FUNDAMENTAL ASPECTS OF PHOTOSENSITIZATION. INTERCOMBINATIONS IN MOLECULES

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• Publication Date: June 15, 1958
• Content Type: REPORT

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TECHNICAL REPORT NO. 2
TO THE
CHEMISTRY DIVISION
OFFICE OF SCIENTIFIC RESEARCH
U. S. AIR FORCE
?
STAT
STAT
FUNDAMENTAL ASPECTS OF PHOTOSENSITIZATION.
INTERCOMBINATIONS IN MOLECULES
JUNE 15, 1958
STAT
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4,
Technical Report No. 2
to the Chemistry Division U. S. Air Force Office of Scientific Research
STAT
FUNDAMENTAL ASPECTS OF PHOTOSENSITIZATION.
INTERCOMBINATIONS IN MOLECULES
4:4
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STAT
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Technical Report No. 2, to the U. S. Air Force Office of
Scientific Research, Air Research and Development Command.
June 15, 1958 STAT
INTERCOMBINATIONS
FUNDAMENTAL ASPECTS OF PHOTOSENSITIZATION.
IN MOLECULES.
Table of Contents
1. Solvent Effects in Merocyanine Spectra, E. G. McRae STAT
(SPectrochimica Acta).*
2. Intramolecular Twisting Effects in Substituted Benzenes.
I. Electronic Spectra, Eion G. McRae and Lionel Goodman.
(J. Molecular Spectroscopy).
3. Intramolecular Twisting Effects in Substituted Benzenes.
II.. Ground State Properties.
(I. ,Chemical Physics).*
if. Energy Transfer in Molecular Complexes of Sym-Trinitrobenzene
with Polyacenes. I. General Considerations,
S. P. McGlynn and J. D. Boggus.
(J. American Chemical Society),*
STAT
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1,2
SOLVENT EFFECTS ON MEROCYANINE SPECTRA
by.E. G. McRae3
Department of Chemistry, University of Western Australia, Nedlands,
Western Australia, and Department of Chemistry, Florida State
University, Tallahassee, Florida.
(1) Taken in part from a thesis submitted by E.-G. McRae for the
degree of M. Sc. at the University of Western Australia.
(2) Part of the work was carried out under a contract between
the U. S. Air Force, Office of Scientific Research, ARDC, and the
Florida State University.
(3) Present address: Department of Chemistry, Indiana University,
Bloomington, Indiana.
(Abstract)
Solvent effects on the visible absorption spectra of three
merocyanine dyes are described. The dyes comprise two (I and II)
of exceedingly high polarity, and a third (III) less polar than
I and II but still highly polar by ordinary standards.
/
I. H3CN/:)=
0..
0-0
/ 1
II. 3H ctsn=cH-en=c14-cw --:.c.\
N.?..1
C '
5 \
= C-14 de4
?
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The absorption curves, values of the extinction coefficient and
frequency at the absorption maxima ( C max and), max respectively)
and oscillator strengths are given for I dissolved in pure
solvents, and for dyes II and III in a variety of both pure and
mixed solvents. For each dye, 6 max and 1) max undergo pro-
nounced solvent effects, but the oscillator strengths are in-
sensitive to solvent perturbations. The results are discussed
in terms of a simple theory in which the combining states are
considered as superpositions of a polar and a non-polar resonance
structure. A more detailed theory is applied in the interpre-
tation of the frequency shifts induced by non-hydrogen bonding
solvents.
I. INTRODUCTION
The visible absorption spectra of highly polar merocyanine
dyes undergo extraordinary solvent effects. The phenomena were
first reported by Brooker and his collaborators,45 who studied
(4) L.G.S. Brooker, G. H. Keyes, R. H. Sprague, R. H. Van Dyke,
E. Van Lare, G. Van Zandt, F. L. White, H.W.J. Crepsman and
S. G. Dent, J. Am. Chem. Soc., 5332 (1951).
(5) L.G.S. Brooker, G. H. Keyes and D. W. Heseltine, J. Am. Chem.
Soc., 2, 5350 (1951).
the spectra ofl several merocyanines dissolved in pyridine - water
mixed solvents. It was found that variation of the percentage
water content of the solvent gives rise to pronounced changes of
both the maximum extinction coefficients, e max' and the corre-
sponding frequencies, 11 max' at the visible absorption maxima.
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The main qualitative features of the solvent effects have
been described in a recent review' by Brooker.6 For an
(6) L. G. S. Brooker, Experientia Supplementum II (XIV the
International Congress of Pure and Applied Chemistry), 229 (1955).
exceedingly highly polar dye in a pyridine - water or lutidine -
water mixed solvent, the progressive addition of water to the
solvent leads to a shift of 1) max to higher frequencies, with
a concomitant diminution of 6 max. The curve of C maxml.), max
has the shape of the "highly polar" branch of the curve shown in
Fig. 1. The arrow indicates the effect of adding water to the
solvent. The opposite behavior is exhibited in the case of a
dye which is comparatively weakly polar (but Which may still be
fairly highly polar by ordinary standards). Here, the plot of
C max vs* I/ max resembleS the "weakly polar" branch (Fig. 1).
For dyes of intermediate polarity, the initial addition of water
to a pure pyridine or lutidine solvent has an effect qualitatively
similar to that observed with weakly polar dyes. Upon further
progressive addition of water to the solvent, C max and
max
pass through extreme values, and the subsequent differential
solvent effect is qualitatively Similar to that observed with
exceedingly highly polar dyes.
For convenience in a. subsequent discussion, we shall refer
to points on the C max X' max max plot as "solvent representative
points" for the dye in question. The point on the ,plot at which
C max attains its maximum value will be called the "reversal point",
and will be thought of as the junction of the two branches.7
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(7) Fig. 1 is slightly idealized in that the minimum of .1,/ max is
shown to coincide with the reversal point. Actually, the
two extremes do not exactly coincide, although in most but not
all cases they lie quite close together.
With this nomenclature, the above description of merocyanine
solvent effects may be summarized as follows: for exceedingly
highly polar dyes, the representative points for pyridine - water
or lutidine - water solvents lie on the highly polar branch, for
relatively weakly polar dyes they lie on the weakly polar branch,
and for dyes of intermediate polarity they straddle the reversal
point.
The work reviewed by Brooker6 is extensive in that it en-
compasses the spectra of dyes covering a wide range of polarity.
However, the published data pertain only to the absorption
maxima, and the solvents used were limited largely to pyridine -
water and lutidine - water mixtures. In this paper, we give a
more detailed description of solvent effects on the visible
absorption spectra of three of the merocyanines previously studied
by Brooker et Al.4'5 Of the three dyes, I and II, which have
the same pair of end-groups, are exceedingly highly polarl while
III has intermediate polarity.8 The absorption curves of II
(8) I and II are labeled XII (n = 1 and n = 2 respectively) in
ref. 4, and III is labeled V in ref. 5.
In pure solvents have been given by Bayliss and McRae, in ?.
preliminary report on the present work.9
(9) N. S. Bayliss and E. G. McRae, J. Am. Cheri. Soc., 21?, 5803 (1952)...
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ii fl.ge.
III
-5-
0
/C-0
C14 -CH C
C14- OW= Ci1-C14 *2=
s\C. = CH =
e 143
Taken together with the data previously published by Brooker
et al,45 our results provide an overall picture of solvent
effects on merocyanine band frequencies, intensities (oscillator
strengths) and band shapes. This information is thought to be
of particular interest in view of several recent discussions,
of the origins of solvent effects on merocyanine spectra.69/10-12
(10) W. T. Simpson, J. Am. Chem. Soc., 21, 5359 (1951).
(11) J. R. Platt, J. Chem. Phys., gl, so (1956).
(12) E. G. McRae, J. Phys. Chem., 61, 562 (1957).
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II. EXPERIMENTAL.
Solvents: - Most of the solvents used in this work have
been described in a previous paper,13 and the remaining solvents
(13) N. S. Bayliss and E. G. McRae, J. Phys. Chem., 1130 1006 (1954).
are described below. Except where other references are given,
the physical constants in parentheses are those quoted by
Timmermans.114.
(14) J. Timmermans, "Physico-chemical Constants of Pure Organic
Compounds", Elsevier Publishing Co., Amsterdam, 1950.
Aniline of a technical grade was dissolved in hydrochloric
acid, and the main impurity, nitrobenzene, was removed by steam
distillation. The aniline hydrochloride was neutralized, and
steam distilled. The distillate was dried with potassium
hydroxide, and fractionated twice under reduced pressure. It
was stored in the dark over potassium hydroxide pellets, and
fractionated again immediately before use. B. P. 94?C/35MM.
(94/35)15; 111)20 1.5860 (1.5863).
(15) Landolt-Bornstein, "Physikalisch-Chemische Tabellan", 5th Ed.,
Eg. III C, Springer, Berlin, 1935, p. 2462.
Dioxane of British Drug Houses Technical grade was refluxed
for ten hours with 1/10 its volume of 0.1N hydrochloric acid.
It was then allowed to stand for one day over scdium hydroxide
sticks, and fractionated. It was kept in the dark and used
within one week of purification. B. P. 101.6?C (101.4);
LID20 1.4215 (1.4214).
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Formamide was prepared from ethyl formate by the method
of Slobodin et al,16 and the product was fractionated under
(16) Ya. M. Slobodin, M. S. Zigel and M. V. Yanishevska, J.
Applied Chem. (U.S.S.R.) 16, 280 (1943). See Chem. Abstr. 32,
702 (1945).
reduced pressure. The formamide was again fractionated immedi-
; np
ately before use. B. P. 116?C/39.2 mm. 2/3 1.4482 (1.4475).
Pyridine of a grade conforming to British Drug Houses
Analar standards (Judex analytical reagent) was allowed to stand
for one week over sodium hydroxide sticks, refluxed for ten
hours over freshly burned calcium oxide, and fractionated.
B. E. 115.2?6 (115)4); 418. 7 1.5106 (1.5106).
Buffer solutions: For the a range 5.0 - 8.0, McIlvaine's
standard buffer solutions17 were prepared, using Analar grade
(17) "Handbook of Chemistry and Physics", 24th Ed., Chemical
Rubber Publishing Co., 1940, p. 1374.
reagents. The solvent of Eli 9 was a 0.05 molar solution of
Analar grade borax.
Merocyanine Dyes: Pure merocyanine dye samples were supplied
by Dr. L. G. S. Brooker,
Solutions: In so far as permitted by the dye solubill.ties,
the dye solutions were prepared to give a minimum transmission
reading between 20 and 70%. This corresponds to a dye concen-
tration in the vicinity of 5 x 10-6M. Where practicable,
solutions of known dye concentration were prepared. Weighed
1 mg. dye samples were dissolved, and the resulting solutions
diluted either by volume or by weight. The latter method was
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used for most of the solutions in mixed solvents. Volume di-
lutions were carried out with a standardized 5 ml. pipette
and standardized 25 ml. flasks. Where weight dilution was
employed, the dye molarity was calculated with the aid of the
tabulated densities of the mixed solvents in question.18
(18) Landolt-Bornstein, "Physikalisch-Chemische Tabellen",
5th ed., Springer, Berlin, 1935.
Spectra': Except in the tests of Beer's law (see below),
all spectra were measured with a Beckman spectrophotometer,
model DU, using matched 1 cm. Corex cells.
Frequencies, V (cm-1), were obtained from the wavelength
settings, no vacuum corrections being applied. The molar ex-
tinction coefficients, E were calculated according to the
formula:
E (1/ed) Ian (100/Z),
where c denotes the molarity, d the path length in cm., and T
the percentage transmission reading. Oscillator strengths, f,
were calculated from the absorption curves according to the
formula19
(19) R. S. Mulliken and C. A. Rieke, Rep. Prog. Physics 8,
231 (1941).
f = 4.32 x 10-9 fE di/
Errors: The errors in the determination of V ranged
max
from 20 to 50 cm-1, depending on the band width.
The errors in the measurement of absolute extinction co-
efficients, which were essentially concentration errors, did
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not exceed 5%. In several cases it was not possible to measure
extinction coefficients, because of sparing dye solubility. In
these cases,
E max was estimated by adjusting the area under
the absorption curve to correspond to the oscillator strength of
the dye dissolved in water. The justification of the procedure
rests on a particular result of the present work, namely that
the oscillator strengths are rather insensitive to solvent per-
turbations. The percentage error of E max determined in this way
is considered not greater than the total percentage variation
of oscillator strength, viz. 20% (Sec. III).
In merocyanine spectra, the visible absorption band is not
overlapped appreciably by bands at higher frequencies; conse-
quently the same errors in the oscillator strengths were only
slightly greater than those in the extinction coefficients.
In a few cases, which are noted individually in the next
section, the errors were probably greater than indicated above.
