- Email: [email protected]
A study of the effects of solvent on overtone frequencies
JOURNAL
OF MOLECULAR
A Study
SPECTROSCOPY
of the Effects
2%
347-359
of Solvent
(1967)
on Overtone
Frequencies
G. DUROCHER AND C. SANI~ORFY Dgpartement de Chimie,
Universit6 de Montrbal,
Mont&al,
Qudbec, Canada
According to Buckingham’s theory on solvent effects the shift caused by solute-solvent interaction should be linearly proportional to the vibrational quantum number of the excited vibrational level which is involved. In order to provide an experimental check on this theory we measured the wave numbers of the OH, NH, or CH fundamentals, their first and second overtones of phenol, 2,6-di-tertiary-butyl-4-methylphenol, N-methylaniline, and chloroform in a series of nonpolar or weakly polar solvents. The results indicate that the agreement with experiment is satisfactory for 2,6-di-tertiary-butyl4-methylphenol and for phenol in the most weakly associating solvents but not for phenol in more strongly associating solvents, or for N-methylaniline, or chloroform. Buckingham’s theory in its original form uses second-order perturbation techniques. We tried to improve the agreement between theory and experiment in taking account of the off-diagonal matrix elements of the quartic potential constant. This way we were able to interpret the main trends observed in the spectra but the need for higher approximations is still indicated. The spectra of 2,6-di-tertiary-butyl-4-methylphenol were also measured at -78°C and, in a solid glass, at -190°C. The observed changes can be interpreted in terms of increased solute-solvent inleractions becoming more significant at liquid air temperature. INTRODUCTION
Buckingham’s theory on solvent effects (1-3) is widely recognized as the soundest approach available to interpret changes in the infrared spectrum due to solut)e-solvent interactions. In this theory t,hc intermolecular potential is expanded in a series, (1) where q is a normal coordinate and U, relates to the vibrational equilibrium position, U’ = (dU/dq) e and U” = (d2U/dq2), . This potential together with the anharmonicity in the free molecule is considered as a, perturbation. Then secondorder perturbation theory is applied yielding the energy levels and other spectral characteristics of the dissolved molecule. There are several points in Buckingham’s theory which lend themselves to experimental verification. Among these we chose the rule that the solvent shift of the first overtone should be double that of the fundamental, the solvent shift of the second overtone triple that of the fundamental, and so on. 347
348
DUROCHER
AND
SANDORFY
Thus we have undertaken a series of measurements of the frequencies of the fundamentals, first and second overtones of the OH, NH, or CH stretching vibrations of a certain number of molecules. These vibrations are known as “good group frequencies” the motion being largely localized in the respective diatomic group. We measured these in a series of solvents which can be supposed to be only slightly perturbing that is, in nonpolar or slightly polar solvents. Our solutes were phenol, 2,6-di-tertiary-butyl-4-methylphenol, N-methylaniline, and chloroform. The solvents were n-hexane, CC&F (freon-11), carbon tetrachloride, chloroform, and carbon disulfide. The perturbing action of these solvents seems to increase in this order, the two first ones having very nearly the same effect. We also used a liquid called F.C. 75 by the Minnesota Mining and Manufacturing Company and which according to this Company’s manuals is a mixture of isomers of perfluoro-n-propylpyrane (4), a perfluorinated cyclic ether with a side chain. It was necessary, however, to mix g per volume of CClsF into it for obtaining a sufficiently high solubility. We also studied the temperature dependence of the anharmonicity of the OH, NH, and CH stretching frequencies of 2,6-di-tertiary-butyl-4-methylphenol, N-methylaniline, and chloroform, respectively. EXPERIMENTAL
Our compounds were purified by distillation, recrystallization, or sublimation according to each case. The preparation of the solutions and the filling of the cells were executed under a dry nitrogen atmosphere. The spectra were measured on a Perkin-Elmer model 112 single beam-double pass instrument mounted with a Bausch and Lomb 300 lines/mm grating blazed at 3 k in the first order in the 2000-4500 cm-l region and with a Perkin-Elmer 640 lines/mm grating blazed at 1.4 ~1in the first order in the 450&11,000 cm-’ area. The spectral slit width was 0.5 cm-l between 3000 and 3600 cm-l, 0.9 cm-’ in the 7000-cm-’ area, and 2.2 cm-’ in the lO,OOO-cm-’ area. The following gases and vapors were used for calibration: (1) 2600-3800 cm-’ : HCI (5), CHr (6)) NH, (7), Hz0 (8, 9) ; (2) 5000-7400 cm-‘: Hz0 (IO), HCI (5), CH4 (11), NH, (1W), Hz0 (15, 14) Hg emission lines (15) ; (3) 8000-10,400 cm-l: Hg emission lines (16), Xe, Iir, A, Ne emission lines (9). We used cells from 2 cm to 1 m. The concentrations between O.OOlM and O.OlM for the fundamental and the of the order of 0.05M for the second overtone. In the low temperature measurements we used two 2.80 cm and 8.90 cm. Their design followed conventional and 1 m cells were used for the vapors.
of the solutions varied first overtone and were cells whose length was lines. Heatable 10 cm,
HIGHER
TERMS
AND
SOLVENT
:WJ
EFFECTS
RESULTS
The results are given in Tables I-XI. The wave numbers of the fundamentals and the first overtones are believed to be correct to &l cm-’ but those of the second overtone only to =t5 cm-‘. (The wave number of the second overtone of the vapor of N-methylaniline is even more uncertain and it is given in brackets. j Accordingly our discussion will be based on the larger differences only. All wave numbers reported in Tables I-VIII were measured at 21°C. In Tables IX-XI the results obtained at different temperatures are shown. The ones in Tables IX and X were measured in a 1: 1 mixture of CCl,F (freon-11) and CF2Br-CF2Br (freon-114B2) which forms a solid glass at liquid air temperature. This solid glass was described in another publication (17). The data in Table XI were measured in liquid solutions as indicated (CSz or CCl,F). The choice of the systems studied at low temperatures was, of course, conditioned by solubility at these temperatures. The wave numbers of the fundamentals of gaseous phenol and 2 ,t%di-tertiarybutyl-4-methylphenol were reported by Ingold (18,19) at 3655 and 3670, respectively. Cole, Little, and Mitchell give 3652 for phenol (20) (3652 and 3667 in our work). Dodd and Stephenson (21) found the NH stretching band of N-methylTABLE I WAVE NUMBERS, yDv IN C!I@ OF THE FUNDAMENTAL, FII~,T OVERTONE, AND SECONI) OVERTONE OF PHENOL IN DIFFERENT SOLVENTS AND THEIR SHIFTS, A~,, IN CK-', FROM THEIR RESPECTIVE VhLcEs IN THE VAPOR Solvent
Vapor
3652
7140
10 448
-
n-Hexnne CCl,F ccl, CHClr cs,
3625 3623 3612 3598 3593
7075 7075 7054 7025 7016
10 10 10 10 10
27 29 40 54 59
TABLE ANHARMONICITY
Vapor n-Hexane CC1,F ccl, CHCla cs,
-
-.
