SATURATED A L D E H Y D E SERIES UDC 539.19
T. T. Merzlyak and L. A. Gribov
In this article we examine results obtained in a direct quantum calculation (based on the semiempirical MINDO/3 method) of the electrooptical parameters (EOPs) and the optimized molecular geometry of a series of saturated aldehydes: formaMehyde, acetaldehyde, propionaldehyde, butyraMehyde, and valeraldehyde. The quantum calculation was performed in a system of dependent natural coordinates. The EOPs of the molecules were found within the framework of a valence--optical scheme and have been used in solving problems of determining intensities of IR absorption bands. Theoretical and experimental curves have been compared.
The problem of calculating absorption band intensities in the IR spectra of polyatomic molecules is becoming more and more urgent. In fact, a calculation of the complete spectral curve is the only way in which the depiction of a model of a complex molecule can be compared correctly with the experimental spectrum. A technique used for this purpose consists of direct quantum calculations of derivatives of the total dipole moment of a molecule (/z) with respect to normal coordinates (Qi) (see for example [1, 2]), and also semiempirical approaches, of which the most widely used is a procedure based on a valence--optical scheme [3-7]. It should be noted, however, that although there has been an insurmountable barrier between these two approaches up until quite recently, both approaches have become equally suitable now that the studies [8, 9] have been published, giving an exact quantum theory of so-called electrooptical parameters. It is another matter that the determination of EOPs for atomic groupings, in view of the transferability of EOPs, makes it possible to calculate -- even using a valence--optical scheme -absorption band intensities in the spectra of very complex molecules, polymers, and crystals. Such calculations, of course, are prohibitive if they are to be based on direct quantum calculations of the derivatives Oi.z/OQi. Today, however, experience in quantum calculations of EOPs is still very limited, and this creates an urgent need for expansion of the statistics. The studies reported in this article had the following goals: To determine~the degree to which sets of EOPs for molecules of a saturated aldehyde series, obtained from an approximate quantum calculation, are applicable to the solution of direct electrooptical problems with subsequent construction of spectral curves; to determine the relationships in the behavior of EOPs; and to develop practical recommendations on forming the structure of sets of EOPs for subsequent calculations of the spectra of saturated aldehydes. The calculations were performed in an IBM PC/AT computer. The determination of the EOPs and the solution of the spectral and electrooptical problems were performed in a system of dependent natural coordinates. The algorithm of the method used in the EOP calculations has been set forth in detail in previous publications by Gribov et al. [8-11]. We used the semiempirical MINDO/3 method in calculating the energies of points on the potential energy surface of the system and in calculating dipole moments of bonds for each deformation. The solution of the spectral and electrooptical problems was performed in accordance with programs given in [12], also realized in an IBM PC/AT computer. The calculations were performed on representatives of a number of saturated aldehydes: H--CO(H), formaldehyde (I); CH3--C O(H), acetaldehyde (2); CH3--CH 2 - CO(H), propionaldehyde (3); CH 3-(CHz)2-CO(H), butyraldehyde (4); and CH3--(CH2)3--CO(H), valeraldehyde (5). The following experimental data were used: For the formaldehyde and acetaldehyde molecules, data on geometric parameters from [13], data on frequencies and absolute integral intensities of absorption bands from [13, 14]; for the propionaldehyde, butyraldehyde, and valeraldehyde molecules, IR absorption spectra from the Sadtler collection [15], numbered 24,003 K, 29,691 K, and 24,167 K, respectively.
K. A. Tirniryazev Agricultural Academy. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 157-168, January-February, 1993. Original article submitted May 19, 1992.