In the cases in which a comparison is possible, our results
agreed with those of Brooker et L1,4$5 within the limits of
error quoted above.
Tests of Beer's Law: Beer's law tests were carried out
using a Beckman spectrophotometer, model DK, with 0.1, 2.0 and
10.00 cm. cells. The spectra of dyes I and III were measured in
the concentration range 3 x 10to 3 x 10-5M. Most of the
measurements were carried out at concentrations near the middle
of this range (iv 5 x 10-6M). The solvents in each case were
pyridine - water mixtures. The solvent for dye I contained 90
mole % pyridine, and that for dye III, 80 mole % pyridine. In
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both cases, Beer's law was obeyed well within the dilution error,
and there was no detectable change of band shape throughout the
hundred-fold range of concentration.
III. RESULTS.
The solvents used in this research are listed in Table 1,
together with their designations in the figures, their relevant
physical properties, and the values of some derived properties
thought to be of importance in the interpretation of the solvent
effects (Sec. IV).
Dyes I and II: The results Obtained with dyes I and II dis-
solved in pure solvents (Table 2, Figs. 2,3) are qualitatively
similar, the solvent effects being somewhat less pronounced in
the case of I. In the case of dye II, the results include the
effects of mixed as well as pure solvents (Table 3, Fig. 4).
The absorption bands of dyes I and II in 0.26N hydrochloric
acid lie at higher frequencies than the corresponding curves for
water solvent. The absorption curves obtained at lower acid
concentration passed through a well-defined isosbestic point,
Indicating that the higher-frequency absorption is due to the
protonated dye in each case.
Freauencies: The pure solvents induce increasing shifts to
higher frequencies in the order: dioxane, chloroform, nitrobenzene
pyridine, acetone, aniline, ethanol, formamide, water. As has
been pointed out previously,9 there is a sharp distinction
between the effects of the hydrogen bonding solvents (last four
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members of the above sequence) and the non-hydrogen bonding
20
solvents (first five members).
(20 It is not clear whether or not. chloroform should be classified
as a hydrogen bonding solvent. Presumably it can form hydrogen
bonds with the dyes, yet its solvent effect is intermediate be-
tween those of dioxane and pyridine. A similar result appeared
. in the writer's analysis of solvent effects on the spectrum of
phenol blue;12 there, it was found that the frequency shift pro-
duced by chloroform was close to that Predicted for a non-
hydrogen bonding Solvent having the same macroscopic properties.
In this paperl chloroform will be considered provisionally as a
non-hydrogen bonding solvent.
In each case, the absorption of the protonated dye lies at
a higher frequency than that of the dye itself dissolved in
water.
Intensities: The band intensities do not undergo pronounced
solvent effects, nor do they show any progressive variation with
the band frequency. Yet, for each dye, some of the observed
oscillator strengths differ significantly from the mean observed
oscillator strength. For example, acetone, and to a smaller
extent, pyridine, appear to cause a relative intensification.
It is noteworthy that the intensity of absorption of the proto-
nated dye is nearly the same as that of the dye itself dissolved
in water.
Band Shapes: The absorption curves for dyes I and II in
dioxane each display a definite shoulder on the high-frequency
side. In the case of dye II, further. structure may be discerned
at still higher frequencies. With dye II, the vibrational
structure is developed even more strongly in benzene-rich-
benzene-acetone and benzene-pyridine mixed solvents, a second
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peak appearing in each case. The separation of the peaks is
1030 ? 100 cm-1.21
(21) The absorption curves obtained with benzene-rich mixed sol-
vents changed slowly with time, probably because of the dye
crystallizing out. They are less accurate than the other curves,
but the frequencies were reproducible within the quoted limits
of error.
The structureless absorption curves become progressively
broader with increasing shift to higher frequencies. On plotting
the corresponding solvent representative points for dye II, it
is found that within the limits of error in the determination of
En , they all lie close to a curve corresponding to the highly
polar branch. (Fig. 5. The values of E for dioxane-water
max
solvents were determined on the assumption of a constant os-
cillator strength. The actual values may be as much as 20%
higher). It is interesting that the point for the protonated
dye lies near the extrapolated curve. The representative points
corresponding to the absorption curves with structure lie close
to a curve corresponding to the weakly polar branch, between the
reversal point and the minimum of )) max*
Dye III: At first sight the absorption curves for dye III
in pure solvents (Table 2, Fig. 6) appear to bear no relation
to those obtained with dyes I and II. However, the results are
readily rationalized with reference to the absorption curves
obtained with mixed solvents (Table 4, Fig. 7), and the C. max
vs? 1) max plot showing points for both pure and mixed solvents
(Fig. 8). Again, the solvent representative points all lie
close to a curve having the general shape of that shown in
Fig. 1.
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The visible absorption of dye III in water is the super-
position of the absorption of the dye itself and a higher-
frequency absorption attributed to the protonated dye. The ab-
sorption curves for the separate components (Fig. 6) were
obtained in. buffer solutions of pH 9 and pH 6 respectively. At
intermediate EU, the composite absorption curves were found to
pass through a definite isosbestic point. A similar result was
obtained with the solvent ethanol, in which the composite ab-
sorption curve varied slowly with time. By observing the ab-
sorption over a period of a few hours, it was resolved into the
two curves shown in Fig. 6, the higher-frequency absorption being
attributed to the protonated dye. The curves obtained with
ethanol solvent are somewhat less accurate than the other curves
shown in Fig. 6. The absorption observed with the solvent formamide
Is thought to be due to the protonated dye.
Freauencies: Of the pure solvents, ethanol has a repre-
sentative point closest to the reversal point. The representa-
tive point for water definitely lies on the highly polar branch
of the C max ma. 11max curve, while the points for the non-
hydrogen bonding solvents all appear to belong to the weakly
polar branch. However, on the weakly polar branch the solvent
order of increasing shift to higher frequencies is not the reverse
of that observed with dyes I and II, as would be expected if
there were a perfectly regular relationship between Emax and
)) max'
,The consideration of band frequencies alone affords no
definite distinction between the effects of hydrogen bonding ?
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and non-hydrogen bonding solvents. Perhaps the most concise
description of the effect of hydrogen bonding, in terms of ex-
perimentally observed quantities, is that it causes a displace-
ment of the solvent representative point in the arrow direction
along the 6 max max
curve (Fig. 1). This does not
22. 11
necessarily imply a large frequency shift.
Intensities: Again, the band intensities appear to be
rather insensitive to solvent perturbations, although the vari-
ation of oscillator strength from solvent to solvent slightly
exceeds the experimental error in a few cases.
Band Shapes: The absorption curves correspondong to repre-
sentative points lying on the weakly polar branch display defi-
nite vibrational structure. A high-frequency shoulder or
second peak is observed in every case, together with some less
pronounced structure at still higher frequencies. As the sol-
vent representative point moves away from the reversal point,
the second peak grows up at the expense of the first, actually
surpassing It in intensity in the case of a benzene-pyridine
solvent.21 (Throughout, C max and )) max refer to the lower-
frequency peak). The separation of the peaks is 1100 100 cm-1
(average of observed separations).
On the high-frequency side of the reversal point, the ab-
sorption curves undergo progressive broadening similar to that
observed with dyes I and II. The trend extends to the absorption
curves of.the protonated dye, the corresponding points lying
near the extrapolated E max
max curve (Fig. 8).
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Gross Features of the Solvent Effects: Inasmuch as the
dyes I-Ill are typical members of the series of dyes studied
by Brooker et al,/5 the gross features of the solvent effects
reported here are probably common to all merocyanine spectra.
They are as follows:
(1) For a given dye, all solvent representative points
lie near part of a curve having the general shape shown in
Fig. 1. The particular part of the curve traced out by the
points for a given series of solvents depends on the dye polarity,
as indicated in Sec. I.
(2) The representative points for hydrogen bonding sol-
vents tend to be displaced in the arrow direction along the
E. max max curve (Fig. 1), compared with non-hydrogen
bonding solvents.
(3) Band intensities (oscillator strengths) are almost
independent of the solvent.
(4) As the solvent representative point moves away from
the reversal point on the weakly polar branch, at least one new
absorption peak grows up on the high-frequency side, at the ex-
pense of the lowest-frequency peak. The peak separation is
1000-1100 cm-1.
IV. DISCUSSION
Frequency Shifts: The gross features of the frequency
shifts have been explained by Brooker6 in terms of the relative
solvent stabilization of the extreme polar and the non-polar
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resonance structures. structures. (IVa and IVb respectively).
? + I
(a)
IV ,
? N?(c=c?)
(b)
Brooker has identified the reversal point with the isoenergetic
point, i.e., the point at which the two structures have the
same energy. The situation in which the polar structure is
the more stable corresponds to the highly polar branch of the
E max vs. y curve, and the opposite situation corresponds
to the weakly polar branch.
Brooker's interpretation has been elaborated by Simpson,10
who has taken into account the interactions between many
resonance structure functions. However, the results of Simpson's
treatment are not in agreement with experiment,9 and the treat-
ment itself has been adversely criticized on the ground that
it is based on an aver-simplified representation of the solvent-
solute22
interaction energy.
Platt11 has pointed out the
(22) Y. Ooshika, J. Phys. Soc. Japan, .24. 594 (1954).
relationship between Brooker's interpretation and an'alternative
scheme in which the frequency shift is related to the relative
magnitudes of the dipole moment of the solute in its ground and
excited states.23
(23) Platt has attributed the latter method of interpretation to
McConne1124 and to Bayliss and McRae 27 Actually, Platt's dis-
cussion represents an advance on the earlier work, which was
based implicitly on the assumption of a rigid solute dipole.
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4t,
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(24) H. McConnell, J. Chem. Phys., 20, 700 (1952).
(25) N. S. Bayliss and E. G. McRae, J. Phys. Chem., 2, 1002 (1954).
Recently, the writer12 has given a general treatment of
frequency shifts arising from dipole interactions. It was shown
that the frequency shift may be expressed in terms of contri-
butions to the environmental electric field at the solute dipole
(all molecular dipoles being treated as point dipoles). In the
case of a merocyanine dye dissolved in a polar solvent, it was .
proposed that as far as the relative frequency shifts induced by
different solvents are concerned, the most important contribution
to the environmental field is the field arising from the oriented
permanent dipoles of the solvent molecules. Denoting the latter
field by R, and neglecting all other contributions to the en-
vironmental field, the following expression was derived for the
frequency shift:
Vrer = (1/ 11- 9-) (Zz-Ze) ?
R r (3/2 h c) (01 - c ) R2 (1)
I e
Here, and 1) ref denote the band frequencies for the dye dis-
solved respectively in the solvent under consideration, and in
a non-polar reference solvent. On the right, h and c.have the
usual meanings, M and 0( respectively signify the permanent
dipole moment and isotropic polarizability of the isolated solute
molecule in its ground electronic state, and Me,o,(e stand for
_ ?
the corresponding quantities for the excited state. The term
Involving R2 represents the quadratic Stark effect.
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It has been shown that with0C oie and M assumed
.g. -e
parallel to ma, Eq. 1 provides a satisfactory interpretation
of the gross features of the frequency shifts in merocyanine
spectra, including the order of magnitude of the shifts.12
From a purely qualitative viewpoint, the description is exactly
the same as that given previously by Platt.11 The important
new feature of the approach based on (1) is the introduction
of the field ,intensity, RI as a parameter to which the frequency
shifts may advantageously be referred.
Probably the most serious errors inherent in (1) are those
incurred through the neglect of environmental field contribu-
tions other than R. This implies the neglect of dispersive
interactions and interactions of the solute permanent dipole-
solvent induced dipole type. In most cases apart from mero-
cyanine spectra, these interactions make an important if not
dominant contribution to the frequency shift. However, they may
be expected to play a relatively small part in the case of mero-
cyanine spectra, because of the high polarity of the merocyanines
compared with ordinary molecules. The extent to which this
expectation is realized is indicated in the following discussion
of the results of the present work; this discussion is based at
first on Eq. 1.
Non-hydrogen Bonding Solvents: In the absence of hydrogen
bonding, the field intensity may be related to macroscopic
properties of the solvent. On the basis of the simplest possible
model for the solute in solution (point dipole at the center of
a spherical cavity in a homogeneous dielectric medium), together
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with certain other simplifying assumptions, there results12
2 M [D - 1 ... no2 - 1
(2)
a3 D "4-2 n02 t. 2J
where a denotes the cavity radium, D the solvent dielectric
constant and no the refractive index of the solvent at zero
frequency. COmbining (1) and (2), assuming Me parallel to ML
in (1) and denoting the expression in brackets (Eq. 2) by F
(9 -D n0 )9 we obtain:
-
ML OIL - F I- (6/ h a6)M
ref = (2/ )1 a3) c_
) F2 (3)
_
According to (3), the band frequencies should vary regularly,
though not necessarily linearly, with F.
