0+L~)/ n z !/2 n z~ / should pass nearer the origin than
l
that of t2vs. (h2_,/2Y12 /) , while stall retaining the
linearity of the latter plot. Because of the difficulty of
estimating Log 11 and B , the possibility of the former plot
cutting the frequency axis far on the red-shift side of the
origin cannot definitely be excluded, although this appears
unlikely if A j.,and B are of comparable magnitude, inspection
of (16) suggests that this is actually the case;A L o probably
predominates slightly in strong transitions, B in weak
transitions.
Electrostatic Interactions.-- The remaining terms in (10)
represent the contribution of electrostatic interactions. The
second term represents the contribution of interactions between
the solute permanent dipoles and the solvent dipoles thereby
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Induced, and the third term represents the contribution of inter-
actions between the permanent dipoles of the solute and solvent
molecules. The fourth term represents the contribution of the
interactions between the permanent dipoles of the solvent mole-
cules and the solute dipoles thereby induced. Since it is pro-
portional to the square of the field intensity produced by the
solvent permanent dipoles, the fourth term may be said to repre-
sent the quadratic Stark effect.
The representation of the electrostatic contribution as a
sum of terms is somewhat artificial, being a consequence of
second-order perturbation theory. The same expressions could
have been derived by the conventional methods of electrostatics,
with due cognizance of the non-equilibrium polarization of the
solvent immediately after the transition. The treatment by per-
turbation theory is preferable, because it is consistent with
the treatment of the dispersive interactions.
In the last three terms in (11+) and in (l+'), the contri-
butions of electrostatic interactions are expressed in terms of
the static dielectric constant of the solvent and the solvent
refractive index extrapolated to zero frequency. It will be
recalled that the third terms were derived on the assumption of
an isotropic solute molecule, and the fourth terms were derived
on an assumption which is likely to be valid only when both
the solvent and the solute are highly polar.
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_3p_
The dependence on the solvent of the frequency difference
between the 0-0 bands of corresponding absorption and fluores-
cence bands should be interpretable in terms of electrostatic
interactions only. Since the interpretation is complicated
neither by the general red shift nor by solute dipole-induced
solvent dipole interactions, concurrent studies of absorption
and fluorescence spectra should provide more definite informa-
tion about the dipole moment of the solute in its lowest excited
singlet state than can be inferred from data on absorption
spectra alone. Eq. (15) represents the frequency difference
mentioned above.
Comparison,woth_Previous Work-- Eq. (1+) may be compared
with the formula derived by Ooshika . As far as the electro-
static contributions are concerned to two expressions appear to
be quite different, but the dlfferece is probably superficial.
However, the present result has the substantial advantage that
the electrostatic contribution is expressed in closed form.
The present theory 1e cis natu~ ~, iy to a classification of
solutions previously adopted by Bay ~ ics and McRae 6. In their
case I (both solute and solvent non?polar) the first term in
(10) alone contributes to the frequency shift. In case II
(solute non-polar, solvent polar) the first and fourth terms
contribute, while in case III (solute polar, solvent non-polar)
the first and second terms contribute. In case IV (both solute
and solvent polar), all four terms make a contribution. Case I
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-31as
has already been discussed above. In the following discussion
of cases II Iv, we shall avoid unnecessary duplication of
that given in the previous paper6 , with which we are sub-
stantially in agreement, confining our attention to certain
modifications or extensions suggested by the present work.
Cases II and III of Bayliss and McRae,-- In the discussion
of case I, it was mentioned that the frequency shifts vary
approximately linearly with na-; l2nz+l . The same
behavior is ordinarily observed in cases II and III, although
in case II, apparently anomalous shifts are produced by highly
polar solvents such as water21, methano124925 and ethanol21,26,
(26) R. Schnurmann and W. F. Maddams, J. Chem. Phys., 19, 1430
(1951).
The phenomena in case II do not necessarily conflict with the
theory, since we may say that the first term in (10) is ordi-
narily much larger than the fourth (i.e. the general red shift
is dominant) but that if the solvent is highly polar the fourth
term (i.e. the quadratic Stark effect) may make an important
contribution. In case III, the dependence of the frequency
shift on the solvent refractive index is represented by the
first two terms in (14) or (14'). Since n0 ordinarily differs
little from n 27, the theory readily explains the observed
behavior.
(27) The solvent water is exceptional in this respect. The value
of no is about 59 while nz for visible light is 1.7728.
(28) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions,"
Butterworth, London, 1955, p. 10.