0022-4766/93/3401-0137512.50
9
Plenum Publishing Corporation
137
TABLE 1. Numbering of Natural Vibrational Coordinates* Mo~ecule
Coordinate numbe:
i ql ql ql ql ql II
4
5
q3
~1 2
Q~ Q~
~2,3
q+
2
1 ] g~ g~ Q~
q~ (2~
q~
q~
q+
qa
q4
15
?4,5
74,~
~5,6
~1,4
~3,4 ~5,6 ~2,3
I+3,~ 15+,7 1+2,+
21
22
23
2&
Q~67
Y7,8 Q22
?7,9 q23
Y8,9 q24
31
32
33
34
(/'1,3
~I+7
13
/~ ?23,34 135,23
1~52~ [310,29 ~1'0,30 42
<~1..38
43
Pc=o
[
Pc=o
CZl,3 q~ qe
9 84
PC=O (Z2,3 0~i,3 . q~ q9
[~3,4
q7
qs
Qio
q7
~6
~7
PC=O
PC=C
[~1,4
18
q9 19
?4,5
15,+,6 I~+.+
22,5
?2,4 ~2,6
?m,+ %,+ 13~,r ~6,7 ~7,8
25
26
~ ~'20,21 35
~0
PC=O
q~
I
8
7
6
q~ q~ Q+ q~
14
[ [~3,5 ~2,3
[ 12
3
27
28
~6,7
29
[ 20
~6,8 qzo
~7,9 30
Pc=o c$21,22 ~:20,22 [~22,28 ~22,24 BC. 5.,22 36
37
38
~9
~}29,30 q35
Q39
40
Pc=o
[~10,31 730,31
729,3I
~38,39
4~
Pc=o
Notes. or) bond angles of the aldehyde group; t) CCH bond angles; ~c) CCC bond angles; 3') HCH bond angles; q is for C--H bonds; Q is for C---O and C--C bonds. The subscripts denote the sequence numbers of the bonds forming the particular angle.
The spatial structures and the systems of independent natural coordinates in which the quantum-chemical and vibrational problems were solved for these particular molecules are presented in Fig. 1 and Table 1. It was shown in [16] that for the formaldehyde and acetaldehyde molecules, the optimized geometry of these structures comes out very close to the experimental geometry, within the limits of accuracy of the calculation. For the formaldehyde and acetaldehyde molecules, therefore, we used their experimental geometries in the calculations. For the propionaldehyde molecule, we used an optimized molecular geometry that we had obtained previously [16]. The structure of the butyraldehyde molecule (trans form) was obtained by "matching" the propionaldehyde molecules and pentane molecules (from a library of molecular fragments [5]) through the No. 5 bond of the pentane molecule. Correspondingly, the initial geometry of the molecule was formed automatically from geometries of the fragments being matched. The length of the C--C bond for which the "matching" was pertbrmed was taken as equal to the length of the C--C bond in molecules of the paraffin series, in order to ensure equivalence of the natural coordinates of C--C bond stretching in the paraffinic radical of the molecule. The structure of the valeraldehyde molecule (trans form) was obtained by "matching" the propionaldehyde molecule and the pentane molecule, but now through the No. 1 bond of the pentane molecule. For the lengths of the bonds 1, 6, and 7 in the valeraldehyde molecule, at the moment of "matching," values were taken as equal to the corresponding bond lengths in the propionaldehyde molecule. The molecular geometries of the butyraldehyde and valeraldehyde molecules that were formed in this manner were then used as input data for the quantum calculation, and were also used in solving the problem of molecular vibrations. During the course of the quantum calculation, we performed the first complete optimization of geometries of the butyraldehyde and valeraldehyde molecules. The results obtained, along with the initial values of the geometric parameters, are presented in Table 2. No experimental data are available in the literature on the geometries of these molecules. With the 138
Valeraldehyde
1,t07
1,137 1,116
t,l'lO t,127 Ii5,8
1,543 1,122
1,099 t ,099
1,093 1,093
1t5,0 1t8,8
C--C4
C--HE,
C--HEm
C --HE,3
C--H M np
C--H m p
CCHA
ttCO
119,3
116,3
1,105
t,iO9
t,tt8
i,510
CCIIEa
CCHE2
CCHE1
CCH M p
CCHMn p
HCHEa HCHM
9
9
))
t09,9 t10,7
tt1,1 11t,2
111,9 111,6
11t,9 tl2,0 109,6 109,3
116,2
1t6,1
t01,2
105,2
t01,0
98,7
[09,2
[09,6
[09,3
[06,3
95,2
110,8 110,2
112,5
)> 9
t10,7
112,7
[09,5
t 24,4
zooptimized ~rdinate value Re.
