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Ground state rotational parameters and fundamental vibration frequencies for isotopically substituted diboranes
JOURNAL
OF MOLECULAR
SPECTROSCOPY
113, 63-76 (1985)
Ground State Rotational Parameters and Fundamental Vibration Frequencies for Isotopically Substituted Diboranes J. L. DUNCAN Department sf Chemistry University of Aberdeen, Meston Walk. Old Aberdeen .4B9 2lJE. Scotland The present spectroscopic structural information on diborane derives from infrared studies of B2H6 and B2D6 species only. Due to the impossibility of selective isotopic substitution in diborane, and the consequent coexistence of a number of isotopic species in any partially deuterated sample, the most probable source of further structural information of quality will be from microwave studies of asymmetrically deuterated species. To assist in the assignment of the overlapping spectra that will occur, accurate rotation and quartic distortion constants are presented for the ground states of all isotopic diboranes in terms of existing zero-point average structural parameters and isotopic changes in these calculated through the harmonic potential function. Sets of fundamental anharmonic vibration frequencies are calculated in order that interference from low-lying vibrations with significant populations at ambient temperatures may be anticipated. 0 1985 Academic Press. Inc. 1. INTRODUCTION
Over the past few years we have made a concerted spectroscopic study of the diborane molecule through the isotopically pure “B2H6, “B2H6, “B2D6, and “B2D6 species. High-resolution rovibration assignment and analysis of a number of isolated bands in the spectrum of each species has enabled rather precise sets of ground state rotational and quartic centrifugal distortion constants to be determined from large basis sets of ground state rotational level combination differences (1-3). As a result of lengthy examination of the infrared and Raman spectra, fairly clear pictures of the major resonance perturbations have been constructed, and the positions of a number of previously uncertain fundamentals have been established, for each isotopic molecule (4). Sets of unperturbed fundamental vibration frequencies which obey closely the Teller-Redlich product rule have then been used to determine for the first time a physically realistic and accurately determined set of harmonic force constants (5), which are completely substantiated by the results of two independent ab initio calculations at the 4-31G level (6, 7). The harmonic potential function has then been used in conjunction with the 12 observed ground state inertial constants to determine the ground state average structure parameters, and their isotopic dependences, for the molecule (8). While this structure appears to be rather precisely defined, not all parameters could be allowed to refine independently, and one of two structural dependences on deuteration had to be constrained to the value predicted using the potential function. The apparent quality of the structure stemmed from the fact that, when either constraint was imposed, the other parameter refined to a value very close to that predicted. In essence, two almost identical sets
63
QO22-2852185$3.00 Copyright 0 1985 by Academic Press. Inc All rights of reproduction in any form reserved.
64
J. L. DUNCAN
of parameters resulted. Nevertheless, at the moment insufficient inertial constant data of quality are available to enable an unequivocal set of structure parameters to be determined for the diborane molecule. 2. FURTHER
PROGRESS
Due to the impossibility of selective deuteration of the molecule at the bridge and terminal positions, a mixture of isotopic species results on partial deuteration of the diborane molecule. This renders detailed spectroscopic studies from either infrared or Raman spectra extremely difficult, to say the least, due to the overlapping of rovibration bands from a minimum of two, and often more, major isotopic species present in the sample. It seems that the most fruitful studies would be those undertaken in the microwave region, where only asymmetrically deuterated species would give rise to absorptions through the small permanent dipole moment introduced by the isotopic substitution. Comparable studies on partially deuterated ethanes (9) and ethylenes (IO) have proven to be highly successful, as well as highly accurate. The problem of blending of absorptions arising from different isotopic species generally does not arise in the microwave experiment. However, assignment work is very much simplified in such cases (and sometimes only possible) when the approximate relative positions of rotational transitions for different isotopic species are known, and when the relative populations of low-lying fundamental vibrations, and hence interference from “hot” transitions, can be