65 65 86 115 124
88 83 108 126 153
II
OF PHENOL AND THE SHIFT OF THE FUNDAMENT.\L ITS HARMONIC VALUE IN VhRIOUs SOLVENTS
CONSTANTS
FROM Solvent
360 365 340 322 295
x12
Xl8
x123
Y123
82 88 86 85 85 85
8i 84 83 80 72 76
71 94 92 95 117 104
2.5 -1.5 -1.5 -2.3 -7 -4.3
08 -
YOL
153 182 178 180 204 190
DUROCHER
350
AND
TABLE
SANDORFY III
WAVE NUMBERS, youIN CM+ OF THE FUNDAMENTAL, FIRST OVERTONE, AND SECOND OVERTONE OF 2,6-DI-TERTIARY-BUTYL-&METHYLPHENOL IN DIFFERENT SOLVENTS AND THEIR SHIFTS,Av..INBM-I,FROMTTHEIRRESPECTIVEVALUESIN +HEVAPOR Solvent Vapor FC-75 CClgF CCla CHCl3 csz
JJ01
PO2
3667 3661 3654 3651 3644 3645
vo3
7164 7154 7141 7133 7112 7118
10 481 10 455 10 436 10 420 10 415 10 405
TABLE
APO1
AV02
A~03
6 13 16 23 22
10 23 31 52 46
26 45 61 66 76
IV
ANHARMONICITY CONSTANTS OF 2,6-DI-TERTIARY-BUTYL+METHYLPHENOL AND THE SHIFT OF THE FUNDAMENTAL FROM ITS HARMONIC VALUE IN VARIOUS SOLVENTS Solvent Vapor FC-75 CClaF ccl, CHC13 CS2
85 84 83 84 88 86
88 92 92 93 84 91 TABLE
78 66 64 63 96 75
1.5 4 4.2 4.6 -1.8 2.4
162 149 148 146 184 161
V
OF THE FUNDAMENTAL, FIRST OVERTONE AND SECOND WAVE NUMBERS, vov IN crl OVERTONEOFTHENHSTREMHINGVIBRATIONOFN-METHYLANILINEINDIFFERENT SOLVENTS AND THEIR SHIFTS,AY~,, IN CI@, FROM THEIR RESPECTIVE VALUES IN THE VAPOR Solvent Vapor CClaF CCll cs2
WI1
WI2
3452 3446 3442 3433
vo3
6760 6742 6732 6716
9916 9874 9850 9830
Avol
Avoz
AI%3
6 10 19
18 28 44
52 66 86
TABLEVI ANHARMONICITY CONSTANTS OFN-METHYLANILINE AND THE SHIFT OF THE FUNDAMENTAL FROM ITS HARMONIC VALUE IN VARIOUS SOLVENTS Solvent Vapor CCl,F ccl, CS*
x12
72 75 76 75
X23
75 80 83 81
X123
65 66 61 61
Yl23
1.5 2.1 3.4 3.2
WC -
YO1
136 140 136 135
HIGHER
TERMS
AND
SOLVENT
TABLE
351
EFFECTS
VII
WAVE NUMBERS, IQ,*INCM-1 OF THE FUNDAMENTAL,FIRSTOVERTONE, AND SECOND OVERTONE OFTHECHSTRETCHINGVIBRATIONOFCHLOROFORMINDIFFERENT SOLVENTS AND THEIR SHIFTS, Av,, IN CM-~, FROM THEIR RESPECTIVE V.~LUES IN THE VAPOR Solvent Vapor FC-75 CCl,F CCI, csn
3033 3028 3025 3021 3011
8731 8695 8683 8662 8640
5943 5926 5914 5904 5888
TABLE ANHARMONICITY
CONSTANTS OFCHLOROFORM ITS HARMONIC VALUE
5 8 12 22
36 48 69 91
17 29 39 55
VIII AND THE SHIFT OFTHE IN VARIOUS SOLVENTS
FUNDAMENTAL
FROM
Solvent 61 65 68 69 67
Vapor FC-75 CCl,F CClr cs,
TABLE
0 0 -2.5 -2 -1.5
61 65 79 78 7-1
61 65 63 65 64
122 130 147 147 142
IX
WAVE NUMBERS, ypU IN c&c1 OF THE FUNDAMENTAL, FIRST OVERTONE, AND SECOND OVERTONE OF 2,6-DI-TERTIARY-BUTYL-4-METHYLPHENOL AT DIFFERENT TEMVALUES PERSTURES AND THEIR SHIFTS, Au DU IN CM-' FROM THEIR RESPECTIVE IN THE VAPOR. SOLVENT: AN 1:l MIXTURE OF CCl,F AND CFeBr-CF9Br
Vapor
3667
7164
10 481
21” -78” -190”
3654 3650 3641
7141 7133 7116
10 442 10 430 10 388
TABLE
13 17 26
-
-
23 31 48
39 51 93
X
ANHARMONICITY CONSTSNTS OF 2,6-DI-TERTIARY-BuTYL-4-METHYLPHENOL SHIFTOFTHEFUNDAMENTALFROM ITSHARMONICVALUEATDIFFERENTTEMPERATURES. SOLVENT: AN 1:l MIXTURE OF CCIaF AND OF CF?Br-CFpBr
Vapor 21” -78” -190”
85 83 84 83
88 90 90 95
78 68 71 57
1.5 3.4 2.9 5.9
AND
162 150 154 138
THE
352
DUROCHER
AND TABLE
SANDORFY XI
WAVE NUMBERS OF THE FUNDAMENTALSAND FIRST OVERTONESAT 21°C AND
Solute 2,6-di-tertiary-butyl-4-methylphenol
N-methylaniline
Chloroform
-78°C
Solvent
T, “C
ml
CCl,F
21” -78”
csz
vo2
Xl2
3654 3650
7141 7134
83 83
21” -78”
3645 3641
7118 7110
86 86
CC&F
221” -78”
3646 3644
6742 6738
75 75
CSZ
21” -78”
3433 3432
6716 6714
75 75
CClsF
21° -78”
3022
5914 5911
68 67
aniline at 3450 in the vapor, (3452). The CH band of chloroform vapor is reported to be at 3033 (22) (3033). Available data on the solution spectra of phenol and chloroform were summarized by Lecomte (28) and are generally in good agreement with our measurements. DISCUSSION
A) SOME CONCLUSIONS FROM BUCKINGHAM’S THEORY In Buckingham’s
theory on solvent effects a vibrational
term is expressed as
Gw=(v+;)ue-(v+3[++‘] +ue-(v+;>“[~-;kr]_.., (2) where v is the vibrational quantum number, wB the “harmonic frequency” in cm-l, and leQand k, are the cubic and quartic potential constants (in cm-‘) for the unperturbed molecule. The whole expression should be averaged to all solvent configurations. Buckingham uses notations where the rotational constant is introduced but since with the molecules examined in this paper we have no hope of using it we simplified the notations. Our Jcs and kd are, of course, the same as Buckingham’s A and B. We preferred these symbols in order to be in accordance with some of our own previous work (24,25). It is important to point out that (2) is obtained through the use of conventional second-order perturbation theory in which the off-diagonal terms of Icaare included (the diagonal term of ka is zero) but the off-diagonal terms of k4 and all higher terms are neglected (26-28).
HIGHER
TERMS
AND
EFFECTS
Xi:<
(v + ,!-i)‘X + U,,
(5)
SOLVENT
If we introduce and
(2) becomes G = (V + !h)w, -
(8 + ,1&@ -
where the bar indicates the presence of the intermolecular potential or its derivatives. From (Fi) we have for the observed fundamental and its first and second overtones : Y,)l = w, -
TV -
2x,
Vi)?= 2w, -
2TP -
vo3 = 3w, - 3?4 -
6X,
12X;
(sj
hence vo1
-
! iv02
=
?+02
-
,;+03
=
x,,
=
x,,
=
(7)
x.