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Case IV of BaYli~s and McRae.-- To simplify this dis-
cussion, we write the last two terms of (10) in the form in-
volving the reaction field, viz.Q f hc) (M o- A4 u). R and
(3/2c)(-c') RZ respectively. Here, the significance
of the reaction field is analagous to that of E" , as dis-
Nw
cussed at the beginning of this Section. The nature of the
phenomena in case IV depends critically on the relative magni-
tude of the above terms. In all cases of practical interest,
the first of the two terms contributes a significant proportion
of their sum. Whether or not the contribution of the second
term is important can only be judged from the experimental
results, because the difference between ground and excited
state polarizabilities (indeed, even the sign of the difference)
is in general difficult to predict.
If the contribution of the quadratic Stark effect is
indeed negligible29, the qualitative interpretation is the same
(29) "Negligible" has a different meaning in the discussion of
case IV than in that of the preceding cases, the discussion of
case IV being carried on at a lower level of approximation.
as that ro osed6
previously p p However we are able to give
semi-quantitative expression to the qualitative theory, with
the aid of (1+) or (i+'). We illustrate this by the applica-
0
tion of an approximate form of (1)+) to the A 5500 A absorp-
tion band of phenol blue.
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Application to Phenol Blue.-- Solvent effects in the phenol
blue spectrum have been studied by Brooker and Sprague309 whose
(30) L. G. S. Brooker and R. H. Sprague, J?Am Chem. Soc., 63 9
~..,
3214 (19).i-1).
results imply that the frequency shifts increase in the order
of solvent dielectric constant. The more extensive study by
LeRosen and Reid31 shows that there is no correlation
with the
(31) A. L. LeRosen and C. E. Reid, J. Chem. Phys., 209 233 (1952).
dielectric constant, but that the shifts induced by hydrocarbon
and aryl halide solvents vary regularly with the solvent re-
fractive index. LeRosen and Reid found no correlation of the
shifts induced by other solvents with any solvent macroscopic
property or combination of such properties. They did, however,
present a qualitative interpretation of the results in terms of
various types of intermolecular interactions, including hydrogen
bonding.
Eq. (l4) may be written in the approximate form
z
(A L o + ~) .n~;! f- C ~ -~ L _ t-:
2r+, LD2
(17)
where refractive indices at all frequencies have been replaced
by the value appropriate to the sodium D line, and the quadratic
Stark effect has been neglected.
A , J3 and C are constants
characteristic of the solute. Fig. 1 illustrates the fit of the
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above equation to the experimental results for phenol blue.
In Fig. 19 points are shown for all solvents whose
effects have been measured30'319 except water. In the case
of water' (17) is inapplicable because of the considerable
difference between /10 and l~T 27,
For saturated hydrocarbon solvents9 bromocyclohexane,
aliphatic alcohols and water, the value of 1_a was taken
0 0
. to be 1000 A9 for other solvents, 1250 A was adopted. The
fit of predicted and observed shifts was insensitive to
E VA p the assumed ratio, which is arbitrary, places equal
weight on AL b and for saturated hydrocarbon solvents.
The best value of C/A was determined by the method of
least squares, omitting the points represented in the
figure by open circles. The value of A was adjusted to
make the theoretical straight line pass through the points
for n-he ptane and pyridine (the vapor spectrum is not
available). The neglect of the quadratic Stark effect is
justified by the fit of the points to a straight line, as
shown in the Figure.
A glance at Fig. 1 shows that the solvents are separated
into two distinct series according to their ability to form a
hydrogen bond with the solute. Although (l4) is not applicable
to the total frequency shifts caused in part by hydrogen bond-
ing, it may be capable of predicting that part of the shift
exclusive of the contribution of hydrogen bonding. The points
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-35--
representing non-hydrogen bonding solvents are fitted to the
full straight line with a root mean square deviation of about
100 cm , which is of the same order of magnitude as the ex-
perimental error in the determination of band frequencies in
solution spectra ( '' 50 cm-1) . The points representing non-
polar solvents illustrate the behavior mentioned above as
typical of class III. The remaining points (non-hydrogen bond-
ing polar solvents) show that frequency shifts in class IV may
be correlated with a particular function of both the dielectric
constant and refractive index of the solvent, even though there
is no general correlation with either quantity separatel.yo
The theory is evidently capable of reproducing the gross
features of the phenomena, but not all of the finer details.
