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Vibrational spectra and normal coordinate calculations for cis- and trans-1,2-dideuteriocyclobutanes
JOURNAL
OF MOLECULAR
SPECTROSCOPY
109,46-59 (1985)
Vibrational Spectra and Normal Coordinate Calculations for cis- and trans-1,2-Dideuteriocyclobutanes A. ANNAMALAIAND T. A. KEIDERLING Deparlmenl of Chemistry. University of Iliinoir at Chicago, Box 4348, Chicago, INinois 60680 Gas-phase FT-IR spectra and liquid-phase Raman spectra have been measured for cis- and Irans-1,2dideuteriocyclobutanes. The bands were assigned by using the results of normal coordinate calculations and Raman depolarization measurements. The initial force constants considered were based on the ab initio scaled force field of Banhegyi et al. [J. Mol. Swucr. 89, l-1 3 (1982)]; they were then optimized using vibrational frequencies of cycIobutane&, and d,, and cis- and trans-cyclobutane- I ,2-d*. The final force field and approximate description of normal modes are reported, and assignment of cyclobutane vibrational spectra is discussed. 0 1985 Academic Press, Inc. INTRODUCTION
In the course of studying the vibrational circular dichroism (VCD) of trans-1,2dideuteriocyclobutane, it became necessary to reinvestigate the normal modes for cyclobutane and its deuterated isotopomers. Many previous investigations have dealt with the vibrational spectra (l-14) and normal modes (13, 14) of cyclobutane with the aim of obtaining satisfactory assignments for this molecule. The most extensive study is by Miller et al. (II), which reports ir and Raman spectra of cyclobutane-& and -d8 for gaseous, liquid, and solid states, and gives assignments that also take into account the earlier work (I-10, 13). Earlier, Lord and Nakagawa (13) developed a force field for cyclobutane, using the frequencies of -d,, and -d8 species, based on the assumption that the molecule behaved as though it had a planar ring. Recently, Banhegyi, Fogarasi, and Pulay (BFP) (14) performed ab initio force field calculations and suggested some modifications to the assignments of Miller et al. (Z1). Since, the force constants calculated at SCF level are generally overestimated, BFP used a systematic method of scaling the ab initio force field. The scale factors were then optimized to fit the experimental frequencies. This approach is quite useful for assignment purposes, particularly when the number of experimental frequencies available is limited, since it uses only a small number of variables in fitting the frequencies. However, since the off-diagonal and diagonal scale factors are not independent, the force field is constrained in such a way that some of the calculated frequencies deviate greatly from the corresponding experimental values. Furthermore, for cyclobutane, BFP kept the scale factors corresponding to the CH stretching and ring-puckering coordinates fixed. This choice was due to both the large anharmonicities in these modes and uncertainties in CH and CD stretching frequency assignments. OO22-2852/85 $3.00 Copyright Q 1985 by Academic Press. Inc. All rights of reproduction in any form reserved.
46
VIBRATIONAL
SPECTRA
OF CYCLOBUTANE-d2
47
During the course of our recent VCD study of [runs-cyclobutane-1,2-d2 (Z5,16), we realized the need for further improvements in the force field of cyclobutane to better understand the experimental results, particularly including the CH and CD stretches. We have measured vapor-phase ir and liquid-phase Raman spectra for cis- and truns-cyclobutane- 1,2-d2. Using these data along with those previously reported for cyclobutane-4 and -dg (Z&12), we have refined the force field in a conventional manner. For these calculations, the initial force field was set up by considering the most significant force constants of the BFP force field (14). Our final force field fits the experimental frequencies very well, and has been found to explain the VCD spectrum of trans-cyclobutane-1,2-d* satisfactorily in both the CH and CD stretching (15) as well as in the mid-ir (16) regions. EXPERIMENTAL
DETAILS
Samples of tram- and cis-cyclobutane-1,2-d2 were kindly supplied to us by Dr. J. S. Chickos. Mass spectral measurements indicated that truns sample had about 9% -dl impurity, whereas the cis sample about 10% -d3, 11% -d, , and 1% -6 impurities (17). These samples were used as such in our studies. Vapor-phase ir spectra of cis- and trans-cyclobutane-1,2-dz were measured in the range 4000-500 cm-’ using a Nicolet MX-5 FT-IR instrument with a resolution of 4 cm-‘. The gas cell used had NaCl windows and a pathlength of 7 cm. Measurements were carried out with different amounts of samples for the ranges 4000-1400 and 1500-500 cm-‘. However, exact gas pressures could not be monitored. Raman spectra were measured, with a resolution of 1 cm-‘, on liquid samples held in sealed ampoules at room temperature, using an instrument constructed in the UK physics department. The excitation source was the 5145-b; line of an argon ion laser. The depolarization ratios obtained are somewhat crude due to instrumental limitations. NORMAL
COORDINATE
ANALYSIS
The geometry of the cyclobutane molecule is well established by both experiment (18-21) and theory (22, 23) as folded with D2d symmetry. A relatively low barrier (9) makes the ring very flexible so that conversion from one puckered conformation to the other is readily accomplished at room temperature. Thus, for trans-cyclobutane1,2-d2 (C, symmetry), two distinct conformers result. In one the deuterium atoms occupy the axial positions, in the other the equatorial positions. Both these are expected to contribute equally to the measured vibrational spectra, and hence were considered in our normal coordinate analysis. However, in the case of cis isomer (C, symmetry), ring puckering does not alter the conformation. We carried out the force field calculations in a conventional manner, i.e., the diagonal and off-diagonal force constants were refined independently. The initial force field was set up by transferring the most significant BFP force constants [from scale factors Set II of Ref. (Z4)]. They include, of course, all diagonal constants; but for interaction force constants, only those having magnitudes greater than 0.04 mdyn/A for stretch-stretch, 0.03 mdyn/rad for stretch-bend and 0.02 mdyn A/t-ad2 for bend-bend were retained. Additionally, all the force constants involving the ring
48
ANNAMALAI
AND
KEIDERLING
puckering coordinate were included. Of 73 possible independent force constants for cyclobutane with D2d symmetry, 35 were considered for the force field. This discrimination, of course, is a constraint on the force field but is very commonly employed and, if properly set up, is not known to affect the frequency fit severely. In the present study, availability of the BFP force field provides an optimal way of setting up the initial force field. The set of internal coordinates considered in the present study is the same as that of Ref. (14). However, to calculate the G matrix elements, we used the ab initio geometry of Cremer (22), which was calculated using a much larger basis set than that used by BFP (14). Generally, small deviations of bond lengths from experimental values, as are usually the case with ab initio calculations, have little effect on the calculated force fields; hence, we did not consider any correction terms. AI1 calculations were performed using Schachtschneider’s GMAT and FPERT programs (24). First, considering the vibrational frequencies of cyclobutane-4 and -ds, and different possible assignments (II, 14), we made several trial refinement calculations and examined the frequency fits. Using the force fields obtained, frequencies for cisand trans-cyclobutane- 1,2-dz were calculated. These frequencies were used along with the Raman depolarization results in assigning the bands for these isomers. The assigned frequencies were then considered for refining the force field further. For cyclobutane-d,,, we have included frequencies corresponding to the A2 vibrations from the lower symmetry solid state (10, 12) in our calculations, though under DIG symmetry these vibrations are both ir and Raman inactive. We faced very little problem with convergence of the force field and in fitting the frequencies, particularly with the use of damped least-squares procedure (25). However, the force constants F6,5 and F13,5were found to be less sensitive to the frequency fit and they showed a great tendency to deviate from the ab initio values. Hence, in the final calculations, these force constants were kept fixed to some intermediate values, and the remaining 33 force constants were refined using 88 frequencies. RESULTS
AND
DISCUSSION
In this section various isotopic species of cyclobutane under consideration wilI be referred to as 6, ds, ciS-dZ, and trans-dz for the sake of brevity. The ir and Raman frequencies and relative peak heights for cis-dz and tram-d2 are listed in Tables I and II, respectively. In Table III are listed the BFP and our final force fields. The calculated and observed frequencies for different isotopic species of cyclobutane are given in Tables IV to VIII, along with the calculated vibrational descriptions.
Cyclobutane-do and -da As seen from Tables IV and V, our calculations reproduce the experimental frequencies quite satisfactorily for 4 and da and, in general, the deviations are less than those obtained in the scaling approach (14). Though vibrational spectra of these species had been studied extensively before, some points regarding the assignments deserve comment. Between the two alternative frequencies suggested
49
VIBRATIONAL SPECTRA OF CYCLOBUTANEdz TABLE I Infrared and Raman Spectra of cis-Cyclobutane- 1,2-d* Infrared Preq.
Assignment
Raman (Liquid)
(Gas) 1nt.”
fan-l) 2978
4400,
cl
2961
3400,
b
2940
2000,
Sh
2882
830.
b
2954
61
2911
19
2871
27
“2 “3
0
510.
1nt.
“1
2218 2199
(cm -11
Freq.
“b
2240
3
2218
16
2196
15
2173
16
2140
2
1448
5
“5’
y17 + “20’
2179
1462
53.
1451
141. 121.
1262
60,
sh
1246
83,
Q
4.
1308
0
9,
“10 “11
P
“12 “13
“b
“14
1221
3
1177
2.
P
“17
1104
3.
P
“10
P
“19 1
“15
1107
7
1095
11.
Q
1097
3,
7.
b
989
100,
P
962
7,
P
sh
933
9,
dp
0
901
4
835
2.
7R5
2
671
1.
998 990 I
8,
942 914
35
901
43,
850
43
837
41
785
22,
676
22
665
24
584
20
571
25
563
60
548
11
sh-shoulder,
peak
pL-eSS”re.
For
correspond
to
b Relative
peak its
P
“25 “26
dp
1. P
dp-depolarized.
“29 ?
p-polarized.
O-O branch,
resonance.