As is seen from (3) the solvent shift depends on the anharmonicity (ka) of the isolated molecule. From the above equations the following predictions can be made: (1) The effect of solvent perturbation on the frequency and therefore, from (6) t,he solvent shifts are, as stated by Buckingham, AQ
=
which are in the ratio 1:2:3. (2,
A /ol -
IF,
Avoz
=
Here Au,, = ;,iAvoz
2w’, vou, gas
= ,$.~AI,, -
Avo3 -
= vm,
;2Auoa
3l1’, soln.
=
(3)
.
0.
(9)
(3) The anharmonicity const’ant (X) is solvent&dependent and, like for an isolated molecule, the same X should be obtained whether we use vol and vwL or v”? an d vo3 (or vol and vo3) in (7). Buckingham’s theory as referred to in t,he present work apphes to diatomic molecules. We are making the assumption throughout that in the X-H stretching vibrations which we examine the motion involves these two atoms only and that, Dhe anharmonic coupling constants between this and the other normal vibrations of the respective molecules are zero. Otherwise the treatment becomes rather more complicated (see Reference S). This approximat’ion is unlikely to impair our conclusions.’ We hope to have a closer look at it in a subsequent work, however. n’ow we turn our attention to the results we obtained to see if they bear out the above expectations. I This is corroborated by the work of M.-T. J. Chi,n. Phys. 57,1103 (1960).
Forel,
J.-P.
Leicknsm,
and M.-L.
Josien,
354
DUROCHER
AND SANDORFY
Phenol The 1: 2 : 3 relation is reasonably followed (Table I) for n-hexane, CC&F, and perhaps CC& if we disregard small variations which may be imputable to experimental error. For the more perturbing solvents, CHCL and CSz , however, a different pattern seems to apply: Av02 is slightly more than the double of Av01 but Avo, is significantly less than thrice Avol . Equation (9) yields the same observation. Table II shows that Xl2 equals X2, within 5 cm-’ like in the vapor for all solvents except CHCI, and CS; , an observation that seems to point in the same direction. 2,6-Di-Tertiary-Butyl-$Methylphenol,
(Tables III and IV)
The sterically shielded OH group is expected to enter less easily into associations than the OH group of phenol. Actually the shifts are invariably smaller for the former. The 1: 2 : 3 relation is roughly obeyed although there are irregularities somewhat exceeding the precision of the measurements. The same applies to the X12 = X23 relation. N-Methylaniline,
(Tables V and VI)
A significant departure of the 1:2:3 rule is observed even though are slight. Avo2is larger than 2Avo1and Avosis much larger than 3Av01. tion of Avos for the vapor is uncertain but CC&F may be taken as a confirming these observations. The departure from the Xxx = X23 rule is relatively slight, about as for the vapor.
the shifts The locastandard, the same
Chloroform, (Tables VII and VIII) This case is similar to the case of N-methylaniline. AVON is significantly larger than 2Avol and Avo3 is even more Iarger than 3Avo1. The Xl2 do not differ much from the XzI, however. To sum up, Buckingham’s theory used with the conventional secondorder perturbation formula is roughly satisfactory for the sterically hindered 2,6-di-tertiary-butyl-4-methylphenol and for phenol in the more weakly associating solvents. It breaks down in the cases of N-methylaniline and chloroform. B) INCLUSIONOF THE OFF-DIAGONALELEMENTSOF led As a next approximation we included the off-diagonal matrix elements of the quartic potential constants into the perturbation calculation as was done by Foldes and Sandorfy (29) in the case of hydrogen bonding. They are given by Barchewitz, for example (28).
HIGHER TERMS AND SOLVENT EFFECTS
Now the multiplier of (v + 35) contains ular potential or its derivatives,
a term independent
355
of the intermolec-
W = 67@/16w,
(11)
and IV = - f$ u” + 3kJJ’/o, The main
novelty
is that
+ Unz/a*B .
now the multiplier
(12)
of (v + $4)” contains
X = 3kJJN/2w,
(13)
representing the solvent dependence of the anharmonicity have a higher anharmonicity constant,
constant
X. We also
Y = 68k‘$16W,) which is seen to be solvent independent With these symbols we can write that G, = (v + %+e
-
and for the wave numbers
[W + lV’] -
V,,Z= 20, -
2[W + w]
=
3w, -
+ WI (v + X)“[X
+ X] -
(v + $i)“Y
(15)
that
VO1= we -
vo3
(14)
in this approximation.
(v + %)[W -
a term
2[X + X] -
3[W + #i’l -
It follows that
,
j.i2vo2=
VOl -
%vo2 -
x
(13/4)Y,
6[X + X] 12[X + X] -
+
_z +
(31/2)Y,
(16)
(17/4)Y.
4.5Y,
$+03 = X + X + 6.5Y,
(17)
and VOl -
102 +
y3vo3 =
--2y.
(18)
Furthermore, Avol = TV + 2X,
where Av,
= vOV ,gas -
A vo2= S@
+ 6-5
Avo3 = 3p
+
VOV ,soln.
128,
(19)
356
DUROCHER
AND SANDORFY
In this approximation the solvent shifts depend on both r and 8 but the effect of solvent on the anharmonicity constant depends only on X. This shows that there is no simple relation between the shift of frequency and the change in anharmonicity caused by the solvent since p and X have a different dependence on the potential constants. The inclusion of the off -diagonal terms of kd as it has been done in this section does not in itself represent a perturbation calculation of a higher order. In particular the lateral terms of ka (not on the row and column in whose intersection the given state is located) may be of the same order of magnitude as the offdiagonal terms of kd . These will introduce terms like ktU’/~z in the coefficient of (v + $4)“. The experimental results seem to indicate that the convergence in the series k3q3,k4q4, * . . is relatively slow but this is unlikely to make these terms negligible. As a consequence the expressions of the anharmonicity constants in terms of the potential constants [Eqs. (ll)-( 14)] would contain some further terms but Eqs. (15) to (20) would not change so that we can base conclusions on the latter. Regular higher order perturbation calculations will be presented later provided forthcoming experimental results warrant their use. Then we expect that (1) The solvent shift will not be linear with the vibrational quantum number and will not obey the 1: 2: 3 relation since according to (19) it now depends on XaswellasonlP. The following example is instructive. Let p be 50 cm-’ and X + 5 and -5 cm-“. Then, from (19) we obtain the following values. _y =
_tf = 5 cm-’
(2)
Avol -
>$Au,,z = j$Avo: -
40 70 90 100 100
60 130 210 300 400
AVOl Al%2 AYo3 AVIM AVOS gAvo3
= --f&
-5cm-’
= -&
(20)
and not zero. (3) The anharmonicity constant X should now depend on the solvent. Xl2 should be different from X23 even for the vapor if Y is not negligible. Let us now have another look at Tables I and VIII. Phenol (Tables I and II). The Avoy seem to indicate that X has a small but non-negligible negative value for CHCI, and CS, , at least. The anharmonicity constants X 123computed from (17) and (18) vary with the solvent about as expected. The shift of the wave number of the fundamental
HIGHER
TERMS AND SOLVENT
EFFECTS
357
from its “harmonic” value, wc - yol varies in a way similar to X1s3 . This could not be predicted since the change in yol depends on both p and X whereas the change in Xl23 only depends on X. Y123has small but, in most cases, negative values and they seem to vary from solvent to solvent. This is incompatible with the approximation applied in this section since according to (14) Y depends only on the square of the quartic constant. A negative value for Y indicates that higher terms like k5 , kg , . . . or u”’ and [,“” are important or, rather, that some of the lateral terms in the secular equation of the perturbation calculation are not negligible. Now, the Y are obtained as small differences between numbers about a thousand times as big and caution should be exercised. It seems, however, that even t,his better approximation is inadequate in this case. 2,6-Di- Tertiary-Butyl-4-Methylphenol
(Tables III
and IV)
This does not require new comments according to what was said above. N-Methylaniline
(Tables V and VI)
The Av,, indicate a positive X as they are divergent. The Y have small posit.ive values which vary little from one solvent to the other. Chlorojom
(Tables VII and VIII)
This too is a case of positive X. Again we find negative Y but they are small. We conclude that the approximation applied in Sec. B interprets correctly the nonlinearity of the solvent shift with the vibrational quantum number. It shows that Avou and the change in anharmonicity do not necessarily parallel one another. It bears out the fact that the anharmonicity constants are solvent dependent. On the other hand, Eq. (20) is not, in general, satisfied. This with the appearance of the negative Y and the slight variation of Y from solvent to solvent shows that even better approximations are needed. For this reason we shall not attempt to compute anharmonicity or potential constants from our data. In cases of stronger perturbations the change in anharmonicity might well be a major cause of the solvent shift. This was pointed out in 1938 by Bauer and ;\lagat (30) and this might have been a more important point of their famous paper than the much discussed Kirkwood-Bauer-Magat formula. A true attempt of using a higher approximation would require a higher precision in the measurement of the frequencies but this is not easily attainable for solution spectra. Work is going on in this laboratory in order to repeat as much as possible of the present work at low temperature. Finally, it is important to note that in a recent paper Vu, Schuller, Atwood, Oksengorn, and Vodar (31) who worked on CO, HCl, and HBr in neutral gas solvents reac*hed concIusions in many respects similar to those of the present paper.