125,0
no.
coI optimized ordinate value
Valeraldehyde
[26,2
initial value
Butyraldehyde
*Bond lengths are given in A, angles in deg. Here and subsequently in the text: A) aldehyde group; E) ethyl; M) methyl; 1, 2, ~, and 4 number the ethyl groups, C--C bonds, and CCC angles in order of increasing distance from the aldehyde group.
119,2
1,109
t,520
t ,543
C--C m HCHE2
CCCa IICHE1
t ,528
1,522
t,543
C--Cs
t ,535
CCC2
t ,498
1,492
1,505
C--C t
CCCI
t,157
1,151
1,157
C--H A
CCO
type of coordinate
Molecules
1,201
t,212
l optimized zoordi- optimized coordinat~ value " Raterdivalue no. no. 1
1,202
initial value
Butyraldehyde
C=O
type of coordinate
Molecules
tABLE 2. Results from Optimization of Molecular Geometry of Butyraldehyde and Valeraldehyde*
H
H
H
H
I IOH, (2J
(1)
H
: (4)
H
(3)
H (5)
Fig. 1. Spatial structure and bond numbering for molecules 1-5.
MINDO/3 method, the bond lengths and angles can be calculated with an average accuracy of 0.02 A and 3 ~ which is fully adequate for the subsequent calculations of vibrational spectra of the molecules. As can be seen from the data of Table 2, within the limits of accuracy of the calculation, the optimized bond lengths in both of the molecules are close to the initial values. The angles in the aldehyde group also maintain values close to those of the corresponding angles in the propionaldehyde molecule, which were taken as initial values. The CCC angles in the butyraldehyde and valeraldehyde molecules proved to be 113 ~ and t 11 o, respectively, slightly greater than the tetrahedral angle that was assumed in the initial geometry. The HCH angles in the ethyl groups of both molecules were found to deviate considerably from tetrahedral. The closer the position of the ethyl group to the aldehyde group, the greater is the deviation from tetrahedral HCH angles. The greatest deviation of this angle from the initial tetrahedral configuration is observed for ethyl groups that are closest to the aldehyde grouping. Thus, in the butyraldehyde molecule, the deviation of this angle from tetrahedral is 14.3% and in the valeraldehyde molecule 10.8 ~ Also deviating from tetrahedral are the CCH angles adjoining the ethyl groups. It should be noted that a decrease of HCH angles in ethyl groups located alongside the carbonyl group (in comparison with the tetrahedral value) has also been observed in optimizing the geometries of the propionaldehyde, methyl ethyl ketone, and diethyl ketone molecules (respective angles HCH E = 101.4, 104.2, 107.6~ For the acetaldehyde and acetone molecules, the optimized HCH angles of the methyl groups also deviate from tetrahedral on the low side; this is consistent with the known experimental data [16]. In the molecules containing more than one ethyl group in the radical attached to the aldehyde group (among the molecules examined in the present work), we can see a very distinct decrease in the influence of the polar group in terms of changing the geometry of the more distant ethyl groups. Clearly, the effect will be the greatest on changes in position of the lightest H atoms from the immediate environment of the polar group. The problem of finding vibrational frequencies of the formaldehyde, acetaldehyde, and propionaldehyde molecules was solved with force fields obtained from a quantum calculation, these values being corrected by solving inverse spectral problems [16]. For the butyraldehyde and valeraldehyde molecules, in solving the analogous problem, we used combined sets of force constants obtained in the process of "matching" without any additional correction: for the aldehyde parts of the molecule as in the propionaldehyde molecule, and for the paraffinic radical as in the pentane molecule. The force constants of the C--C bonds at which the "matching" of fragments was performed in the butyraldehyde and valeraldehyde molecules were taken as equal to the force constants of C--C bonds in the propionaldehyde and pentane molecules, respectively. In Tables 3 and 4 we have listed sets of EOPs of the aldehyde molecules that had been found as a result of the direct quantum calculation. Analysis of the calculated dipole moments of the bonds shows that there is a considerable scatter in the error of calculation of these quantifies. We were able to determine the dipole moments of the bonds of the most polar aldehyde group with the smallest calculational errors. Thus, the relative error in calculations of the dipole moment of the C----~-Obond was no greater than 1%, and that for the C--H bonds of the aldehyde group no greater than 7%. The greatest errors in the calculation pertain to the dipole moments of the weakly polar C--C bonds, the absolute values of which are close to zero. The errors in calculating dipole moments of the C--C bonds of the ethyl and methyl groups are intermediate between these two extremes. Their scatter ranges from =20% to 80%; i.e., a well-known mathematical rule is observed: The smaller the 140
T A B L E 3.