(abaorbances,
frequencies
with
should
0 branch,
depend the
upon gas
listed
values
0 branch.
heights
plane
“23 “24
568
heights
the
“22 7
“28 7
P.R.-Fermi
v-very,
a Relative
Q
“20 cyclobutawd3
“27
b-broad,
Abbreviations:
“7’ “4 P.R.?
“9
1314
64
1310
-1165
i
eh 0
1326
dent
10
2”lR. 2” 19’
2187
having
2”
“6’ F.R.
of
corresponding polarization
to parallel
the
scattered to
that
radiation of
the
inci-
light.
by BFP (14) for Al scissoring of d,, (v~), 1468 cm-’ fits better in our calculations. This assignment is in accordance with Ref. (II). BFP assigned the 1153- and 1006cm-’ bands, respectively, to & and ds A, rocking modes (Q). We are able to fit the 1153-cm-’ band very well. But, our calculations consistently place the u4 mode for
50
ANNAMALAI AND KEIDERLING TABLE II
I .2-d*
Infrared and Raman Spectra of fran.KyclobutaneInfrared Freq.
Raman
(Gas)
(‘nl-1l
Freq.
1nt.a
2978
4200,
0
2958
3400,
b
2882
810,
0
Assignment
(Liquid) (cm-l)
1nt.b
2954
64
2929
32
2913
26
2871
35
Axial form
-
;z;;torial
“1’ “17
“I
“19
“19 “3’
2”21 F.R.
“3,
2260 “8
2223 630.
b
2194
520,
b
2181
1462
51,
1451
141,
1310
57
1296
84
1246
82.
1447
4,
dP
sh
1320
2.
P
1304
2
901
33,
sh
22,
b
“6
797
27.
b
775
35
“7’ 1218
3.
dP
1110
6.
p
ilon
3.
1016
13.
P
996
25.
p
980
100.
p
911
8.
586
55
569
27,
558
35
548
45
See
“4’
“9
sh.p
coresponding
“24 “10
“10
“11
cyclobutane-dl? “11
“12
b.dP
“13
2.
“13’
“26
“14,
“28
dp “14
778
2.
dP
669
1,
P
“28
b “29
“29 23
“22
“23
“24 “8
683 667
’
“26 R27
826
arb
“5 “21
“6
0
0
21,
“5 “21
“22
57.
689
“11’
F.R.?
32
0
912
R14 I
+
“4, “20 P.R.?
Sh
33,
-1325
2v21 F.R.
2”lO’
2243
2178
“1R
“2
I
2197
“17
’
“2’
“15
“15 “30
sh
"30
footnotes
and
abbreviations
to
Table
I.
ds at -975 cm-‘, thus indicating that the 1006-cm-’ band for this mode may not be appropriate. The experimental spectra, however, do not reveal the presence of any band around 975 cm-’ that can reliably be assigned to u4 of ds. In the case of B, species, our calculations support the recent assignment of Aleksanyan and Antipov (12) for the u9 and vIo modes of & to the solid-state Raman bands at 1234 and 1139 cm-‘, respectively. The calculated frequencies (1234 and 1124 cm-‘, respectively) both evidence wag and twist contributions; v9 has a larger contribution from the twist whereas ulo from the wag. A total agreement between our and BFP’s results is obtained for B2 species, and we confirm that the 892-cm-’ band is appropriate for v15of dc,.
VIBRATIONAL
SPECTRA
OF CYCLOBLJTANEd2
51
TABLE III Force Constants for Cyclobutane Ref. (14)=
This work
Ref. (14)
This work
F2,1
0.0531
0.1060
F3,l
0.1365
0.1023
F5,2
-0.0093
-
F5,5
4.8000
4.7513 O.Olllb
Ref. (14)
F1.1
3.8998
P5,l
0.0352
F6.1
0.0702
0.1574
F6.2
-0.0183
-
F6,5
0.0475
F6,6
4.8109
4.7296
F7,5
-0.0098
-
F7.6
0.0148
F8.6
0.0029
-
F9,3
0.0074
-
F9,6
0.0009
F10,6
0.0065
-
F 13,5
-0.0147
-0.0012b
F13,6
F13,13
1.4859
1.4827
F14,l
-0.1639
-0.2113
F14,5
0.0917
0.0726
F14,6
0.1016
0.1152
F14,8
-0.0008
Fl4,9
-0.0064
F14
13
0.0099
FM,5
0.0916
F18.8
-
-
0.1070
F16,14
3.8513
0.1021
F14,14
0.0880
-0.0073
-
-0.0163
F18,6
-0.0713
F18,9
-0.0022
-0.0104
F14,2
0.0258
0.0744
F14,7
-0.0017
-
F 14,10
-0.0039
-
F15,14
0.0050
-
F 18,2
-0.0183
-
F16,7
0.0185
-
-
F18 1o -0.0144
-
-
F 18,15
-
0.6938 -0.0395
F18,13
0.0779
F18,14
0.0061
FM,16
0.0058
-
F18,18
0.4316
0.4612
Fig
F20
0.0135
-
F22,l
0.2016
0.2279
F22.2
18
0.0742
F18,l
-
-0.0814
-
0.7110
This work
-0.0044
18
0.0122
-
0.0075
-
F22,7
0.0094
-
F22.6
0.0006
F22,1g
0.0122
-
F22,22
0.6957
0.6793
F 23,22
-0.0203
F24,22
-0.0163
'26.1
0.0745
0.0347
F26,2
-0.0064
F26,8
-0.0178
-
F 26,15
-0.0106
F26,22
0.0050
-
F26,23
-0.0208
-0.0453
F26,7
0.0213
F26,19
0.0518
-0.0189 0.0673
-
F22
15 -0.0035
-0.0397 -
'26.24
0.0078
-
F26,26
0.7158
0.7145
F 27,26
-0.0738
-0.0572
F29,26
-0.0150
-
F30,l
0.0236
0.0172
F30,5
0.0114
0.0106
F30,6
-0.0190
-0.0475
14 -0.0250
0.0103
F30,18
0.0804
0.0530
F30.30
0.1084
0.1532
units:
stretch-stretch
mdyn
A/ead2.
a -Ab
initio
b
In the
force
final
field
PjO
in mdyn/A,
after
refinements,
stretch-bend
scaling
these
with
force
scale
constants
in rdyn/rad
factors were
Set
kept
and bend-bend
II of Ref.
in
(14).
fixed.
Miller et al. (II) assigned 1042 and 1054 cm-‘, respectively, to u9 (I?,) and v20 (E) of ds, whereas BFP reversed this. Furthermore, BFP proposed that v19(E) of d8 could be either the 1112- or 1153-cm-’ band, instead of the 1065cm-’ band as originally assigned by Miller et al. Our calculations support the assignment of Miller et al. for all the three modes. The two A2 vibrations (IJ, and v*) should be both ir and Raman inactive under D2d symmetry. The frequencies of these modes calculated by BFP for d,, are - 1250 and -950 cm-‘, whereas for ds they are - 1005 and -675 cm-‘. Before the ab initio results (14) were published, in solid-state experiments, Castellucci et al. (10) assigned the weak Raman bands at 1258 and 1228 cm-‘, respectively, to v7 and v8 of 4 based on the early normal coordinate results (13). The BWs results, however,
52
ANNAMALAI AND KEIDERLING TABLE IV Assigned and Calculated Frequencies (cm-‘) for Cyclobutane-d,
Ref. (111
This work stretch
asym.
2974‘
2962
2965
CH~
2
2905
2905
2900
CR2 sym.
A1 1
A2
This work=
Ref. (14)
descriptionb
Approx.
ca1c.
Assignment
NO.
stretch
3
1469
1468(1518)
1469
1468
Scissor
4
737
1153
1153
1149
Rock
5
1005
1005
1005
1004
Ring
stretch
6
199
199
199
199
Ring
pucker
7d
1255e
125EE
1259
8d
951*
943g
939
wag
+ twist
Twist
+ wag + wag + ring
g 10
1225h
1204e
1234g
1234
Twist
1234
1153
11399
1124
wag + twist
11
926
926
926
932
R* 12
Sl
E
Ring
2987
2987
2972
CR2 asym.
29451
2915i
2908
CH2 sym.
14
1454
1454
1454
Scissor
892
896
Ring
626
626
Rock + ring
1454
stretch stretch
15
9997
16
626
17
2965
2968
2972
CH~ asym.
18
2887
288Oj
2901
CH2 sym.
19
1452
1452
1452
1449
scissor
20
1260
1260
1260
1256
Twist
21
1224
1224
1224
1220
Wag + twist
22
901
901
901
RY4
Ring
23
749
749
749
750
Rock + twist
.a All
frequencies
refinement
energy
from
the
Ref.
we use
this
column
diagonal
distribution
were
used
2962 cm-’
were
symmetry
are
Eat
are
this
for
was
obtained
the
and solid
phase
using to
that
in Ref.
110).
g Assignment
similar
to
that
in Ref.
(12).
b Calculated
from
force
Ref.
force
field
that
present
work.
for
D2d symmetry
of
lowering
of
Set
II
in
Ref.
(14).
rule.
2945 and
-1 2915 cm
are
gas
phase
(11)
is
believed
ir
values
Ill).
2887 cm-’
Though field
scalefactors
product
frequencies in
j The frequency
influenced
stretch
(10.12).
similar
the
+ ring
potential
the
because
values
in error.
stretch stretch
+ wag + ring
by considering
Raman inactive
Assignment
the
bend
mode.
ir
’
reported
our
with
In
pairs.
e Calculated
i Roth
in
+ rock
10%.
resorlance
both
ohserved
constants
than
frequency
2962 cm-l
d A2 vibrations
force
greater
this
(11).