358
DUROCHER
AND SANDORFY
C. THE EFFECT OF TEMPERATURE
The solubility of 2,6-di-tertiary-butyl-4-methylphenol was sufficient to measure its spectrum in a 1: 1 mixture of CCIBF and CF2Br-CF2Br down to liquid air temperature (Tables IX and X). At 21°C the wave numbers are very close to those for CC&F given in Table III. Only slight bathochromic shifts are observed at -78” but at -190” the change is significant. The fundamental shifts by 13 cm-l from 21°C to -190°C. This seems to show that at liquid air temperature associations are appreciably stronger. Also the 1: 2 : 3 ratio is maintained at 21° and -78” but the AvoWdiverge at -190”. Thus the lowering of temperature is seen to increase the strength of the solvent effect. The changes become significant at temperatures close to liquid air temperature only (when the solvent becomes a glass), as shown by Table XI. CONCLUSIONS
The data contained in this paper lead to the generalization that Buckingham’s theory on solvent shifts when used with the conventional second order perturbation formula is adequate in cases of very weak interactions only. For cases of stronger perturbations higher terms have to be included. The inclusion of the off-diagonal matrix elements of the quartic potential constant improves the situation inasmuch as the explanation of the observed trends is concerned but it does not lead to a quantitative agreement with experiment. The inclusion of higher terms seems to be indicated. ACKNOWLEDGMENT
We are indebted to Professor A. D. Buckingham for a stimulating exchange of letters. We express our thanks to the National Research Council of Canada for financial help and for granting a scholarship to G.D. Our very sincere thanks are due to Mr. G. Belanger and P&e J. Lajoie from this laboratory who measured the spectra of the vapors. RECEIVED: August 3, 1966 REFERENCES 1. A. D. BUCKINGHAM, Proc. Roy. Sot. A248, 169 (1958). 8. A. D. BUCKINGHAM, Proc. Roy. Sot. M66, 32 (1960). 9. A, D. BUCKINGHAM, Trans. Faraday Sot. 66, 753 (1960). 4. “Fluorochemicals.” Technical Data Sheet, Minnesota Mining and Manufacturing Company, St. Paul, Minnesota, 1957. 6. C. F. MEYER AND A. A. LEVIN, Phys. Rev. 34, 44 (1929). 6. A. H. NIELSEN AND H. H. NIELSEN, Phys. Rev. 46, 864 (1935). 7. G. A. STINCHCOMB AND E. F. BARKER, Phys. Rev. 33, 305 (1929). 8. E. K. PLYLER AND W. W. SLEATER, Phys. Rev. 37, 1493 (1931). 9. “Tables of Wavenumbers for the Calibration of Infrared Spectrometers.” International Union of Pure and Applied Chemistry. Butterworths, London, 1961. 10. E. K. PLYLER, J. Res. Natl. Bur. Std. (U.S.) 40, 221 (1952).
HIGHER
TERMS
AND
SOLVENT
EFFECTS
359
11. R. C. NELSON, E. K. PLYLER, AND W. S. BENEDICT, J. Res. Natl. Bur. Std. (U.S.) 41, 615 (1948). 12. H. J. UNGER, Phys. Rev. 43, 123 (1933). 13. H. H. NIELSEN, Phys. Rev. 62, 422 (1942). 14. E. K. PLYLER, N. M. GAILLAR, AND T. A. WIGGINS, J. Res. Natt. Bur. Std. (U.S.) 48, 221 (1952). 15. E. K. PLYLER AND C. W. PETERS, J. Res. Natl. Bur. Std. (U.S.) 46, 462 (1950). 16. E. D. MCALISTER, Phys. Rev. 34, 1142 (1929). 17. G. DUROCHER AND C. SANDORFY, J. Mol. Spectry., 20,410 (1966). 18. K. U. INGOLD, Can. J. Chem. 40, 111 (1962). 19. K. U. INGOLD AND D. R. TAYLOR, Can. J. Chem. 39, 471 (1961). 20. A. R. H. COLE, L. H. LITTLE, AND A. J. MICHELL, Spectrochim. Acta 21, 1169 (1965). 2f. R. E. DODD AND G. W. STEPHENSON, in “Hydrogen Bonding.” (D. Hadgi, ed.), p. 177. Pergamon Press, New York, 1959. 2.2. N. GINSBURG, quoted by H. H. Voge and J. E. Rosenthal, J. Chem. Phys. 4,137 (1936). 23. J. LECOMTE, Spectroscopic dans l’infrarouge. In S. Flugge’s “Handbuch der Physik,” Vol. 26, pp. 361 and 486. Springer Verlag, Berlin, 1958. 24. C. BERTHOMIEU AND C. SANDORFY, J. Mol. Spectry. 16, 15 (1965). 26. G. DUROCHER AND C. SANDORFY, J. Mol. Spectry. 16, 22 (1965). 86. G. HERZBERG, “Molecular Spectra and Molecular Structure,” Vol. I, p. 90. Van Nostrand, Princeton, New Jersey, 1950. 27. E. B. WILSON, JR., J. C. DECIUS, AND P. C. CROSS, “Molecular Vibrations,” p. 193. McGraw-Hill, New York, 1955. 28. P. BARCHEWITZ, “Spectroscopic Infrarouge, I. Vibrat,ions Moleculaires,” p. 189. Gauthier-Villars, Paris, 1961. 29. A. FOLDES AND C. SANDORFY, J. Mol. Spectry., 20, 262 (1966). 30. E. BAUER AND M. MAG.~T, J. Phys. Radium 9, 319 (1938). 31. H. Vu, F. SXULLER, M. R. ATWOOD, B. OKSENGORN, AND B. VODSR, J. Chim. Phys. 61, 263 (1964).