Figs. 9 and 10 show graphically the relationship between
F and the observed band frequencies for dyes II and III dissolved
in non-hydrogen bonding solvents. The corresponding plot for
dye I is similar to that for dye II. The values of F for the
pure solvents are taken from Table 1 (here and elsewhere in this
paper, all refractive indices are replaced by LID for the purpose
of numerical calculation). For the benzene-pyridine mixed
solvents, the dielectric constants are interpolated from the
data of Lange.26 It is seen that there is a definite though
(26) L. Lange, Z. Physik 2a, 169 (1925).
imperfect correlation between the frequency shifts and the corre-
sponding values of F. The points obtained for dye II lie near
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a curve having the shape expected from (1) and (2), with
M M and 0( )0( .
Z.
The irregularities in the relationship between band fre-
quency and solvent F may be discussed in terms of the super-
posed effects of dispersive interactions and of interactions
of the dipole-induced dipole type; as noted above, both types
of interaction were neglected in the derivation of (1).
Dispersive interactions invariably give rise to a shift
to lower frequencies, relative to the vapor frequency (the
"general red shift"). The general red shift is expected to be
particularly large for strong bands such as appear in the
visible spectra of dyes, and the relative magnitudes of the
red shifts produced by different solvents are known to depend
primarily on the solvent refractive index.12,22,26,27
(27) The general red shift was called the "polarization red
shift" in ref. 25.
Dipole-induced dipole interactions are expected to produce
a shift to lower frequencies relative to the vapor frequency if
the solute dipole moment of the dissolved dye molecule is
greater in the excited state than in the ground state; other-
wise, a shift to higher frequencies is expected. For a particu-
lar solute, the magnitudes of the shifts induced by different
solvents are expected to depend on the solvent refractive
index. 12,22,25
Accepting the above description of the dispersive and
dipole-induced dipole effects, we conclude that the dipole-
induced dipole shift augments the general red shift in the case
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of dye III and opposes it in the case of dye II. Upon ref-
erence to Figs. 9 and 10, we find that the most noticeable
irregularities occur with dye III in nitrobenzene and acetone.
Now these two solvents have respectively the highest and the
lowest refractive indices of the series. By virtue of the
superposed effects of dispersive and dipole-induced dipole
interactions, the two solvents are expected respectively to pro-
duce larger and smaller red shifts, compared with a reference
solvent of intermediate refractive index, than predicted on
the basis of the solvent F alone. The corresponding irregular-
ities in the case of dye II in nitrobenzene and acetone are
much less pronounced, as is expected in view of the partial
cancellation of the dispersive and dipole-induced dipole shifts.
A similar explanation can be advanced for most of the remaining
irregularities; however, it is most likely that those irregu-
larities reflect the limitations of the simple theory in which
the solvent is treated as a homogeneous dielectric medium.
It is readily shown that the above discussion involves
quantities of the correct order of magnitude. The curves super-
posed on Figs. 9 and 10 represent the behavior predicted by (3),
with M x: 10 Debye, a = 42, and c< = 0.1+ x 10-23 cm3
for each of the two dyes, M - M = 0.05 Debye for dye II and
7e-
M M = -1.7 Debye for dye III. It may be noticed that the
curves are drawn on the assumption that the value of
(04E 11is the same for both dyes; this is to be expected
in view of the general similarity of the spectra of the two dyes.
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It is noteworthy that the difference between the ground and
excited state polarizabilities need not be particularly large
to account for the observed trends. The chosen value of the
difference is about one-quarter of the contribution of a
strong visible transition to the ground state polarizability.
For strong transitions, such as those considered here,
the general red shift is given approximately by12
-14 Lf
,J0 (dispersive) -2.14 x 10 - 1
2n2 t- 1
where L and n respectively denote the "weighted mean wavelength"
and refractive index of the solvent at the band frequency, f
denotes the oscillator strength of the transition in question,
and a again denotes the cavity radius. The minus sign indi-
cates that the shift is to lower frequencies, relative to the
vapor frequency. Adopting L = 1250 A, 4 i and f 0.8,
we obtain
2
- nb ?
4 ?,(dispersive) go 3390 (4)
2nt 4- 1
as - rough estimate (cm-1) of the general red shift.
The
literal application of the above formula (refractive indices
from Table 1) accounts for a little over half the frequency
separation of the points on Fig. 10 for dye III in nitrobenzene
and acetone.
According to a formula given previously,12 the dipole-
induced dipole shift, relative to the vapor frequency, is
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given by
.8.0 (dipole-induced dipole) =
2 2 2 - 1
4 - /6 no
hca32n02 r 1
Actually, the above formula does not apply accurately to the
merocyanines, because it is based on the assumption of a rigid
solute dipole. In a more elaborate discussion, we would have
to replace M and M by appropriate expressions for the dipole
-e
moments of the dissolved dye. Bearing that in mind, the above
formula suffices to show that if, for the dissolved dye, the
ground and excited state dipole moments differ by less than
2 Debye, then the magnitude of the dipole-induced dipole shift
is approximately equal to or less than that of the general
red shift.
We have shown, first, that the observed frequency shifts
display a definite though imperfect correlation with the sol-
vent F, which has been defined with a reference to Eq. 2;
second, that the observed behavior conforms approximately to
that predicted by (3), with plausible values for the dipole
moments and polarizabilities of the dyes; third, that the most
noticeable discrepancies which do occur are of the nature and
approximate magnitude to be expected from the superposition of
dispersive and dipole-induced dipole effects. The evidence
leaves little cause to doubt that the frequency shifts are
caused primarily by dipole-dipole interactions, with the quad-
ratic Stark effect playing an important or dominant role.
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?
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Hydrogen Bonding Solvents: Although the order in which
the hydrogen bonding solvents induce shifts to higher fre-
quencies is the same as that of increasing F, it is clear from
the magnitudes of the shifts that they correspond, in a
formal sense, to values of R much larger than those calculated
from (2). It appears that the quadratic Stark effect makes a
dominant contribution to the frequency shift.
Even when the quadratic Stark effect has been taken into
account, there seems to be no simple explanation of the results
in terms of hydrogen bonding. To take an extreme example, in
the spectrum of dye II, the solvent water induces a shift of
about 4500 cm-1 to higher frequencies, referred to acetone.
If we allow 500 cm-1 for the change of Ft there remains 4000 cm-1
or about 12 Kcal/mole, to be accounted for by hydrogen bonding.
This appears to be too large a shift to be attributable to the
formation of a single hydrogen bond. Again the case of dye II
the shift induced by water is about twice as great as that
induced by formamide, and about four times as great as that ?
induced by ethanol (all referred to acetone), though the three
solvents presumably form hydrogen bonds of about the same
strength. On the other hand, the band frequencies for dye II
in ethanol and aniline exceed by about the same amount (^'1200 cm-1)
those expected on the basis of the solvent F alone.
We suggest that in the case of the solvent water, and
possibly formamide, two or more solvent molecules simultaneously
form strong hydrogen bonds with one dye molecule to form a com-
plex of structure V. In each of the dyes 1-III only one dye
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atom can can be strongly hydrogen bonded, namely the carbonyl
V.
*0
oxygen. The formation of two or more strong hydrogen bonds
would therefore be sterically hindered or prohibited in
ethanol and aniline solvents.
This possibility has been considered previously for
another solute by Professor G. Pimentel in a discussion of
solvent spectral shifts ?28
(28) G. Pimentel, University of California, private communica-
tion to M. Kasha.
Intensities: A simple theory of solvent effects on mero-
cyanine band intensities has been proposed by McConne11.29
(29) H. McConnell, quoted by Platt.11
The theory is based on the assumption that the ground and ex-
cited electronic state functions for the strong visible transi-
tion may be considered as linear combinations of the electronic
state functions appropriate to the isoenergetic point. This
assumption differs only formally from that upon which Brooker
based his interpretation of the frequency shifts. There results
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=
(5)
where f and respectively denote the oscillator strength
and frequency of a band, and the subscript refers to the iso-
energetic point.
The theory is not supported by the results of the present
work. Whereas the frequencies of the bands of known inten-
sity undergo a total variation of 20% and 30% for dyes I and
II respectively, the oscillator strengths show no progressive
variation with band frequency beyond the experimental error
of 5%. With dye III, the band frequencies do not cover a
sufficiently large range to permit a valid test of the theory.
Band Shapes: Platt11 has shown that Brooker's interpre-
tation of the frequency shifts can be extended to explain
the concomitant changes of band width. At the isoenergetic
point, the equilibrium nuclear configuration of the dye does
not change upon excitation, so that only the 0-0 vibronic band
appears strongly. As the solvent representative point moves
away from the isoenergetic point, the equilibrium length of
each bond in the C-C chain suffers a progressively more pro-
nounced change upon excitation. According to the Franck-
Condon principle, this should lead to the growing up of
higher-frequency vibronic bands at the expense of the 0-0 band
with frequency separations corresponding to the C.-C stretch-
ing frequency.
The above interpretation is strongly supported by the
results of the present work. The absorption curves corre-
sponding to representative points near the reversal point and
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on the weakly polar branch
ture, which changes in the
sentative point moves away
separation of the vibronic
factory agreememt with the
Vibrational structure does
corresponding to points on
because of the blurring of
-27-
show definite vibrational struc-
predicted manner as the repre-
from the reversal point. The
peaks (1000-1100 ce-1) is in satis-
C-C stretching frequency.
not appear in the absorption curves
the highly-polar branch, probably
structure normally associated with
strong solvent-solute interaction. Nevertheless, the broaden-
ing may be attributed to changes of the relative intensity of
the underlying vibronic transitions. It can be seen from the
absorption curves that if it were possible to plot E max
against the 0-0 frequency rather than against Ilmax, the highly-
polar and weakly-polar branches would be nearly superposed.
This tends further to substantiate Platt's interpretation,
since the ground and excited-state potential energy curves for
C-C stretching are presumably nearly symmetrical near their
respective minima.
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Acknowledgements: Most of the work described above was
carried out under the supervision of Professor N. S. Bayliss,
to whom the writer is indebted for encouragement and helpful
criticism. The writer is glad to thank Dr. L. G. S. Brooker
for the gift of the merocyanine dye samples, and Professors
N. S. Bayliss and M. Kasha for reading this paper prior to
publication. Financial assistance provided by the University
Research Fund (University of Western Australia), including the
award of a studentship, is gratefully acknowledged, as is
also the award of a Hackett Studentship by the University of
Western Australia.
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TABLE- 1
SOLVENT DESIGNATIONS AND PROPERTIES
Solvent
Desig-
nation
Da
Benzene
2.3
Dioxane
Chloroform
2.2
CF
5.2
Nitrobenzene NB 35
Pyridine
Ace t one
12.4
Ac
21
Aniline An 7.3
- Ethanol
28
Formamide
109
Water W 79
F(D,A3)e
2 1
n D
2n2D r 1
1.4-98
0
0.23
1.421
0.03
0.20
1.446
0.32
0.21
1.555
0.60
0.24-
1.511
0.49
0.23
1.359
0.65
0.18
1.586
0.34
0.25
1.363
0.68
0.18
1.448
0.71
0.21
1.333
0.76
0.17
(a) Dielectric constant
(b) Refractive index (sodium D
(c.) F(P_1nD) = (D - 1)/(D t 2) - (n2'- ) /(Z2 t- 2)
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TABLE 2
DYES 1-III IN PURE SOLVENTS
Solvent
Vmax x 10-4 (cm-1)
Dioxane
1.864
1.559
III
1.838,
1.947a
1.773
Chloroform
1.883
1.570
1.888b
Nitrobenzene
1.920
1.629
1.753
1.85313
1.768,
Pyridine
1.935
1.638
1.883u
1.804
Acetone
1.970
1.681
1.920
*Aniline
1.986
1.690
Ethanol'
2.071
1.002
2.333"
Foimamide
2.115
1.890
2.351d
2.292
2.132
2.028e
Water
2.615?
2.4800
2.463f
-3
max 10
I 11 III I 11 III
58.0a 82.5a 53.0a ,
52.6a9u
74.0
103.5
90.4
50.41)
89.0,
66.5
92.9
49.7"
98.0
80.5
112.8
58.ob
76.0
78.0
103.6
50.5b
67.5
79.3
0.65 0.74 0.82
0.63 0.79 0.80
-
0.70 0.91 0.81
0.74 0.94 0.74
0.64 0.82
113.0
51.0 510.7 41.4d
0.90,
0.62 0.85 0.82a
46.0 42.5 35.9d 0.62 0.82 0.73d
37.5 36.7 43.3!
29.00 26.0c 33.5'
0.63 0.80 0.74e
0.62c 0.80c 0.72f
(a) Adjusted to conform to an oscillator strength equal to that for the same dye in water.
(b) Refers to a second maximum.
(c) Protonated dye. Solvent: 0.26N HCL.
