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Molecular force field of 1,1′-dicyanoethene from vibrational and microwave data
JOURNAL
OF
MOLECULAR
Molecular
SPECTROSCOPY
76, 104- 117 (1979)
Force Field of 1 ,I ‘-Di~yanoethene Vibrational and Microwave Data”
B. T. TAN, J. DEMAISON,~ Department
of Chemistry,
University
AND
From
H. D. RUDOLPH
of Urn, D-7900 Ulm, Federal
Republic
of Germany
Vibrations Raman frequencies were used in conjunction with the centrifugti distortion, constants determined from. the microwave rotational spectrum to calculate a (simplified) harmonic force field by a least-squares fit for the molecules CH,C(CN), and CD2C(CN),. As a check, the inertial defects of the ground state and the lowest vibrational states for both isotopes were calculated from this force field and found to be in good agreement with the experimental values obtained from the microwave spectra. The calculated values for c:b,,, and AE,0,18 of the two Coriolis-interacting vibrational states uIO= 1 and u,~ = 1 in CD,C(CN)e likewise agreed satisfactorily with those derived from the microwave spectra. INTRODUCTION
Molecular force fields have, in the past, been determined almost exclusively from the fundamental frequencies. In general, there are more force constants than observed fundamentals. The rotation-vibration interaction parameters observed in the microwave spectrum provide additional data for the determination of a force field. In Ref. (I) the microwave spectra of l,l’-di~yanoethane CH,C(CN), and its deuterated species CD,C(CN), were reported in their ground and lowest excited vibrational states. These vibrational states originated from combinations of the two C-CSN bending motions. The molecule dicyanoethene is of symmetry Czu. All vibrational modes are Raman active; the vibrations of the species Al, B1, and B2 are also infrared active. The infrared spectrum of the normal isotope of dicyanoethene has been studied by Rosenberg and Devlin (2) and the Urey-Bradley force constants for the in-plane vibrations were calculated by these authors. The Raman spectra of both isotopic forms were available to us. The symmetry of dicyanoethene reduces the number of symmetry force constants to 58. For their determination, there are only the 2 x 18 normal frequencies of CH&(CN), and CD,C(CN),. The 2 x 5 centrifugal distortion constants, obtained from the microwave spectra, provide additional experimental data which should allow a better force field to be calculated. In order to check the force field so determined we have calculated the inertial defects of the ground state and the lowest vib~tional states for both isotopes ’ Dedicated to Professor Yonezo Morino at the occasion of his 70th birthday. 2 Department of Physics, University of Lille, F-59650 Villeneuve d’Ascq, France. 0022-2852/79/070104-14%02.00/O Copyright All rights
0
1979 by Academic
of reproduction
in any
Press. form
Inc. reserved.
104
MOLECULAR
FORCE FIELD OF DICYANOETHENE
105
and compared the results of the calculation with the experimentally determined values obtained from the microwave spectra. A similar check was made by the comparison of the calculated values of the Coriolis coupling constant and the energy difference of the two interacting states u10 = 1 and o18 = 1 with their experimental counterparts. RAMAN
SPECTRA
OF DICYANOETHENE
AND THEIR ASSIGNMENT
Assuming that di~yanoethene is planar and has C,, symmet~, frequencies are expected with the following species
I8 normal
7A, + 3B1 + 2Az + 6Bz, where the vibrations of species A, and B2 are the in-plane and those of species B, and A2 are the out-of-plane vibrational motions. In the present work we have used the same designation and numbering of the symmetry coordinates for the in-plane vibrations as Rosenberg and Devlin. However, our normal coordinate work was carried out on a GVFF basis, not on a UBFF basis as these authors have done. The Raman spectra (Fig. 1) were recorded in the region from 100 to 3200 cm-‘. The spectrum of the normal isotope consists of bands at 157,720,764,1398,1594, 2246, and 3036 cm-‘, which were assigned to species A 1 due to their small degree of depolarization. The band at 157 cm-’ had earlier been predicted by Rosenberg and Devlin. The bands of species B2 at 494, 940, 1257,2246, and 3137 cm-r agree with those measured by Rosenberg and Devlin. These authors had suggested that the absorption at 239 cm-’ is also of species Bz, but, from the analysis of the Coriolis interaction as described in our previous paper (I), we believe that this absorption belongs to species Bl. Two of the three symmetrical out-of-plane vibrations (B,) have been observed previously (2), the CHZ and CC, wagging at 986 cm-’ and 620 cm-‘, respectively. The third vibration of species B, is the out-of-plane C-C=N bending. As mentioned before, we identify this vibration with the band observed at 239 cm-’ (see previous paper). From the intensity measurements of the rotational transitions, the frequency of the antisymmetric out-of-plane C-C=N bending (A,) was expected to be near 390 cm-‘. The Raman spectrum displays a band at 368 cm-l, and, because there appears to be no other choice, we have assigned this band to species A%. The other Raman-active band of species A2 is the C=C torsion. This normal vibration was observed in ethylene (3) at a frequency of 825 cm-’ and in CH,=CF,(I) at a frequency of 714 cm-*. In CH,C(CN), a depolarized band was measured at 740 cm-‘, and hence we assign this to the C=C torsion. The assignment of the Raman spectrum of the d, isotope of dicyanoethene was carried out in a manner similar to that used for the normal isotope. SYMMETRY
COORDINATES
The symmetry coordinates for the species Al, AZ, Bz are normalized, whereas those of species B1 are given here without the normalizing factor to maintain clarity. The internal coordinates are displayed in Fig. 2.
I
3000
.
.
.
L
I
’
2500
.
.
.
*
FIG. 1. Laser Raman spectra of CH,C(CN)2 bands is given in Table I.
CM-4
CM
*
’
.
.
.
2000
I,
I
and CD,C(CN),
.
*
.a
.
.
.
1500
1
I
.,
.
.
.,
-.
1000
,
1
*
*
h
.
'16
“8
*.
in the region 100 to 3200 cm- ]. The assignment
.
I
.
500
.
-
of the overtones
.
I
500
y5 i""
"6 I
‘1
“10
100
100
v7
.’
and combination
..I
-
"18
MOLECULAR
107
FORCE FIELD OF DICYANOETHENE TABLE I
Ram-m Spectra of CH&(C!N), and CD2C(CN),
SYm-
NOIllE.1
metry
Vibration
-1 " (cm 1 =P
,C&C(cm
us(C-H)
3036
3032
2192
3205
vs(CIN)
2246
2235
2246
2255
vtc=cj
1594
1600
1543
1538
-1
1
Species
Al
"1 "2 v3
6s(HCH)
1398
1381
1062
1097
vstd-ct
764
755
692
689
V6
6sfCCC)
596
599
608
598
"7
Gs(C-CINI
157
151
156
150
"6
wfCH2)
986
986
794
794
"9
"4 %
Bl
A2
%!
w(CC2)
620
622
608
607
"lo ys(C-GIN)
239
241
239
234
"11 r(C=C)
740
740
569
569
92
y,,(C-EN)
368
368
341
341
Y_
v,,(C-HI
3137
3137
?352
~~4 vas(C:N)
2246
2246
2?46
"15 Uas(C"C)
1257
1255
1?17
~16 p(CH2)
940
935
750
VI7 P(CE*)
494
491
460
"18 Gas(C-CsN)
258
260
?39
(Impurity? Overtones and Combination TOW;
720(Al)
v15+u16=2197 2194(Al) "3 +%
=?!I922975(Al)
(Impurity
720tAl)
v4+v17=1522 1513 (?12vg=1588 1569(Al) 22337 2310 "3+"8 v7tviq=240? 2380 2v16
Note. Polarized lines are denoted force field of Table III.
with (A,).