OF MOLECULAR
A Study
SPECTROSCOPY
of the Effects
2%
347-359
of Solvent
(1967)
on Overtone
Frequencies
G. DUROCHER AND C. SANI~ORFY Dgpartement de Chimie,
Universit6 de Montrbal,
Mont&al,
Qudbec, Canada
According to Buckingham’s theory on solvent effects the shift caused by solute-solvent interaction should be linearly proportional to the vibrational quantum number of the excited vibrational level which is involved. In order to provide an experimental check on this theory we measured the wave numbers of the OH, NH, or CH fundamentals, their first and second overtones of phenol, 2,6-di-tertiary-butyl-4-methylphenol, N-methylaniline, and chloroform in a series of nonpolar or weakly polar solvents. The results indicate that the agreement with experiment is satisfactory for 2,6-di-tertiary-butyl4-methylphenol and for phenol in the most weakly associating solvents but not for phenol in more strongly associating solvents, or for N-methylaniline, or chloroform. Buckingham’s theory in its original form uses second-order perturbation techniques. We tried to improve the agreement between theory and experiment in taking account of the off-diagonal matrix elements of the quartic potential constant. This way we were able to interpret the main trends observed in the spectra but the need for higher approximations is still indicated. The spectra of 2,6-di-tertiary-butyl-4-methylphenol were also measured at -78°C and, in a solid glass, at -190°C. The observed changes can be interpreted in terms of increased solute-solvent inleractions becoming more significant at liquid air temperature. INTRODUCTION
Buckingham’s theory on solvent effects (1-3) is widely recognized as the soundest approach available to interpret changes in the infrared spectrum due to solut)e-solvent interactions. In this theory t,hc intermolecular potential is expanded in a series, (1) where q is a normal coordinate and U, relates to the vibrational equilibrium position, U’ = (dU/dq) e and U” = (d2U/dq2), . This potential together with the anharmonicity in the free molecule is considered as a, perturbation. Then secondorder perturbation theory is applied yielding the energy levels and other spectral characteristics of the dissolved molecule. There are several points in Buckingham’s theory which lend themselves to experimental verification. Among these we chose the rule that the solvent shift of the first overtone should be double that of the fundamental, the solvent shift of the second overtone triple that of the fundamental, and so on. 347
348
DUROCHER
AND
SANDORFY
Thus we have undertaken a series of measurements of the frequencies of the fundamentals, first and second overtones of the OH, NH, or CH stretching vibrations of a certain number of molecules. These vibrations are known as “good group frequencies” the motion being largely localized in the respective diatomic group. We measured these in a series of solvents which can be supposed to be only slightly perturbing that is, in nonpolar or slightly polar solvents. Our solutes were phenol, 2,6-di-tertiary-butyl-4-methylphenol, N-methylaniline, and chloroform. The solvents were n-hexane, CC&F (freon-11), carbon tetrachloride, chloroform, and carbon disulfide. The perturbing action of these solvents seems to increase in this order, the two first ones having very nearly the same effect. We also used a liquid called F.C. 75 by the Minnesota Mining and Manufacturing Company and which according to this Company’s manuals is a mixture of isomers of perfluoro-n-propylpyrane (4), a perfluorinated cyclic ether with a side chain. It was necessary, however, to mix g per volume of CClsF into it for obtaining a sufficiently high solubility. We also studied the temperature dependence of the anharmonicity of the OH, NH, and CH stretching frequencies of 2,6-di-tertiary-butyl-4-methylphenol, N-methylaniline, and chloroform, respectively. EXPERIMENTAL
Our compounds were purified by distillation, recrystallization, or sublimation according to each case. The preparation of the solutions and the filling of the cells were executed under a dry nitrogen atmosphere. The spectra were measured on a Perkin-Elmer model 112 single beam-double pass instrument mounted with a Bausch and Lomb 300 lines/mm grating blazed at 3 k in the first order in the 2000-4500 cm-l region and with a Perkin-Elmer 640 lines/mm grating blazed at 1.4 ~1in the first order in the 450&11,000 cm-’ area. The spectral slit width was 0.5 cm-l between 3000 and 3600 cm-l, 0.9 cm-’ in the 7000-cm-’ area, and 2.2 cm-’ in the lO,OOO-cm-’ area. The following gases and vapors were used for calibration: (1) 2600-3800 cm-’ : HCI (5), CHr (6)) NH, (7), Hz0 (8, 9) ; (2) 5000-7400 cm-‘: Hz0 (IO), HCI (5), CH4 (11), NH, (1W), Hz0 (15, 14) Hg emission lines (15) ; (3) 8000-10,400 cm-l: Hg emission lines (16), Xe, Iir, A, Ne emission lines (9). We used cells from 2 cm to 1 m. The concentrations between O.OOlM and O.OlM for the fundamental and the of the order of 0.05M for the second overtone. In the low temperature measurements we used two 2.80 cm and 8.90 cm. Their design followed conventional and 1 m cells were used for the vapors.
of the solutions varied first overtone and were cells whose length was lines. Heatable 10 cm,
HIGHER
TERMS
AND
SOLVENT
:WJ
EFFECTS
RESULTS
The results are given in Tables I-XI. The wave numbers of the fundamentals and the first overtones are believed to be correct to &l cm-’ but those of the second overtone only to =t5 cm-‘. (The wave number of the second overtone of the vapor of N-methylaniline is even more uncertain and it is given in brackets. j Accordingly our discussion will be based on the larger differences only. All wave numbers reported in Tables I-VIII were measured at 21°C. In Tables IX-XI the results obtained at different temperatures are shown. The ones in Tables IX and X were measured in a 1: 1 mixture of CCl,F (freon-11) and CF2Br-CF2Br (freon-114B2) which forms a solid glass at liquid air temperature. This solid glass was described in another publication (17). The data in Table XI were measured in liquid solutions as indicated (CSz or CCl,F). The choice of the systems studied at low temperatures was, of course, conditioned by solubility at these temperatures. The wave numbers of the fundamentals of gaseous phenol and 2 ,t%di-tertiarybutyl-4-methylphenol were reported by Ingold (18,19) at 3655 and 3670, respectively. Cole, Little, and Mitchell give 3652 for phenol (20) (3652 and 3667 in our work). Dodd and Stephenson (21) found the NH stretching band of N-methylTABLE I WAVE NUMBERS, yDv IN C!I@ OF THE FUNDAMENTAL, FII~,T OVERTONE, AND SECONI) OVERTONE OF PHENOL IN DIFFERENT SOLVENTS AND THEIR SHIFTS, A~,, IN CK-', FROM THEIR RESPECTIVE VhLcEs IN THE VAPOR Solvent
Vapor
3652
7140
10 448
-
n-Hexnne CCl,F ccl, CHClr cs,
3625 3623 3612 3598 3593
7075 7075 7054 7025 7016
10 10 10 10 10
27 29 40 54 59
TABLE ANHARMONICITY
Vapor n-Hexane CC1,F ccl, CHCla cs,
-
-.