predicted. These require, respectively, a prior knowledge with reasonable assurance of (a) the ground state rotational (or inertial) constants and centrifugal distortion constants, and (b) the fundamental vibration frequencies of the isotopic modifications concerned. We have at our disposal the means for predicting these spectroscopic phenomenological parameters to high accuracy for any isotopic modification of the diborane molecule. In this paper we list the appropriate data for all isotopic forms of diborane which contain either the i”B or “B nuclides. Calculations for “mixed” “B”B species have not been made because of their very large number, and because preparation prior to effective study would always be made in terms of an isotopically pure starting material. Calculations of this kind, carried out previously for isotopic species of ethylene (1 I) and ethane (12), have proven of great value to subsequent spectroscopic investigations on new isotopic species (9, 13-l@, ground state rotational constants being predicted to within 0.05% and centrifugal distortion constants generally being reliable to much better than 5%. Table I compares the ground state phenomenological parameters for isotopic ethylenes predicted in 1974 (II) with the experimental values which have been determined subsequently through infrared or microwave studies, to give some idea of the quality of prediction which is possible. 3. CALCULATIONAL
PROCEDURE
AND RESULTS
(a) Ground State Rotational Constants The harmonic potential function may be used to correct ground state rotational constants, B$, for the effects of averaging over the harmonic atomic displacements in the ground vibrational state, and for the very much smaller centrifugal distortion effects, to yield zero-point average constants, B; (19). No corrections for electronic
SPECTROSCOPIC
PARAMETERS
65
FOR DIBORANE
TABLE I Comparison of Ground State Phenomenological Parameters (in cm-‘) for Isotopic Ethylenes Predicted in 1974a with Experimental Values Determined Subsequently 13 ‘2”4 Pred.
Exp.(l8)
Pred.
IR
Exp. ( 16) IR
3.4860
3.48608
0.95067
0.91654
0.9163250
0.84798
0.8478267
0.83324
0.83297
0.79331
0.74406
0.7437726
0.67401
0.6737685
0.67091
0.67063
0.95068 0.79342
IO’ . A”R
Pred.
Mw 3.324541
Ro
A’,
Exp.(lO)
3.3256
Co
IO6 . AoJK
Pred.
ml 4.005888
4.86452
,06.
Exp.(lO)
4.0068
4.8656
A0
t~XWC2H2D2
cis-C2H2D4
‘ZH3’
1.31
I .332
1.27
1.3019
I. 16
1.20
1.05
1.089
9.94
9.659
6. I8
6.0174
3.82
3.90
3.04
2.85
48.66
54. I
55.21
82.1
82.05
66.8
70.595
45.6
I06 . 60J
0.234
0.2354
0.275
0.2803
0.280
0.2884
0.241
0.257
106 . 60K
8.97
8.97
7.60
8.132
6. I3
6.558
5.45
6.5
a Ref.
(II)
contributions to the moments of inertia, and hence rotational constants, are necessary for diborane, since there are neither lone pairs of electrons nor multiple bonds to give off-axis inertial contributions. The B; constants are compatible within any single isotopic molecular species (although isotopic dependences still remain), and enable one to calculate average structure parameters and the major isotopic dependences of these. Minor isotopic dependences, e.g., on substituting “B for “B, are small, but important to the overall quality and reliability of the determined parameters. These are estimated through the harmonic potential using a simple diatomic approximation to enable the anharmonic contribution to be calculated (20). Through the reverse calculation, starting with the average structure parameters and allowing for the particular isotopic dependences calculated through the potential function, a set of ground state rotational constants may be estimated for any isotopic modification desired. The set of harmonic force constants used are listed in Table V of Ref. (5) where the symmetry coordinates and molecular geometry to which they refer are also defined. The average structure parameters used are essentially those of Ref. (8) but are modified very slightly here due to a recent update of isotopic atomic masses (21). The recalculated average structure parameters for diborane are listed in Table II. Isotopic changes were calculated for these zero-point average distance parameters between bonded nuclei according to the relation (18) 6r, = s(Ar),
- X,,,
where (A$,, is the average displacement of the bonded distance, and 6Ko is a correction for the effect of nuclear displacements perpendicular to the bond. The subscript zero refers to 0 K, since the ground state is being considered. By treating
66
J. L. DUNCAN TABLE II Zero-Point Average Structural Parameters for the Diborane Molecule” Parameter
Value
rZ(“BHt)
1.1939’;1
0.001’3
+“BHb)
1.327238
0.00046
LZ(Ht’o~~t) LZ(Hb’O~Hb)
121.5Y”
0.19
96.42’
0.04
6rz(‘o~~t
- ‘OmJ
0.00’808
Gr=(“B”b
- “BDb)
0.003732
0.00038
0. ‘50
0.05
6LZ(Ht”BHt “8H
6’&(Hb 6r
z
(“BH
6rZ(loBHb
a See
Table
due
to
The
number
Constrained function, a(BHb)
t
-Dt”BDt)
b
-D
=
“BD,)
b
-“8H
t
-0.