Dipole Moments of Bonds gi (D) and Relative Errors in Their
Calculation e (%) Molecule
Bond t y p e
3
2
t
s 60 4t
C=0
3 t
C _ . (nonplanar
-l~in-p
lanel
--0,59 --2,80
5 1 0,16 16 --0,03 76
C--HEI
C--HE2 C--HE3 C--C I
0,10
21
C--C 2 C--C 3 C--C~
TABLE 4. Elec~oopfical Parameters Calculation e (%) Type of parameter
i
2
dgildq ]
t
CHA/CH A
c~A/co CHA/CCz(CH)A
CHA/HCO CHA/CCHA(HCH) CO/CH A COtCO CO/GO: co/gco C0/CC0
CCl/CHA CCIlCO CGz/CC1 CCz/CCO CCI,ICCHA
CH~/CC~ CH~/CH~ CH~/CCH~* CHM/HCH~t* CHEI'/CttE t ....
2
d.ai/dq i
7
--0,78 --2,68 --0,06 -i' --0,16 1, 0,06 6:
t,95
Molecule 3 r
81 51 t1 9~ 8! 4i 11
3,76 0,4i 9,28
I
0,52 0,32 0,83
CHE]C.cTrE
0,43 0,37
CCJCCCI CCJCC2HE t
CC2/CC2HE2
CHE2/CHE2 CHF~/CC~H E2 CHE 2/HCYIE2
7
2 2,28 2 0,87 5 0,551 .i 0,95 ' 7 0,47 6 -3,65 l t 0,86l 3 I 0,36l t [ 0,47 8 I -0,88 7 ] -2,i6 3 I 0,77 7 I -0,4i :oS -0,6i Lst -i,06
2
5 r
.2,34
1,04 3,44 3,58
0,2~"
4
d~i/dqj
CHEI/HCH E : CHE JCC2H E i c c J c o (CH/CO) CCjCC~ CCJCHE2
--0,72 --2,75 --0,07
--0,73 7 --2,71 t --0,14 24 --0,09 --0,14 28 0,07 0,10 5O --0,14 --0,13 34 --0,t2 3O --0,10 5, --0,05 --0,04 t41 0,i5 2 --0,26 0,21 29 0,08 0,10 5t --0,t2 54 (D/A) and Relative Errors in Their
6
:,97 .~,05 ),7i ),43 ),76 ),44 ],52 ),86 ),35 ),42 ?,70
5
a#ilOqj
3
2 2 6 .0 9 3 1
4
tti
8
9
--2,t5 2,22 0,74 0,30 0,80 0,42 --3,68 0,89 0,37 0,44 -0,87 --2,t8 0,77
3 3 8 ~,8 [0 5 t 3 9 7 7 3 9
-0,35 25
0,24 3 I --t,04 8 0,4t L2 I 0,42 4 --0,84 .1 .l
0,40; .0
0,28 0,12 0,49 --0,t6 --0,t7 0,t8 --0,60 --0,52 0,4fl --t,15 0,42 0,44
9 2 7 7 6
io
ti
--2,11 2 2 2,31 6 0,81 0,48 14 0,8t 8 5 0,39 --3,68 o l 0,90 2 0,30 9 7 0,36 6 -0,86 3 -2,t6 7 0,86 -0,51 i7 -0,51 17 9 0,37 3 --t,i8 0,39 i0 0,28 i5 0,77 . 6
23 0,38 56! 0,I c 13 0,47 38 0,1~ 47 0,t( 30 --0,0~ 13 --0,3~ t5 0,5,: t4 0,0~ 4 --1,1~ t5 0,4'-; 13 0,4(
16 32 i2 38 46 30 19 14 16 3 i1 il
*Angle formed by same C - - H bond. 141
of vibrations may affect the changes in dipole moments of not only the adjacent bonds, but also those that are positioned at a distance of one bond away. The calculation showed that in the molecules 3-5, the order of magnitude of this parameter proves to be the same as that of the derivatives of the bond dipole moment with respect to the angular coordinate; however, the relative error in determining this parameter is somewhere near 40% in a number of cases. It should also be noted that for the acetaldehyde molecule, only for one conformation of the molecule -- specifically, the conformation in which the CH bond lying in the plane of symmetry of the molecule has the cis position relative to the C~-----Obond of the aldehyde group -- were absolute magnitude of the sought parameter, the lower will be the accuracy of its calculation. As a consequence of the small magnitudes and large errors in calculating dipole moments of the C--C bonds and the C--H bonds in ethyl and methyl groups, we will not attempt to judge the signs of the dipole moments obtained in the course of these quantum calculations. It must be noted, however, that for molecules having more than one ethyl