2991 and
but
under
bend
calculations.
b Inferred
= In
626
listed
we considered
calculations,
by strong
Fermi
in
Ref.
the
28SO cm-’
we believe resonance
that
band
for
this
band
interactions.
stretch
stretch
13
892(868)
(breath) + rock
See
to
be
v18 in is text.
stretch stretch
53
VIBRATIONAL SPECTRA OF CYCLOBUTANEd2 TABLE V Assigned and Calculated Frequencies (cm-‘) for Cyclobutaneds Assignment
NO. Ref. (11)
Al
B2
2210
2213=
2213
CD2
asym.
2120
2114’
2117
CD2
sym.
3
1169
1169
1166
1169 1006
+
ring
5
884
884
8R4
876
Ring
stretch
157
157
157
156
Ring
pucker
limd
’
9
1042
10
925
a47d
11
748
748
12
2243
1084
1084
15
1036
1042
Ring
stretch
Twist
748
753
wag
+
2205
CD2
asym.
stretch
212se
2121
CD2
sym.
stretch
lOR4
1084
Scissor
ring
775
775
771
Ring
bend
480
480
483
Rock
+
stretch
+
17
2234E
2224f
2212
CD~
asym.
1s
2129
21094
2108
CD2
sym.
19
1065
1112(1153?)
1065
1071
Wag
+
20
1054
1042(1054)
1054
1058
Scissor
21
944
944
944
945
Twist
22
730
730
730
734
Ring
stretch
23
556
556
55R
553
Rock
+
See
corresponding
d
Calculated
e
This
f
Gas
phase
Raman
L7 Gas
phase
ir
band
values values
band
in
footnotes of
was
Ref.
the using
scale
assigned
in
frequencies
frequency
to
resonance
Table
ill)
reported
previously
bend
stretch stretch
ring
+
stretch
rock +
wag
twist
IV.
pairs
considered
factors
Ref.
rock
ring
480
Average
scissor
+ wag
830
16
c
+
rock
Twist
672
1054(1042)
(breath) +
wag
1002
674d
stretch
Rock
6
14
alb
stretch stretch
Scissor
978
13
E
descriptionb
This work
1
8
Bl
This work’
2
4
A2
rlpprox.
CE?lC.
Ref. (14)
Set to
II
in in
Ref.
Ref.
(111.
(14).
~1~.
in assigned
Ref.
(11). to
a
combination
(111.
led Aleksanyan and Antipov (12) to assign the solid-phase Raman band at -940 cm-’ to v8 of &. These authors also predicted that the v7 mode to have a frequency of - 1340 cm-’ based on an analysis of their cyclobutane-dl spectra. However, 1258 cm-’ for v7 and 943 cm-’ (II) for v8 are well fit by our calculations. In Ref. (12), the solid-phase Raman bands at 1252 and 1256 cm-’ were interpreted as the two components of v20 E mode arising because of splitting due to lowering of symmetry. The present and previous calculations (14) would seem to indicate that the higher-frequency band, at least in part, belongs to u7 A2 vibration of do. In Ref. (ZO), the A2 vibrations of ds were assigned to weak Raman bands at 10 17 and 891 cm-’ observed for the solid phase. While the former is close to the calculated value of - 1005 cm-‘, the latter is very different from our predicted -675 cm-‘. Though
54
ANNAMALAI AND KEIDERLING TABLE VI Observed and Calculated Frequencies (cm-‘) for cisCyclobutane- 1.2-dz ObS .
NO.
2972
CH2 asp.
(2961)
2969
c!i2
asym.
(29401
2944
C-H
stetch
2932
C-H
stretch sym.
stretch
sym.
stretch
I2978
8
)b
descriptiona
Approx.
C?llC.
Stretch
stretch (axial) (equatorial)
(2911lC
2904
(2882)
2900
CH2 CH~
(2179)
2168
C-D
stretch
(axial)
(2140)'
2153
C-D
stretch
(equatorial)
9
1462
1459
CH2
scissor
(in-phase)
10
1451
1451
CH2
scissor
(out-of-phase)
11
1326
1318
CHD
scissor
(in-phase)
12
1310
1312
CHD
scissor
(out-of-phase)
13
1262
1256
wag
+ twist
14
1246
1246
Wag
+ twist
15
1221=
1227
Twist
1205
Wag
+ twist
+ rock
+ scissor
1177=
1179
Wag
+ twist
+ ring
stretch stretch
16 17
+ ring
stretch
18
1107
1104
Wag
+ twist
+ ring
19
1095
1080
Rock
+ wag
+ scissor
989
Ring
stretch
(breath)
20
989C
21
+ scissor
+ wag
983
Ring
stretch
+ twist
933=
931
Ring
stretch
+ twist
+ wag
23
901
901
Ring
stretch
+ twist
+ rock
24
850
855
Ring
bend
25
837
839
Ring
stretch
+ wag
+ rock
26
785
785
Twist
+ wag
+ rock
+ ring
27
676
677
Rock
28
665
663
Rock
+ twist
29
563
565
Rock
+ ring
bend
187
Ring
pucker
+ rock
30 .a Inferred tion
from
greater
b Frequencies
the diagonal than
within
+ twist
force
constants
with
+ ring
stretch
+ wag
+ ring
+ ring
stretch
+ rock
+ twist
22
+ rock
+ ring
+ wag
stretch
stretch
stretch
potential
energy
distribu-
10%. the parentheses
were
not
fit
in the
force
field
calcula-
tions. c Raman
frequencies
far
the
liquid
phase.
there is no evidence for the presence of a 1017-cm-’ band in the Raman spectra measured by Miller et al., weak ir bands do appear around 1025 cm-’ for the solid phase of ds. One of these bands may correspond to the v7 mode of d8. (We have not included this frequency in force field calculations.) The CH and CD stretching regions of the spectra of d,, and d8 are less understood because of their complexity due to overlapping and Fermi resonance of several fundamental and combination bands (II). We believe that the assignments given in Ref. (11) are the best available so far for these regions, but no calculations had previously been carried out using these assignments. Our calculations necessitated some modifications in these assignments. In general, the frequencies assigned by Miller et al. (II) for v13 of 6, and v,~, v17, and v18 of d8 are found to be too high. The details about our revised assignments are given in Tables IV and V. This does
VIBRATIONAL SPECTRA OF CYCLOBUTANE-d2
55
TABLE VII Observed and Calculated Frequencies (cm-‘) for the Axial Form of trans-Cyclobutane-1 ,2-dz ObS.
NO. A
1
(297t))b
2969
2
(2929lC
2927
CH2 asym. C-H
stretch
sym.
stretch
3
(28821
2900
CH2
sym.
stretch
4
12178)
2173
C-D
sym.
stretch
5
(1462)
1459
CH2
scissor
6
132oC
1327
CHD
scissor
7
1246
1251
Wag
+
twist
+
ring
stretch
8
1218C
1220
Wag
+
twist
+
ring
stretch
9
1110=
1124
wag
+
twist
1080
Rock
+
11
1016C
1023
Ring
stretch
+
12
98OC
987
Ring
stretch
(breath)
stretch
10
(Iloo)=
ring
13
(912)
913
Ring
14
814
807
Ring
stretch
15
667
668
Rock
+
187
Ring
pucker
2972
CH2
asym.
2936
C-H
asym.
2904
CH2
sym.
16
R
description”
Approx.
ca1c.
17
129781
1.4 19
(2913)’
20
C-D
asym.
CH2
scissor
22
1296
1295
CHD
scissor
1257
Wag
+
1246
Wag
+
1131
Twist
901
26 27
+
rock
stretch
twist twist
+
ring
+
+
scissor
wag
901
Ring
stretch
885
Ring
bend
+ f
773
Twist
683
680
Rock
+
twist
+
30
548
551
Rock
+
ring
bend
corresponding
footnotes
to
wag
Table
+
ring
+ wag
stretch +
rock
rock
775
+
stretch
twist
29
See
wag
+ wag
28
“b’c
+
stretch
1451
25
rock
stretch
2162
1246
+
stretch
1451
24
twist
twist
21
23
stretch
+
rock
+
ring
stretch
wag
VI.
not, however, mean that the problem of assigning these modes is now settled, since there can certainly be alternate assignments. In Table 3 of Ref. (12) a frequency of 2887 cm-’ is listed for VI8 of &. This value seems to be in error, since there is no observed band at this position in the reported spectra and since there was no mention of any other alternative consideration in obtaining this value. However, there are two bands close to this value at 2877 and 2880 cm-’ in the gas-phase ir spectrum. The Raman spectra have a band at 2878 cm-’ for the gas and at 2870 cm-’ for the liquid. We considered the 2880cm-’ band for vi8 but obtained a poor fit (Table IV) with a calculated frequency of 2901 cm-‘. cis- and tram-d* species also exhibit an ir band at 2882 cm-’ for the gas phase and a Raman band at 2871 cm-’ for the liquid phase (Tables I and II). As in the case of d,,, the closest of our calculated frequencies for the dz species is 2900 cm-‘. These findings suggest that the origin of the 2880-cm-i band in d,,, cisdZ, and trans-dz may be the same. AI1 three species have scissoring modes at - 1450 cm-‘, corresponding to vi9 (E) in 4, vIo in ci+d2, and v2, (B) in tram-d2. The first
56
ANNAMALAI AND KEIDERLING TABLE VIII Observed and Calculated Frequencies (cm-‘) for the Equatorial Form of truns-Cyclobutane- 1,2-d* Obs.
NO.
A
Approx.
ca1c.
description”
1
(297n)b
2968
CH2 asym.
2
(2954)
2945
C-H
3
(2882)
2900
CH2 sym.
stretch
2149
C-D
sym.
stretch
02
scissor
4
Stretch
stretch
syn.
5
(1462)
1459
6
1310
1310
CHD scissol:
1234
Twist
i2iac
1216
wag
+ twist
+ rock
1206
Wag + twist
+ ring
1llOC
1124
Rock + ring
stretch
7
a 9 10
9aoc
11 12
+ wag + ring
982
Ring
stretch
(breath)
968
Ring
stretch
+ rock
stretch
13
(9121
914
Ring
14
797
795
Wag + ring
15
1667)
669
Rock + twist
186
Ring
16 B 17
pucker
2912
CH2 asym.
stretch
2944
C-H asym.
stretch
19
(2913)C
2905
CH2 sym.