)
- “BHb)
7 of
Ref.
a recent
consistency b
Uncertainty
of
(8).
update decimal
in
the
to
values
using 0-I 1.8A
6rL .
‘3O
0.04
0.000’2;1
constrainedb
0.00008;;
constrainedb
Individual of
isotopic
places
constrainedb
values atomic
quoted
are
are
slightly
masses.
required
See for
changed text.
internal
calculations. estimated = 3a&&2>0 See
through -
the
6Ko with
harmonic a(BHt)
potential 0-l = 2.5A and
text.
bonded distances in the diatomic approximation (equivalent to considering only the cubic stretching force constant for the bond in the light of its dominance over all others), the anharmonic contribution (Ar),, may be approximated to 3a(Az2)0/2. Here (Az2),-, is the mean square parallel amplitude of vibration, and a is the cubic anharmonicity constant for the bond in question, arising from the potential energy expansion for a diatomic molecule, I/ = $(Az2 - aAz3 + - - - ). On the basis of our structural calculations, supported by ab initio calculations, values of a(BH’) = 2.5 A-’ and a(BHb) = 1.8 A-’ were chosen for diborane (8) and are used here. The changes to the zero-point average BH distances may then be estimated for any isotopic substitution by calculation of the mean square parallel and perpendicular amplitudes through the harmonic potential function and application of the equation 6r, = 3a6(Az2j0/2 - 6K0. The zero-point average isotopic structural changes thus estimated for isotopic diboranes are collected in Table III. The numbering used for the atoms is given in Fig. 1.
SPECTROSCOPIC
PARAMETERS
67
FOR DIBORANE
TABLE III Calculated Zero-Point Average Structural Changes from “B2H6 for Isotopic Diboranes (negative and positive signs denote bond shortenings and lengthenings, respectively) Isotopic substitution
1lB 2 Dl DlDZ DlD8 D1D7 DlDZD7 DlD2D7D8 DqD5 DlD4D5 DlD2D4D5 DDDD 1458 DlD4D5D7 DDDDD 12457 DlD2D4D5D7D8 D4 DlD4 D1D2D4 DlD4D8 DlD4D7 DlD2D4D7 DlD2D4D7D8
5%
B"4
BHg
B"7
B%
10-4x
10-4x
10-4%
ld4R
10-4x
lO-48
-1.2
-1.2
-0.8
-0.8
-1.2
-1.2
-9
+2
-1
-1
-5
-6
-8
-8
-2
-2
-11
-11
-15
-2
-4
-4
-2
-15
-13
-4
-4
-4
-13
-4
-12
-13
-5
-5
-18
-7
-17
-17
-7
-7
-17
-17
-3
-3
-32
-32
-3
-3
-12
0
-33
-33
-7
-8
-11
-11
-34
-34
-11
-11
-16
-4
-36
-36
-4
-16
-15
-5
-36
-36
-15
-5
-14
-15
-36
-36
-20
-8
-18
-18
-38
-38
-18
-18
-2
-2
-27
-7
-2
-2
-11
+1
-28
-6
-6
-7
-10
-10
-33
-6
-11
-11
-16
-3
-32
-9
-3
-16
-14
-5
-32
-9
-14
-5
-13
-14
-33
-8
-19
-8
-17
-17
-36
-10
-17
-17
For interbond angles no comparable calculations can be made. Isotopic changes were assumed pro rata with respect to those experimentally determined on deuteration, and listed in Table II, with no changes on boron substitution. Some form of check on the validity of these last simplistic assumptions could be made by calculating the resulting nonbonded distance changes on partial deuteration and comparing these with values calculated using Eqn. (39) of Nakata et al. (22), derived for XY2 molecules as a development of the diatomic approximation. Using averages of their (approximately constant) estimates for the appropriate anharmonic constants, good agreement for H--H nonbonded distance changes on deuteration was observed. Consequently, our simple method for estimating isotopic angle changes was assumed to be a reasonable one.