(d) Protonated dye.
(p) Solvent: buffer solution, RH 9.
.(1) Protonated dye. Solvent: buffer solution, pH 6.
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TABLE 3
DYE II IN MIXED SOLVENTS
Solvent Mole%a
'max x lo -4 (cm-1) x 10-3
ma.x
Dioxane-water
Benzene-pyridine
Benzene-acetone
Acetone-water
95.0 1.570 90.0
90.0 1.590 85.5
78.4 1.660 62.0
64.2 1.713 59.0
44-.6 1.770 49.8
20.0 1.885 43.0
11.7 1.958 40.4
98.1 1.533 76.2
1.636c 56.40
78.2 1.554 90.7 -
52.7 1.589 102.0 -
24.6 1.618 90.0
98.3 1.534 75.2
1.631c 53.7c
94.9 1.542 81.4 -
91.7 1.549 100.0 -
78.9 1.573 105.2 0.84
49.3 1.618 117.7 0.93
37.0 1.632 109.0 0.89
12.4 1.661 105.0 0.94
99.0 1.682 106.5 0.96
95.4 1.695 103.8 0.99
72.4 1.750 66.4 0.89
57.9 1.776 63.8 0.91
35.6 1.870 47.0 0.82
22.2 1.927 46.0 o.86
9.4 2.010 38.4 0.77
=IP
OM.
WEI
41=11
Om
ftellet
(a) Refers to first-named solvent component.
(b) Where no oscillator strengths are given, the extinction coefficients are adjusted to conform
to.an oscillator strength equal to that for the same dye in water.
(c) Refers to a second maximum..
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TABLE 4
DYE III IN MIXED SOLVENTS
-2b
Solvent Mole 11max x 10-4(cm 1)max x 10
1.813
Dioxane-water 96.3 1.9250
1.791,
88.7 1.908?
77.7 1.785
61.1 1.791
42.2 1.803
23.1 1.835
12.0 1.892
Benzene-pridine 98.9 1.835
1.930e
70.3 1.798
1.914e
46.3 1.784
1.895?
22.4 1.775
, 1.890e
, 1.766
Pyridine-water 92.3 1.876e
82.0 1.764
48.4 1.785
34.5 1.801
4.2 1.913
0.8 1.992
58.0
50.0c
75.5?,
49.o-
103.5
107.0
96.0
70.0
55.5
52.0
52.470.5c
60.51/4*
84.0
60.5c
93.0
6o.oc
112.0,
56.5`'
125.5
1?4.5
77.0
55.4
45.5
.11
SIM
11.
0.83
0.86
0.86
0.84
0.85
0.80
0.72
0.82
0.78
(a) Refers to first-named solvent component.
(b) Where no oscillator strengths are given, the extinction coefficients are adjusted to an
oscillator strength equal to that for the same dye in water.
(c) Refers to a second maximum.
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-
(Captions for Figures)
Fig. 1. E max vaL V max plot (schematic).
Fig. 2. Absorption curves for dye I in pure solvents. For
solvent designations, see Table I. A prime indi-
cates an absorption curve for the protonated dye.
Fig. 3. Absorption curves for dye II in pure solvents.
Fig. 4. Absorption curves for dye II in acetone-water and
benzene-acetone mixed solvents. The numbers denote
mole percentages of the first-named solvent component.
The curve for pyridine-water solvents is redrawn from
the data of Brooker et al.4
Fig. 5. C vs.max plot for dye II.
max
Fig. 6. Absorption curves for dye III in pure solvents.
Fig. 7. Absorption curves for dye III in benzene-pyridine
and pyridine-water mixed solvents.
Fig. 8. Emaxma. max plot for dye III.
Fig. 9. (No caption).
Fig. 10. (No caption).
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TOX
100
niREVERSAL
POINT
HIGHLY POLAR
BRANCH
WEAKLY POLAR
BRANCH
5000
?
V max
X (A)
4000
80
6 x10-3
60
CF
NB
Ac
40
20
?
1.8 2.0 2.2 12.4 4 2.6
V (cm) 110-
3.0
Fi4 1
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7000 6000
MA)
5000
80
? x10-
6 0
7000 6000
MA) 4000
5000
B-Ac r% f
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? %MAW. --vfe-vo.,r44t4tam.Qsth.i4OeV,
INTRAMOLECULAR TWISTING EFFECTS IN
SUBSTITUTED BENZENES. I. ELECTRONIC SPECTRA.1 '2
By Eion G. McRae and Lionel Goodman
Departments of Chemistry, Florida State University, Tallahassee,
Florida and The Pennsylvania State University, University Park,
Pennsylvania.
1
Taken from a dissertation submitted by E. G. McRae for the
degree of Ph.D. at Florida State University, 1957. Presented in
part at the symposium on Molecular Structure and Spectroscopy,
Columbus, Ohio, June 1955.
2 The work was carried out under a contract between the U. S.
Air Force, Office of Scientific Research, ARDC, and the Florida
State University. Supported in part by a grant from Research
Corporation.
3 Present addresses: E. G. M. -'Chemical Physics Section,
C.S.I.R.O., Melbourne, Australia; L. G. (to whom reprint requests
should be addressed) - Department of Chemistry, Pennsylvania
State University, University Park, Pennsylvania.
(Abstract)
The electronic spectral effects of twisting a substituent
group about the substituent -ring bond in substituted benzenes
are analyzed from the viewpoint of semi-empirical MO theory in-
cluding zeroth and first order configuration interaction. The
substituent orbital iso is expressed as a linear combination
of two functions, Ox and Or which are respectively anti-symmetric
and symmetric with respect to reflection in the ring plane:
1. cos eOx 4- sin 9 fy.. Transition energies and intensities
are discussed with reference to the twisting parameter 9.
? Ordinarily, 9 increases as the substituent is twisted, and can
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be evaluated explicitly when the molecular geometry is known.
The treatment is carried through both with and without cogni-
zance of the nearest-neighbor overlap integrals, and the in-
ductive effect of the substituent is discussed. Particular
attention is given to the question of self-consistency.
The theory applies especially to those transitions which
correspond to transitions observed in the spectrum of benzene
("benzene-analogue" transitions). Three possible types of ()-
dependence of transition energies are distinguished, and the
conditions under which each might be realized are specified.
Of the four benzene-analogue singlet-singlet transitions con-
sidered, the two of lowest energy are ordinarily predicted to
suffer a decrease of intensity as A increases, while the inten-
sities of the remaining two transitions are predicted to be
insensitive to twisting perturbations. "Charge transfer"
transitions are also considered, though in less detail.
The theory is applied in a detailed discussion of the ultra-
violet absorption spectra of N,N-dimethylaniline and related
molecules in which the dimethylamino substituent is twisted
as a result of ortho substitution or intramolecular bridge
formation.
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?
1. INTRODUCTION
vorl&-sigo--...VOrlatiArimitist."1,,arkrastxttgsst4:2..
In several series of substituted benzenes, the twisting of
the substituent group about the substituent-ring bond leads to
pronounced changes in electronic properties. For example, the
effect of twisting is revealed particularly clearly in the
spectra and some ground-state properties of N,N-dimethylaniline
and related molecules.4-8 In this and other series of substituted
if
5
B. M. Wepster? Rec. Tray. Chim. gtz, 411 (1948); 1159 (1952);
, 335 (1957); 2k, 357 (1957).
B. M. Wepster, Rec. Tray. Chim. 23w, 661 (1953).
6 H. B. Klevens and J. R. Platt, J. Am. Chem. Soc., 17.19 1714
(1949).
7
W. R. Remington, J. Am. Chem. Soc., 6Z, 1838 (151+5).
8
9
Ref. 4-7 are to literature on spectra.
including references to the literature
ties, are given in the following paper
Further references,
on ground-slate proper-
(paper II).Y
E. G. McRae and L. Goodman, J. Chem. Phys. za, 0000 (1958).
benzenes, twisting may be produced either as a steric effect of
ortho-substitution, or as a result of intramolecular bridge
formation.
This paper is devoted to an analysis, from the molecular
orbital (MO) viewpoint, of the effects of twisting perturbations
on substituted benzene spectra. In the following paper9, we
apply a similar theory to ground-state properties such as
dipole moment and resonance energy.
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2. GENERAL APPROACH
We consider a substituted benzene in which a particular
substituent group is attached to the ring by a bond between the
substituent atom, 7, and the adjacent ring carbon atom, 1. The
other ring carbon atoms are numbered consecutively around the
ring (See Fig. lb). The 1-7 bond is assumed to lie on the pro-
jection of the line joining carbon atoms 1 and 4, but the sub-
stituent group itself is supposed not to be axially symmetric
with respect to the 1.4 line.
Let us suppose that the substituent interacts conjugatively
with the ring via the single atomic orbital (A0) is?, centered
on 7. We assume that in the ground configuration there are
formally two electrons in ?scs. In a future publication we shall
consider the case of a substituent with several AO's capable of
interacting with the ring carbon 201r AO's.10
10 L.
Frolen and L. Goodman, work in progress.
We wish to discuss the spectral effects of twisting the
substituent group about the 1-7 bond. The effect of twisting
is observed experimentally as a regular relationship between the
spectra and the twist angle1112. In order to discuss twisting
11 The observed spectra should be corrected, if necessary, to
allow for the direct influence of the substituent or sub-
stituents responsible for twisting. For an example, see
Table 6, footnote (b).
12
The definition of the twist angle is arbitrary to some extent,
as there are in general various ways of incorporating the
part of the twist angle corresponding to the change of shape
of the substituent as it is twisted.
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effects from the theoretical viewpoint, we express is? as a
linear combination of two normalized functions, Ox and 07, which
are respectively anti-symmetric and symmetric with respect to
reflection in the ring plane:
is? = cos 0 ix 6, sing fy ?
(1)
We require that Ox remain effectively unchanged during the twist-
ing of the substituent. However, we place no such restriction
on O.
Because of its symmetry, the function Oy in Eq. I may be
assumed not to interact appreciably with the ring 17-MO's.
Consequently, the parameter 9 enters into the theory in a par-
ticularly simple way. For this reason, and also because the
twisting of the substituent ordinarily corresponds to an increase
of 9, it is convenient to break the problem into two parts:
First, to deduce the 9-dependence of the spectra, and, second,
to relate 9 to the angle of twist. In this paper, except where
otherwise mentioned, we will be concerned with the first part of
this program. The second part is difficult to treat generally;
it could easily be carried through for any particular substituted
.benzene if its geometry were known. If fs? is a pure 2p AO,
the parameter 9 takes on an especially simple meaning; it is the
angle of twist of ks?, and hence of the substituent group, with
respect to the ring plane (Fig. lc).
For the substituted benzene, we anticipate four low-energy
singlet excited states, corresponding respectively to the
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7
following states states in benzene: 1B2u (energy )+.9 e. v. above
ground state, 1Bin (6.2 e. v.) all.: the components of lEiu
(7.0 e. v. ).
In the foregoing, the benzene state energies
refer to the absorption band centers, the symmetry designations
pertain to the Doi group, and the assumed assignments are those
?
fairly generally accepted at the present time.13 We shall
13 D. P. Craig, Revs. Pure and Applied Chem. (Roy. Australian
Chem. Inst.) a, 207 (1953).
refer to the above states of the substituted benzene as "benzene
analogue" (BA) states. In addition to the BA states, we antici-
pate at least two low energy singlet "charge transfer" (CT)
states, arising formally from the excitation of one of the sub-
stituent electrons to a vacant benzene 11-140. For each of the
above states, we naturally anticipate a corresponding low-energy
triplet state. In particular, we expect a lowest-energy trip-
let corresponding to B in benzene (absorption band center
13
3.8 e. v.).
The treatment of CT transitions is rendered comparatively
difficult by a number of factors, among which may he mentioned
the possible inapplicability of the approximation in which the
same effective Hamiltonian is deemed appropriate to both the
ground and the excited states. A detailed discussion of that
question is beyond the scope of the present work. Accordingly,
only the BA states are treated in detail in this paper. The CT
states, and the possible importance of BA-CT configuration inter-
action are also discussed, but in a purely qualitative way.
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3. TREATMENT OF BENZENE ANALOGUE TRANSITIONS
The method of treatment adopted in this paper is based on
the semi-empirical MO procedure developed by Goodman and Shull,
14. L. Goodman and H. Shull, J. Chem. Phys. 220 33 (1955).
and applied by them in a systematic interpretation of the spectra
of substituted benzenes.15. The above two papers should be con-
15 L. Goodman and H. Shull, J. Chem. Phys. 22, 1388 (1957).
suited for those details of the method which are omitted in the
present paper; to facilitate reference, the notation in the
present paper has been made to conform as closely as practicable
to that of Goodman and Shull.