65 65 86 115 124
88 83 108 126 153
II
OF PHENOL AND THE SHIFT OF THE FUNDAMENT.\L ITS HARMONIC VALUE IN VhRIOUs SOLVENTS
CONSTANTS
FROM Solvent
360 365 340 322 295
x12
Xl8
x123
Y123
82 88 86 85 85 85
8i 84 83 80 72 76
71 94 92 95 117 104
2.5 -1.5 -1.5 -2.3 -7 -4.3
08 -
YOL
153 182 178 180 204 190
DUROCHER
350
AND
TABLE
SANDORFY III
WAVE NUMBERS, youIN CM+ OF THE FUNDAMENTAL, FIRST OVERTONE, AND SECOND OVERTONE OF 2,6-DI-TERTIARY-BUTYL-&METHYLPHENOL IN DIFFERENT SOLVENTS AND THEIR SHIFTS,Av..INBM-I,FROMTTHEIRRESPECTIVEVALUESIN +HEVAPOR Solvent Vapor FC-75 CClgF CCla CHCl3 csz
JJ01
PO2
3667 3661 3654 3651 3644 3645
vo3
7164 7154 7141 7133 7112 7118
10 481 10 455 10 436 10 420 10 415 10 405
TABLE
APO1
AV02
A~03
6 13 16 23 22
10 23 31 52 46
26 45 61 66 76
IV
ANHARMONICITY CONSTANTS OF 2,6-DI-TERTIARY-BUTYL+METHYLPHENOL AND THE SHIFT OF THE FUNDAMENTAL FROM ITS HARMONIC VALUE IN VARIOUS SOLVENTS Solvent Vapor FC-75 CClaF ccl, CHC13 CS2
85 84 83 84 88 86
88 92 92 93 84 91 TABLE
78 66 64 63 96 75
1.5 4 4.2 4.6 -1.8 2.4
162 149 148 146 184 161
V
OF THE FUNDAMENTAL, FIRST OVERTONE AND SECOND WAVE NUMBERS, vov IN crl OVERTONEOFTHENHSTREMHINGVIBRATIONOFN-METHYLANILINEINDIFFERENT SOLVENTS AND THEIR SHIFTS,AY~,, IN CI@, FROM THEIR RESPECTIVE VALUES IN THE VAPOR Solvent Vapor CClaF CCll cs2
WI1
WI2
3452 3446 3442 3433
vo3
6760 6742 6732 6716
9916 9874 9850 9830
Avol
Avoz
AI%3
6 10 19
18 28 44
52 66 86
TABLEVI ANHARMONICITY CONSTANTS OFN-METHYLANILINE AND THE SHIFT OF THE FUNDAMENTAL FROM ITS HARMONIC VALUE IN VARIOUS SOLVENTS Solvent Vapor CCl,F ccl, CS*
x12
72 75 76 75
X23
75 80 83 81
X123
65 66 61 61
Yl23
1.5 2.1 3.4 3.2
WC -
YO1
136 140 136 135
HIGHER
TERMS
AND
SOLVENT
TABLE
351
EFFECTS
VII
WAVE NUMBERS, IQ,*INCM-1 OF THE FUNDAMENTAL,FIRSTOVERTONE, AND SECOND OVERTONE OFTHECHSTRETCHINGVIBRATIONOFCHLOROFORMINDIFFERENT SOLVENTS AND THEIR SHIFTS, Av,, IN CM-~, FROM THEIR RESPECTIVE V.~LUES IN THE VAPOR Solvent Vapor FC-75 CCl,F CCI, csn
3033 3028 3025 3021 3011
8731 8695 8683 8662 8640
5943 5926 5914 5904 5888
TABLE ANHARMONICITY
CONSTANTS OFCHLOROFORM ITS HARMONIC VALUE
5 8 12 22
36 48 69 91
17 29 39 55
VIII AND THE SHIFT OFTHE IN VARIOUS SOLVENTS
FUNDAMENTAL
FROM
Solvent 61 65 68 69 67
Vapor FC-75 CCl,F CClr cs,
TABLE
0 0 -2.5 -2 -1.5
61 65 79 78 7-1
61 65 63 65 64
122 130 147 147 142
IX
WAVE NUMBERS, ypU IN c&c1 OF THE FUNDAMENTAL, FIRST OVERTONE, AND SECOND OVERTONE OF 2,6-DI-TERTIARY-BUTYL-4-METHYLPHENOL AT DIFFERENT TEMVALUES PERSTURES AND THEIR SHIFTS, Au DU IN CM-' FROM THEIR RESPECTIVE IN THE VAPOR. SOLVENT: AN 1:l MIXTURE OF CCl,F AND CFeBr-CF9Br
Vapor
3667
7164
10 481
21” -78” -190”
3654 3650 3641
7141 7133 7116
10 442 10 430 10 388
TABLE
13 17 26
-
-
23 31 48
39 51 93
X
ANHARMONICITY CONSTSNTS OF 2,6-DI-TERTIARY-BuTYL-4-METHYLPHENOL SHIFTOFTHEFUNDAMENTALFROM ITSHARMONICVALUEATDIFFERENTTEMPERATURES. SOLVENT: AN 1:l MIXTURE OF CCIaF AND OF CF?Br-CFpBr
Vapor 21” -78” -190”
85 83 84 83
88 90 90 95
78 68 71 57
1.5 3.4 2.9 5.9
AND
162 150 154 138
THE
352
DUROCHER
AND TABLE
SANDORFY XI
WAVE NUMBERS OF THE FUNDAMENTALSAND FIRST OVERTONESAT 21°C AND
Solute 2,6-di-tertiary-butyl-4-methylphenol
N-methylaniline
Chloroform
-78°C
Solvent
T, “C
ml
CCl,F
21” -78”
csz
vo2
Xl2
3654 3650
7141 7134
83 83
21” -78”
3645 3641
7118 7110
86 86
CC&F
221” -78”
3646 3644
6742 6738
75 75
CSZ
21” -78”
3433 3432
6716 6714
75 75
CClsF
21° -78”
3022
5914 5911
68 67
aniline at 3450 in the vapor, (3452). The CH band of chloroform vapor is reported to be at 3033 (22) (3033). Available data on the solution spectra of phenol and chloroform were summarized by Lecomte (28) and are generally in good agreement with our measurements. DISCUSSION
A) SOME CONCLUSIONS FROM BUCKINGHAM’S THEORY In Buckingham’s
theory on solvent effects a vibrational
term is expressed as
Gw=(v+;)ue-(v+3[++‘] +ue-(v+;>“[~-;kr]_.., (2) where v is the vibrational quantum number, wB the “harmonic frequency” in cm-l, and leQand k, are the cubic and quartic potential constants (in cm-‘) for the unperturbed molecule. The whole expression should be averaged to all solvent configurations. Buckingham uses notations where the rotational constant is introduced but since with the molecules examined in this paper we have no hope of using it we simplified the notations. Our Jcs and kd are, of course, the same as Buckingham’s A and B. We preferred these symbols in order to be in accordance with some of our own previous work (24,25). It is important to point out that (2) is obtained through the use of conventional second-order perturbation theory in which the off-diagonal terms of Icaare included (the diagonal term of ka is zero) but the off-diagonal terms of k4 and all higher terms are neglected (26-28).
HIGHER
TERMS
AND
EFFECTS
Xi:<
(v + ,!-i)‘X + U,,
(5)
SOLVENT
If we introduce and
(2) becomes G = (V + !h)w, -
(8 + ,1&@ -
where the bar indicates the presence of the intermolecular potential or its derivatives. From (Fi) we have for the observed fundamental and its first and second overtones : Y,)l = w, -
TV -
2x,
Vi)?= 2w, -
2TP -
vo3 = 3w, - 3?4 -
6X,
12X;
(sj
hence vo1
-
! iv02
=
?+02
-
,;+03
=
x,,
=
x,,
=
(7)
x.