68
J. L. DUNCAN c
I-
a
b
t
a
FIG. 1. Numbering of atoms and orientation of inertial axes for the diborane molecule.
Application of the structural data in Tables II and III enables the zero-point average inertial constants, Z;, to be calculated for any isotopic diborane, as listed in Table IV. Through application of the harmonic potential function and use of the relevant perturbation expressions (8, 23, 24), the zero-point harmonic vibrational (AZ&) and centrifugal distortion (AZ&,) contributions to the ground state I$ constants may be calculated, as listed in Table V. These enable zero-point average and ground state inertial constants to be interconverted for any isotopic diborane according to the relation
The data of Tables IV and V may finally be combined through this relation to predict the appropriate ground state rotational constants for any deuterated diborane, using the conversion B*/MHz = 505 379.0 pA2/Za. These constants are collected in Table VI. From our previous experiences, and from the quality of the empirical data used in their estimation, it is considered that these ground state rotational parameters should be reliable to considerably better than 1 part in 2000 in any predictive or comparative spectroscopic capacity. (b) Centrifusal Distortion Constants The quartic distortion constants are functions of the harmonic potential function and may be used to assist in its determination. Accordingly, values may be predicted for any isotopic modification through a reliably determined potential function. Strictly, these are hypothetical values at the equilibrium configuration rather than ground state values. Since the vibrational dependences of the constants are not known, the two are normally equated. It is our experience that differences are seldom greater than 5% in these small constants (see Table I), although in exceptional cases differences of 10% appear to be possible (25). Calculated quartic distortion constants consistent with a Z’A axis representation (A, B, C - z, x, y) are collected in Table VII for all deuterated diboranes.
SPECTROSCOPIC
PARAMETERS
69
FOR DIBORANE
TABLE IV Calculated Zero-Point Average Inertial Constants (in pA2) for Deuterated Diboranes from the Parameters of Tables II and III as-
BZ”6
'lB
"B
t
t
B2"5D
B2"4D2
"B
B2"4D2
t
t B2"3D3
B2H2D4t 10.68199
6.35090
7.30065
8.51935
8.12611
0.37229
I;
27.87255
30.05830
31.91115
32.58303
32.19284
34.38669
36.51320
I= z
30.27651
33.41236
36.48450
36.76433
36.62032
39.90739
43.25216
Ia z
6.35202
7.29261
a.52090
a.10100
8.36362
9.45706
10.68397
I;
26.31714
28.50471
30.33635
31.05608
30.63917
32.83599
34.96096
IC z
28.72175
31.85025
34.91077
35.21180
35.05751
38.34836
41.70143
trans-
cis-
B2D3"3
as-
t
B2D4"2t
B2D4"2
t B2D4"2
t B2D5"
B2D6
Ia z
a.30801
9.25960
10.47593
10.08152