2158
C-D asym.
1451
1451
CH2 scissor
22
1310
1309
CHD scissor
23
1246
1252
Wag + twist
24
121ac
1214
Wag + twist
1060
Wag + ring
27
923
Twist
a69
Rock + ring
stretch
+ scissor stretch
+ wsg
+ twist
+ ring bend
stretch + twist
2R
797
798
Ring
stretch
+ ring
bend
29
683
682
Rock + twist
+ ring
bend
30
586
586
Rock + ring
s’b’c
see
corresponding
footnotes
+ twist
stretch
stretch
21
912
+ rock
+ wag
+ rock
129541
25
+ twist
+ ring
(2978)
26
stretch
stretch
18 20
stretch
to Table
+ ring + twist
stretch + wag
bend “I.
overtone of these modes thus lies in the vicinity of 2900 cm-‘. We believe that the Fermi resonance of these overtones with the fundamentals calculated at about 2900 cm-’ could be the main source of the 2880-cm-’ band in all three isotopomers. cis and tram-Cyclobutane-d2
We believe that the assignments given in Table I and II for cis- and tram-d2 are quite reliable for frequencies below 1500 cm-‘, since they are fit extremely well in our calculations. However, the assignments for the CH and CD stretching spectral regions of cis- and trans-d2 must remain tentative for the same reasons as discussed for 4 and ds. The spectra in these regions are so complicated that no detailed attempt could be made to analyse them. For example, all Raman bands in these regions appear to be polarized. (This may be due to the crude nature of our Raman depolarization ratios.) We assigned the observed frequencies to the vibrational modes having closest calculated frequency values. But, due to the uncertainty in
VIBRATIONAL SPECTRA OF CYCLOBUTANE-&
57
the CH and CD stretching frequencies, we did not include them in our force field refinement calculations. The ir spectra of both cis- and truns-dZ have a Q branch at 1451 cm-‘. The corresponding Raman band is observed at 1447 cm-‘. For the tram isomer this band is depolarized, but for the cis isomer it is less certain. This band corresponds to CH2 scissoring B mode of both axial and equatorial forms of transd;!. For cisdZ this is assigned to the out-of-phase CH2 scissoring mode. The corresponding A modes of truns and in-phase mode of cis appear as shoulders in the ir spectra at 1462 cm-‘. The CHD scissoring modes appear between 1290 and 1330 cm-‘; our calculations predict that the A modes of trans and the in-phase mode of cis have higher frequencies than the corresponding B and out-of-phase modes, as in the case of CH2 scissors. The ring-breathing modes appear as characteristic polarized Raman bands at 989 cm-’ for cis-dz and 980 cm-’ for tram-d2. These are the strongest Raman bands in these spectra. The calculated frequencies agree well with these values but have a difference of 5 cm-’ between the axial and equatorial forms of the trans isomer. The Raman spectrum of this isomer has a polarized band at 996 cm-’ as a shoulder of the 980-cm-’ band. This may be due to the ring breathing of cyclobutanedi impurity. This value agrees with the frequencies, for C-D axial and C-D equatorial forms of cyclobutaned,, calculated using our final force field. The ir spectra of cyclobutane-d, reported in Ref. (12) show a weak band at about this position. However, this impurity band in the cis spectrum seems to be completely enveloped in the 989~cm-’ band. The polarized Raman band at 962 cm-’ in the cis spectrum may correspond to the ring breathing mode of the dd3 impurity present in this sample as evidenced by the mass spectral analysis (27). Both the ir and Raman spectra of the truns isomer have a band at -912 cm-‘. The Raman band is clearly depolarized and should, at least in part, belong to a B mode. This is assigned to vz6 B mode of the equatorial form of this isomer, which has a calculated frequency of 923 cm -I. The calculations also indicate that both the axial and equatorial forms have a ring-stretching A mode (vi3) at -912 cm-‘. Hence, the observed band may also belong to this mode. However, in our force field refinement calculations we used the experimental 912~cm-’ band only for the v26 B mode of the equatorial form. Cyclobutane-4 and -dl are known to exhibit some “hot band”-like features in the region 680-580 cm-’ (7, 8). We have made similar observations for cis and truns-cyclobutane-d2. Except for a very few modes like the CH2 and CHD scissoring, and ring breathing, our calculations indicate strong mixing of internal coordinates in the low-frequency modes. The C-H and C-D stretches mix among themselves in the usual manner. However, it is interesting to note the minimal mixing, predicted in our calculations, between the axial and equatorial C-H (or C-D) stretches corresponding to the -CHD- moieties in cis-dZ species (Table VI), though their calculated frequencies lie very close to each other. Force Field The final force field obtained from this work is reported in Table III. This force field was developed by taking advantage of both theory and experiment. To obtain
58
ANNAMALAI
AND
KEIDERLING
this force field we fit the vibrational frequencies of c&d2 and tram-d2 as well as those of & and d8 used in previous work (13, 14). As can be seen from Tables IV to VIII the force field reproduces the experimental frequencies very well. The final force constants do not seem to differ much from the ab initio scaled force constants. However, it is well known that even very small differences, particularly in the interaction force constants, can significantly alter the calculated frequencies. Recently, we demonstrated that this kind of alteration in the calculated frequencies can lead to great differences in the calculated VCD spectra for chiral tram-d2 using both the fixed partial charge and localized molecular orbital models (15, 16). While theory of VCD is still in a developing stage, these models appear to provide a reasonable description of hydrocarbon VCD. It should be noted that the final force field reported here explained the observed VCD better than any other force field considered in Ref. (15). Furthermore, it gave a satisfactory representation of the mid-ir (1500-900 cm-‘) VCD using no change in the parameterization (16). In some sense, these VCD calculations provide an additional level of test for the force field. Since VCD is dependent on the relative motion of atoms in a vibrational mode, its description is more sensitive to the detailed characteristics of the normal mode than are the frequencies. In the future, it may prove that such optical activity measurements will provide a more constrained test of calculated force fields than the traditionally used isotopic frequencies. Additionally, we have shown (15) that frequency overlap can dramatically affect the calculated VCD. This may also provide a means of relooking at crowded spectral regions in future studies. All diagonal constants in the final force field have standard deviations below 2% except for the ring-puckering constant, whose deviation is - 15%. The interaction constants not involving the C-H stretching or ring-puckering coordinates indicate deviations within 25%. But, it is found that the interaction constants involving the C-H or ring-puckering coordinates show very large errors. The errors are one to five times the corresponding calculated force constant values if one such coordinate is involved, but are much larger for F30,5 and F30,6. These must be regarded as undetermined. These large deviations are understandable for the following reasons. The C-H stretching and ring-puckering modes are highly anharmonic and are poorly represented in a harmonic approximation. Furthermore, in refining the force field, only a limited number of C-H stretching and ring-puckering frequencies could be used. Moreover, as indicated before, the C-H stretching frequencies used may have large errors due to the complexity of this spectral region. Our primary goal was to obtain a force field which would yield a good frequency fit as well as explain the experimental VCD satisfactorily. The force field reported here satisfies these requirements. CONCLUSIONS
In summary, we have measured the ir and Raman spectra of cis- and transcyclobutane-1,2-d*, and have assigned the bands. We believe that the assignments for the bands below 1500 cm-’ are quite reasonable. We have demonstrated that the ab initio scaling approach of BFP, combined with the conventional force field
VIBRATIONAL
SPECTRA
59
OF CYCLOBUTANE-d2
refinement procedure, fits the experimental frequencies very well and is quite useful whenever such a high-quality frequency fit is very important, as was the case of our VCD studies (IS, 16). This method takes advantage of both theory and experiment, and is justified in terms of obtaining the initial and final estimates for the force constants. ACKNOWLEDGMENTS We gratefully acknowledge the National Science Foundation (CHEI l-04497) and the National Institutes of Health (GM-30147) for support of this research. We thank Professor Larry Abels for assistance in
obtaining the Raman spectra, the Nicolet Corporation for the loan of an FT-IR spectrometer, and Professor J. S. Chickos for kindly supplying the cyclobutane-d, samples. RECEIVED:
July
18,
1984 REFERENCES
1. P. WILSON, J. Chem. Phys. 11, 369-378 (1943). 2. G. W. RATHJENS,JR., N. K. FREEMAN,W. D. GWINN, AND K. S. PITZER,J. Amer. Chem. SOC.75, 5634-5642 (1953). 3. D. G. REA, Ph.D. Thesis, Massachusetts Institute of Technology, 1954. 4. D. A. Dows AND N. RICH, J. Chem. Phys. 47, 333-334 (1967). 5. T. UEDA AND T. SHIMANOUCHI,J. Chem. Phys. 49, 470-471 (1968). 6. V. T. ALEKSANYAN,G. M. KUZYANTS, M. Yu. LLJKINA,S. V. ZOTOVA, AND E. I. VOSTOKAVA,J. Struct. Chem. (USSR) 9, 123-125 (1968). 7. J. M. R. STONEAND I. M. MILLS, Mol. Phys. 18, 631-652 (1970). 8. V. T. ALEKSANYAN,Opt. Spectrosc. 29, 574-575 (1970). 9. F. A. MILLER AND R. J. CAPWELL,Speetrochim. Acta A 27, 947-956 (1971). 10. E. CASTELLUCCI,M. G. MIGLIORINI,AND P. MANZELLI, Acta Crystallogr., Sect. A 28, 432-440 (1972). F. A. MILLER, R. J. CAPWELL, R. C. LORD, AND D. G. REA, Spectrochim. (1972). 12. V. T. ALEKSANYANAND B. G. ANTIPOV, J. Mol. Struct. 89, 15-24 (1982). 13. R. C. LORD AND I. NAKAGAWA,J. Chem. Phys. 39, 2951-2965 (1963). 14. G. BANHEGYI,G. FCCARASI,AND P. PULAY, J. Mol. Struct. 89, l-13 (1982). II.