As is seen from (3) the solvent shift depends on the anharmonicity (ka) of the isolated molecule. From the above equations the following predictions can be made: (1) The effect of solvent perturbation on the frequency and therefore, from (6) t,he solvent shifts are, as stated by Buckingham, AQ
=
which are in the ratio 1:2:3. (2,
A /ol -
IF,
Avoz
=
Here Au,, = ;,iAvoz
2w’, vou, gas
= ,$.~AI,, -
Avo3 -
= vm,
;2Auoa
3l1’, soln.
=
(3)
.
0.
(9)
(3) The anharmonicity const’ant (X) is solvent&dependent and, like for an isolated molecule, the same X should be obtained whether we use vol and vwL or v”? an d vo3 (or vol and vo3) in (7). Buckingham’s theory as referred to in t,he present work apphes to diatomic molecules. We are making the assumption throughout that in the X-H stretching vibrations which we examine the motion involves these two atoms only and that, Dhe anharmonic coupling constants between this and the other normal vibrations of the respective molecules are zero. Otherwise the treatment becomes rather more complicated (see Reference S). This approximat’ion is unlikely to impair our conclusions.’ We hope to have a closer look at it in a subsequent work, however. n’ow we turn our attention to the results we obtained to see if they bear out the above expectations. I This is corroborated by the work of M.-T. J. Chi,n. Phys. 57,1103 (1960).
Forel,
J.-P.
Leicknsm,
and M.-L.
Josien,
354
DUROCHER
AND SANDORFY
Phenol The 1: 2 : 3 relation is reasonably followed (Table I) for n-hexane, CC&F, and perhaps CC& if we disregard small variations which may be imputable to experimental error. For the more perturbing solvents, CHCL and CSz , however, a different pattern seems to apply: Av02 is slightly more than the double of Av01 but Avo, is significantly less than thrice Avol . Equation (9) yields the same observation. Table II shows that Xl2 equals X2, within 5 cm-’ like in the vapor for all solvents except CHCI, and CS; , an observation that seems to point in the same direction. 2,6-Di-Tertiary-Butyl-$Methylphenol,
(Tables III and IV)
The sterically shielded OH group is expected to enter less easily into associations than the OH group of phenol. Actually the shifts are invariably smaller for the former. The 1: 2 : 3 relation is roughly obeyed although there are irregularities somewhat exceeding the precision of the measurements. The same applies to the X12 = X23 relation. N-Methylaniline,
(Tables V and VI)
A significant departure of the 1:2:3 rule is observed even though are slight. Avo2is larger than 2Avo1and Avosis much larger than 3Av01. tion of Avos for the vapor is uncertain but CC&F may be taken as a confirming these observations. The departure from the Xxx = X23 rule is relatively slight, about as for the vapor.
the shifts The locastandard, the same
Chloroform, (Tables VII and VIII) This case is similar to the case of N-methylaniline. AVON is significantly larger than 2Avol and Avo3 is even more Iarger than 3Avo1. The Xl2 do not differ much from the XzI, however. To sum up, Buckingham’s theory used with the conventional secondorder perturbation formula is roughly satisfactory for the sterically hindered 2,6-di-tertiary-butyl-4-methylphenol and for phenol in the more weakly associating solvents. It breaks down in the cases of N-methylaniline and chloroform. B) INCLUSIONOF THE OFF-DIAGONALELEMENTSOF led As a next approximation we included the off-diagonal matrix elements of the quartic potential constants into the perturbation calculation as was done by Foldes and Sandorfy (29) in the case of hydrogen bonding. They are given by Barchewitz, for example (28).
HIGHER TERMS AND SOLVENT EFFECTS
Now the multiplier of (v + 35) contains ular potential or its derivatives,
a term independent
355
of the intermolec-
W = 67@/16w,
(11)
and IV = - f$ u” + 3kJJ’/o, The main
novelty
is that
+ Unz/a*B .
now the multiplier
(12)
of (v + $4)” contains
X = 3kJJN/2w,
(13)
representing the solvent dependence of the anharmonicity have a higher anharmonicity constant,
constant
X. We also
Y = 68k‘$16W,) which is seen to be solvent independent With these symbols we can write that G, = (v + %+e
-
and for the wave numbers
[W + lV’] -
V,,Z= 20, -
2[W + w]
=
3w, -
+ WI (v + X)“[X
+ X] -
(v + $i)“Y
(15)
that
VO1= we -
vo3
(14)
in this approximation.
(v + %)[W -
a term
2[X + X] -
3[W + #i’l -
It follows that
,
j.i2vo2=
VOl -
%vo2 -
x
(13/4)Y,
6[X + X] 12[X + X] -
+
_z +
(31/2)Y,
(16)
(17/4)Y.
4.5Y,
$+03 = X + X + 6.5Y,
(17)
and VOl -
102 +
y3vo3 =
--2y.
(18)
Furthermore, Avol = TV + 2X,
where Av,
= vOV ,gas -
A vo2= S@
+ 6-5
Avo3 = 3p
+
VOV ,soln.
128,
(19)
356
DUROCHER
AND SANDORFY
In this approximation the solvent shifts depend on both r and 8 but the effect of solvent on the anharmonicity constant depends only on X. This shows that there is no simple relation between the shift of frequency and the change in anharmonicity caused by the solvent since p and X have a different dependence on the potential constants. The inclusion of the off -diagonal terms of kd as it has been done in this section does not in itself represent a perturbation calculation of a higher order. In particular the lateral terms of ka (not on the row and column in whose intersection the given state is located) may be of the same order of magnitude as the offdiagonal terms of kd . These will introduce terms like ktU’/~z in the coefficient of (v + $4)“. The experimental results seem to indicate that the convergence in the series k3q3,k4q4, * . . is relatively slow but this is unlikely to make these terms negligible. As a consequence the expressions of the anharmonicity constants in terms of the potential constants [Eqs. (ll)-( 14)] would contain some further terms but Eqs. (15) to (20) would not change so that we can base conclusions on the latter. Regular higher order perturbation calculations will be presented later provided forthcoming experimental results warrant their use. Then we expect that (1) The solvent shift will not be linear with the vibrational quantum number and will not obey the 1: 2: 3 relation since according to (19) it now depends on XaswellasonlP. The following example is instructive. Let p be 50 cm-’ and X + 5 and -5 cm-“. Then, from (19) we obtain the following values. _y =
_tf = 5 cm-’
(2)
Avol -
>$Au,,z = j$Avo: -
40 70 90 100 100
60 130 210 300 400
AVOl Al%2 AYo3 AVIM AVOS gAvo3
= --f&
-5cm-’
= -&
(20)
and not zero. (3) The anharmonicity constant X should now depend on the solvent. Xl2 should be different from X23 even for the vapor if Y is not negligible. Let us now have another look at Tables I and VIII. Phenol (Tables I and II). The Avoy seem to indicate that X has a small but non-negligible negative value for CHCI, and CS, , at least. The anharmonicity constants X 123computed from (17) and (18) vary with the solvent about as expected. The shift of the wave number of the fundamental
HIGHER
TERMS AND SOLVENT
EFFECTS
357
from its “harmonic” value, wc - yol varies in a way similar to X1s3 . This could not be predicted since the change in yol depends on both p and X whereas the change in Xl23 only depends on X. Y123has small but, in most cases, negative values and they seem to vary from solvent to solvent. This is incompatible with the approximation applied in this section since according to (14) Y depends only on the square of the quartic constant. A negative value for Y indicates that higher terms like k5 , kg , . . . or u”’ and [,“” are important or, rather, that some of the lateral terms in the secular equation of the perturbation calculation are not negligible. Now, the Y are obtained as small differences between numbers about a thousand times as big and caution should be exercised. It seems, however, that even t,his better approximation is inadequate in this case. 2,6-Di- Tertiary-Butyl-4-Methylphenol
(Tables III
and IV)
This does not require new comments according to what was said above. N-Methylaniline
(Tables V and VI)
The Av,, indicate a positive X as they are divergent. The Y have small posit.ive values which vary little from one solvent to the other. Chlorojom
(Tables VII and VIII)
This too is a case of positive X. Again we find negative Y but they are small. We conclude that the approximation applied in Sec. B interprets correctly the nonlinearity of the solvent shift with the vibrational quantum number. It shows that Avou and the change in anharmonicity do not necessarily parallel one another. It bears out the fact that the anharmonicity constants are solvent dependent. On the other hand, Eq. (20) is not, in general, satisfied. This with the appearance of the negative Y and the slight variation of Y from solvent to solvent shows that even better approximations are needed. For this reason we shall not attempt to compute anharmonicity or potential constants from our data. In cases of stronger perturbations the change in anharmonicity might well be a major cause of the solvent shift. This was pointed out in 1938 by Bauer and ;\lagat (30) and this might have been a more important point of their famous paper than the much discussed Kirkwood-Bauer-Magat formula. A true attempt of using a higher approximation would require a higher precision in the measurement of the frequencies but this is not easily attainable for solution spectra. Work is going on in this laboratory in order to repeat as much as possible of the present work at low temperature. Finally, it is important to note that in a recent paper Vu, Schuller, Atwood, Oksengorn, and Vodar (31) who worked on CO, HCl, and HBr in neutral gas solvents reac*hed concIusions in many respects similar to those of the present paper.