The frequencies
=243Y 2423(Ai)
vpalc were calculated
Species A, ~~n-Pl~n~ Vibr~~i~ns~ S, = (1/21’2)(Arxz + Ar13)
stretch
dC---H)
Sz = (1/21’2)(Ar56 + ArT8)
stretch
vs(C%N)
S3 = Ar,,
stretch
v(C=C)
with the
108
TAN, DEMAISON,
bend
MHCW
S, = (1/21’2)(Ar45 + Arb,)
stretch
%(C-C)
S6 = ( l/2”2)(Aa5 + Aas)
bend
MCCC)
S, = (1/2’9(AL\ps + A&)
bend
a,( C-C=N)
S, = (1/29(Aa2
Species
AND RUDOLPH
B, (out-of-Plane
+ AaJ
Vibrations)
Ss = tgaz *A+, - (ATE - 6~)
S, = -2*ctgaz.A&
4CJ&)
wag
@4CC*)
bend
ys( C---C=N)
- (2.ctg2cyz + l)*tga5+ A44 - (Ar1 - Arz)
Sm = AR + A-Y, S& = 2*ctgaz*A#,
wag
- 23p.~,*A&~
+ (AT, - 6~~)
redundant
FIG. 2. Internal coordinates of the molecule dicyanoethene. All internal coordinates, including the torsions T~(H2C 1C4C 5) and -r2(H,C,C,C,), were chosen according to Wilson, Decius, and Cross (17).
MOLECULAR
Species AZ (out-of-Plane
FORCE FIELD OF DICYANOETHENE
109
Vibrations)
SI1 = (1/2l’9(A7, + AT+J
torsion
7(C==c)
Slz = (1/21’2)(Ay, - Ay,)
bend
Y&-C-N)
Species B2 (in-Plane Vibrations) S13 = (1/21’2)(Ar,2 - Ar13)
stretch
dc--HI
S,, = (1/21’2)(Ar,, - Ar,J
stretch
u,,( C-N)
S,, = (1/21’2)(Ar,, - Ar4r)
stretch
&&--4
SIG = (1/21’2)(Aa2 - A
rock
PWM
S,, = (1/21’2)(Aa5 - A
rock
PWG)
Sls = ( 1/21’2)(A& - A/3,)
bend
a,,( C-C=N)
FORCE CONSTANT
The calculations
CALCULATIONS
were carried out with the following assumed structure: rCH = 1.091 8,
9(HCH = 118.70”
rczc = 1.309 L&
rc-c = 1.446 A
QCCN = 180”
rc_N = 1.163 .& In terms of the symmetry coordinates the eigenvalue problem factorizes into four symmetry blocks of ranks 7(A,), 3(B,), 2(A,), and 6(B,). The number of independent (symmetry) force constants Fssl hence totals 58; 49 for the in-plane vibrations of species A, and B2 and 9 for the out-of-plane vibrations of species A, and B,. For a planar molecule the centrifugal distortion constants do not depend on the out-of-plane vibrations. This follows from the expression for the centrifugal constants (5). T,PYS =
-T
&$I:::; clPY6
* s
The quantities a,, where aFp) is the partial derivative of the component Zap of the inertial tensor with respect to the normal coordinate Qs, vanish ifs denotes an out-of-plane vibration. The centrifugal distortion constants can therefore, in principle, provide no additional data for the determination of the out-of-plane force field of a planar molecule. For the calculation of the out-of-plane force constants, three of species Az and six of species B,, we are provided with four and six fundamental frequencies, respectively. Only for species AZ does the number suffice to truly fit the force constants F1l,ll, F12,12rand F,,,,, to the four vibrational frequencies. For the species B,, initially only the diagonal force constants were allowed to vary during the fitting. F 1O,,,,is strongly correlated with F9,@and both
110
TAN, DEMAISON,
AND RUDOLPH
constants cannot be determined independently. We have hence assigned F,o,lo the fixed value 0.35 mdyne/A which had earlier (6) been determined for the same motion in the molecule CH2(CN)2. The deviation of the calculated frequency Q from the experimental was rather large, 21 cm-‘. This difference could be reduced to 0.3 cm-l if one allows the off-diagonal element Fsp9 to vary. In contrast to the force constants of species A2 and B1, those of the species A, and Bz do depend on the centrifugal distortion constants. The calculation of the latter force constants was carried out by combining the experimental vibrational frequencies and the distortion constants. In order to evaluate appropriate relative weights for the vibrational frequencies and the centrifugal distortion constants in the required least-squares calculation of the force constants, recourse was taken to a suggestion made earlier in a different, though similar, context by Kuchitsu, Fukuyama, and Morino (7) and by Kuchitsu and Cyvin (8). After weighting each datum by a factor proportional to the inverse square of the experimental error, which is standard procedure, the weights were further adjusted until the residuals of the vibrational frequencies remained below 3% while the residuals of the distortion constants appeared to be comparable with their inherent inaccuracies, which were estimated to be of the order of 10 to 20%. This is in obvious contrast to the precision with which these constants can be determined from the rotational spectra (cf. Table II). However, the above centrifugal distortion expression, which enters the least-squares calculation and yields the calculated values of Table II, is only a harmonic approximation which might indeed be in error by the estimated amount. The additional weight factor used was 36 x lo6 in favor of the vibrational frequencies. Without this factor the influence of the distortion constants would be overwhelming and practically exclude the vibrational frequency data from the fit, as can be seen from a consideration of the extremely small magnitude of a typical Jacobian matrix element G(force constant)B(vibrational frequency) compared with the large value of G(force constant)/&(distortion constant): For a diatomic molecule with rotational constant B and vibrational TABLE II Centrifugal Distortion Constants of CH,C(CN), and CD,C(CN),
I
I
CH,C(CN);, Calc. from
Exp. from
Force Field
MW Spectrum
(kHz) 1.056 -8.564 (25)
( 6K
1 1.331 (33)
r
CD,C(CN12
(kHz)
(195)
1.195
(4)
-7.403 (1160)
-6,823 (27)
27.61
22.88
(468)
0.467
(90)
1.075
(256)
0.542
(3) (3)
1.050 (36)
I
Force Field
1.002
19.67
0.828
Note. In parentheses uncertainties in units of the last digit; for calculated much larger due to unfavorable weight factor, see text.