For example, all of the points representing the aliphatic ethers
lie near the full straight line, but the relative shifts
induced by different members of this group of solvents do not
support the theory. No doubt the discrepancies are due in
part to the simplifying assumptions about the refractive index
and the weighted mean wavelength, the crudity of the model, and
the anisotropy of phenol blue. At least one of the dis-
crepancies, in the case of the solvent dioxane, may reflect a
more fundamental failure of the approach based on (i+). The
dioxane molecule has two non-adjacent dipolar groups whose
moments cancel, so that the effective reaction field R is
Yw
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_36.
probably greater than is indicated by the macroscopic properties
(cf. the discussion of (10) at the beginning of this Section).
LeRosen and Reid31 tried to explain the results which they
obtained with non-hydrogen bonding solvents in terms of solute
dipole-induced solvent dipole interactions only. The present
work indicates that permanent dipole interactions make an im-
portant contribution to the frequency shifts induced by polar
solvents.
The constant C , which appears in the approximate form
of (1}+), corresponds to(2/hca)(M a--M ). tv/ In (i+),
so that from the best value of C found as indicated above
(-1530 cm) we may calculate the excited state permanent
dipole moment of phenol blue. The ground state dipole
moment is 5.80 Debye32. The most appropriate cavity radius
(32) C. P. Smyth, "Dielectric Behavior and Structure,"
McGraw Hill , New York, 1955, p. 3~+8.
0 0
probably lies between A and 5 A. If we assume that the
ground and excited state dipole moments are parallel, we
calculate the excited state dipole moment to be between
0 0
7.5 Debyes (a . )+ A) and 9.1 Debyes (a 5 A) . Both are
of the expected order of magnitude, but they do not offer
strong support for the suggestion30 that a Zwitterion
structure contributes heavily to the excited state.
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Application to Merocyan nes. We now discuss the remark-
able solvent-induced frequency shifts observed in the lowest-
frequency singlet-singlet absorption bands of merocyanine dyes.
The results of extensive studies, mainly by Brooker and co-
workers33934 are typified
9 by those illustrated in Fig. 2a. The
(33) L. G. S. Brooker, G. H. Keyes, R. H. Sprague, R. H. Van
Dyke, E. Van Lare, G. Van Zandt, F. L. White, H. 0 J. Cressman
and S. G. Dent, J_. Am, Chem. Soc., , 5332 (1951).
(34) L. G. S. Brooker, G. H. Keyes and D. vi. Heseltine,
J. Am. Chern. Soc., 73, 5350 (1951) .
Brooker and co-workers have studied solvent effects on maximum
extinction coefficients as well as band frequencies0
three dyes IV, V and IX (notations of Brooker, Keyes and
3)+
Heseltine)have
a common acidic (electron-attracting) nucleus,
and basic (electron-repelling) nuclei whose basicity decreases
in the order Iv > V,> IX3, Almost certainly, this i
is the order
of decreasing ground state permanent dipole moment. The out-
standing feature of the frequency shifts, as revealed by
Fig. 2a, is that the band of the most highly polar dye (IV)
shifts to higher frequencies as the water content of the solvent
is increased, while the band of the least polar dye (Ix) shifts
initially to lower, and then to higher frequencies. Intermediate
behavior is exhibited by the dye of intermediate dipole moment.
The phenomena have been interpreted by Br ooker5 in terms
of the relative solvent stabilization of polar and non-polar
resonance structures, and this approach has been elaborated by
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(i//ic)( M- A4).7 *(/2hc)(o-cj'r)N2( 18>
-38-
Simpson35 and b platt36. As
by a particular application of the
(35) ,r. T. Simpson, J. Am. Chem, Soc, 5359 (1951).
(36) J. R. Platt, J. Chem. Phys.,~?2~j99b ?i956).
present theory, we advance an alternative (but not funda-
mentally different) explanation in terms of the quadratic
Stark effect.
The merocyanine dyes have just the right combination of
properties to favor the quadratic Stark effect. First, they
are highly polar, implying that in moderately or highly polar
solvents R (and hence R Z ) is particularly large; second,
the first singlet transition is strong ( f N 1) . The second
property makes it reasonable to assume, as is necessary in the
following interpretation, that the polarizability of any given
dye in its lowest singlet excited state is considerably less
than in its ground state. This can be understood upon in-
spection of the usual formula for the polarizability10. The
lowest singlet transition, being strong, makes a sizeable con-
tribution to the ground state polarizability, and a negative
contribution of the same magnitude to the lowest excited
singlet state polarizability.