10.33792
11.42318
12.63831
I;
29.66518
31.84024
33.70474
34.35900
33.96702
36.15995
38.27312
IC z
30.10694
33.23468
36.31669
36.57926
36.44372
39.72192
43.05280
8.30936
9.25205
10.47773
10.05663
10.33069
11.41595
12.64055
I;
28.12181
30.29950
32.14487
32.84372
32.42519
34.62131
36.73214
IC z
28.56448
31.68607
34.75829
35.03843
34.89395
38.17534
41.51317
trans-
cis-
b B2"5D
B H DbDt 24
B H DbD t 23 2
bt B2"3D D2
bt B2"3D D2
bt B2D4H H
b B2D5"
as-
"B
B*"4D*t
I:
B2D2"4t
"B
cis-
9.46493
t
1lB
trans-
1:
7.29374
a.24574
9.46287
9.32183
10.41173
11.62909
Ib z
28.72693
30.91701
32.76736
33.43457
33.04250
35.23985
37.35912
I= z
30.18489
33.32620
36.39447
36.66643
36.53048
39.81415
43.15099
Ia z
7.29250
8.23562
9.46233
9.04307
9.31168
10.40214
11.62927
I;
27.17653
29.36818
31.19732
31.91134
31.49239
33.69304
35.81061
c
28.63753
31.77139
34.82736
35.12163
34.97420
38.26119
41.60578
(c) Fundamental
9.07025
Vibration Frequencies
The determination of the molecular harmonic potential function requires that observed (anharmonic), unperturbed fundamental frequencies are “harmonized” so as to obey the product rule predictions as well as possible. In the absence of experimental anharmonicity constants, we have used a simple Dennison’s Rule approach with the original data on “B2H6, “B2H6, “BzD6, and “B2D6 (4). By
-0.14(-0.14)
0.23(0.23)
103.AI&
103.AIc;nt
-O.Ol(-0.01)
103.AIv;b
a cent
-71.00(-68.66)
-29.65(-27.66)
I03.AIvbib
103.AI
-3.85(-4.36)
B2H5D
b
0.17(0.16)
-O.ll(-0.10)
-O.Ol(-0.01)
-31.28(-29.27)
-67.73(-65.54)
-3.98(-4.57)
0.28(0.27)
-0.16(-O.
-O.Ol{-0.01) 15) 0.38(0.37)
-O.Zl(-0.20)
-O.OZ(-0.02)
-24.08(-22.41)
b
-82.75(-80.44)
-8.94(-9.51)
B2H3D
as-
-27.18(-25.42)
bc D
-76.89(-74.44)
-6.59(-7.08)
B2H4D
0.29(0.28)
-0.17(-O.
-0.13(-0.12)
0.21(0.20)
-O.OZ(-0.02)
-25.74(-24.16)
-O.Ol(-0.01)
-79.37(-77.14)
-7.99(-8.60)
-28.89(-27.15)
l7(-6.74)
B2D4H2
-73.46(-71.25)
-6.
B2D3H3
as-
B2D2H4t
t
-0.02(-0.02)
-O.Ol(-0.01)
0.33(0.32)
103.AIv\b
103.AI
=
= Cent
b. vrb
103.AIc;nf
103.AI
lo3.AI”~b
103.AI
103.AIv;b
103.AIr;nr
-20.24(-18.60)
-23.05(-21.31)
0.50(0.49)
18)
-86.52(-83.97)
-80.62(-78.98)
-0.26(-0.25)
-0.19(-O.
103.AIc;nt
t
t
16)
D2
t
-9.55(-10.10)
B2H4D2
0.38(0.37)
-O.Ol(-0.01)
V
t
13)
t
b
H
t
0.27(0.26)
-0.15(-O.
-O.Ol(-0.01)
0.30(0.29)
-0.16(-O.
-O.Ol(-0.01)
0.34(0.33)
-0.18(-O.
-0.02(-0.02) 17)
0.33(0.32)
-0.17(-O.
-O.OZ(-0.02)
-18.70(-17.38)
-10.69(-11.28)
B2D5H
-87.85(-85.73)
-9.90(-10.45)
B2D4H
-21.66(-20.26)
16)
D2
-85.35(-83.06)
b
-24.82(-23.26)
-8.89(-9.41)
B2H3D
-82.83(-80.64)
14)
D2
cis-
0.26(0.26)
-0.14(-O.
-24.76(-23.23)
b
0.26(0.25)
-0.02(-0.02)
-79.17(-76.82)
-7.83(-8.28)
B2H3D
trans-
0.20(0.20)
t
-0.13(-O.
-0.12(-O.
-0.15(-0.14)
-O.Ol(-0.01)
-O.Ol(-0.01)
0.23(0.22)
-O.Ol(-0.01)
-26.46(-24.91)
b
ll(-18.80)
-84.71(-82.65)
-26.42(-24.90)
-75.89(-73.68)
-20.