(193)
(3212)
(222)
values intentionally
MOLECULAR
frequency V, the centrifugal obtain (F = force constant) -SD/&
FORCE FIELD OF DICYANOETHENE
distortion
constant
= -@F/6v)/(W6D)
111
is D = 4B3/v2, from which we
= (~B/v)~,
which is roughly of the order of lOME. Most of the initial values of the diagonal force constants for the in-plane vibrations were calculated from the UBFF given by Rosenberg and Devlin, and all off-diagonal elements were initially set equal to zero. In species A, strong correlations were observed between Fz,z and F5,5 and between F6,6 and F,,,. Since the calculated frequency v2, produced by allowing F2,* to vary, was in good agreement with the observed frequency without further off-diagonal constants, F,,, was held fixed at its initial UBFF value 6.97 mdynel& Further, it is probably more correct to transfer the value for F,., from the molecule CH2(CN), (6) than that for F6,6, because the different hybridization of the central C atom of the two molecules should have less effect on F,,, (v, = G,(C--CN)) than on F,, (v6 = S,(CCC)). Consequently, F,,, was assumed equal to 0.333 mdyne/A, as determined for the C-C=N bending motion in CH,(CN),. In order to reduce the deviation of the calculated frequencies of vq and vg from the experimental ones, the off-diagonal force constant F4,5 was set free. The remaining discrepancy of vg was further reduced by allowing F3,5 to vary. The calculated frequency for vg for CH,C(CN), was 22 cm-’ lower than that observed, but, by allowing F,,6 to vary, better agreement could be obtained (see Table I). The calculated constants AJKfor both isotopes were 33% smaller than the observed values; this discrepancy could be reduced to 13% by fitting the offdiagonal element F,,, (see Table II). In species B,,F,,,,, was found to be strongly correlated with F,5,1s. Hence one of these force constants had to be kept fixed during the fitting process. Since the calculated frequency v,~, produced by allowing F14,14to vary, was in good agreement with the observed frequency without further off-diagonal constants, F,j,ls was held fixed at its initial UBFF value of 5.56 mdyne/A. The calculated frequency for v17 was 14 cm-’ lower than the observed frequency, but, by allowing the off-diagonal constant F15,17to vary, this difference could be reduced to 5.4 cm-‘. As an-effect of varying F15,16, this difference was further reduced to 3 cm-’ (see Tables I and III). Rosenberg and Devlin have supposed the band which we observed in the Raman spectrum at 764 cm-l to be the combination band vg + v7 (expected at 753 cm-l), while they assigned the band at 720 cm-l to the fundamental vibration vs. However, since the Raman intensity of the band at 764 cm-’ is larger than that of vg, it can hardly be the combination band vg + v7, and we propose that this band is in fact the fundamental I+. The assignment of vg to the band at 596 cm-’ (Fig. 1) was a little uncertain due to the presence of a Raman line at 720 cm-l which is polarized and appears in the spectra of both CH,C(CN), and CD,C(CN),. Initially we assumed this line to be v6. However, the frequency vg calculated with this assumption was much too low (670 cm-l), and the deviation of the centrifugal distortion constants increased to
112
TAN, DEMAISON,
AND RUDOLPH
TABLE III Symmetry Force Constants of Dicyanoethene
Species A1
F
11
r22
9.122 (0.314)
I‘44
=
1.241 (0.047)
=
6.97
2.408 (0.7%)
=
0.333 (fixed)
=
0.157 (0.007)
=
0.292 (0.079)
q
0.35
=
0.255 (0.029)
12,L2 =
0.360 (0.0781
'88 1‘99 FlOJO
fll,ll F
p13,13 =
Pl4,lii= 17.009 CO.4781 f15,15 = F16,16 F
17,17
F18,18
F45 F56 F67
= q
2.217 10.275) -0.631 (0.112)
= -0.543 (0.527) =
0.113 (0.093)
F89
= -0.104 CO.0231
(fixed)
5.174 (0.014)
5.56
r35
(fixed)
=
p71
Species B2
= 16.530 (0.415) =
F66
Species A2
5.160 (0.01s)
F 33
F55
Species B1
=
F = -0.048 (0.039) 11,12
F15,16 F15,17
= -0.030 (0.086) =
0.431 (0.373)
(fixed)
=
0.540 (0.036)
q
0.839 (0.236)
=
0.265 (0.102)
Note. The units for stretch vibration are mdyne/& for angle deformation mdyne/i\, and for stretch-bend interaction mdyne. The errors are composed of the standard errors and the estimated errors of the assumed force constants. For force constants kept fixed during fit, see text.
25%. Therefore it seems reasonable to assume that the band at 720 cm-l originated from an impurity. We summarize the results of the fit as follows. Species AI, B,: Using 2 x 13 vibrational frequencies and 2 x 5 centrifugal distortion constants for both isotopes, allowing 10 diagonal and 6 nondiagonal force constants to vary while keeping 3 diagonal force constants at fixed values, and fixing the remaining nondiagonal force constants at zero, the fit presented a maximum deviation of 35 cm-l for v4 in the d, species and of 21% for & in the d, species. Species A,: Complete agreement between the 2 x 2 experimental and calculated frequencies could be obtained by varying all 3 force constants. Species B,: The 3 x 2 vibrational frequencies were reproduced with a maximum difference of 5 cm-l for Ye,,in
MOLECULAR
FORCE FIELD OF DICYANOETHENE
113
the d, species by allowing 2 diagonal and 1 nondiagonal force constants to vary and keeping 1 diagonal force constant fixed (value transferred) and the other nondiagonal force constants fixed at zero. In species A, the stretch v5 = v,(C-C) = 764 cm-’ has been found at a much lower frequency than the angle deformation v4 = G,(HCH) = 1398 cm-l. Rosenberg and Devlin have assumed the same sequence for the stretch v,,(C-C) and the rock p(CHz) (which actually also is a CH,-angle defo~ation) in the B2 species. In contrast to this assignment, the potential energy distribution in Table IV shows that the stretching frequency u&C--C) is higher than the rocking frequency p(CH.J. The same situation has been encountered in the molecule CH,=CF, (9-11) regarding the angle defo~ation of the CH2 group and the stretch v(C-F). TABLE IV Potential Energy Dist~bution of CH,C(CN), and CD&(CN), N0lTl.21
CH,C(CN),
Coordinates
CD2C(CN12
"1
u,fC-H)
s1:o.99
Sl:0.49, S2:0.42
"2
vs(C:N)
S2:0.84
s1:o.43, s2:o.43
v3
" cc=c1
S3:0.83, s4:0.24, s5:o.09
s3:0.91, sq:o.05, s5:o.12
uil ssmtcaf
S3:0.16, 6430.65, S5:0.08
S3:0.01, S4:0.60, S5:0.1E
v5
vs(C-C)
Sq:0.16, S6:0.66, S6:O.U
5,+:0.38,S5:0.57, S6:0.08
V6
6scccc)
s5:o.19, S5:0.36, s7:o.m
S5:0.17, S6:0.37, S7:0.29
"7
G,fC-EN)
s6:0.1;?,S7:0.67
sg:o.‘k7,57:0.67
v8
w (CH2)
ss:1.15
y9
w
S9:0.73, Slo:0.42
"lo
y,(C-EN)
sg:o.55, slo:o.58
S9:0.55, Slo:0.56
VI1 .T cc=c) "12 Y,,(C-C:N)
v13 v_(C-H)
S13:o.99
v14 vas(C:N)
s14:o.85, s16:o.16
VI5 v_(C-C)
s15:o.64, s16:o.30
VI6
P iCH*)
5_:0.30, s16:O_54, s17:o.20
v17
P (CC,)
S17:0.59, S18:0.26
v18 Aas(C-C8N)
S17:o.25, s18:o.76
Note. Symmetry Coordinates
S1, . . . , S,, as shown in text.