Acta A 28, 603-618
15. A. ANNAMALAI, T. A. KEIDERLING,AND J. S. CHICKOS, J. Amer. Chem. Sot. 106, 6254-6262 ( 1984). 16. A. ANNAMALAI,T. A. KEIDERLING,AND J. S. CHICKOS,J. Amer. Chem. Sot., in press. 17. J. S. CHICKOS,private communication. 18. A. ALMENNIGEN,0. BASTIANSEN,AND P. N. SKANCKE, Acta Chem. Stand. 15, 7 I I-712 (I 961). 19. S. MEIBOOMAND L. C. SNYDER, J. Amer. Chem. Sot. 89, 1038-1039 (1967). 20. S. MEIBOOMAND L. C. SNYDER,J. Chem. Phys. 52, 3857-3863 (1970). 21. F. TAKABAYOSHI,H. KAMBARA, AND K. KUCHITSU, in “Proceedings, 7th Austin Symposium on
Gas Phase Molecular Structure,” Austin, Texas, March I, 1978; paper WA6. 22. D. CREMER,J. Amer. Chem. Sot. 99, 1307-1309 (1977). 23. P. N. SKANCKE, G. FOGARASI,AND J. E. BOGGS, J. Mol. Struct. 62, 259-273 (1980). 24. J. H. SCHACHTSCHNEIDER, unpublished results. 2s. D. PAPOUSEK,S. TOMAN, AND J. PL~VA,J. Mol. Spectrosc.
15, 502-505
(1965).
OF MOLECULAR
SPECTROSCOPY
109,46-59 (1985)
Vibrational Spectra and Normal Coordinate Calculations for cis- and trans-1,2-Dideuteriocyclobutanes A. ANNAMALAIAND T. A. KEIDERLING Deparlmenl of Chemistry. University of Iliinoir at Chicago, Box 4348, Chicago, INinois 60680 Gas-phase FT-IR spectra and liquid-phase Raman spectra have been measured for cis- and Irans-1,2dideuteriocyclobutanes. The bands were assigned by using the results of normal coordinate calculations and Raman depolarization measurements. The initial force constants considered were based on the ab initio scaled force field of Banhegyi et al. [J. Mol. Swucr. 89, l-1 3 (1982)]; they were then optimized using vibrational frequencies of cycIobutane&, and d,, and cis- and trans-cyclobutane- I ,2-d*. The final force field and approximate description of normal modes are reported, and assignment of cyclobutane vibrational spectra is discussed. 0 1985 Academic Press, Inc. INTRODUCTION
In the course of studying the vibrational circular dichroism (VCD) of trans-1,2dideuteriocyclobutane, it became necessary to reinvestigate the normal modes for cyclobutane and its deuterated isotopomers. Many previous investigations have dealt with the vibrational spectra (l-14) and normal modes (13, 14) of cyclobutane with the aim of obtaining satisfactory assignments for this molecule. The most extensive study is by Miller et al. (II), which reports ir and Raman spectra of cyclobutane-& and -d8 for gaseous, liquid, and solid states, and gives assignments that also take into account the earlier work (I-10, 13). Earlier, Lord and Nakagawa (13) developed a force field for cyclobutane, using the frequencies of -d,, and -d8 species, based on the assumption that the molecule behaved as though it had a planar ring. Recently, Banhegyi, Fogarasi, and Pulay (BFP) (14) performed ab initio force field calculations and suggested some modifications to the assignments of Miller et al. (Z1). Since, the force constants calculated at SCF level are generally overestimated, BFP used a systematic method of scaling the ab initio force field. The scale factors were then optimized to fit the experimental frequencies. This approach is quite useful for assignment purposes, particularly when the number of experimental frequencies available is limited, since it uses only a small number of variables in fitting the frequencies. However, since the off-diagonal and diagonal scale factors are not independent, the force field is constrained in such a way that some of the calculated frequencies deviate greatly from the corresponding experimental values. Furthermore, for cyclobutane, BFP kept the scale factors corresponding to the CH stretching and ring-puckering coordinates fixed. This choice was due to both the large anharmonicities in these modes and uncertainties in CH and CD stretching frequency assignments. OO22-2852/85 $3.00 Copyright Q 1985 by Academic Press. Inc. All rights of reproduction in any form reserved.
46
VIBRATIONAL
SPECTRA
OF CYCLOBUTANE-d2
47
During the course of our recent VCD study of [runs-cyclobutane-1,2-d2 (Z5,16), we realized the need for further improvements in the force field of cyclobutane to better understand the experimental results, particularly including the CH and CD stretches. We have measured vapor-phase ir and liquid-phase Raman spectra for cis- and truns-cyclobutane- 1,2-d2. Using these data along with those previously reported for cyclobutane-4 and -dg (Z&12), we have refined the force field in a conventional manner. For these calculations, the initial force field was set up by considering the most significant force constants of the BFP force field (14). Our final force field fits the experimental frequencies very well, and has been found to explain the VCD spectrum of trans-cyclobutane-1,2-d* satisfactorily in both the CH and CD stretching (15) as well as in the mid-ir (16) regions. EXPERIMENTAL
DETAILS
Samples of tram- and cis-cyclobutane-1,2-d2 were kindly supplied to us by Dr. J. S. Chickos. Mass spectral measurements indicated that truns sample had about 9% -dl impurity, whereas the cis sample about 10% -d3, 11% -d, , and 1% -6 impurities (17). These samples were used as such in our studies. Vapor-phase ir spectra of cis- and trans-cyclobutane-1,2-dz were measured in the range 4000-500 cm-’ using a Nicolet MX-5 FT-IR instrument with a resolution of 4 cm-‘. The gas cell used had NaCl windows and a pathlength of 7 cm. Measurements were carried out with different amounts of samples for the ranges 4000-1400 and 1500-500 cm-‘. However, exact gas pressures could not be monitored. Raman spectra were measured, with a resolution of 1 cm-‘, on liquid samples held in sealed ampoules at room temperature, using an instrument constructed in the UK physics department. The excitation source was the 5145-b; line of an argon ion laser. The depolarization ratios obtained are somewhat crude due to instrumental limitations. NORMAL
COORDINATE
ANALYSIS
The geometry of the cyclobutane molecule is well established by both experiment (18-21) and theory (22, 23) as folded with D2d symmetry. A relatively low barrier (9) makes the ring very flexible so that conversion from one puckered conformation to the other is readily accomplished at room temperature. Thus, for trans-cyclobutane1,2-d2 (C, symmetry), two distinct conformers result. In one the deuterium atoms occupy the axial positions, in the other the equatorial positions. Both these are expected to contribute equally to the measured vibrational spectra, and hence were considered in our normal coordinate analysis. However, in the case of cis isomer (C, symmetry), ring puckering does not alter the conformation. We carried out the force field calculations in a conventional manner, i.e., the diagonal and off-diagonal force constants were refined independently. The initial force field was set up by transferring the most significant BFP force constants [from scale factors Set II of Ref. (Z4)]. They include, of course, all diagonal constants; but for interaction force constants, only those having magnitudes greater than 0.04 mdyn/A for stretch-stretch, 0.03 mdyn/rad for stretch-bend and 0.02 mdyn A/t-ad2 for bend-bend were retained. Additionally, all the force constants involving the ring
48
ANNAMALAI
AND
KEIDERLING
puckering coordinate were included. Of 73 possible independent force constants for cyclobutane with D2d symmetry, 35 were considered for the force field. This discrimination, of course, is a constraint on the force field but is very commonly employed and, if properly set up, is not known to affect the frequency fit severely. In the present study, availability of the BFP force field provides an optimal way of setting up the initial force field. The set of internal coordinates considered in the present study is the same as that of Ref. (14). However, to calculate the G matrix elements, we used the ab initio geometry of Cremer (22), which was calculated using a much larger basis set than that used by BFP (14). Generally, small deviations of bond lengths from experimental values, as are usually the case with ab initio calculations, have little effect on the calculated force fields; hence, we did not consider any correction terms. AI1 calculations were performed using Schachtschneider’s GMAT and FPERT programs (24). First, considering the vibrational frequencies of cyclobutane-4 and -ds, and different possible assignments (II, 14), we made several trial refinement calculations and examined the frequency fits. Using the force fields obtained, frequencies for cisand trans-cyclobutane- 1,2-dz were calculated. These frequencies were used along with the Raman depolarization results in assigning the bands for these isomers. The assigned frequencies were then considered for refining the force field further. For cyclobutane-d,,, we have included frequencies corresponding to the A2 vibrations from the lower symmetry solid state (10, 12) in our calculations, though under DIG symmetry these vibrations are both ir and Raman inactive. We faced very little problem with convergence of the force field and in fitting the frequencies, particularly with the use of damped least-squares procedure (25). However, the force constants F6,5 and F13,5were found to be less sensitive to the frequency fit and they showed a great tendency to deviate from the ab initio values. Hence, in the final calculations, these force constants were kept fixed to some intermediate values, and the remaining 33 force constants were refined using 88 frequencies. RESULTS
AND
DISCUSSION
In this section various isotopic species of cyclobutane under consideration wilI be referred to as 6, ds, ciS-dZ, and trans-dz for the sake of brevity. The ir and Raman frequencies and relative peak heights for cis-dz and tram-d2 are listed in Tables I and II, respectively. In Table III are listed the BFP and our final force fields. The calculated and observed frequencies for different isotopic species of cyclobutane are given in Tables IV to VIII, along with the calculated vibrational descriptions.