A particularly simple discussion is made possible by
writing (10) in a form appropriate to the limiting case of
large R viz.
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where represents the frequency shift induced by a
non-polar reference solvent, and the frequency shift as again
expressed in terms of R instead of E . We assume that
in order to preserve the orthogonality of ground and excited
electronic state functions in a series of merocyanines of
decreasing ground state dipole moment, the excited state dipole
moments either stay nearly constant or tend to increase in the
same order as the ground state dipole moments decrease. In
Fig. 2b, the frequency shift L V - Q Ref is plotted against
R in the three possible cases: /V1 A'1~ greater than,
less than and equal to zero. (In the discussion of visible
merocyanine spectra, the ground and excited state permanent
dipole moments may be considered parallel). The comparison of
Figs. 2a and 2b shows that (18) is capable of reproducing the
gross features of the phenomena, for R may be assumed to in-
crease monotonically with water content in an aqueous pyridine
solvent. The comparison must remain purely qualitative, because
there is in this case no reliable way of relating R to the
solvent composition. Indeed, the reaction field has only
formal significance in the present application. The reason for
this has been explained, with explicit reference to
at the beginning of this Section, Eq. (18) itself is far from
realistic, because the first two terms in (10) may well suffer
significant changes on passing from solvent to solvent. However
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it is unlikely that the consideration of the general red shift,
for example, would alter the qualitative conclusions drawn here.
In spite of the drastic simplifications which have
been introduced, the present discussion is readily shown
to involve quantities of the correct order of magnitude.
For this purpose the ordinate in Fig. 2b was chosen to run
to 2 x l05 e.s.u,, which is the order of magnitude of the
reaction field indicated by the simple model, for a solvent
u
of high dielectric constant and M00 = 10 Debyes. The
difference between the ground and excited state permanent
dipole moments is almost certainly of the order of a few
Debyes, and 1.5 Debyes was chosen for the sake of illus-
tration. In order to reproduce the gross features of the
phenomena within the chosen range of R , the difference
between the ground and excited state isotropic polariza-
bilities must be 0.5 - 1.0 x l0123 cm3, i,ee, about one-
third of the contribution of a strong visible transition
to the ground state polarizability.
In his discussions of the phenomena, Brooker5 has
focused attention on the plot of the peak extinction co-
efficient E against the corresponding wavelength A m , and
he has associated the maxima in such curves with the iso-
energy point, at which the principal polar and non-polar
resonance structures have equal energies. At the isoenergetic
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point the ground and excited state dipole moments of the solute
in solution should be equal. From (18) we find that the condition
for a minimum value of Lxv- LSVRef (iW u, Al o) is
Moo f 3~i~ R - M u t3a u . For a rod-like solute
molecule, 3aa and 3a are polarizabilities appropriate to
a field directed parallel to the dipole moments, so that
AAU U < u
`V00 ~ 3ao ' and ~t?~ ' 3q'? irs:: represent dipole
moments of a rod-like solute molecule in solution. Since the
merocyanines may be considered nearly rod-like, the present
theory suggests that in the approximation of neglecting the first
two terms in (10), the minimum in Q 72 -- LS 717 f should be
associated with the isoenergetic point. The minimum in
and the maximum in the plot of E,~ vs.
ordinarily occur at nearly the same solvent composition37. The
(37) This is not the case in the curves for Brooker, Keyes and
Heseltlnets dyes IX and x3. However, since these dyes are
relatively weakly polar, the first two terms in (10) may make an
important contribution.
present discussion thus tends to support the views previously
expressed b Brooke and fact indicates that Brooker's con
clusions remain valid even if there are more than two resonance
structures making important contributions to the combining
states.
Other Interactions.-- Finally we point out that not all
~'~NWVY~Nti1/Y~rYIY~Y
frequency shifts are caused entirely by dipole interactions, but
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that other types of interaction may make important or even
dominant contributions in certain cases. For example, charge--
transfer complex formation is generally accompanied by shifts
in band frequencies; this topic has been reviewed recently38,
(38)(a) L. J. Andrews, Chem. Revs., 54, 713 (1954)9
(b) L. E. Orgel, quart,. Rev. Chem. Soc., 8, 422 (1951+).