114
TAN, DEMAISON,
AND RUDOLPH
The errors of the force constants in Table III, shown in parentheses, comprise the standard errors and the assumed errors of the fixed force constants. The estimated error is 1.O mdyne/A for the force constants F,,, and F,,,, and 0.1 mdyne/A for the constants F,,, and F1O,lO,all of which were kept fixed in the fitting process. These errors amount to 16 and 29% of the values of the respective force constants. The standard errors of most force constants did not increase significantly when the estimated errors of the fixed force constants were taken into account. Only the errors of Fta2,Fs,s, F9,9, and F14,14became up to 5 times larger (in Table III, already included), because these force constants are strongly correlated with the fixed constants. From an inspection of Table III it is obvious that significant values have been determined for the diagonal force constants, with the possible exception of the very small constant F18,18, where the error is almost half as large as the quantity itself. However, out of the eight nondiagonal force constants only three, Fa5, Fa5,and F,,, can be considered as significantly determined by the fit. Nonetheless, all of these constants were quite effective in the fitting process and improved the agreement between the experimental and calculated vibrational frequencies and/or centrifugal distortion constants. In our final choice of which nondiagonal force constants to admit to the fit, we were guided by the desire to find the minimum number of most effective nonzero constants. Table II compares Watson’s centrifugal distortion constants AJ, AJx, AR, &, & calculated from the force field with the experimental values obtained from the microwave spectra. While sign and magnitude are correctly reproduced, the calculated numbers are consistently too small. A similar observation had been made earlier in the case of the planar molecule S(CN), by Pierce et al. (12). A possible explanation of this fact may be the missing anharmonic and/or terms in P6 in the calculated values. CHECK OF THE CALCULATED
FORCE FIELD
Apart from the usually small contributions from the centrifugal and electron-rotation interaction, the inertial defect can be expressed
distortion as (13):
A = C (v, + ‘+$)+A,. s TABLE V Rotation-Vibration
Contributions l8 to Principal Moments of Inertia and Contributions Inertial Defects As for Several Vibrations of CH,C(CN),
to
MOLECULAR
FORCE FIELD OF DICYANOETHENE
115
TABLE VI Inertial Defects A = I, - (I, + &,) for Ground State and Excited Vibrational States of CH,C(CN), b
exp (am”.X2)
from MW Spectrum
d
talc (amu.X2)
calculated from Force Field
G.S.
0.404
0.374
-1
1.031
0.957
v7 =2
1.656
1.541
v7 =3
2.278
2.124
v7 -4
2.898
2.708
=5
3.520
3.291
VIO:l
-0.785
-0.912
=2 "10 '10=1, v7 -1
-1.771
-2.198
-0.182
-0.329
=1 "12
0.255
0.299
1.464
1.519
2.080
2.103
v7
v7
-1
“18 J18=1. Y7 =1
A, = 6,” - $ - r,b is the contribution of the sth vibration of the inertial defect. To the second order of approximation, it has been found that for planar molecules the inertial defect contributions A, do not involve the vibrational anharmonicity constants (13, Id), in contrast to the vibrational cont~butions E: to the principal moments of inertia which depend on the harmonic und anharmonic force constants. The harmonic part of the E; may be expressed as
TABLE VII Inertial Defects for Ground State and Excited Vibrational States of CD&(CN), b exp hnu.X2) ffom MW Spectrum
B
tale
(.m”.X2)
calculated from Force Field
G.S.
0.410
0.380
"7 -1
1.058
0.980
Y7 -2
1.701
1.579
VIO‘l
-2.564
-2.161
v12=I
0.331
0.376
V&l
2.941
2.766
116
TAN, DEMAISON,
AND RUDOLPH
TABLE VIlI Energy Difference at AE and Coriolis Coupling Constant g&8 of CD,C(CN),
AE = Y,~ - q0 i%!1*
Exp. from MW
Calc. from force field
5.9 cm-’ 0.40
8,6 cm-’ 0.56
In Table V we have compared the observed contributions ES”(for s = 7, 10, 12, 18) with the respective harmonic parts calculated from the force field established. As expected, there are considerable disagreements due to the missing anharmanic portions. In Table V we have also compared the observed inertial defect contribution A8 for the same vibrational modes s with those calculated from the force field as A, = egC(harm.) - &harm.) - &harm.). There is obviously no discrepancy, which shows that the inertial defect is indeed determined solely by the harmonic part of the force field (to second order). In our case we also take the good agreement as a successful check of the correctness of the harmonic force field established. Table V also confirms that the low-lying in-plane vibrations usually make a positive contribution and the low-lying out-of-plane vibrations make a negative contribution to the inertial defect (25, 16). The parameters AE = q8 - vlo and Q& of the interacting vibrations vlo and pX8in the dz species provide a further check of the calculated force field. AE and 4X18 calculated from the force field are listed in the right-hand column of Table VIII, and the values obtained from the microwave rotational spectra in the left-hand column. The sign of { cannot be obtained from the analysis of the rotational spectrum. From the force field calculation, {$,\18was found to be positive. The agreement of AE and LJ 1&s calculated from the force field with the values obtained from the microwave spectrum is satisfactory though not exact. A possible explanation of the remaining small differences may again be the missing anharmanic and/or the terms in P6 contributions in the calculated values. The good agreement of the inertial defects and the fair reproduction of the energy difference AE and the Coriolis coupling constant @j& confirm that the calculated force field is, in principle, correct and that the rotational spectra in the vibrationally excited states have been correctly identified. ACKNOWLEDGMENTS The authors are grateful to Dr. V. Typke for computer programs for the calculation of the force fields and to the Vibrational Spectroscopy Section of the Department of Chemistry, University of Ulm, for making available the Raman spectra of the molecule. The calculations have been carried out at the Computing Center of the University of Ulm. The investigation has been supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.
RECEIVED:
September
12, 1978
MOLECULAR
FORCE FIELD OF DICYANOETHENE
117
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. IO. Il. 12. 13. 14. 15. 16. 17.