Cyclobutane-do and -da As seen from Tables IV and V, our calculations reproduce the experimental frequencies quite satisfactorily for 4 and da and, in general, the deviations are less than those obtained in the scaling approach (14). Though vibrational spectra of these species had been studied extensively before, some points regarding the assignments deserve comment. Between the two alternative frequencies suggested
49
VIBRATIONAL SPECTRA OF CYCLOBUTANEdz TABLE I Infrared and Raman Spectra of cis-Cyclobutane- 1,2-d* Infrared Preq.
Assignment
Raman (Liquid)
(Gas) 1nt.”
fan-l) 2978
4400,
cl
2961
3400,
b
2940
2000,
Sh
2882
830.
b
2954
61
2911
19
2871
27
“2 “3
0
510.
1nt.
“1
2218 2199
(cm -11
Freq.
“b
2240
3
2218
16
2196
15
2173
16
2140
2
1448
5
“5’
y17 + “20’
2179
1462
53.
1451
141. 121.
1262
60,
sh
1246
83,
Q
4.
1308
0
9,
“10 “11
P
“12 “13
“b
“14
1221
3
1177
2.
P
“17
1104
3.
P
“10
P
“19 1
“15
1107
7
1095
11.
Q
1097
3,
7.
b
989
100,
P
962
7,
P
sh
933
9,
dp
0
901
4
835
2.
7R5
2
671
1.
998 990 I
8,
942 914
35
901
43,
850
43
837
41
785
22,
676
22
665
24
584
20
571
25
563
60
548
11
sh-shoulder,
peak
pL-eSS”re.
For
correspond
to
b Relative
peak its
P
“25 “26
dp
1. P
dp-depolarized.
“29 ?
p-polarized.
O-O branch,
resonance.
(abaorbances,
frequencies
with
should
0 branch,
depend the
upon gas
listed
values
0 branch.
heights
plane
“23 “24
568
heights
the
“22 7
“28 7
P.R.-Fermi
v-very,
a Relative
Q
“20 cyclobutawd3
“27
b-broad,
Abbreviations:
“7’ “4 P.R.?
“9
1314
64
1310
-1165
i
eh 0
1326
dent
10
2”lR. 2” 19’
2187
having
2”
“6’ F.R.
of
corresponding polarization
to parallel
the
scattered to
that
radiation of
the
inci-
light.
by BFP (14) for Al scissoring of d,, (v~), 1468 cm-’ fits better in our calculations. This assignment is in accordance with Ref. (II). BFP assigned the 1153- and 1006cm-’ bands, respectively, to & and ds A, rocking modes (Q). We are able to fit the 1153-cm-’ band very well. But, our calculations consistently place the u4 mode for
50
ANNAMALAI AND KEIDERLING TABLE II
I .2-d*
Infrared and Raman Spectra of fran.KyclobutaneInfrared Freq.
Raman
(Gas)
(‘nl-1l
Freq.
1nt.a
2978
4200,
0
2958
3400,
b
2882
810,
0
Assignment
(Liquid) (cm-l)
1nt.b
2954
64
2929
32
2913
26
2871
35
Axial form
-
;z;;torial
“1’ “17
“I
“19
“19 “3’
2”21 F.R.
“3,
2260 “8
2223 630.
b
2194
520,
b
2181
1462
51,
1451
141,
1310
57
1296
84
1246
82.
1447
4,
dP
sh
1320
2.
P
1304
2
901
33,
sh
22,
b
“6
797
27.
b
775
35
“7’ 1218
3.
dP
1110
6.
p
ilon
3.
1016
13.
P
996
25.
p
980
100.
p
911
8.
586
55
569
27,
558
35
548
45
See
“4’
“9
sh.p
coresponding
“24 “10
“10
“11
cyclobutane-dl? “11
“12
b.dP
“13
2.
“13’
“26
“14,
“28
dp “14
778
2.
dP
669
1,
P
“28
b “29
“29 23
“22
“23
“24 “8
683 667
’
“26 R27
826
arb
“5 “21
“6
0
0
21,
“5 “21
“22
57.
689
“11’
F.R.?
32
0
912
R14 I
+
“4, “20 P.R.?
Sh
33,
-1325
2v21 F.R.
2”lO’
2243
2178
“1R
“2
I
2197
“17
’
“2’
“15
“15 “30
sh
"30
footnotes
and
abbreviations
to
Table
I.
ds at -975 cm-‘, thus indicating that the 1006-cm-’ band for this mode may not be appropriate. The experimental spectra, however, do not reveal the presence of any band around 975 cm-’ that can reliably be assigned to u4 of ds. In the case of B, species, our calculations support the recent assignment of Aleksanyan and Antipov (12) for the u9 and vIo modes of & to the solid-state Raman bands at 1234 and 1139 cm-‘, respectively. The calculated frequencies (1234 and 1124 cm-‘, respectively) both evidence wag and twist contributions; v9 has a larger contribution from the twist whereas ulo from the wag. A total agreement between our and BFP’s results is obtained for B2 species, and we confirm that the 892-cm-’ band is appropriate for v15of dc,.
VIBRATIONAL
SPECTRA
OF CYCLOBLJTANEd2
51
TABLE III Force Constants for Cyclobutane Ref. (14)=
This work
Ref. (14)
This work
F2,1
0.0531
0.1060
F3,l
0.1365
0.1023
F5,2
-0.0093
-
F5,5
4.8000
4.7513 O.Olllb
Ref. (14)
F1.1
3.8998
P5,l
0.0352
F6.1
0.0702
0.1574
F6.2
-0.0183
-
F6,5
0.0475
F6,6
4.8109
4.7296
F7,5
-0.0098
-
F7.6
0.0148
F8.6
0.0029
-
F9,3
0.0074
-
F9,6
0.0009
F10,6
0.0065
-
F 13,5
-0.0147
-0.0012b
F13,6
F13,13
1.4859
1.4827
F14,l
-0.1639
-0.2113
F14,5
0.0917
0.0726
F14,6
0.1016
0.1152
F14,8
-0.0008
Fl4,9
-0.0064
F14
13
0.0099
FM,5
0.0916
F18.8
-
-
0.1070
F16,14
3.8513
0.1021
F14,14
0.0880
-0.0073
-
-0.0163
F18,6
-0.0713
F18,9
-0.0022
-0.0104
F14,2
0.0258
0.0744
F14,7
-0.0017
-
F 14,10
-0.0039
-
F15,14
0.0050
-
F 18,2
-0.0183
-
F16,7
0.0185
-
-
F18 1o -0.0144
-
-
F 18,15
-
0.6938 -0.0395
F18,13
0.0779
F18,14
0.0061
FM,16
0.0058
-
F18,18
0.4316
0.4612
Fig
F20
0.0135
-
F22,l
0.2016
0.2279
F22.2
18
0.0742
F18,l
-
-0.0814
-
0.7110
This work
-0.0044
18
0.0122
-
0.0075
-
F22,7
0.0094
-
F22.6
0.0006
F22,1g
0.0122
-
F22,22
0.6957
0.6793
F 23,22
-0.0203
F24,22
-0.0163
'26.1
0.0745
0.0347
F26,2
-0.0064
F26,8
-0.0178
-
F 26,15
-0.0106
F26,22
0.0050
-
F26,23
-0.0208
-0.0453
F26,7
0.0213
F26,19
0.0518
-0.0189 0.0673
-
F22
15 -0.0035
-0.0397 -
'26.24
0.0078
-
F26,26
0.7158
0.7145
F 27,26
-0.0738
-0.0572
F29,26
-0.0150
-
F30,l
0.0236
0.0172
F30,5
0.0114
0.0106
F30,6
-0.0190
-0.0475
14 -0.0250
0.0103
F30,18
0.0804
0.0530
F30.30
0.1084
0.1532
units:
stretch-stretch
mdyn
A/ead2.
a -Ab
initio
b
In the
force
final
field
PjO
in mdyn/A,
after
refinements,
stretch-bend
scaling
these
with
force
scale
constants
in rdyn/rad
factors were
Set
kept
and bend-bend
II of Ref.
in
(14).
fixed.
Miller et al. (II) assigned 1042 and 1054 cm-‘, respectively, to u9 (I?,) and v20 (E) of ds, whereas BFP reversed this. Furthermore, BFP proposed that v19(E) of d8 could be either the 1112- or 1153-cm-’ band, instead of the 1065cm-’ band as originally assigned by Miller et al. Our calculations support the assignment of Miller et al. for all the three modes. The two A2 vibrations (IJ, and v*) should be both ir and Raman inactive under D2d symmetry. The frequencies of these modes calculated by BFP for d,, are - 1250 and -950 cm-‘, whereas for ds they are - 1005 and -675 cm-‘. Before the ab initio results (14) were published, in solid-state experiments, Castellucci et al. (10) assigned the weak Raman bands at 1258 and 1228 cm-‘, respectively, to v7 and v8 of 4 based on the early normal coordinate results (13). The BWs results, however,
52
ANNAMALAI AND KEIDERLING TABLE IV Assigned and Calculated Frequencies (cm-‘) for Cyclobutane-d,
Ref. (111
This work stretch
asym.
2974‘
2962
2965
CH~
2
2905
2905
2900
CR2 sym.
A1 1
A2
This work=
Ref. (14)
descriptionb
Approx.
ca1c.
Assignment
NO.
stretch
3
1469
1468(1518)
1469
1468
Scissor
4
737
1153
1153
1149
Rock
5
1005
1005
1005
1004
Ring
stretch
6
199
199
199
199
Ring
pucker
7d
1255e
125EE
1259
8d
951*
943g
939
wag
+ twist
Twist
+ wag + wag + ring
g 10
1225h
1204e
1234g
1234
Twist
1234
1153
11399
1124
wag + twist
11
926
926
926
932
R* 12
Sl
E
Ring
2987
2987
2972
CR2 asym.
29451
2915i
2908
CH2 sym.
14
1454
1454
1454
Scissor
892
896
Ring
626
626
Rock + ring
1454
stretch stretch
15
9997
16
626
17
2965
2968
2972
CH~ asym.