Zeroth Order: - In the zeroth order of approximation, in
which the substituent is considered not to interact with the ring,
(Fig. la) the orbitals fpr the substituted benzene comprise the
substituent AO fs?,,and the benzene 1T'-MO's. We denote the
10.4-4-evo
.1.171WW?OA.
ii? (i 8.01 1, 1, 2, 3), and express them as linear
combinations of AO's (ICAO):
6 -
o
c544 Ofi. 9
= 1
where 0/14, denotes the 2p/r AO belonging to atom, a , all AO's
having positive lobes on the same side of the ring plane.
The value of the carbon AO Coulomb integral, ,.is chosen
as the zero.of MO energy, and the orbital energies are expressed
throughout in terms of the semia,empirical.CC resonance integra11/5
(2)
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In the zeroth order, let ei? denote the energy of the orbital
ii?. We write
ei = ni
where ni? is the orbital energy factor for The AC co-
efficients and energy factors for the benzene MO's, either
with or without nearest-neighbor overlap integrals included, may
be obtained from the formulas given by Wheland.16
For the C-C
16 G. W. Wheland, "Resonance in Organic Chemistry", John Wiley
and Sons, New York, 1955, p. 666.
overlap integral in benzene, the value 1/4 is adopted for cal-
culations with overlap included. The barred and unbarred MO
subscripts respectively signify MO's belonging to A and B reps
(irreducible representations)17 of the C2 group (see below).
17 M. A. Melvin, Revs. Mod. Phys. aai 18 (1956).
Intramolecular twisting destroys the C2v symmetry of a sub-
stituted benzene, and in this paper we assume that the effective
Hamiltonian has C2 symmetry. Accordingly, we adopt the C2
symmetry classification of wave functions, and consider only
those interactions which are between functions of the same C2
symmetry type. As a particular consequence of the destruction
of the C2v symmetry by intramolecular twisting, it is no longer
strictly meaningful to draw a distinction between W-- andlc
Ir-electrons, because a Molecule with a twisted substituent
group no longer has a plane of symmetry containing the con-
jugated atoms. However, the ring carbon AO's which are anti-
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....mnerastemungINOICIIIIMIIIMMOINIPINOMPhk
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symmetric with respect to reflection in the ring plane may be
distinguished from the other ring carbon AO's, and it is con-
venient to refer to them still as 2pIr AO's and to the occu-
pying electrons as 71'-electrons. Similarly the two electrons
in the substituent AO fs remain sharply differentiated from
the other substituent electrons. For similar reasons, the
Te-electron approximation is no longer strictly applicable.
We retain it in, the sense that we consider interactions between
only those AO's which are anti-symmetric with respect to re-
flection in the ring plane ---viz. fx and the ring carbon 207-A0ts.
The ground state function is approximated throughout by a
single (closed shell) configuration function, and the zeroth-
order ground state function is denoted by 00. The zeroth-
order state functions for the substituted benzene must be built
up from the orbitals with due cognizance of zeroth-order con-
figuration interaction (CI). There results, for the four low-
energy singlet excited states,
4
O , - 2-1/2
(x12 - x/2,,
I24'1/2 (xl
2 12
-1/2 o o
- 2 ,
(x12 12
x- )
o
y
.
- r1/2 (X% ?x?? )
le 12 9
(3)
where x12, for example, denotes the zeroth-order singlet con-
figuration function arising from the configuration .
)2 0) 2 4 1 1)2 2)1. Similar expressions can of course be
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written down for the triplet state functions. In the notation
for the state functions, as in that for the MO's, a barred sub-
script signifies an A-type function and an unbarred subscript
a B -type function. The correspondence between the benzene
states and the above functions is as follows: Alg; l''-B;
Biu; 212'E1.
Interactions: - When the interactions between substituent
and ring are taken into account, the new MO's are given in DCMO
form,
3
Aij f3
j se sO
by solution of the MO secular equation
det {111.3 - e Si33 = o.
Hij = Her f; d v,
(ilj s, 0,1, 1, 1, 2, 3)
Here,
Heft denoting the ,effective Hamiltonian, and
sii
ej v.
In solving the secular equation, we follow Goodman and
Shull, who have described a method for solving Eq. under
the following conditions:
s15cil r s,
Hij in cii e31 difi 9
n?116 r end' 1j5
His sit cii ffi
(i s)
(i 3, i # st 3 # 5)
(i # s)
(i # s)
(10
( 5 )
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?9?
Here, S denotes the C-C overlap integral, and
si7/s
where s17 denotes the 1-7 overlap integral. The assumption
(6)
/917/14 (
(7)
is implicit in the expression for His in (5). ignmans the
Coulomb integral at atom 7, and dT1/6 represents the increment
of the Coulomb integral at atom 1, due to the substituent. Thus,
represents the inductive effect Of the substituent.
The conditions (5) embody the approximation, frequently
Introduced, of neglecting interactions between non-nearest
neighbor atoms. Two other common approximations, namely the
neglect of overlap and the neglect of the inductive effect, may
be brought in through (5). The neglect of overlap corresponds
to putting s sl7 = O. This implies that the benzene MO's and
MO energy factors are to be taken without overlap. The neglect
of the 'inductive effect corresponds to putting 6 = 0.
The present problem is characterized by the condition that
/7 varies approximately as cos 0, while cr remains approximately
constant as the substituent is twisted'. Therefore, we may
appropriately specialize the conditions (5) by superposing the
following conditions:
= /00 cos At (8a) .
cr independent of 0, (8h)
.14
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where po is independent of 9. From Eqs. 7 and 88.118 we have
18
The parameter is assigned different values for the A-type
as distinct frd the B-type states. Therefore, in principle,
p in 8c should be assigned different values so as to give
/17 the same value in all states for any particular value
of U. However, in this paper, we adopt for simplicity a
single parameter to.
= f2ofl
cos O. .(8c)
The configuration functions are altered as a result of the
orbital perturbations. Also, the mixing of configurations is
no longer symmetrical, the new state functions being determined
by solution of the state secular equations.15 The new state
functions are of the form
pi . co. ( 1T14f - AA) x12 -
. sin ( 11/4 - AA) x12 4.
sin( 11/4 - AA) xn
cos ( 7r/4 - A)x
-A' /
1 cos ( - B) x6.2 sin ( 104- - AB) x/2 ,
i2 sin ( irA - AB) x3.2 -
cos ( - A ) x
B- 12 /
(9)
where AA and AB are numbers measuring the asymmetry of mix-
ing between the respective pairs of configurations.
In order to evaluate "As AB and the BA state energies
from (9), it is necessary first to evaluate the configuration
energies and CI integrals. The former are given in the semi-
empirical method as orbital energy differences, i.e.
ej - ei = (nj - ni)fi 9
where the MO energy factors are obtained from (4), and is
evaluated empirically. The CI integrals may be evaluated with
(10)
-
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-11 -
the aid of the approximation15
Mij lkA, ail aj j akk att
where Mijtia. is a general MO electron repulsion integral and
MulkL 0 denotes the corresponding integral for benzene. Then
Hti. and Hg can be expressed in terms of the zeroth-order integrals
(benzene integrals), H?A and H?B respectively, and the latter
may be evaluated empirically. k similar method applied to
triplet states.. The empirical parameters are evaluated from the
spectrum of benzene, as described in Ref. 15. The values of the
parameters used in the present work are shown in Table 1.
From Eq. 9 the transition moments governing the BA transition
intensities are given by
MI -- cos AA 4 4- sin AA tit2
62 - -sin AA
-
NI e.. c OS A A 4
_ - c os A B 4 ? sin AB 4
tf2 = --sin AB 81 r cos A mt
B ?2
(12)
Here Mil for example, denotes the integral
Sio d v
where is the perturbed ground state (one-configuration)
function and M denotes the classical dipole moment vector. .4
and 0::2 correspond to the allowed components of the Aig Elu
transition in benzene, but are modified by the orbital perturbations.
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Thus, for example
2-1/2 jr 0 M
(x12 x--) d v.
12
Mi and Mi similarly correspond respectively to the forbidden
Alg Blu and Aig B2u transitions in benzene.
The orbitally perturbed transition moments, 4, etc., can
be evaluated in terms of the C-C distance in benzene. The
method used in this paper is to express the transition moments
In terms of the appropriate integrals involving MO's, to expand
those integrals in terms of AO integrals, and to evaluate the
AO integrals by the formulas
0.4 ?
tel o,
dv Ervtt.
dv (1/2) ? rp ) s?,,y , ( /1.4, .1) )
where rilk denotes the position vector of the,m,th atom,
8 ? j'?Ofy dv, and C stands for the electronic charge. For
(13)
simplicity, the 1-7 bond length is assumed equal to the C-C
distance. For the purpose of calculating BA transition ,intensi-
ties, we choose the C-C distance to be 1.0 i; with that value, ,
Eq. 13 reproduces the observed oscillator strength, f 1.2,
for the Algu transition in benzene vapor.19
19 L. W. Pickett, M. MUntz, and E.
21, 4862 (1951).
J. Romand and B. Vodiar, Compt.
M. McPherson, J. Am. Chem. Soc.
rend. lal, 930 (1951).
4. FOUNDATION OF THE METHOD
We describe the foundation of the semi-empirical method
with reference to a formal LCAO SCF treatment of Intramolecular
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4.211
-13 -
twisting perturbations in substituted benzenes. We pay special
attention to the conditions (8), which for the purpose of the
present problem are superposed on Goodman and Shull's con-
ditions (5). Also, we discuss the constancy of the important
empirical parameter g . Where feasible, the discussion is
supported by numerical calculations.
SCF Method:--Following a procedure similar to that described
by Roothaan,20 we consider the derivation of the "best possible"
20 C. C. J. Roothaan, Revs. Mod. Phys. ga, 69 (1951).
LCAO MO for the ground configuration of a substituted benzene
represented by Fig. lc. We begin with the same orbitals as
before, namely the benzene MO and the substituent AO 07(07 !n).
For 0 . we adopt the form (1). The ground configuration MO
7'
energies and MO are found by the iterative solution of the
secular equation
where Fij
r 0
detij - g S = 0,
F
volving the Hartree-Fock Hamiltonian, F.
In the first cycle of the iterative process, the Hartree-
Fock Hamiltonian is constructed with the zeroth-order MO's
(Eq. 2). In a given subsequent cycle, the Hartree-Fock
Hamiltonian is constructed with the MO's resulting from the
previous cycle. Let ct (It = s, 0, y, 22 3) denote these
dv is an MO interaction integral in-
MO's and let ir denote summation over the subscripts of the
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MOlk occupied in the ground configuration. Then the MO inter-
action integrals of the cycle in question are given in con-
ventional notation by
- j(T
Fii 1 90-
? dv t?7 (II q? ?)
2(ficik;WP-(fki7;Okri)
where T denotes the electronic kinetic energy operatio4U
c/.4,
the electrostatic potential due to the/a, th core, and in the
notations for the electron repulsion integrals, the functions
of one electron are written on the left and those of the other
electron on the right.
The above MO interaction integrals may be expanded in
terms of the changes in the AO interaction integrals
= F i5, dv resulting from the interaction between
ring and substituent. Let F? denote the Hartree-FoCk
Hamiltonian for the situation represented by Fig. la. The change
In L is given by
Then we have
and
A L
6 6
F -dv - 1.64, F? six 'dv.
F44 LI JE. C C
.1.4 #44 la ji =1 V4' ix)
6 0
Fii = ? .ca
,A? =1 or. 94'
F = ;E: 6 c 4L,7,
Fss = e ? AL77.
, 3; i, j 5)
z L/444, , s)
(i i 5)
(110
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Comparison of Semi-empirical ard SCF Methods:--We shall
assume for the moment that all bond lengths are independent of
0, in which case condition 8(a) is automatically satisfied.
On comparing corresponding semi-empirical and SCF NO integrals
in Eqs. 5 and 14, we see that in order to substantiate con-
ditions 8(h) and 8(c) we must have respectively:
L77 independent of 0,
L
- L7 cos et (AA_ 17).
.44-7 '44
Also, in order that /9 be independent of 0, we must have:
4 1 independent of 0, (A,
As explained later in this section, the above condition is
necessary but not sufficient for the constancy arig
We first consider the 0-dependences of the SCF AO integrals
in the first cycle of the iterative process. We have
=(107:0!01.1)) 4.2(137070,,44-13.1))41371f.i4 ;15761 )9(AIP 47)
= sr 7 5/47 z6 : 07)
0
r [ 2(t!,4057) -(1 t;c ; 1: 07) , i 7)
kk'6'
"17167) Isk 4i1); '137?7)4 157 ?k?t57)3
? (07 07; 47 i7).
We may express each core integral as the sum of a penetration
integral and an AO electron repulsion integral,21 ? e.g.