B. T. TAN, J. DEMAISON,AND H. D. RUDOLPH,J. Mol. Spectrosc. 71, 471-487 (1978). A. ROSENBERG AND J. P. DEVLIN, Spectrochim. Acta 21, 1613-1623 (1%5). G. HERZBERG,“Infrared and Raman Spectra,” Van Nostrand, New York, 1962. W. F. EDGELLAND W. E. BYRD, J. Chem. Phys. 17, 740-741 (1949). E. B. WILSON AND J, B. HOWARD, J. Chem. Phys. 4, 260-268 (1935). E. HIROTA,J. Mol. Spectrosc. 7, 242-260 (l%l). K. KUCHITSU,T. FUKUYAMA, AND Y. MORINO,J. Mol. Structure 1, 463-479 (1967-68). K. KUCHITSUAND S. J. CYVIN, in “Molecular Structure and Vibrations” (S. J. Cyvin, Ed.), Elsevier, Amsterdam, 1972. Y. MORINO, K. KUCHITSU,AND T. SHIMANOUCHI,.I. Chem. Phys. 20, 726-733 (1952). R. J. SCHERERAND J. OVEREND,J. Chem. Phys. 32, 1720-1731 (196O). D. C. SMITH, J. R. NIELSEN, AND H. H. CLAASSEN,J. Chem. Phys. 18, 326-331 (1950). L. FIERCE,R. NELSON, AND C. THOMAS,J. Chem. Phys. 43, 3423-3431 (1965). T. OKA AND Y. MORINO,J. Mol. Spectrosc. 6, 472-482 (1961). B. T. DARLINGAND D. M. DENNISON,Phys. Rev. 57, 128-139 (1940). W. G~RDY AND R. L. COOK, “Microwave Molecular Spectra,” Interscience, New York, 1970. D. R. HERSCHBACH AND V. W. LAURIE,J. Chem. Phys. 40, 3142-3153 (1%4). E. B. WILSON, JR., J. C. DECIUS, AND P. C. CROSS, “Molecular Vibrations,” McGraw-Hill, New York, 1955.
OF
MOLECULAR
Molecular
SPECTROSCOPY
76, 104- 117 (1979)
Force Field of 1 ,I ‘-Di~yanoethene Vibrational and Microwave Data”
B. T. TAN, J. DEMAISON,~ Department
of Chemistry,
University
AND
From
H. D. RUDOLPH
of Urn, D-7900 Ulm, Federal
Republic
of Germany
Vibrations Raman frequencies were used in conjunction with the centrifugti distortion, constants determined from. the microwave rotational spectrum to calculate a (simplified) harmonic force field by a least-squares fit for the molecules CH,C(CN), and CD2C(CN),. As a check, the inertial defects of the ground state and the lowest vibrational states for both isotopes were calculated from this force field and found to be in good agreement with the experimental values obtained from the microwave spectra. The calculated values for c:b,,, and AE,0,18 of the two Coriolis-interacting vibrational states uIO= 1 and u,~ = 1 in CD,C(CN)e likewise agreed satisfactorily with those derived from the microwave spectra. INTRODUCTION
Molecular force fields have, in the past, been determined almost exclusively from the fundamental frequencies. In general, there are more force constants than observed fundamentals. The rotation-vibration interaction parameters observed in the microwave spectrum provide additional data for the determination of a force field. In Ref. (I) the microwave spectra of l,l’-di~yanoethane CH,C(CN), and its deuterated species CD,C(CN), were reported in their ground and lowest excited vibrational states. These vibrational states originated from combinations of the two C-CSN bending motions. The molecule dicyanoethene is of symmetry Czu. All vibrational modes are Raman active; the vibrations of the species Al, B1, and B2 are also infrared active. The infrared spectrum of the normal isotope of dicyanoethene has been studied by Rosenberg and Devlin (2) and the Urey-Bradley force constants for the in-plane vibrations were calculated by these authors. The Raman spectra of both isotopic forms were available to us. The symmetry of dicyanoethene reduces the number of symmetry force constants to 58. For their determination, there are only the 2 x 18 normal frequencies of CH&(CN), and CD,C(CN),. The 2 x 5 centrifugal distortion constants, obtained from the microwave spectra, provide additional experimental data which should allow a better force field to be calculated. In order to check the force field so determined we have calculated the inertial defects of the ground state and the lowest vib~tional states for both isotopes ’ Dedicated to Professor Yonezo Morino at the occasion of his 70th birthday. 2 Department of Physics, University of Lille, F-59650 Villeneuve d’Ascq, France. 0022-2852/79/070104-14%02.00/O Copyright All rights
0
1979 by Academic
of reproduction
in any
Press. form
Inc. reserved.
104
MOLECULAR
FORCE FIELD OF DICYANOETHENE
105
and compared the results of the calculation with the experimentally determined values obtained from the microwave spectra. A similar check was made by the comparison of the calculated values of the Coriolis coupling constant and the energy difference of the two interacting states u10 = 1 and o18 = 1 with their experimental counterparts. RAMAN
SPECTRA
OF DICYANOETHENE
AND THEIR ASSIGNMENT
Assuming that di~yanoethene is planar and has C,, symmet~, frequencies are expected with the following species
I8 normal
7A, + 3B1 + 2Az + 6Bz, where the vibrations of species A, and B2 are the in-plane and those of species B, and A2 are the out-of-plane vibrational motions. In the present work we have used the same designation and numbering of the symmetry coordinates for the in-plane vibrations as Rosenberg and Devlin. However, our normal coordinate work was carried out on a GVFF basis, not on a UBFF basis as these authors have done. The Raman spectra (Fig. 1) were recorded in the region from 100 to 3200 cm-‘. The spectrum of the normal isotope consists of bands at 157,720,764,1398,1594, 2246, and 3036 cm-‘, which were assigned to species A 1 due to their small degree of depolarization. The band at 157 cm-’ had earlier been predicted by Rosenberg and Devlin. The bands of species B2 at 494, 940, 1257,2246, and 3137 cm-r agree with those measured by Rosenberg and Devlin. These authors had suggested that the absorption at 239 cm-’ is also of species Bz, but, from the analysis of the Coriolis interaction as described in our previous paper (I), we believe that this absorption belongs to species Bl. Two of the three symmetrical out-of-plane vibrations (B,) have been observed previously (2), the CHZ and CC, wagging at 986 cm-’ and 620 cm-‘, respectively. The third vibration of species B, is the out-of-plane C-C=N bending. As mentioned before, we identify this vibration with the band observed at 239 cm-’ (see previous paper). From the intensity measurements of the rotational transitions, the frequency of the antisymmetric out-of-plane C-C=N bending (A,) was expected to be near 390 cm-‘. The Raman spectrum displays a band at 368 cm-l, and, because there appears to be no other choice, we have assigned this band to species A%. The other Raman-active band of species A2 is the C=C torsion. This normal vibration was observed in ethylene (3) at a frequency of 825 cm-’ and in CH,=CF,(I) at a frequency of 714 cm-*. In CH,C(CN), a depolarized band was measured at 740 cm-‘, and hence we assign this to the C=C torsion. The assignment of the Raman spectrum of the d, isotope of dicyanoethene was carried out in a manner similar to that used for the normal isotope. SYMMETRY
COORDINATES
The symmetry coordinates for the species Al, AZ, Bz are normalized, whereas those of species B1 are given here without the normalizing factor to maintain clarity. The internal coordinates are displayed in Fig. 2.
I
3000
.
.
.
L
I
’
2500
.
.
.
*
FIG. 1. Laser Raman spectra of CH,C(CN)2 bands is given in Table I.
CM-4
CM
*
’
.
.
.
2000
I,
I
and CD,C(CN),
.
*
.a
.
.
.
1500
1
I
.,
.
.
.,
-.
1000
,
1
*
*
h
.
'16
“8
*.
in the region 100 to 3200 cm- ]. The assignment
.
I
.
500
.
-
of the overtones
.