group (butyraldehyde, valeraldehyde), we observe an alternation of signs of the dipole moments of the ethyl-group C--H bonds as the distance from the aldehyde group is increased. It should also be noted that the method used in the calculation gives different values for the dipole moments of the C--H bonds of the methyl group for bonds located in the plane of the molecule and outside the plane. As regards the derivatives of the dipole moments of the bonds with respect to the natural coordinates, we find that for all of the molecules participating in the calculation, we were able to obtain stable sets of monotypical EOPs with a good degree of calculational accuracy. On the level of the quantum calculation, we can clearly follow transferability of EOPs in this series of related molecules. At the same time, the method of calculation is sensitive to individual features of the molecules. Thisis clearly evident in the example of the EOPs of the aldehyde group: In the series of molecules I-5, beginning with the propionaldehyde molecule, the character of the aldehyde group environment no longer changes; and this is manifested in closer calculated values of the dipole moments of the ~ O and C--I-I bonds of this group in molecules 3-5 in comparison with molecules 1 and 2 (see Table 3). The same can be said of the parameters 0~(C~---H)/0q(C-H), 0/~(C-H)/0q(C---~O), O/z(C=O)/0q(C~------O). The same effect is observed in the behavior of the parameter OIx(C--H)/Oq(C--H) of the terminal methyl group (see Table 4). The sets of EOPs of molecules that have been reported in the literature [5, 6, 13, 14], obtained by empirical means, in the case of bonds forming tetrahedral structures (methyl or ethyl groups) usually include derivatives of the dipole moment of the bond with respect to the angular coordinate formed by the same bond, and also with respect to the angular coordinate formed by neighboring bonds. This experience was utilized in making up the sets of EOPs subject to determination from the quantum calculation. However, as the calculation showed, we were not able to determine both parameters simultaneously with an adequate degree of accuracy. Simultaneous determination of parameters results in much greater errors in determining each of them. For the acetaldehyde molecule, for example, when the parameters 0/z(CH)/0#(CCI-I) and 0/~(CH)/0/~(CCHadj) are determined simultaneously, the respective relative errors were 246% and 54%. By excluding the second parameter from the set of EOPs in the calculation, we were able to determine the first parameter with a relative error no greater than 11%. A similar result was observed for the parameters 0/~(CH)/0~(HCH) and 0/L(CH)/0/3(HCHadj). This fact provides clear evidence of a linear dependence of parameters of this type, and it can serve as grounds for reducing the number of EOPs describing a molecular model; in turn, this is important for the solution of the inverse electrooptical problem. It was of interest to estimate the orders of magnitude of derivatives of a bond dipole