(15)
21 M. Goeppert-Mayer and A. I. Sklar, J. Chem. Phys. 6, 645 (1938).
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$i 02) (12.14' : 151 02) - (#41,!f,44- : 152)P
where triA, denotes the electrostatic potential due to neutral
On expressing 07, where appropriate, in the form (1)1
we obtain
da LA40 (ii : 'Sy )
c
(15xf&O,44 ) (044- ;f5x?51/ ) os2
g. 2 (tiziy.;6,44, ) - (044, ;034 ) cos 9 sin 0
r (034;144, ) ( SOCA, ;clip ) sin2 0 Ca., V A a)
r o 6
.44-7
s sAzx (U.a- I 1/04. tCx)
t.
AL al
occ
C [2( lc(); ffx) ke. /14" ;i: ox)]
0,44, ; ix)]
occ
,
6
L77 (11 : 07 07)
[2( kO;Ox 0x) ix;
-/44,k ? (?4,15//.4. ;t5x 03c)i cos2 0
ie 2 r 2(i ko ko;0x -y)k L -(-o
k ex; f: iy)J
?; ss
11,4& x '15r)
1 cos sin
[2( kc) k?; Oy tly)
k 7.1c
(io ; Ao 0w)]
6
?Z (Ii?, ; 0y) .? 81n29
frxi
- (07 071- 07 07).
In the expression for LA7 the notation sAta = dv has been,
introduced, and we have taken note of the vanishing of all
cos e (.As)
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integrals in which 'Sy appears only once.
It is seen that in the approximation we are considering
(first SCF cycle, bond lengths fixed), the integrals L/.47 are
strictly proportional to cos 0. A detailed discussion of the
0-dependence of the integrals L/44, (,14.,y 4 7) and L77 would
require the knowledge of all the relevant penetration and AO
electron repulsion integrals; however, some general conclusions
can be drawn by referring to tables of two-center AO Coulomb
integrals22,23 ( we neglect three- and four-center integrals,
22
23
R. G. Parrand and B. L. Crawford, J. Chem. Phys. 114 1049
(1948).
C. C. J. Roothaan, "Tables of Two-center Coulomb Integrals
between is, 2s, and 2p Orbitals", Special Technical Report,
University of Chicago, 195$.
which are relatively small). If we take 4 to be a 2p AO with
axis perpendicular to the ring plane, and assume in turn that idy
is a 2s AO and either of the two 2p AO's orthogonal to 4, in
no case do we find (4 /1,40!,st.) and (0y 160 J1144,44) to differ
by more than about ten per cent. Also, these integrals are at
least an order of magnitude greater than the largest integrals
involving both idx and 'dye It follows that, in the first cycle
of the iterative process, 1,,,ax (AGP 7) and L77 are nearly
independent of 0.
We now discuss the more realistic case in which the
Hartree-Fock Hamiltonian is constructed with MO's of the general
form ik = f.aki = s, 0, * 1). Retaining only the
one-center and two-center Coulomb electron repulsion integrals,
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we find
L = (U07' ere IS- )
/4))
?18-
- 1/2 4 r!so, (Ida. ;95.1) t5y )1(/44 V;Ap .3) 4 7)
4 LI., = (u7 :0 ) .1/2 419A (ei4- '0 . "
/5 0 )
c /44 ,1?4
6
I. v ) + "417(44. ;15707)/
6
LA47 =e sAku e. (13$44. rd1,44 157)- 1/2 31,4* 7(14, 4. 07,57) l( /AcX 7)
/4,--
6
and 4 L? = (lje :07$7) * 1/2 4 Q7 (e7o7, '57,57) (151)
la A
6
+ .9),?
,,c=1
where
occ
2
2 eE
k 4-1
n 0 , A p
'4/44. 1Sa' gj "44'
aki Ci/A. 9
akj CD)
j:444. v
(superscripts
denote zeroth-order quantities).
If the MO's are derived with neglect of overlap, Q/41 repre-
sents the Tr-charge density at the /44th atom, and pay represents
the order of the Tr-bond joining atoms,, and 1/. Since the
semi-empirical MO integrals Hij have been shown to be of approx-
imately the correct form as judged by comparison with the first-
cycle SCF integrals F1it is not inappropriate to invoke semi-
empirical charge densities and bond orders in order to discuss
more fully the foundation of the semi-empirical method. Utiliz-
ing the semi-empirical MO's of Table 2 (overlap neglected),
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tabulated values of the appropriate AO electron repulsion
1ntegrals2224 and again assuming all bond lengths fixed, we
24 The adopted values were those for an effective nuclear charge
of 3A2 a.u. and a nearest-neighbor internuclear distance of
1.4 X (these are the parameters appropriate to benzene itself).
find that the integrals L/14 (' A,A. 7). vary (-4- 0.01 e.v.) as
"
cos 0:
LA,7 = k cos 0, (16a)
while the integrals L44.1) (1491, 7) and L77 contain additive -
parts which vary approximately (4-0.05 e.v.) as cos2 0:
(A) ac L1,4), 17/2) 154.), cos2 Oi (,a,IP i 7) (16b)
L77 (0) a L77 ( 1T/2) + k77 cos2 9. (16c)
The constants 1!./44.y are easily evaluated if it is assumed
that the integrals 12,4) are exactly constant in the first cycle;
in that case, the values of the constants measure. the 9-dependence
of the integrals, resulting from the redistribution of charge
accompanying twisting of the substituent. For the integrals
/" (iu.i 7) we find (e.v.)24: k -0.17, 1c22 = -0.03,
"
k33 = smo.65, k44 = 4.0.57. A positive sign indicates that the
amount of electron repulsion decreases as 9 increases; i.e., the
electrons become more tightly bound as 9 increases. For the
integrals LAy (,)/ denoting adjacent carbon atoms), we find
24
(e?v?)-- 'k12 = *0.217 k23 = -0.04, k34 '40.03. A positive
sign indicates that the magnitude of 1.,/z" increases as in-
creases; i.e., the bond between atoms/kandy becomes stronger
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as.0 increases. The integral 1,77 has a slightly greater ()-
dependence; we find24 k77 = *0.78 e.v. If the substituent
atom 7 were more electronegative than carbon, the value of k77
would be greater. For example, for nitrogen we have25
25 The integral (47 47; 47 47) was assigned the value appro-
priate to an effective nuelear charge of 3.9 a. u4 The
other AO electron repulsion integrals were assigned the
- same values as before.
k77? 4.1.02 e.v. It is notewtirthy that the sum(,5,404,,0147$7)
is almost independent of 9, so that most of the 0 -depencence of
L77 comes from (1/2) 6(47 (4747; 4747).
We now consider the effect of the 0-dependence of the 7-1
bond length. Changes in the other bond lengths are relatively
small, and are therefore not discussed. Assuming a linear
relationship between bond length and MO bond order,26 and assum -
26 C. A. Coulson, "Valence", Oxford University Press, London,
1952, p. 253.
ing Li7 inversely proportional to the bond length, we obtain
d1-d2
L17 = k17 cos 9 k17 P17 cos2 0 +....
dl
Here, d1 and d2 respectively denote the lengths of single and
double 7-1 bonds, and k17 is the value of L17(0)/c0s 0 for a
fixed bond length equal to 41. A similar formula applies for
017. We note that P17 is almost exactly proportional to cos 09
(the order of the 7-1 IT-bond is of course proportional to
P17 cOs 9, in view of Eq. 1). Therefore the second term is
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really proportional to cos3 9. If we take (d1-d2)/d1g"! 0.2/1.51
and P(9 . 0.3, we see that the second term is not more
than five per cent of the first.
We return now to discuss the conditions (8). We assume
for the moment the is really a constant (see below). Con-
dition 8c holds with an error in 0-dependence not greater than
five per cent, the error arising almost entirely from the
lengthening of the 7-1 bond as 0 increases. A similar remark
applies to 8a, but in this case the error arises solely from
the bond lengthening. The applicability of 8b may be judged
from the 0-dependence of the integral L77. Changes in L77 arise
mainly from charge redistribution, although the slight ()-
dependence of the AO electron repulsion integrals such as
(g5,a, t6/44 08) could also play a part. The calculated change in
L77 throughout the range of 9,A-1 e.v., implies a change of dr'
of about 0.3 VA: -3 eev.). Previous experience15 indicates
that this change, while by no means negligible, is not suf-
ficient to upset qualitative conclusions drawn by assuming
constant.
The question that remains to be discussed is that of the
constancy of,. We have stated that a necessary condition for
the constancy of /g is that the integrals 1,1441 (14+9) 7) be
independent of 0, and the foregoing discussion show that this
condition is appraximately satisfied. To complete the dis-
cussion, we note that in the semi-empirical method the configu-
ration energies are taken to be orbital energy differences (Eq. 10),
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whereas in the SCF method the configuration energies are given by
=e - - (Jil = Ki) Kil (101)
where the els are SCF orbital energies and Ji/ and Ku are
respectively Coulomb and exchange MO electron repulsion integrals
(the upper sign applies to singlet, the lower to triplet con -
_figurations). Now the semi-empirical and SCF orbital energies
may be assumed to vary proportionately under perturbations, so
that the assumption of a constant A is justified to the extent
that the electron repulsion integrals vary in proportion to the
corresponding semi-empirical configuration energies.
The 0-dependences of the electron repulsion integrals have
been introduced through Eq. 11. With the aid of the MO's and
MO energies of Table 2 (overlap neglected), we find that the
ratios(all a22)2/(e2-e1), (a11)2/(eE - el) and (a22)2/(e2 -el)
respectively undergo variations of 30%, 20% and 10% throughout
the entire range of 0. The errors come in mainly at values of
approaching 900. In the range of 9 between 0 and 45?, the
variations in these ratios do not exceed 5%. The semi-empirical
procedure for the configuration energies is thus leen to be
securely founded on the SCF method, especially at lower values
of 0.
5. GENERAL CONCLUSIONS
Benzene-analogue Transitions:--In order to arrive quickly
at the qualitative Conclusions of the theory, we handle the
orbital perturbations by means of second-order perturbation
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theory. The MO energy factors are given by an expression of
the form
ni - ni Ai + Bi cos2 A,
(17)
where for the constant Ai and Bi we adopt expressions conforming
to conditions (5) and (8):
cil2 Bi = /002
A c 12 (1 - s n1?)2/(n1?? ).
-
A term involving di2 has been neglected in the above expression
for Al. The effect of overlap on the MO energies is illustrated
In Fig. 2.
For the BA state energies, three possible types of behavior
under twisting perturbations may be classified and interpreted
In terms of the relative magnitudes of Bi and B,2 (Note that B1 and
B5 are always zero under the conditions specified in this paper).
Let us consider either of the two pairs of interacting configu-
rations, and the states arising from them. Where I B11 >, 1B21,
both state energies increase initially upon twist (increase of 0).
We designate that behavior as Type i. Where the lower state
energy initially increases and the higher state energy initially
decreases upon twist, we speak of Type ii behavior; it would
appear if (B11 11321 . Finally, where IBil 44 IB21,
both the state energies would initially decrease upon twisting,
and we refer to that behavior as belonging to Type iii. The
three types of behavior are illustrated in Fig. 3.
The above classification is based on the, Initial behavior
as 9 is increased. The theory does not necessarily imply that
the state energies should vary monotonically with 4; Non-
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monotonic behavior behavior could result from the variation of the CI
integral. Also any non-monotonic trend in the mean configura-
tion energy, such as might arise as a result of deviations from
(17), could be reflected in a similar trend in one or both
state energies.
Twisting effects on the BA singlet-singlet intensities
depend primarily on the variation of the /1's in Eq. 12 rather
than on the much less marked variation of the orbitally perturbed
transition moments. Now for either pair of interacting configu-
rations, the appropriate ( lijk or Al B) approaches zero as the
configuration functions become more nearly degenerate; Keeping
that in mind, the qualitative intensity predictions of the
theory may be inferred by inspection of Eq. 12.
Let us first consider the case where both the inductive
effect and the overlap integrals are neglected. We have
A A2
(B11 - - 2
B1(
0
B21
(18a)
(18b)
In view of (18b), each pair of transition .energies must conform
either to Type i or Type ii behavior. Because of (18a), the
configuration energies become degenerate at 9 = 1T/2. The theory
OW
thus predicts that the 6 and 0 ?01 transitions should each
shift initially to the blue upon twisting, with a progressive
diminution of' intensity. The intensities of the other two
transitions should he relatively insensitive to twisting.27 As
27 In speaking of intensity changes, we refer to percentage changes
of the oscillator strength.
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0 approaches 1172, the frequencies and intensities of all four
transitions should approach those of the corresponding benzene
transitions.