I
500
y5 i""
"6 I
‘1
“10
100
100
v7
.’
and combination
..I
-
"18
MOLECULAR
107
FORCE FIELD OF DICYANOETHENE TABLE I
Ram-m Spectra of CH&(C!N), and CD2C(CN),
SYm-
NOIllE.1
metry
Vibration
-1 " (cm 1 =P
,C&C(cm
us(C-H)
3036
3032
2192
3205
vs(CIN)
2246
2235
2246
2255
vtc=cj
1594
1600
1543
1538
-1
1
Species
Al
"1 "2 v3
6s(HCH)
1398
1381
1062
1097
vstd-ct
764
755
692
689
V6
6sfCCC)
596
599
608
598
"7
Gs(C-CINI
157
151
156
150
"6
wfCH2)
986
986
794
794
"9
"4 %
Bl
A2
%!
w(CC2)
620
622
608
607
"lo ys(C-GIN)
239
241
239
234
"11 r(C=C)
740
740
569
569
92
y,,(C-EN)
368
368
341
341
Y_
v,,(C-HI
3137
3137
?352
~~4 vas(C:N)
2246
2246
2?46
"15 Uas(C"C)
1257
1255
1?17
~16 p(CH2)
940
935
750
VI7 P(CE*)
494
491
460
"18 Gas(C-CsN)
258
260
?39
(Impurity? Overtones and Combination TOW;
720(Al)
v15+u16=2197 2194(Al) "3 +%
=?!I922975(Al)
(Impurity
720tAl)
v4+v17=1522 1513 (?12vg=1588 1569(Al) 22337 2310 "3+"8 v7tviq=240? 2380 2v16
Note. Polarized lines are denoted force field of Table III.
with (A,).
The frequencies
=243Y 2423(Ai)
vpalc were calculated
Species A, ~~n-Pl~n~ Vibr~~i~ns~ S, = (1/21’2)(Arxz + Ar13)
stretch
dC---H)
Sz = (1/21’2)(Ar56 + ArT8)
stretch
vs(C%N)
S3 = Ar,,
stretch
v(C=C)
with the
108
TAN, DEMAISON,
bend
MHCW
S, = (1/21’2)(Ar45 + Arb,)
stretch
%(C-C)
S6 = ( l/2”2)(Aa5 + Aas)
bend
MCCC)
S, = (1/2’9(AL\ps + A&)
bend
a,( C-C=N)
S, = (1/29(Aa2
Species
AND RUDOLPH
B, (out-of-Plane
+ AaJ
Vibrations)
Ss = tgaz *A+, - (ATE - 6~)
S, = -2*ctgaz.A&
4CJ&)
wag
@4CC*)
bend
ys( C---C=N)
- (2.ctg2cyz + l)*tga5+ A44 - (Ar1 - Arz)
Sm = AR + A-Y, S& = 2*ctgaz*A#,
wag
- 23p.~,*A&~
+ (AT, - 6~~)
redundant
FIG. 2. Internal coordinates of the molecule dicyanoethene. All internal coordinates, including the torsions T~(H2C 1C4C 5) and -r2(H,C,C,C,), were chosen according to Wilson, Decius, and Cross (17).
MOLECULAR
Species AZ (out-of-Plane
FORCE FIELD OF DICYANOETHENE
109
Vibrations)
SI1 = (1/2l’9(A7, + AT+J
torsion
7(C==c)
Slz = (1/21’2)(Ay, - Ay,)
bend
Y&-C-N)
Species B2 (in-Plane Vibrations) S13 = (1/21’2)(Ar,2 - Ar13)
stretch
dc--HI
S,, = (1/21’2)(Ar,, - Ar,J
stretch
u,,( C-N)
S,, = (1/21’2)(Ar,, - Ar4r)
stretch
&&--4
SIG = (1/21’2)(Aa2 - A
rock
PWM
S,, = (1/21’2)(Aa5 - A
rock
PWG)
Sls = ( 1/21’2)(A& - A/3,)
bend
a,,( C-C=N)
FORCE CONSTANT
The calculations
CALCULATIONS
were carried out with the following assumed structure: rCH = 1.091 8,
9(HCH = 118.70”
rczc = 1.309 L&
rc-c = 1.446 A
QCCN = 180”
rc_N = 1.163 .& In terms of the symmetry coordinates the eigenvalue problem factorizes into four symmetry blocks of ranks 7(A,), 3(B,), 2(A,), and 6(B,). The number of independent (symmetry) force constants Fssl hence totals 58; 49 for the in-plane vibrations of species A, and B2 and 9 for the out-of-plane vibrations of species A, and B,. For a planar molecule the centrifugal distortion constants do not depend on the out-of-plane vibrations. This follows from the expression for the centrifugal constants (5). T,PYS =
-T
&$I:::; clPY6
* s
The quantities a,, where aFp) is the partial derivative of the component Zap of the inertial tensor with respect to the normal coordinate Qs, vanish ifs denotes an out-of-plane vibration. The centrifugal distortion constants can therefore, in principle, provide no additional data for the determination of the out-of-plane force field of a planar molecule. For the calculation of the out-of-plane force constants, three of species Az and six of species B,, we are provided with four and six fundamental frequencies, respectively. Only for species AZ does the number suffice to truly fit the force constants F1l,ll, F12,12rand F,,,,, to the four vibrational frequencies. For the species B,, initially only the diagonal force constants were allowed to vary during the fitting. F 1O,,,,is strongly correlated with F9,@and both
110
TAN, DEMAISON,
AND RUDOLPH
constants cannot be determined independently. We have hence assigned F,o,lo the fixed value 0.35 mdyne/A which had earlier (6) been determined for the same motion in the molecule CH2(CN)2. The deviation of the calculated frequency Q from the experimental was rather large, 21 cm-‘. This difference could be reduced to 0.3 cm-l if one allows the off-diagonal element Fsp9 to vary. In contrast to the force constants of species A2 and B1, those of the species A, and Bz do depend on the centrifugal distortion constants. The calculation of the latter force constants was carried out by combining the experimental vibrational frequencies and the distortion constants. In order to evaluate appropriate relative weights for the vibrational frequencies and the centrifugal distortion constants in the required least-squares calculation of the force constants, recourse was taken to a suggestion made earlier in a different, though similar, context by Kuchitsu, Fukuyama, and Morino (7) and by Kuchitsu and Cyvin (8). After weighting each datum by a factor proportional to the inverse square of the experimental error, which is standard procedure, the weights were further adjusted until the residuals of the vibrational frequencies remained below 3% while the residuals of the distortion constants appeared to be comparable with their inherent inaccuracies, which were estimated to be of the order of 10 to 20%. This is in obvious contrast to the precision with which these constants can be determined from the rotational spectra (cf. Table II). However, the above centrifugal distortion expression, which enters the least-squares calculation and yields the calculated values of Table II, is only a harmonic approximation which might indeed be in error by the estimated amount. The additional weight factor used was 36 x lo6 in favor of the vibrational frequencies. Without this factor the influence of the distortion constants would be overwhelming and practically exclude the vibrational frequency data from the fit, as can be seen from a consideration of the extremely small magnitude of a typical Jacobian matrix element G(force constant)B(vibrational frequency) compared with the large value of G(force constant)/&(distortion constant): For a diatomic molecule with rotational constant B and vibrational TABLE II Centrifugal Distortion Constants of CH,C(CN), and CD,C(CN),
I
I
CH,C(CN);, Calc. from
Exp. from
Force Field
MW Spectrum
(kHz) 1.056 -8.564 (25)
( 6K
1 1.331 (33)
r
CD,C(CN12
(kHz)
(195)
1.195
(4)
-7.403 (1160)
-6,823 (27)
27.61
22.88
(468)
0.467
(90)
1.075
(256)
0.542
(3) (3)
1.050 (36)
I
Force Field
1.002
19.67
0.828
Note. In parentheses uncertainties in units of the last digit; for calculated much larger due to unfavorable weight factor, see text.