-79.43(-77.41)
B2D6 -9.16(-9.78)
-82.04(-79.89)
-8.68(-9.28)
B2D5Ht
-8.08(-8.67)
cis-
0.41(0.40)
-23.30(-21.87)
-7.04(-7.56)
B2D4H2
tra”S-
12)
-0.20(-O.
0.43(0.42)
-O.Zl(-0.21)
19)
-0.20(-O.
-0.19(-O. 0.40(0.39)
-O.OZ(-0.02)
-0.02(-0.02)
-O.Ol(-0.01)
0.3610.35)
-15.46(-14.17)
-l8.17(-16.69)
-21.12(-19.50)
-9l.l2(-88.83)
-O.Ol(-0.01)
-ll.97(-12.52)
B2H2D4
-20.79(-19.22)
18)
t
-88.81(-86.48)
-10.81(-11.32)
B2H3D3
-86.49(-84.12)
t
-82.84(-80.29)
B2H4D2
cis-
-9.30(-9.77)
t
-8.23(-8.63)
B2H4D2
tl-C%lS?
and Centrifugal Contributions (in rAZ) to Ground State Inertial “B Diboranes (values for ‘“B diboranes in parentheses)
-O.Zl(-0.20)
-25.32(-23.27)
‘. vlb
103.AI
-74.87(-72.32)
-6.53(-6.98)
-3.11(-3.58)
103. AIctnt
103.AIvbib
I03.Alv~.
BZH5D
t
Harmonic Vibrational Constants for Deuterated
B2"6
Calculated
TABLE
16)
13)
19)
t
71
SPECTROSCOPIC PARAMETERS FOR DIBORANE TABLE VI Predicted Ground State Rotational Constants (in MHz) for Deuterated Diboranes as-
11B
"B
trans-
cis-
B2H6=
t BZ"5D
t B2"4D2
B2H4D2t
B2H4D2t
t B2"3D3
t B2H2D4
A0
79 615
69 286
59 388
62 255
60 430
53 456
47 364
B 0
18 181
16 859
15 880
15 550
15 741
14 735
13 876
C 0
16 706
15 136
13 859
13 754
13 808
12 669
11 689
A
79 607
69 367
59 381
62 451
60 496
53 503
47 358
B.
19 256
17 778
16 705
16 315
16 540
15 432
14 481
Co
17 610
15 878
14 404
14 360
14 424
13 184
12 123
trans-
cis-
0
as-
t
"B
"B
B2D2H4t
B2D3"3t
B2D4H2
B2D4H2t
t B2D4H2
t B2D5"
B2D6a
A0
60 860
54 615
48 278
50 164
48 923
44 276
40 017
B 0
17 075
15 910
15 030
14 742
14 913
14 008
13 234
Co
16 805
15 219
13 926
13 826
13 878
12 730
11 744
A0
60 854
54 663
48 273
50 291
48 961
44 306
40 012
B0
18 013
16 719
15 760
15 422
15 623
14 631
13 790
Co
17 711
15 963
14 550
14 434
14 494
13 246
12 179
trans-
cis-
asb
B2H5D
"B
"B
a
bt B2H4D D
bt B2H3D D2
bt B2H3D D2
bt B2H3D D2
bt B2D4H H
b B2D5H
A0
69 326
61 339
53 457
55 766
54 266
48 586
43 498
B 0
17 635
16 387
15 462
15 151
15 333
14 376
13 559
Co
16 758
15 176
13 895
13 792
13 844
12 700
11 717
A0
69 343
61 418
53 463
55 937
54 328
48 633
43 500
B0
18 643
17 252
16 241
15 875
16 089
15 037
14 146
Co
17 644
15 919
14 520
14 399
14 460
13 216
12 152
me
fit (observed - calculated) to the spectroscopic rotational constants A,, Bo, C 0
in MHz for B2H6 and B2D6 species are: 11B2H6 (0,2,1), 1°B2H6 (O,-2,-2), "B2D6
(-3,-3,-l), 1°B2D6 (1.0,2).