Next, we take up the case where the inductive effect is
included but the overlap integrals are neglected. In place of
(18a), we now have
A - A 0
1 - 2 9
and the B configuration energies become degenerate at a value of
0 less than I1/2. The intensity of the 5 ?0.1 transition should
initially decrease upon twisting, the transition should become
accidentally forbidden at an intermediate value of 9 (cf. Fig 5b),
and subsequently the intensity should increase until 0 becomes
1r/2. No other new features are brought in, except in that, when
0 = 17/2, the transition frequencies are no longer expected to
revert exactly to the corresponding benzene frequencies.
Finally, we consider the case where the inductive effect
is again neglected, but the overlap integrals are taken into
account. The effect of overlap is to decrease by a substantial
amount the numerator of B19 and at the same time to increase
that of B2 by about the same amount. Therefore, where overlap
is includedi the predicted behavior of the band frequencies tends
more nearly to conform to Type iii than to where overlap is
neglected. Type i behavior might still be predicted, however,
if d' were sufficiently close to n10 As the configurational
interaction integrals depend only slightly on the AO overlap
integrals, it follows that the calculated electronic state
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energies are substantially increased by the inclusion of Over-
1ap28 (cf. Figs. 2,4). Since B1 .and B2 may now become equal,
28 In the SCF method upon which the present semi-empirical
treatment is based, the difference between the ground and
excited state effectivR Hamiltonians is allowed for only in
a crude approximation.29 Some preliminary calculations by
29 P. 0. Lowdin, Advances in Physics 1, 1 (1956).
the authors3? indicate that, if a more accurate correction
30 E. G. McRae and L. Goodman, unpublished.
were applied in the semi-empirical method, the calculated
energy of the state would be lowered relative to the ground
state (i.e., in opposition to the effect of inclusion of
overlap) and the energies of the other three BA states would
be increased., A corresponding correction for CT transitions
would probably be especially large.
there exists the possibility of the 5 I transitions being
accidentally forbidden throughout the range of O. In any case,
with overlap included, the predicted intensity is smaller than
with overlap neglected.
Charge - Transfer Transitions:--The lowest energy CT con-
figurations, together with the corresponding singlet configu-
rational functions, are as follows:
s) 1 0)2 1)2 1) 2 2)1;
01 0)2 1)2 1)2 2)1;
Xs2
x32. A
Although the n -+1t* and fl r -01r* classification of electronic
transitions is not strictly applicable in the cases we are dis-
cussing here (C2 symmetry), it is helpful and not too inaccurate
to think of the CT transition changing from the IT --pir to the
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n ir* type as 9 runs from 0 to 17/2. Since n -oir* transi-
tions are generally weak as compared with those of the 71r471*
type, it is to be expected that the CT oscillator strengths
should decrease upon twisting. By analogy with n --)fr * tran-
sition intensities in substituted benzenes (not heterocyclics),
an upper limit for the CT oscillator strength at 0 Tr/2 may
be set at 0.001.
As for CT transition intensities at 0 < 1172, we may be
guided to some extent by the values of the one-configuration
transition moments such as
iils2
=
1 r3
p-21 d v,
which are given in Table 5. It must be kept in mind, however,
that the CT intensities could be greatly increased through
Interaction between BA and CT configurations.31 As the relevant
3;. Conversely, the BA transition energies and intensities could
be affected by low-energy CT configurations. A possible
case of this is discussed in Sec. 6.
CI integrals all tend to zero (or to very small values) as 0
approaches 1T72, there is no need to revise our conclusion con-
cerning the limiting CT intensity as 0 approaches 11/2.
6. APPLICATION TO N.IN-DIMETHYLANILINE AND RELATED MOLECULES.
Assignment of Transitions:--The effects of intramolecular
twisting on the spectra of N,N-dimethylaniline and related
molecules have been studied experimentally by Wepdter,'5 by
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Klevens and Platt6 and by Remington.7 A representative
selection of the experimental data is reproduced in Table 6.
The structures of the less familiar molecules figuring in Table
6 are shown below.
In the molecules listed in Table 5, ortho-substitution or
intramolecular bridge formation leads to twisting of the amino
group about the bond joining the nitrogen atom to the adjacent
ring carbon atom. There is little doubt that the observed
intensity changes may be *attributed primarily to intramolecular
twisting perturbations, since in the absence of intramolecular
twisting, alkyl chloro- or bromo- substitution has a
relatively small effect on band intensities. In order approxi-
mately to eliminate the direct effects of substitution on the
band frequencies, the observed frequencies are corrected by
adding the difference between the corresponding band frequencies
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for benzene and for an appropriate substituted benzene.32 The
32 The ortho substituent correction of the ? -41 and '6 I
transitions in Table 6 represent the difference between the 1
and 0 -.4 1 o-o band energies of benzene and the corresponding
alkyl or halo benzene applied to the band maxima of the dimethyl
aniline derivative. For the 0 -42,2 transitions band maxima
are used throughout.
This procedure is justified on the following grounds: The
calculations reported in this paper assume the same molecular
dimensions in the ground and excited states and therefore apply
to vertical transitions. On first thought, this would imply
that an experimental band maximum Is to be used for comparison
with a theoretical excitation energy. However, the problem is
complicated by the 0 1 and 0 I transitions becoming for-
bidden, or nearly forbidden as runs to 1172. (The presence
of an inductive effect will remove the formal forbiddeness at
al 1772, but will in general not change the sense of the
following argument.) A weakly perturbed transition may be re-
garded as retaining "memory" of the forbiddeness and therefore
possesses a weak o-o band.53 In the following series of sub -
33 W. W. Robertson and F. A. Matsen, J. Am. Chem. Soc. 7, 5252 (1950).
stituted benzenes of Increasing substituent perturbation
(benzene, toluene, chlorobenzene, fluorobenzene), the o-o band
In the vapor spectrum increases in strength until the band
maximum occurs at the o-o transition. For these cases the ver-
tical transition is likely the o-o one. Since our corrections
are for the alkyl and halogen groups it seems clear that the
substituent correction should be the difference in the o-o band
energies of benzene and the substituted benzene for the 0 1
and 0 transitions; but for the allowed 0 transitions
the difference in band maxima. These corrections are applied to
the band maxima of the Dimethylanilines since o-o forbiddeness
is believed to be sufficiently removed for the maximum to be
the vertical transition. This procedure may be open to some
question in VII, where the 6 -41 transitions show benzene
structure and the vertical transition is not completely unam-
biguous. We note 'that this implies a small error in our empirical
parameters since benzene band maxima were used throughout.
corrected band frequencies are given in Table 6. The corrections
actually depend in part on the band assignments indicated below.
The nine molecules appearing in the table are designed numeri-
cally in what is thought to be the order of increasing*twist
angle, the twist-angle being defined, following KleVens and Platt,6
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as the angle of inclination to the ring plane of the line join-
ing the amino carbon atoms. Except for VII and possibly lie,
it is not possible to specify, actual values of 9 because the
tolecular geometries are not known. On the basis of symmetry,
we can say fairly certainly that the twist angle in VII (benzo-
quinuclidine) is 900, and that in He (Trogerls base) it
probably lies close to 45(:).5 The upper and lower limits for
the twist angles are reproduced in Table 7. The figures quoted
there provide the basis for the ordering of molecules in Table 6.
The parameter 0 cannot be identified with the twist angle,
because at a given twist angle 9 depends on the type of hybri-
dization of the nitrogen valence orbitals. The values of 9
corresponding to the limiting twist angles are shown in Table 7.
From this table, we conclude that 0 increases monotonically with
twist angle.
The trends in the observed absorption energies and inten-
sities are illustrated in Figs. 4a and 5a respectively. The
trends in the spectra as the twist angle approaches iir/2 suggest
definite assignments for each of the observed absorptions. Thus
the lowest-frequency transition, which in I appears weakly
(f = 0.04) at 4.2 shifts sharply to the blue with pronounced
diminution in intensity. In VII, the band has a- frequency 'very
close to that of the Alg B2u band in benzene, and has similar
vibrational structure. Accordingly the band may be attributed
to the 'BA transition 5 1.34'35 We should not be surprised
34 This is contrary to an assignment made by Klevens and Platt.6
35 See also the similar assignments of Goodman and Shull.15
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ea,
-31 -
that the 5 -41 band intensity in VII is considerably larger
(by a factor of four) than that of the benzene Ag --o B2u band,
since this effect is predicted theoretically (see below). How-
ever, the intensities of the other BA bands are expected to
revert to those of the corresponding benzene bands as 9 approaches
1T/2.
The next band is fairly strong (f 7. 0.28) in I. It loses
intensity upon twisting and disappears altogether in VII
(f ( 0.001). The band frequency suffers relatively little
change upon twisting, remaining close to 5.0 e.v. The transition
must be of the CT type; otherwise, its intensity would approach
that of one or other of the benzene transitions, all of which
have oscillator strengths in excess of 0.001. By similar reason-
ing, the band at 6.2 e.v. in I (f s 0.54) may be attributed to
the BA transition 5.. As the twist angle increases, the
band shifts to the red with a fairly pronounced drop in intensity.
Finally, the absorption at 7.0 e.v. in I (f r. 0.79) may be
attributed to the remaining two BA transitions, 5 -.4.2 and 5 .?
which presumably lie so close together that they appear as one.15
Its behavior is different from that of. the other three bands,
in that its intensity' undergoes only a small fractional change
as a result. of intramolecular twisting. ThUs, its intensity in
VI is twenty per cent less than in I while the intensities of
each of the other three bands are diminished by a factor of three
or more.
Empirical Parameters: - -In order to apply the theory described
in Sec. 3, we choose values of (which, for 921,01 lead to
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-32-
approximately the correct intensity for the 1 transitions
in I. With overlap neglected, we adopt la 1.5,36 and with
36 In Ref. 15 we have estimated it- 1.0 for I by fitting the
energy of the Z5 1 transition. Our conclusions are rather in-
sensitive to the particular numerical values assigned to the
parameters, except where otherwise noted, and are therefore con-
sidered to be fairly generally applicable. We note that the
intensity of the ? --k1 transition should be highly sensitive to
assymmetry of'chargerlY and thus valid for conjugative parameter
37 L. Goodman, I. G. Ross and H. Shull, J. Chem. Phys. 26, 474 (1957).
correlation.
overlap included oral 1.0. Where the inductive effect is in-
eluded, we adopt cir, . 0.2g. Throughout, we choose
This means that, where overlap is included, the 7-1 overlap
integral at = 0 is taken equal to the C-C overlap integral.
These values are appropriate to a substituent which interacts
rather strongly with the ring. In particular, it is considered
to represent with reasonable accuracy the strength of the 7-1
IT-bond in N,N-dimethylaniline. We note that setting /00 = 1
(implying gi7 -/g at Q is 0) does not imply equality between the
7-1 and C-C 1r-bond strengths, because /9' is diminished in mag-
nitude by the term involving MO electron repulsion integrals
while gi7 does not contain a term of this type. Since in sub-
stituted 'benzenes the 7-1 bonds are somewhat weaker than the
bonds between ring carbon atoms, the adopted 7-1 overlap integral
value may be viewed as an upper limit. In conformity with the
above assumptions about the overlap integrals, we assume all
bond lengths equal, and equal to the carbon-carbon bond length
in benzene (1.4 h. For purely conjugative substituents, the MO
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?33?
secular equation was solved by the method of Goodman and Shull,
as described in Sec. 3. The inductive effect was treated by
first-order perturbation theory,38 adopting the MO's .for the
38 H. Eyring, J. Walter, and G. E. Kimball, "Quantum Chemistry",
Wiley and Sons, New York, 1944, p. 95.
purely conjugative case as zeroth-order functions. All solutions
were obtained subject to conditions (5) and (8). The results of
the calculations are given in Tables 3 and 4. To illustrate an
intermediate stage of calculation, the MO's and MO energies are
given in Table 2.
Bepzene -analogue Transitions:--The behavior of the Observed
A .4A transition energies is on the borderline between Types ii
and iii while the A --"B transition energies exhibit Type ii
behavior (Fig. 4a). The trends predicted by the thdory with
overlap neglected belong to Type i, and thus conflict with experi-
ment. The inclusion of overlap leads to a better agreement with
experiment, Type iii behavior being predicted for the A-4.A,
and Type ii for the A B transition energies (Fig. )+b). Actually,
the predicted trends tend to be too much like Type iii. However,
we have probably overestimated the 7-1 overlap integral in
adopting Po = 1, and a smaller estimate of the 7-1 overlap
integral at G= 0 would lead to an improved agreement with ob-
servation. In comparing the calculated and observed trends in
transition energies, it should be kept in mind that, in the
transition, the error incurred through neglect of overlap tends
to be cancelled out by the Hamiltonian approximation inherent
In the MO method.28
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The highest-energy absorption shows a definite red shift
in the series I, IV, VI. It is natural to expect that, if
the observations were extended to VII, the absorption energy
would revert approximately to that for the corresponding ab-
sorption in benzene. The implied non-monotonic behavior is
correctly predicted by the theory with overlap included,
according to which both the 5 -.2 and S a transition energies
pass through minima at intermediate values of O. The theory
predicts deviations from monotonic behavior for the other band ener-
gies, but these are relatively slight and are not observed
experimentally.