(193)
(3212)
(222)
values intentionally
MOLECULAR
frequency V, the centrifugal obtain (F = force constant) -SD/&
FORCE FIELD OF DICYANOETHENE
distortion
constant
= -@F/6v)/(W6D)
111
is D = 4B3/v2, from which we
= (~B/v)~,
which is roughly of the order of lOME. Most of the initial values of the diagonal force constants for the in-plane vibrations were calculated from the UBFF given by Rosenberg and Devlin, and all off-diagonal elements were initially set equal to zero. In species A, strong correlations were observed between Fz,z and F5,5 and between F6,6 and F,,,. Since the calculated frequency v2, produced by allowing F2,* to vary, was in good agreement with the observed frequency without further off-diagonal constants, F,,, was held fixed at its initial UBFF value 6.97 mdynel& Further, it is probably more correct to transfer the value for F,., from the molecule CH2(CN), (6) than that for F6,6, because the different hybridization of the central C atom of the two molecules should have less effect on F,,, (v, = G,(C--CN)) than on F,, (v6 = S,(CCC)). Consequently, F,,, was assumed equal to 0.333 mdyne/A, as determined for the C-C=N bending motion in CH,(CN),. In order to reduce the deviation of the calculated frequencies of vq and vg from the experimental ones, the off-diagonal force constant F4,5 was set free. The remaining discrepancy of vg was further reduced by allowing F3,5 to vary. The calculated frequency for vg for CH,C(CN), was 22 cm-’ lower than that observed, but, by allowing F,,6 to vary, better agreement could be obtained (see Table I). The calculated constants AJKfor both isotopes were 33% smaller than the observed values; this discrepancy could be reduced to 13% by fitting the offdiagonal element F,,, (see Table II). In species B,,F,,,,, was found to be strongly correlated with F,5,1s. Hence one of these force constants had to be kept fixed during the fitting process. Since the calculated frequency v,~, produced by allowing F14,14to vary, was in good agreement with the observed frequency without further off-diagonal constants, F,j,ls was held fixed at its initial UBFF value of 5.56 mdyne/A. The calculated frequency for v17 was 14 cm-’ lower than the observed frequency, but, by allowing the off-diagonal constant F15,17to vary, this difference could be reduced to 5.4 cm-‘. As an-effect of varying F15,16, this difference was further reduced to 3 cm-’ (see Tables I and III). Rosenberg and Devlin have supposed the band which we observed in the Raman spectrum at 764 cm-l to be the combination band vg + v7 (expected at 753 cm-l), while they assigned the band at 720 cm-l to the fundamental vibration vs. However, since the Raman intensity of the band at 764 cm-’ is larger than that of vg, it can hardly be the combination band vg + v7, and we propose that this band is in fact the fundamental I+. The assignment of vg to the band at 596 cm-’ (Fig. 1) was a little uncertain due to the presence of a Raman line at 720 cm-l which is polarized and appears in the spectra of both CH,C(CN), and CD,C(CN),. Initially we assumed this line to be v6. However, the frequency vg calculated with this assumption was much too low (670 cm-l), and the deviation of the centrifugal distortion constants increased to
112
TAN, DEMAISON,
AND RUDOLPH
TABLE III Symmetry Force Constants of Dicyanoethene
Species A1
F
11
r22
9.122 (0.314)
I‘44
=
1.241 (0.047)
=
6.97
2.408 (0.7%)
=
0.333 (fixed)
=
0.157 (0.007)
=
0.292 (0.079)
q
0.35
=
0.255 (0.029)
12,L2 =
0.360 (0.0781
'88 1‘99 FlOJO
fll,ll F
p13,13 =
Pl4,lii= 17.009 CO.4781 f15,15 = F16,16 F
17,17
F18,18
F45 F56 F67
= q
2.217 10.275) -0.631 (0.112)
= -0.543 (0.527) =
0.113 (0.093)
F89
= -0.104 CO.0231
(fixed)
5.174 (0.014)
5.56
r35
(fixed)
=
p71
Species B2
= 16.530 (0.415) =
F66
Species A2
5.160 (0.01s)
F 33
F55
Species B1
=
F = -0.048 (0.039) 11,12
F15,16 F15,17
= -0.030 (0.086) =
0.431 (0.373)
(fixed)
=
0.540 (0.036)
q
0.839 (0.236)
=
0.265 (0.102)
Note. The units for stretch vibration are mdyne/& for angle deformation mdyne/i\, and for stretch-bend interaction mdyne. The errors are composed of the standard errors and the estimated errors of the assumed force constants. For force constants kept fixed during fit, see text.
25%. Therefore it seems reasonable to assume that the band at 720 cm-l originated from an impurity. We summarize the results of the fit as follows. Species AI, B,: Using 2 x 13 vibrational frequencies and 2 x 5 centrifugal distortion constants for both isotopes, allowing 10 diagonal and 6 nondiagonal force constants to vary while keeping 3 diagonal force constants at fixed values, and fixing the remaining nondiagonal force constants at zero, the fit presented a maximum deviation of 35 cm-l for v4 in the d, species and of 21% for & in the d, species. Species A,: Complete agreement between the 2 x 2 experimental and calculated frequencies could be obtained by varying all 3 force constants. Species B,: The 3 x 2 vibrational frequencies were reproduced with a maximum difference of 5 cm-l for Ye,,in
MOLECULAR
FORCE FIELD OF DICYANOETHENE
113
the d, species by allowing 2 diagonal and 1 nondiagonal force constants to vary and keeping 1 diagonal force constant fixed (value transferred) and the other nondiagonal force constants fixed at zero. In species A, the stretch v5 = v,(C-C) = 764 cm-’ has been found at a much lower frequency than the angle deformation v4 = G,(HCH) = 1398 cm-l. Rosenberg and Devlin have assumed the same sequence for the stretch v,,(C-C) and the rock p(CHz) (which actually also is a CH,-angle defo~ation) in the B2 species. In contrast to this assignment, the potential energy distribution in Table IV shows that the stretching frequency u&C--C) is higher than the rocking frequency p(CH.J. The same situation has been encountered in the molecule CH,=CF, (9-11) regarding the angle defo~ation of the CH2 group and the stretch v(C-F). TABLE IV Potential Energy Dist~bution of CH,C(CN), and CD&(CN), N0lTl.21
CH,C(CN),
Coordinates
CD2C(CN12
"1
u,fC-H)
s1:o.99
Sl:0.49, S2:0.42
"2
vs(C:N)
S2:0.84
s1:o.43, s2:o.43
v3
" cc=c1
S3:0.83, s4:0.24, s5:o.09
s3:0.91, sq:o.05, s5:o.12
uil ssmtcaf
S3:0.16, 6430.65, S5:0.08
S3:0.01, S4:0.60, S5:0.1E
v5
vs(C-C)
Sq:0.16, S6:0.66, S6:O.U
5,+:0.38,S5:0.57, S6:0.08
V6
6scccc)
s5:o.19, S5:0.36, s7:o.m
S5:0.17, S6:0.37, S7:0.29
"7
G,fC-EN)
s6:0.1;?,S7:0.67
sg:o.‘k7,57:0.67
v8
w (CH2)
ss:1.15
y9
w
S9:0.73, Slo:0.42
"lo
y,(C-EN)
sg:o.55, slo:o.58
S9:0.55, Slo:0.56
VI1 .T cc=c) "12 Y,,(C-C:N)
v13 v_(C-H)
S13:o.99
v14 vas(C:N)
s14:o.85, s16:o.16
VI5 v_(C-C)
s15:o.64, s16:o.30
VI6
P iCH*)
5_:0.30, s16:O_54, s17:o.20
v17
P (CC,)
S17:0.59, S18:0.26
v18 Aas(C-C8N)
S17:o.25, s18:o.76
Note. Symmetry Coordinates
S1, . . . , S,, as shown in text.