using the same procedure in reverse, the predicted unperturbed anharmonic fundamental frequencies for any isotopic modification may be calculated through the potential function. The predicted values are considered to be reliable to within 10
72
J. L. DUNCAN TABLE VII Quartic Centrifugal Distortion Constants (in kHz) for Deuterated “B diboranes in the I’A Representation (z, x, y - A, B, C) (values for “B diboranes in parentheses)
B2H6 t B2”5D t
as-B2H4D2
t
tram-B2H4D2 t
cis-B2R4D2 t B2H3D3 t B2H2D4 t B2D2H4 t B2D3H3 t
as-B2D4H2
t
tram-B2D4H2
t B2D5H B2D6 b B2H5D b
B2H4D D
t
as-B2H3D
t D2 b
trans-B2H3D cis-B2H3D
b
D2
t D2 t
a
If
a IrS
molecules, values
2.28(2.66)
27.OC29.4)
42.9C42.6)
500(498)
2.82C3.27)
22.2C24.0)
74.7C77.6)
292(287)
2.82C3.23)
50.4(53.
21.7C23.4)
30.2C28.9)
411(411)
2.59C2.95)
31.3C32.2)
24.2(26.4)
12.2C8.8)
461(462)
3.4lC3.95)
42.OC44.2)
18.9C20.4)
37.7C37.5)
274(272)
2.82C3.20)
41.5C43.5)
15.8Cl6.9)
32.9C32.5)
190(189)
2.6OC2.92)
36.5C38.0)
27.4C29.6)
33.8C37.8)
297(292)
0.04(0.
23.2C25.0)
23.2C24.3)
279(277)
0.95(1.14)
-llV(-129)
lV.l(20.5)
43.2C45.5)
168(164)
l.30(1.50)
-38.9(-42.4)
relations
1.35(0.28) 31.4C32.5)
IO)
228(227)
l.lS(l.32)
-55.7(-61.1)
3.76C2.26)
270(271)
I .76(2.06)
-40.4(-43.9)
16.4(17.6)
22.OC22.4)
162(161)
1.56Cl.79)
-15.5(-17.3)
13.7C14.6)
20.5C20.7)
ll5(114)
l.57Cl.78)
29.6C32.0)
47.4C51.7)
395(388)
1.10(1.31)
-151(-165) -53.9(-58.8)
17.8(18.
I)
I)
32.8C33.5)
376(374)
I .86(2.17)
20.6C22.2)
57.6C60.3)
222(218)
2.03C2.33)
20.2C21.7)
24.2C24.0)
307(307)
I .84(2,
I)
-3.02(-3.70)
-6.71(-8.00) IO)
-24.6(-27.6) -10.7(-12.1)
354(356)
2.57(2.99)
17.6(19.0)
29.5C29.7)
21 l(2lO)
2.17(2.47)
3.62(3.
14.7Cl5.8)
26.5C26.6)
148(147)
2.07C2.33)
l0.1(10.1)
7.99C5.75)
representation
this in
is
preferred
corresponding table
Table
and I
of
constants the
Ref.
rotational
for
these DJ,
nearly
prolate
. . . . d2 may be
constants
in
Table
I)
-463(-504)
20.8(22.5)
the in
6K
503(497)
22.4(24.4)
B D HbHt 2 4 b B2D5H
J
61.5C65.4)
25.0(27. b
6
31.9C34.7)
18.8(20.
t
cis-B2D4H2
A K
A JK
AJ
asymetric
calculated VI,
using
18)
top from
the
the
(a).
cm-’ or 1% (whichever is smaller) at worst, but most should be reliable to within 5 cm-‘.’ It must be emphasized here that the values are free from all effects of Fermi resonance, which does not exist within the harmonic model. In B2H6 and BzD6 species, Fermi resonance perturbations of up to 50 cm-’ have been observed ’ The standard deviation of the overall fit for B2H6 is 4.2 cm-r on frequencies and 0.4 cm-’ on “‘B isotopic shifts; for B2D6, 4.5 cm-’ on frequencies and 0.4 cm-’ on “‘B isotopic shifts.