We draw attention to the predicted 0-dependence of the
lowest-energy singlet-triplet transition energy given in
Table 3. In order to carry out the calculation, the hiu state
In benzene was assumed to lie at 4.8 e.v., and the lowest-
energy triplet state was assumed to be Bia (3.8 e.v.). Generally
speaking, the trends in corresponding singlet-singlet transi-
tions under intramolecular twisting. However, in each case some
A
differences are expected because of the changed magnitudes of
the relevant CI integral. The parallelism between the calcu-
lated variations of corresponding triplet and singlet state
energies is not greatly disturbed either by the inclusion of
overlap or by the choice of different limiting values for the
benzene 3E state energy.
la
As far as transition energies are concerned, qualitative
conclusions drawn from the calculations for a purely conjuga-
tive substituent are not altered by inclusion of-the inductive
effect.
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_31f...
The highest-energy absorption shows a definite red shift
in the series I, IV, VI. It is natural to expect that, if
the observations were extended to VII, the absorptiOn energy
would revert approximately to that for the corresponding ab-
sorption in benzene. The implied non-monotonic behavior is
correctly predicted by the theory with overlap included,
aCCording to which both the 6 -4.2 and 6 transition energies
pass through minima at intermediate values of 0. The theory
predicts deviations from monotonic behavior for the other band ener-
gies, but these are relatively slight and are not observed
experimentally.
We draw attention to the predicted 0-dependence of the
lowest-energy singlet-triplet transition energy given in
Table 3. In order to carry out the calculation, the 3Ela state
In benzene was assumed to lie at 4.8 e.v., and the lowest-
energy triplet state was assumed to be 3B1a (3.8 e.v.). Generally
speaking, the trends in corresponding singlet-singlet transi-
tions under intramolecular twisting. However, in each case some
differences are expected because of the changed magnitudes of
the relevant CI integral. The parallelism between the calcu-
lated variations of corresponding triplet and singlet state
energies is not greatly disturbed eitherby the inclusion of
overlap or by the choice of different limiting values for the
benzene 3E1a state energy.
As far as transition energies are concerned, qualitative
conclusions drawn from the calculations for a purely conjuga-
tive substituent are not altered by inclusion of the inductive
effect.
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-35..
The trends in the observed band intensities are shown, in
Fig. 5, in indirect comparison with those predicted theoreti-
cally. As predicted, the 6 1 and 5 .451 transition intensities
decrease upon twisting, while the 6 42 and S -0 a intensity sum
is relatively insensitive to twisting perturbations.
The fact that the 6-101 intensity in VII (9 = 1/2) is
substantially greater than that of the Aig -frB2u transition in
benzene may be attributed to the inductive effect of the sub -
stituent. For the 6 -*1 transition, the accidental forbiddeness
predicted at an intermediate twist angle cannot be discerned with
certainty in the experimental results. However, the relationship
between the observed transition intensities and energies, which
is shown in Fig. 6a, indicates indirectly that it does occur in
fact (see below).
The theory fails to account for the high intensity of the
S-01 transition at small twist angles. With overlap neglected,
the calculated oscillator strength (9 = 0) is less than half that
observed in the spectrum of I, and a still smaller intensity is
predicted with overlap included.39 In agreement with observation,
39 The condition of "accidental forkiddeness", which was mentioned
in Sect 5 with reference to the "6 1 transition, is approached
closely with the present set of parameters. This is a fortuitous
circumstance, however, and is not an essential implication of the
theory as applied here. To illustrate this, we .point out that ?
the consideration of the inductive effect, with overlap included,
could lead to a considerable increase of the predicted intensity.
the observed intensities in the series I, II(b), III, IV, V, VI
are related linearly to the corresponding transition energies
(Fig. 6a). The points for II(a) and II(c) depart somewhat from
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the main trend, while the point for VII lies well above the
straight line passing through the points for I and V. The
shapes of the corresponding theoretical curves are shown in
Fig. 6b. At low energies, the observed linear relationship
is reproduced in all three curves. This comes about from the
approximate cos2 9 dependence of both the intensity and exci-
tation energy for small and moderate 9 values. For larger twist
angles the intensity, in particular, deviates markedly from
Cos2 9 behavior. At higher energies, the observed behavior
appears to conform qualitatively to that predicted with the
Inductive effect included. The probable trend followed by the
experimental points, including that for VII, is indicated by
the broken line in Fig. 6a. From the figure, it is seen that
the available information definitely suggests that the intensity
of the ? -1,01 transition should pass through a minimum value at
an intermediate value of 9, as predicted theoretically. We note
that the data for II(a), II(b) and II(c) implies that the
nitrogen - atom valence states for those molecules may be
different from the unbridged cases.
The Oscillator Strength Sum: --Klevene and Platt have
pointed out that the sum of the oscillator strengths for the
observed transitions decreases upon twisting, from 1.7 in I to
0.9 in VI. In qualitative accord with that result, the sum of
squares of the transition moments listed in Table 5 decreases
with increasing O. The predicted trend is not' so pronounced as
that observed. However, the agreement between theory and
experiment would be improved by taking more :transition moments
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into account, and by allowing appropriately for changes in
the transition energies.
previous Worl?--The theory of twisting effects on the
spectra of ortho-substituted N,N-dimethylanilines has been
discussed recently by MUrrell.40 Although MUrrell's method of
40 J. W. Murrell, J. Chem. Soc. ?1956, 3779.
treatment is quite different from that adopted in the present
work, it is gratifying that his conclusions are almost identical
with some of those of the present study.
Acknowledgments: - -We thank Professor M. Kasha for pro-
viding the opportunity to undertake this study. We thank
Professors M. Kasha and H. Shull for many helpful discussions;
and Dr. P. 0. Lowdin for some helpful suggestions, which have
been followed in this paper.
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Table 1
EMPIRICAL PARAMETERS
Overlap
Approximation
Excited
State
,(e.v.)
CI
Integral
Overlap
Neglected
Overlap
Included
1A
1B
3A
1A
1B
3A
-3.30
-2.98
-2.15
-3.09
-2.79
-2.02
0.121e
0.353,
0.233/
0.129p
0.377fg
0.21+8 le
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Table 2
MO% AID NO ElIERGY WITS?
(*)
I
Overlap neglected
aio - atm ail
a12
a13
a
aio
Overlap included
ais ail' ai2
ai3
ni
0
30
-60
90
0 0.7219
:.0.6748
1 .0.1501
2 .0.0280
0 0.7706
? -0.6227
1 -0.1332
2 .0.0217
0 0.9127
$ -0.4021
1 -0.0731
2 -0.0076
0 1
s 0
1 0
2 0
0.6264
0.5490
0.4929
0.2146
0.5852
0.6123
0.040
0.1899
0.3930
0.8162
0.4038
0.1135
0
1
i)
0
0.2671
0.4747
-0.8363
.0.0582
0.2307
0.4615
-0.8510
-.0.0433
0.0367
0.023
-0.9093
-0.0162
0
0
, 1
0
0.1078
0.1188
0.1714
.0.9694
0.0895
0.1155
0.1411
-0.9777
0.0196
0.0912
0.0623
.0.9931
0
0
0
1
0.0588
04611
0.0756
0.1005
0.0485
0.0593
0.0630
0.0743
0.0196
0.0464
0.0287
0.0240
0
0
0
0
2.3543
1.6678
0.6597
-1.1278
2.2685
1.6523
0.7156
-1.0971
2.0879
1.5856
0.8718
-1.0330
-1.0000
1.0000
1.50000
1.0000
0.7027
.0.6857
.,0.1982
.0:11548
0.7605
-0.6262
.0.1799
?0.0429
0.9185
.0.3814
-.0.1107
.0.0153
1
0
0
1
0.5554
0.4937
0.5733
0.3483
0.5188
0.5564
0.5751
0.3103
0.3367
0.7580
0.5300
0.1873
0
1
0
0
0.2570
0.4979
.0.8306
-0.1033
C).2238
0.5056
.0.8362
.0.0811
0.0996
0.4864
-0.8698
.0.0296
0
0
1
0
0.0819
0.0935
0.1845
-0.9820
0.0682
0.0921
0.1541
.0.9880
0.0272
0.0757
0.07735
-0.9970
0
0
0
1
0.0389
0.0392
0.0648
0.1223
0.0302
0.0385
0.0550
0.0899
0.0119
0.0313
0.0273
0.0283
0
0
0
0
1.4%1
1.1631
0.4870
-1.6683
1.4584
1.1506
0.5335
-1.5865
1.3734
1.0925
0.6690
-1.4181
1.3333
1.0000
0.8000
-1.3333
(a) Inductive effect neglected.
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( 0 )
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Table 3
CALCULATED TRANSITION ENERGIES AND INTENSITIES
Upper Overlap neglected Overlap neglected Overlap included
State Inductive effect neglected Inductive effect included Inductive effect
neglected
E(e.v.) f
3A, 3.61 -
1- 4.53 0.041
0 1 5.77 0.139
2 6.73 0.447
2 6.73 0.537
3A 3.64 -
11 4.63 0.028
30 1 5.84 0.109
2 6.71 0.472
2 6.75 0.548
3A 3.74 -
11 4.83 0.004
60 1 6.05 0.029
2 6.79 0.597
2 6.84 0.590
3A1
3.80
1 4.90 o
90 1 6.20 0
2 7.00 0.600
2 7.00 0.600
E(e.v.) f
3.54 -
4.6o 0.018
.5.65 0.156
6.54 0.468
6.71 0.507
3.58 -
4.69 0.008
5.73 0.130
6.54 0.491
6.72 0.516
3.70 -
4.83 0.002
5.97 0.046
6.68 0.528
6.80 0.558
3.80 -
4;86 0.012
6.20 0
6.03 0.581
7.00 0.600
E(d.v.) f
3.91 -
4.74 0.058
6.31 0.022
7.23 0.462
6.96 0.769
3.86 -
4.8o 0.041
6.25 0.014
7.06 . 0.486
6.91 0.743
3.82 _
4.93 0.006
6.18 0.014
6.84 0.547
6.88 0.646
3.80 -
14.90 o
6.20 o
7.00 0.600
7.00 0.600
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Overlap neglected
G (?) ' Inductive effect neglected
AA (0) AB (0)
Table 4
STATE FUNCTIONS
Overlap neglected
Inductive effect included
"A (o) A B (0)
Overlap included
Inductive effect neglected
AA (0) AB (?)
24.0
19.7
26.3
14.8
-3.0
30
21.3
16.7
24.5
10.7
1.8
.60
11.7
7.1
10.5
-0.2
5.8
90
0
0
Oa
-8.o
0
23.3
20.0
9.2
0
, (a) Higher order approximations than first-order perturbation theory will cause 11A to be .
slightly different from zero in the presence of an inductive perturbation.
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0(0) 1,41
0 .007
30 .003
60 .016
90 0
?
Table 5
a-c
TRANSITION MOMENTS
.937
.944
.966
1.0000
Ml141
Ml
m, m53
.2 m13
.095 1.095 .383 .239 .166 2.32
.078 1.078 .382 .198 .162 2.27
.029 1.029 .334 .062 .128 2.12
0 1.000 0 0 0 2.00
(a) Both overlap and inductive effect neglected.
(b) The magnitudes of the transition moments are given in units of ER,
where denotes the electronic charge and R denotes the C-C
bond length. The m's denote one-configuration transition moments,
and denotes the sum of squares of the transition moments in
columns 2-8.
(c) The following were found to be less than 0.1 CR at 9 = 0:
12282r m029 m02.
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Table 6
SPECTRA OF N,N-DIMETBYLANILINE AND RELATED MOLECULESa
Substance
Emaxx10-3
Eobs(e.v.) E (e.v.)b f sum
corr
I. N,N-Dimethylaniline
ha. N-Metbylindoline
b. N-Methyl-homo-tetrahydro-
quinoline
c. Troger's Base
III. o -Chloro-NIN -dimethylaniline
IV. N,N-Dimethy1-2-toluidine
V. 2-Isopropyl -N,N -dimethylaniline
2,6-NIN-Tetramethylaniline
VII. Benzoquinuclidine
2.39
15.50
22.2
36.6
2.9
10.0
2.0
8.5
2 x 1.11
2 x 4.25
1.8
7.6
18.5
36.10
1.30
6.36
3.1.4
30.8
1.17
4.30
(12.0)
2.09
8.6
36.1
0.5
(0.4)
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0.036
0.29
0.54
0.79
0.041
0.21
0.021
0.17
2 x 0.017
2 x 0.08
0.026
0.14
0.39
0.72
0.014
0.128
0.23
0.69
0.013
0.089
I= NO
?
(