358
DUROCHER
AND SANDORFY
C. THE EFFECT OF TEMPERATURE
The solubility of 2,6-di-tertiary-butyl-4-methylphenol was sufficient to measure its spectrum in a 1: 1 mixture of CCIBF and CF2Br-CF2Br down to liquid air temperature (Tables IX and X). At 21°C the wave numbers are very close to those for CC&F given in Table III. Only slight bathochromic shifts are observed at -78” but at -190” the change is significant. The fundamental shifts by 13 cm-l from 21°C to -190°C. This seems to show that at liquid air temperature associations are appreciably stronger. Also the 1: 2 : 3 ratio is maintained at 21° and -78” but the AvoWdiverge at -190”. Thus the lowering of temperature is seen to increase the strength of the solvent effect. The changes become significant at temperatures close to liquid air temperature only (when the solvent becomes a glass), as shown by Table XI. CONCLUSIONS
The data contained in this paper lead to the generalization that Buckingham’s theory on solvent shifts when used with the conventional second order perturbation formula is adequate in cases of very weak interactions only. For cases of stronger perturbations higher terms have to be included. The inclusion of the off-diagonal matrix elements of the quartic potential constant improves the situation inasmuch as the explanation of the observed trends is concerned but it does not lead to a quantitative agreement with experiment. The inclusion of higher terms seems to be indicated. ACKNOWLEDGMENT
We are indebted to Professor A. D. Buckingham for a stimulating exchange of letters. We express our thanks to the National Research Council of Canada for financial help and for granting a scholarship to G.D. Our very sincere thanks are due to Mr. G. Belanger and P&e J. Lajoie from this laboratory who measured the spectra of the vapors. RECEIVED: August 3, 1966 REFERENCES 1. A. D. BUCKINGHAM, Proc. Roy. Sot. A248, 169 (1958). 8. A. D. BUCKINGHAM, Proc. Roy. Sot. M66, 32 (1960). 9. A, D. BUCKINGHAM, Trans. Faraday Sot. 66, 753 (1960). 4. “Fluorochemicals.” Technical Data Sheet, Minnesota Mining and Manufacturing Company, St. Paul, Minnesota, 1957. 6. C. F. MEYER AND A. A. LEVIN, Phys. Rev. 34, 44 (1929). 6. A. H. NIELSEN AND H. H. NIELSEN, Phys. Rev. 46, 864 (1935). 7. G. A. STINCHCOMB AND E. F. BARKER, Phys. Rev. 33, 305 (1929). 8. E. K. PLYLER AND W. W. SLEATER, Phys. Rev. 37, 1493 (1931). 9. “Tables of Wavenumbers for the Calibration of Infrared Spectrometers.” International Union of Pure and Applied Chemistry. Butterworths, London, 1961. 10. E. K. PLYLER, J. Res. Natl. Bur. Std. (U.S.) 40, 221 (1952).
HIGHER
TERMS
AND
SOLVENT
EFFECTS
359
11. R. C. NELSON, E. K. PLYLER, AND W. S. BENEDICT, J. Res. Natl. Bur. Std. (U.S.) 41, 615 (1948). 12. H. J. UNGER, Phys. Rev. 43, 123 (1933). 13. H. H. NIELSEN, Phys. Rev. 62, 422 (1942). 14. E. K. PLYLER, N. M. GAILLAR, AND T. A. WIGGINS, J. Res. Natt. Bur. Std. (U.S.) 48, 221 (1952). 15. E. K. PLYLER AND C. W. PETERS, J. Res. Natl. Bur. Std. (U.S.) 46, 462 (1950). 16. E. D. MCALISTER, Phys. Rev. 34, 1142 (1929). 17. G. DUROCHER AND C. SANDORFY, J. Mol. Spectry., 20,410 (1966). 18. K. U. INGOLD, Can. J. Chem. 40, 111 (1962). 19. K. U. INGOLD AND D. R. TAYLOR, Can. J. Chem. 39, 471 (1961). 20. A. R. H. COLE, L. H. LITTLE, AND A. J. MICHELL, Spectrochim. Acta 21, 1169 (1965). 2f. R. E. DODD AND G. W. STEPHENSON, in “Hydrogen Bonding.” (D. Hadgi, ed.), p. 177. Pergamon Press, New York, 1959. 2.2. N. GINSBURG, quoted by H. H. Voge and J. E. Rosenthal, J. Chem. Phys. 4,137 (1936). 23. J. LECOMTE, Spectroscopic dans l’infrarouge. In S. Flugge’s “Handbuch der Physik,” Vol. 26, pp. 361 and 486. Springer Verlag, Berlin, 1958. 24. C. BERTHOMIEU AND C. SANDORFY, J. Mol. Spectry. 16, 15 (1965). 26. G. DUROCHER AND C. SANDORFY, J. Mol. Spectry. 16, 22 (1965). 86. G. HERZBERG, “Molecular Spectra and Molecular Structure,” Vol. I, p. 90. Van Nostrand, Princeton, New Jersey, 1950. 27. E. B. WILSON, JR., J. C. DECIUS, AND P. C. CROSS, “Molecular Vibrations,” p. 193. McGraw-Hill, New York, 1955. 28. P. BARCHEWITZ, “Spectroscopic Infrarouge, I. Vibrat,ions Moleculaires,” p. 189. Gauthier-Villars, Paris, 1961. 29. A. FOLDES AND C. SANDORFY, J. Mol. Spectry., 20, 262 (1966). 30. E. BAUER AND M. MAG.~T, J. Phys. Radium 9, 319 (1938). 31. H. Vu, F. SXULLER, M. R. ATWOOD, B. OKSENGORN, AND B. VODSR, J. Chim. Phys. 61, 263 (1964).