Again, a large frequency shift may arise from intermolecular
repulsive forces, in the event that the solute molecule suffers
a marked change of equilibrium size 39 or shape 4o941 upon
(39)(a) N. S. Bayliss and A. L. G. Rees, J. Chem. Phys., 8, 377
(19)-f0); w
(b) N. S. Bayliss, A. R. H. Cole and B. G. Green,
Australian J. Sci. Res., Al, 472 (1948)9
c) A. L. G. Rees, J. hem. Phys., $, 429 (1940)0
(40) k. W. Hausser, R. Kuhn and E. Kuhn, Z, phy skalChem.,
B29, 1+17 (1935).
This work has been summarized and discussed by Forster 1.
(41) Reference 25, p, 136.
excitation.
Acknowledgements.-.... The writer gladly acknowledges the
award of a Hackett Studentship by the University of Western
Australia, and the kind interest of Dr. N. S. Bayliss, Dr.
H. C. Longuet-Higgins, Dr. M. Kasha and Mr. M. F. O'Dwyer.
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 Sanitized Copy Approved for Release 2010108109: CIA-RDP81-01043R000200200012-0
(Caption to Fig. 1)
Fig. 1. Calculated vs, observed frequency shifts in the
0
5500 A band of phenol blue. The frequency shifts are cal-
culated from Eq. (17) ( A = -5.5 x 108 cm-2 9 B1 . -5500 cm 1
,
C = -1530 cm ). Hydrogen bonding solvents (open circles) are
indicated by name. The remaining solvents (full circles) are
indicated as shown below. In the following list of solvents, the
refractive index and static dielectric constant of each solvent
are quoted in that order. In a few cases, static dielectric
constants are not available; values estimated from those for
related compounds were used in the calculation, and the estimated
values are given below in parentheses= The solvents are listed
in the order in which they induce increasing red shifts.
H Heptane 1.390 1.9 Ac Acetone 1.360 21.0
Oc Octane 1.391 1.9 C1B Chlorobenzene 1.519 5.5
Ch Cyclohexane 1.419 2.0 CD Carbon disulfide 1.618 2.6
Dd D odecane 1.417 2.0 BrCh Bromocyclohexane 1.491 7.9
EtE Ethyl ether 1.345 4.4 CiT p-Chlorotoluene 1.516 5.6
BuE Butyl ether 1.193 (3.4) An Anisole 1.509 4,3
IpE Isopropyl ether 1.363 (3,9) PhE Phenyl ether 1.574 3.7
AmE Amyl ether 1.409 2.8 BrB Bromobenzene 1.553 5.2
D Dioxane 10417 2.2 IT o-Iodotoluene 1.603 (5)
B Benzene 1.493 2.3 P Pyridine 1.502 12.4
IN 1-Iodonapthalene 1.695 (4)
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 D
C CI~lOYOf~r~~
j3utariol
M etho r o I
'4cetu Acid d
H ~Ch
ac, I . J 1
C
1000 - 2OO
abse rved F=rc9uehc y Shifts (cm``)
(Relo h ye 1c) that fncicieed b y lriefjtar
Fig I
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-1.000
INS
v (cm')
(Eq. 1 7)
X000
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CjB
CT'
Ah
CIr
Bra
Ac
 Sanitized Copy Approved for Release 2010108109: CIA-RDP81-01043R000200200012-0
(Caption to Figs. 2a and 2b).
Fig. 2a (top). Variation of merocyanine band frequency
with percentage of water in aqueous pyridine solvent. The
abscissa is the frequency shift relative to the shift
induced by pure pyridine. Curves are drawn for three mero-
cyanine dyes, whose ground state dipole moments are considered
to decrease in the order: IV > V } IX (see text). The
optical data and dye notations are those of Brooker, Keyes
and Heseltine34.
Fig. 2b (bottom). Variation of band frequency with the
reaction field, according to Eq. (18) (~o "ate
/1 4 - - 1.5 0 -1.5 Debyes).
o.67 x lo'23 cm3 9 Mc tt
These curves are meant to illustrate the general behavior
predicted by the theory. The numbers are considered to be of
the correct order of magnitude (see text), but are otherwise
arbitrary. The curves do not refer specifically to the
dyes of Fig. 2a.
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 Sanitized Copy Approved for Release 2010108109: CIA-RDP81-01043R000200200012-0
60
i
V /afet_
"a
0
;
-'.
\')
40o -.200 0 200 1-00 60o
CbservEd Fi-Qqu~nc y Shifts (cm-')
(Relative to T i induced by ,yt-iCine)
/V/," /W L
O'15
.~ -
1< X (0 C.,U.
.010
0
-40o
200
C)
20() 400
V - ~VRQF (crm"')
Fiq. 2
E9. Is)
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(;OU
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