18
2887
288Oj
2901
CH2 sym.
19
1452
1452
1452
1449
scissor
20
1260
1260
1260
1256
Twist
21
1224
1224
1224
1220
Wag + twist
22
901
901
901
RY4
Ring
23
749
749
749
750
Rock + twist
.a All
frequencies
refinement
energy
from
the
Ref.
we use
this
column
diagonal
distribution
were
used
2962 cm-’
were
symmetry
are
Eat
are
this
for
was
obtained
the
and solid
phase
using to
that
in Ref.
110).
g Assignment
similar
to
that
in Ref.
(12).
b Calculated
from
force
Ref.
force
field
that
present
work.
for
D2d symmetry
of
lowering
of
Set
II
in
Ref.
(14).
rule.
2945 and
-1 2915 cm
are
gas
phase
(11)
is
believed
ir
values
Ill).
2887 cm-’
Though field
scalefactors
product
frequencies in
j The frequency
influenced
stretch
(10.12).
similar
the
+ ring
potential
the
because
values
in error.
stretch stretch
+ wag + ring
by considering
Raman inactive
Assignment
the
bend
mode.
ir
’
reported
our
with
In
pairs.
e Calculated
i Roth
in
+ rock
10%.
resorlance
both
ohserved
constants
than
frequency
2962 cm-l
d A2 vibrations
force
greater
this
(11).
2991 and
but
under
bend
calculations.
b Inferred
= In
626
listed
we considered
calculations,
by strong
Fermi
in
Ref.
the
28SO cm-’
we believe resonance
that
band
for
this
band
interactions.
stretch
stretch
13
892(868)
(breath) + rock
See
to
be
v18 in is text.
stretch stretch
53
VIBRATIONAL SPECTRA OF CYCLOBUTANEd2 TABLE V Assigned and Calculated Frequencies (cm-‘) for Cyclobutaneds Assignment
NO. Ref. (11)
Al
B2
2210
2213=
2213
CD2
asym.
2120
2114’
2117
CD2
sym.
3
1169
1169
1166
1169 1006
+
ring
5
884
884
8R4
876
Ring
stretch
157
157
157
156
Ring
pucker
limd
’
9
1042
10
925
a47d
11
748
748
12
2243
1084
1084
15
1036
1042
Ring
stretch
Twist
748
753
wag
+
2205
CD2
asym.
stretch
212se
2121
CD2
sym.
stretch
lOR4
1084
Scissor
ring
775
775
771
Ring
bend
480
480
483
Rock
+
stretch
+
17
2234E
2224f
2212
CD~
asym.
1s
2129
21094
2108
CD2
sym.
19
1065
1112(1153?)
1065
1071
Wag
+
20
1054
1042(1054)
1054
1058
Scissor
21
944
944
944
945
Twist
22
730
730
730
734
Ring
stretch
23
556
556
55R
553
Rock
+
See
corresponding
d
Calculated
e
This
f
Gas
phase
Raman
L7 Gas
phase
ir
band
values values
band
in
footnotes of
was
Ref.
the using
scale
assigned
in
frequencies
frequency
to
resonance
Table
ill)
reported
previously
bend
stretch stretch
ring
+
stretch
rock +
wag
twist
IV.
pairs
considered
factors
Ref.
rock
ring
480
Average
scissor
+ wag
830
16
c
+
rock
Twist
672
1054(1042)
(breath) +
wag
1002
674d
stretch
Rock
6
14
alb
stretch stretch
Scissor
978
13
E
descriptionb
This work
1
8
Bl
This work’
2
4
A2
rlpprox.
CE?lC.
Ref. (14)
Set to
II
in in
Ref.
Ref.
(111.
(14).
~1~.
in assigned
Ref.
(11). to
a
combination
(111.
led Aleksanyan and Antipov (12) to assign the solid-phase Raman band at -940 cm-’ to v8 of &. These authors also predicted that the v7 mode to have a frequency of - 1340 cm-’ based on an analysis of their cyclobutane-dl spectra. However, 1258 cm-’ for v7 and 943 cm-’ (II) for v8 are well fit by our calculations. In Ref. (12), the solid-phase Raman bands at 1252 and 1256 cm-’ were interpreted as the two components of v20 E mode arising because of splitting due to lowering of symmetry. The present and previous calculations (14) would seem to indicate that the higher-frequency band, at least in part, belongs to u7 A2 vibration of do. In Ref. (ZO), the A2 vibrations of ds were assigned to weak Raman bands at 10 17 and 891 cm-’ observed for the solid phase. While the former is close to the calculated value of - 1005 cm-‘, the latter is very different from our predicted -675 cm-‘. Though
54
ANNAMALAI AND KEIDERLING TABLE VI Observed and Calculated Frequencies (cm-‘) for cisCyclobutane- 1.2-dz ObS .
NO.
2972
CH2 asp.
(2961)
2969
c!i2
asym.
(29401
2944
C-H
stetch
2932
C-H
stretch sym.
stretch
sym.
stretch
I2978
8
)b
descriptiona
Approx.
C?llC.
Stretch
stretch (axial) (equatorial)
(2911lC
2904
(2882)
2900
CH2 CH~
(2179)
2168
C-D
stretch
(axial)
(2140)'
2153
C-D
stretch
(equatorial)
9
1462
1459
CH2
scissor
(in-phase)
10
1451
1451
CH2
scissor
(out-of-phase)
11
1326
1318
CHD
scissor
(in-phase)
12
1310
1312
CHD
scissor
(out-of-phase)
13
1262
1256
wag
+ twist
14
1246
1246
Wag
+ twist
15
1221=
1227
Twist
1205
Wag
+ twist
+ rock
+ scissor
1177=
1179
Wag
+ twist
+ ring
stretch stretch
16 17
+ ring
stretch
18
1107
1104
Wag
+ twist
+ ring
19
1095
1080
Rock
+ wag
+ scissor
989
Ring
stretch
(breath)
20
989C
21
+ scissor
+ wag
983
Ring
stretch
+ twist
933=
931
Ring
stretch
+ twist
+ wag
23
901
901
Ring
stretch
+ twist
+ rock
24
850
855
Ring
bend
25
837
839
Ring
stretch
+ wag
+ rock
26
785
785
Twist
+ wag
+ rock
+ ring
27
676
677
Rock
28
665
663
Rock
+ twist
29
563
565
Rock
+ ring
bend
187
Ring
pucker
+ rock
30 .a Inferred tion
from
greater
b Frequencies
the diagonal than
within
+ twist
force
constants
with
+ ring
stretch
+ wag
+ ring
+ ring
stretch
+ rock
+ twist
22
+ rock
+ ring
+ wag
stretch
stretch
stretch
potential
energy
distribu-
10%. the parentheses
were
not
fit
in the
force
field
calcula-
tions. c Raman
frequencies
far
the
liquid
phase.
there is no evidence for the presence of a 1017-cm-’ band in the Raman spectra measured by Miller et al., weak ir bands do appear around 1025 cm-’ for the solid phase of ds. One of these bands may correspond to the v7 mode of d8. (We have not included this frequency in force field calculations.) The CH and CD stretching regions of the spectra of d,, and d8 are less understood because of their complexity due to overlapping and Fermi resonance of several fundamental and combination bands (II). We believe that the assignments given in Ref. (11) are the best available so far for these regions, but no calculations had previously been carried out using these assignments. Our calculations necessitated some modifications in these assignments. In general, the frequencies assigned by Miller et al. (II) for v13 of 6, and v,~, v17, and v18 of d8 are found to be too high. The details about our revised assignments are given in Tables IV and V. This does
VIBRATIONAL SPECTRA OF CYCLOBUTANE-d2
55
TABLE VII Observed and Calculated Frequencies (cm-‘) for the Axial Form of trans-Cyclobutane-1 ,2-dz ObS.
NO. A
1
(297t))b
2969
2
(2929lC
2927
CH2 asym. C-H
stretch
sym.
stretch
3
(28821
2900
CH2
sym.
stretch
4
12178)
2173
C-D
sym.
stretch
5
(1462)
1459
CH2
scissor
6
132oC
1327
CHD
scissor
7
1246
1251
Wag
+
twist
+
ring
stretch
8
1218C
1220
Wag
+
twist
+
ring
stretch
9
1110=
1124
wag
+
twist
1080
Rock
+
11
1016C
1023
Ring
stretch
+
12
98OC
987
Ring
stretch
(breath)
stretch
10
(Iloo)=
ring
13
(912)
913
Ring
14
814
807
Ring
stretch
15
667
668
Rock
+
187
Ring
pucker
2972
CH2
asym.
2936
C-H
asym.
2904
CH2
sym.
16
R
description”
Approx.
ca1c.
17
129781
1.4 19
(2913)’
20
C-D
asym.
CH2
scissor
22
1296
1295
CHD
scissor
1257
Wag
+
1246
Wag
+
1131
Twist
901
26 27
+
rock
stretch
twist twist
+
ring
+
+
scissor
wag
901
Ring
stretch
885
Ring
bend
+ f
773
Twist
683
680
Rock
+
twist
+
30
548
551
Rock
+
ring
bend
corresponding
footnotes
to
wag
Table
+
ring
+ wag
stretch +
rock
rock
775
+
stretch
twist
29
See
wag
+ wag
28
“b’c
+
stretch
1451
25
rock
stretch
2162
1246
+
stretch
1451
24
twist
twist
21
23
stretch
+
rock
+
ring
stretch
wag
VI.
not, however, mean that the problem of assigning these modes is now settled, since there can certainly be alternate assignments. In Table 3 of Ref. (12) a frequency of 2887 cm-’ is listed for VI8 of &. This value seems to be in error, since there is no observed band at this position in the reported spectra and since there was no mention of any other alternative consideration in obtaining this value. However, there are two bands close to this value at 2877 and 2880 cm-’ in the gas-phase ir spectrum. The Raman spectra have a band at 2878 cm-’ for the gas and at 2870 cm-’ for the liquid. We considered the 2880cm-’ band for vi8 but obtained a poor fit (Table IV) with a calculated frequency of 2901 cm-‘. cis- and tram-d* species also exhibit an ir band at 2882 cm-’ for the gas phase and a Raman band at 2871 cm-’ for the liquid phase (Tables I and II). As in the case of d,,, the closest of our calculated frequencies for the dz species is 2900 cm-‘. These findings suggest that the origin of the 2880-cm-i band in d,,, cisdZ, and trans-dz may be the same. AI1 three species have scissoring modes at - 1450 cm-‘, corresponding to vi9 (E) in 4, vIo in ci+d2, and v2, (B) in tram-d2. The first
56
ANNAMALAI AND KEIDERLING TABLE VIII Observed and Calculated Frequencies (cm-‘) for the Equatorial Form of truns-Cyclobutane- 1,2-d* Obs.