114
TAN, DEMAISON,
AND RUDOLPH
The errors of the force constants in Table III, shown in parentheses, comprise the standard errors and the assumed errors of the fixed force constants. The estimated error is 1.O mdyne/A for the force constants F,,, and F,,,, and 0.1 mdyne/A for the constants F,,, and F1O,lO,all of which were kept fixed in the fitting process. These errors amount to 16 and 29% of the values of the respective force constants. The standard errors of most force constants did not increase significantly when the estimated errors of the fixed force constants were taken into account. Only the errors of Fta2,Fs,s, F9,9, and F14,14became up to 5 times larger (in Table III, already included), because these force constants are strongly correlated with the fixed constants. From an inspection of Table III it is obvious that significant values have been determined for the diagonal force constants, with the possible exception of the very small constant F18,18, where the error is almost half as large as the quantity itself. However, out of the eight nondiagonal force constants only three, Fa5, Fa5,and F,,, can be considered as significantly determined by the fit. Nonetheless, all of these constants were quite effective in the fitting process and improved the agreement between the experimental and calculated vibrational frequencies and/or centrifugal distortion constants. In our final choice of which nondiagonal force constants to admit to the fit, we were guided by the desire to find the minimum number of most effective nonzero constants. Table II compares Watson’s centrifugal distortion constants AJ, AJx, AR, &, & calculated from the force field with the experimental values obtained from the microwave spectra. While sign and magnitude are correctly reproduced, the calculated numbers are consistently too small. A similar observation had been made earlier in the case of the planar molecule S(CN), by Pierce et al. (12). A possible explanation of this fact may be the missing anharmonic and/or terms in P6 in the calculated values. CHECK OF THE CALCULATED
FORCE FIELD
Apart from the usually small contributions from the centrifugal and electron-rotation interaction, the inertial defect can be expressed
distortion as (13):
A = C (v, + ‘+$)+A,. s TABLE V Rotation-Vibration
Contributions l8 to Principal Moments of Inertia and Contributions Inertial Defects As for Several Vibrations of CH,C(CN),
to
MOLECULAR
FORCE FIELD OF DICYANOETHENE
115
TABLE VI Inertial Defects A = I, - (I, + &,) for Ground State and Excited Vibrational States of CH,C(CN), b
exp (am”.X2)
from MW Spectrum
d
talc (amu.X2)
calculated from Force Field
G.S.
0.404
0.374
-1
1.031
0.957
v7 =2
1.656
1.541
v7 =3
2.278
2.124
v7 -4
2.898
2.708
=5
3.520
3.291
VIO:l
-0.785
-0.912
=2 "10 '10=1, v7 -1
-1.771
-2.198
-0.182
-0.329
=1 "12
0.255
0.299
1.464
1.519
2.080
2.103
v7
v7
-1
“18 J18=1. Y7 =1
A, = 6,” - $ - r,b is the contribution of the sth vibration of the inertial defect. To the second order of approximation, it has been found that for planar molecules the inertial defect contributions A, do not involve the vibrational anharmonicity constants (13, Id), in contrast to the vibrational cont~butions E: to the principal moments of inertia which depend on the harmonic und anharmonic force constants. The harmonic part of the E; may be expressed as
TABLE VII Inertial Defects for Ground State and Excited Vibrational States of CD&(CN), b exp hnu.X2) ffom MW Spectrum
B
tale
(.m”.X2)
calculated from Force Field
G.S.
0.410
0.380
"7 -1
1.058
0.980
Y7 -2
1.701
1.579
VIO‘l
-2.564
-2.161
v12=I
0.331
0.376
V&l
2.941
2.766
116
TAN, DEMAISON,
AND RUDOLPH
TABLE VIlI Energy Difference at AE and Coriolis Coupling Constant g&8 of CD,C(CN),
AE = Y,~ - q0 i%!1*
Exp. from MW
Calc. from force field
5.9 cm-’ 0.40
8,6 cm-’ 0.56
In Table V we have compared the observed contributions ES”(for s = 7, 10, 12, 18) with the respective harmonic parts calculated from the force field established. As expected, there are considerable disagreements due to the missing anharmanic portions. In Table V we have also compared the observed inertial defect contribution A8 for the same vibrational modes s with those calculated from the force field as A, = egC(harm.) - &harm.) - &harm.). There is obviously no discrepancy, which shows that the inertial defect is indeed determined solely by the harmonic part of the force field (to second order). In our case we also take the good agreement as a successful check of the correctness of the harmonic force field established. Table V also confirms that the low-lying in-plane vibrations usually make a positive contribution and the low-lying out-of-plane vibrations make a negative contribution to the inertial defect (25, 16). The parameters AE = q8 - vlo and Q& of the interacting vibrations vlo and pX8in the dz species provide a further check of the calculated force field. AE and 4X18 calculated from the force field are listed in the right-hand column of Table VIII, and the values obtained from the microwave rotational spectra in the left-hand column. The sign of { cannot be obtained from the analysis of the rotational spectrum. From the force field calculation, {$,\18was found to be positive. The agreement of AE and LJ 1&s calculated from the force field with the values obtained from the microwave spectrum is satisfactory though not exact. A possible explanation of the remaining small differences may again be the missing anharmanic and/or the terms in P6 contributions in the calculated values. The good agreement of the inertial defects and the fair reproduction of the energy difference AE and the Coriolis coupling constant @j& confirm that the calculated force field is, in principle, correct and that the rotational spectra in the vibrationally excited states have been correctly identified. ACKNOWLEDGMENTS The authors are grateful to Dr. V. Typke for computer programs for the calculation of the force fields and to the Vibrational Spectroscopy Section of the Department of Chemistry, University of Ulm, for making available the Raman spectra of the molecule. The calculations have been carried out at the Computing Center of the University of Ulm. The investigation has been supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.
RECEIVED:
September
12, 1978
MOLECULAR
FORCE FIELD OF DICYANOETHENE
117
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