moment with respect to a bond located one bond away from the given bond. Sets of empirically determined EOPs usually do not include parameters of this type. In Table 4 we have included results of a calculation of the parameter 3/~(CCEt)/0Q(C~------O). The introduction of this particular parameter into the set of EOPs in the calculation has a specific physical justification. Since the C ~ O bond in aldehyde molecules is a region of excess concentration of electron density, we can expect that its deformation in the course we able to determine the parameter 0/~(CH)/O/z(CmO) with acceptable accuracy: Ol~(CH)/Olz(C~----O)(cis) = 0.22; e = 12%. In the case of the trans position of these bonds, the error in determining the parameter was greater than 300%, and the calculated value of the parameter was 0.01 D/A. Thus, in the case of conformers, the parameter may prove to be either necessary or superfluous, depending on the conformation under consideration. The sets of EOPs obtained from the quantum calculation were used without correction in solving the direct electrooptical problem. In Figs. 2-6, along with the experimental spectra, we show theoretical spectra constructed on the basis of a solution of the direct electrooptical problem with EOPs obtained from the quantum calculation. In the following discussion, these spectral curves will be called "quantum curves" in the interest of brevity. For the molecules 3 and 4, the experimental curves were taken from the Sadfler collection. For molecules 1 and 2, the role of experimental spectral curves is played by theoretical curves obtained by solving the electrooptical problem with empirical EOPs that were found by solving inverse electrooptical problems using experimental data on absolute integral intensities that were taken from the literature 142
TABLE 5. EOP Parameters (Olzi/Oqj) and Vibration Intensities (0 and Frequencies (p) of Formaldehyde Molecule Form of vibration Q(c=o)
a(HCH) q(CH +) q(CH-) g(HCO) PC=O
I, 108 cm 2 Isec.mole
%)~ C m - I
exp.
talc.
1746 1500 2766 2843 t247 t169,5
1746 t508 2768 } 2828 t256 } tt65
exp.
Empirical EOPs type
calc.
29,1 4,6
29,t3 4,3
63,8
gCH
Pc=o CH/CH
40,3
CH/CO CH/HCO CH/HCH CO/CO
t,5 }4,9 3,4
4,9
value
--0,55 t,97 t,55 0,20 0,25 --0,03 --t,75
TABLE 6. EOP Parameters (Op.ilOqj) and Vibration Intensities (0 and Frequencies
(~) of Acetaldehyde Molecule Form of vibration
M ~
I, lO s cm2/sec.mole
c m -I
exp.
exp.
talc.
PC=O Q(c-c) p(CCH) ~(CCH)
7(HCII*) a(HCO)
?(HCtt) 7(HCH) O(C=O) q(C--H)A
8,3
9,7 6,4
IZc_c IXC--HM CHA/CttA CH./C=O C=O/C=O
3,2i26,1 2,9]
27,0
74,8 58,2 6,5
73,0 56,1
2994 2995
[~C--IIA
3,615,8 2,2) 9,5 4,0 tt,1} 8,91
5,7
289~ }
q(C--H) M
q(C--tt)~ q(C--It)M
type
calc.
8,t
5t9 873 } 934 10Sl tt24 t35t 1409 1445 1447 1763 2740
~(cco)
Empirical EOPs
CO/HCO COICCO CC/CCO CO/Cell A
CHM/CHM
11,2
CHM/CH~ CHM/HCH
value --0,55 t,98 0,35
-o,4o t ,57 0 --4,40 --O, iO --0,24
0,4 --0,43 0,54 0,21 0
{
! u t
J
I
~
I
!r
2
I
2~OO
2400
~ooo
~8oo
12oo
Fig. 2. Experimental (1) and theoretical (2) IR spectra of
formaldehyde molecule.