NO.
A
Approx.
ca1c.
description”
1
(297n)b
2968
CH2 asym.
2
(2954)
2945
C-H
3
(2882)
2900
CH2 sym.
stretch
2149
C-D
sym.
stretch
02
scissor
4
Stretch
stretch
syn.
5
(1462)
1459
6
1310
1310
CHD scissol:
1234
Twist
i2iac
1216
wag
+ twist
+ rock
1206
Wag + twist
+ ring
1llOC
1124
Rock + ring
stretch
7
a 9 10
9aoc
11 12
+ wag + ring
982
Ring
stretch
(breath)
968
Ring
stretch
+ rock
stretch
13
(9121
914
Ring
14
797
795
Wag + ring
15
1667)
669
Rock + twist
186
Ring
16 B 17
pucker
2912
CH2 asym.
stretch
2944
C-H asym.
stretch
19
(2913)C
2905
CH2 sym.
2158
C-D asym.
1451
1451
CH2 scissor
22
1310
1309
CHD scissor
23
1246
1252
Wag + twist
24
121ac
1214
Wag + twist
1060
Wag + ring
27
923
Twist
a69
Rock + ring
stretch
+ scissor stretch
+ wsg
+ twist
+ ring bend
stretch + twist
2R
797
798
Ring
stretch
+ ring
bend
29
683
682
Rock + twist
+ ring
bend
30
586
586
Rock + ring
s’b’c
see
corresponding
footnotes
+ twist
stretch
stretch
21
912
+ rock
+ wag
+ rock
129541
25
+ twist
+ ring
(2978)
26
stretch
stretch
18 20
stretch
to Table
+ ring + twist
stretch + wag
bend “I.
overtone of these modes thus lies in the vicinity of 2900 cm-‘. We believe that the Fermi resonance of these overtones with the fundamentals calculated at about 2900 cm-’ could be the main source of the 2880-cm-’ band in all three isotopomers. cis and tram-Cyclobutane-d2
We believe that the assignments given in Table I and II for cis- and tram-d2 are quite reliable for frequencies below 1500 cm-‘, since they are fit extremely well in our calculations. However, the assignments for the CH and CD stretching spectral regions of cis- and trans-d2 must remain tentative for the same reasons as discussed for 4 and ds. The spectra in these regions are so complicated that no detailed attempt could be made to analyse them. For example, all Raman bands in these regions appear to be polarized. (This may be due to the crude nature of our Raman depolarization ratios.) We assigned the observed frequencies to the vibrational modes having closest calculated frequency values. But, due to the uncertainty in
VIBRATIONAL SPECTRA OF CYCLOBUTANE-&
57
the CH and CD stretching frequencies, we did not include them in our force field refinement calculations. The ir spectra of both cis- and truns-dZ have a Q branch at 1451 cm-‘. The corresponding Raman band is observed at 1447 cm-‘. For the tram isomer this band is depolarized, but for the cis isomer it is less certain. This band corresponds to CH2 scissoring B mode of both axial and equatorial forms of transd;!. For cisdZ this is assigned to the out-of-phase CH2 scissoring mode. The corresponding A modes of truns and in-phase mode of cis appear as shoulders in the ir spectra at 1462 cm-‘. The CHD scissoring modes appear between 1290 and 1330 cm-‘; our calculations predict that the A modes of trans and the in-phase mode of cis have higher frequencies than the corresponding B and out-of-phase modes, as in the case of CH2 scissors. The ring-breathing modes appear as characteristic polarized Raman bands at 989 cm-’ for cis-dz and 980 cm-’ for tram-d2. These are the strongest Raman bands in these spectra. The calculated frequencies agree well with these values but have a difference of 5 cm-’ between the axial and equatorial forms of the trans isomer. The Raman spectrum of this isomer has a polarized band at 996 cm-’ as a shoulder of the 980-cm-’ band. This may be due to the ring breathing of cyclobutanedi impurity. This value agrees with the frequencies, for C-D axial and C-D equatorial forms of cyclobutaned,, calculated using our final force field. The ir spectra of cyclobutane-d, reported in Ref. (12) show a weak band at about this position. However, this impurity band in the cis spectrum seems to be completely enveloped in the 989~cm-’ band. The polarized Raman band at 962 cm-’ in the cis spectrum may correspond to the ring breathing mode of the dd3 impurity present in this sample as evidenced by the mass spectral analysis (27). Both the ir and Raman spectra of the truns isomer have a band at -912 cm-‘. The Raman band is clearly depolarized and should, at least in part, belong to a B mode. This is assigned to vz6 B mode of the equatorial form of this isomer, which has a calculated frequency of 923 cm -I. The calculations also indicate that both the axial and equatorial forms have a ring-stretching A mode (vi3) at -912 cm-‘. Hence, the observed band may also belong to this mode. However, in our force field refinement calculations we used the experimental 912~cm-’ band only for the v26 B mode of the equatorial form. Cyclobutane-4 and -dl are known to exhibit some “hot band”-like features in the region 680-580 cm-’ (7, 8). We have made similar observations for cis and truns-cyclobutane-d2. Except for a very few modes like the CH2 and CHD scissoring, and ring breathing, our calculations indicate strong mixing of internal coordinates in the low-frequency modes. The C-H and C-D stretches mix among themselves in the usual manner. However, it is interesting to note the minimal mixing, predicted in our calculations, between the axial and equatorial C-H (or C-D) stretches corresponding to the -CHD- moieties in cis-dZ species (Table VI), though their calculated frequencies lie very close to each other. Force Field The final force field obtained from this work is reported in Table III. This force field was developed by taking advantage of both theory and experiment. To obtain
58
ANNAMALAI
AND
KEIDERLING
this force field we fit the vibrational frequencies of c&d2 and tram-d2 as well as those of & and d8 used in previous work (13, 14). As can be seen from Tables IV to VIII the force field reproduces the experimental frequencies very well. The final force constants do not seem to differ much from the ab initio scaled force constants. However, it is well known that even very small differences, particularly in the interaction force constants, can significantly alter the calculated frequencies. Recently, we demonstrated that this kind of alteration in the calculated frequencies can lead to great differences in the calculated VCD spectra for chiral tram-d2 using both the fixed partial charge and localized molecular orbital models (15, 16). While theory of VCD is still in a developing stage, these models appear to provide a reasonable description of hydrocarbon VCD. It should be noted that the final force field reported here explained the observed VCD better than any other force field considered in Ref. (15). Furthermore, it gave a satisfactory representation of the mid-ir (1500-900 cm-‘) VCD using no change in the parameterization (16). In some sense, these VCD calculations provide an additional level of test for the force field. Since VCD is dependent on the relative motion of atoms in a vibrational mode, its description is more sensitive to the detailed characteristics of the normal mode than are the frequencies. In the future, it may prove that such optical activity measurements will provide a more constrained test of calculated force fields than the traditionally used isotopic frequencies. Additionally, we have shown (15) that frequency overlap can dramatically affect the calculated VCD. This may also provide a means of relooking at crowded spectral regions in future studies. All diagonal constants in the final force field have standard deviations below 2% except for the ring-puckering constant, whose deviation is - 15%. The interaction constants not involving the C-H stretching or ring-puckering coordinates indicate deviations within 25%. But, it is found that the interaction constants involving the C-H or ring-puckering coordinates show very large errors. The errors are one to five times the corresponding calculated force constant values if one such coordinate is involved, but are much larger for F30,5 and F30,6. These must be regarded as undetermined. These large deviations are understandable for the following reasons. The C-H stretching and ring-puckering modes are highly anharmonic and are poorly represented in a harmonic approximation. Furthermore, in refining the force field, only a limited number of C-H stretching and ring-puckering frequencies could be used. Moreover, as indicated before, the C-H stretching frequencies used may have large errors due to the complexity of this spectral region. Our primary goal was to obtain a force field which would yield a good frequency fit as well as explain the experimental VCD satisfactorily. The force field reported here satisfies these requirements. CONCLUSIONS
In summary, we have measured the ir and Raman spectra of cis- and transcyclobutane-1,2-d*, and have assigned the bands. We believe that the assignments for the bands below 1500 cm-’ are quite reasonable. We have demonstrated that the ab initio scaling approach of BFP, combined with the conventional force field
VIBRATIONAL
SPECTRA
59
OF CYCLOBUTANE-d2
refinement procedure, fits the experimental frequencies very well and is quite useful whenever such a high-quality frequency fit is very important, as was the case of our VCD studies (IS, 16). This method takes advantage of both theory and experiment, and is justified in terms of obtaining the initial and final estimates for the force constants. ACKNOWLEDGMENTS We gratefully acknowledge the National Science Foundation (CHEI l-04497) and the National Institutes of Health (GM-30147) for support of this research. We thank Professor Larry Abels for assistance in
obtaining the Raman spectra, the Nicolet Corporation for the loan of an FT-IR spectrometer, and Professor J. S. Chickos for kindly supplying the cyclobutane-d, samples. RECEIVED:
July
18,
1984 REFERENCES
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