143
/
i.
,
9
! " I
t
I
I
"t
" E
" t
rI'" i
h
;000
"I
r
2~7r
.6"0~
Fig. 3. Experimental (1) and theoretical (2) IR spectra of acetaldehyde molecule.
I
,5~0~
|
I
f~,;":.~,;"' "
2200
1
i
780C
]
1
7400
]
I
7000
i
I
I
~00 .
Fig. 4. Experimental (1) and theoretical (2) IR spectra of propionaldehyde molecule.
(Tables 5 and 6; the dimensions of/t/and O/ti/Oqi are the same as indicated in Tables 3 and 4). A comparison of the quantum spectra with the experimental spectra shows that, even though there is no exact agreement between the absolute integral intensities of the experimental and calculated absorption bands, the quantum spectra are fully comparable to the experimental spectra in all of the cases examined. The EOPs obtained from the quantum calculation do transmit correctly the ratio of intensities of the absorption bands that are characteristic with respect to frequency and intensity, in comparison with other absorption bands of these molecules. This is true for the region of stretching vibrations of the C~---O bond {= 1700 cm-l), and also in the region of stretching vibrations of the C--H bond of the aldehyde group ( = 2700 c m - 1). In the molecules 3-5, we also find completely satisfactory transmission of the structurally more complex region of bending vibrations, as well as the region of stretching vibrations of the methyl and ethyl groups. We could hardly expect in advance that there would be any satisfactory agreement between the quantum and experimental spectra, since substantial simplifications have been made in the algorithm used for the quantum calculation of the EOPs: In calculating the bond dipole moments, only the charges on the atoms are taken into account, while the bond and vector contributions are ignored; in the model representation of a bond dipole moment in the form of a power polynomial in natural coordinates, only second derivatives of the dipole moment of the bond with respect to bond stretching coordinates are assumed to be nonzero [17]. The positive result that we obtained is apparently related to the lower sensitivity of the electrooptical problem to errors in determining EOPs, in comparison with the problem of finding vibration frequencies. Thus, a change in the EOPs, even a two-fold change, will change only the band shape in the 144
0
I
I
I
1
1
i
I
I
1
I
I
1
I
I
t
l'ilAl
[
5000
2800
r
2200
7400
~ooo
200
~oo
Fig. 5. Experimental (1) and theoretical (2) IR spectra of butyraldehyde molecule.
r ip
1
I
i
I"
'l
'
|
i
ii
II
|l,
1
v
-~
2
V AJ ,/V ,
3000
i
|
2800
1
s
2200"
s
L
r
t
|
~400
|
I I 7000
Il '
I
t
6'00
i
I
2OO
Fig. 6. Experimental (1) and theoretical (2) IR spectra of valeraldehyde molecule.
spectrum; i.e., the absorption band may become broader or narrower, but there will be no shift of the band. Therefore, with good agreement between experimental and calculated frequencies, a spectral curve obtained with EOPs taken directly from a quantum calculation is qualitatively similar to the corresponding experimental spectrum.
REFERENCES 1.
2. 3. .
M. V. Korolevich, Author's Abstract of Candidate's Dissertation, Minsk (1987). M. V. Korolevich, V. A. Lastochldna, and R. G. Zhbankov, Zh. PriN. Spektrosk., 52, No. 1, 68-76 (1990). M. V. Vol'kenshtein, M. A. El'yashevich, and B. I. Stepanov, Vibrations of Molecules [in Russian], Vols. 1 and 2, Gostekhizdat, Moscow (1949). L. A. Gribov, Theory of Intensities in Infrared Spectra of Monatomic Molecules [in Russian], Izd. Akad. Nauk SSSR, Moscow (1963).
145
. . . .
9. 10. 11. 12. 13. 14. 15. 16. 17.
146
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