SPECTROSCOPIC
PARAMETERS
13
FOR DIBORANE
TABLE VIII Anharmonic Fundamental Frequencies (in cm-‘) for all Deuterated “B Diboranes (associated upward “B isotopic shift below each frequency) tran.s-
ast
t B2H6
t
t
t
B2H4D2
B2H4D2
B2H5D
cis-
t B2H4D2
B2H3D3
B2H2D4 D2h
D2h 2526
2521
2521
1898
1842
6.6
5.9
5.9
13.3
12.9
9.2
8.5
2096
2102
2105
2108
2109
2112
2114
1.8
0.8 a
a
g
u
1187
b2u
Ig
b l"
b3g A
b 3u
1.9 a~
II81
3.0
2.9 a
g 1086
al
1083
3.0 a
1080
3.1 ag
917
6.3
6.3
7.7
7.2
6.8
788
761
744
721
753
718
708
31.1
21.1
19.1
15.6
21.0
13.4
13.6
833
709
648
646
624
0.0
5.0
2.0
5.7
1.8
704 fa2
a
00
"
vt 1754
1752
1752
4.2
4.3
4.4
4.4
860
850
13.9
9.2
2613 15.0
a
1752
a
a
593 "
11 1750
0.0 1747
4.5
770
850
716
13.3
14.0
9.4
14.9
2606
2605
2570
2574
2568
1975
14.7
14.7
II.1
II.4
II.0
20.8
951
940
940
880
865
4.3
7.1
7.0
II.4
4.9
343
326
323
320
0.3
0.2
0.0
al
bl
b2
b
717
g
a2
20.0
4.4
367
b
II81
6.2
1756
b2g
a
1837
867
b u
5.0
al
a'
4.6 b2g
703 16.1
860
b 2u
3.6
306
291
0.1
0.1
0.0
0.0
2597
2566
1968
2564
2560
1968
1961
14.3
II.1
20.9
11.0
10.6
20.8
21.0
918
836
796
781
771
14.0
19.5
10.5
25.9
14.0
15.1
13.4
1924
1922
1920
1920
1920
1918
1916
10.7
10.6
10.5
10.5
10.5
10.4
924
834
974
a
88 942
bl
a g
a
924
u
bl
b Ig
738
10.3
b
11 839
I11 744
5.0
6.2
7.2
997
1012
985
0.9
0.8
0.9
a
4.7
4.2
1023
1015
0 0
0.4
2518
1899
1842
1905
1900
1899
5.3
13.7
9.2
14.2
14.6
13.9
10.0
1615
' 1612
1608
1609
1609
1 1605
1601
a
7.8
824
998 La2
=I
3.9 b g
00
4.5
4.2
1175
1080
901
6.4
6.7
16.8
3.5
b u
3.8
b2
bl
a
b A 3g
943 00 1847
b 3"
2.5
3.8
3.2
1073
1077
903
878
5.5
6.5
16.9
7.1
(4), the largest associated with the bridge deformation vibration, v13. It seems likely that this resonance will persist through many isotopic diboranes. Other identified resonance perturbations in B2H6 and BzD6 species were not greater than 20 cm-‘.
74
J. L. DUNCAN TABLE VIII-Continued
B2D2"4 D2h 2523
~-
a"
tra”St %D4"2
BzD4"2
BzD5"
B2D6
Cs(a,b)
C*"(a)
C2h(C)
C2"(b)
Cs(ab)
D
2520
2520
1906
1'112
1905
1858
5.7
5.8
15.7
15.4
15.0
II.8
1506
1506
1506
1504
1501
2.3
I.8
I.9
I.9
1.4
a
'
=I
g
1084
5.6
6.2
720
792
719
706
18.9
15.7
23.9
12.8
13.7
664
643
644
621
I.6
5.2
I.3
1291
4.7
794
741
30.5
24.0
833
682
0.0
3.8
no
="
6.6
6.6
6.6
860
a52
____~ 13.6
9.7
2605 15.0
a
0,
18.9
a
593 u
1288
0.0 1286
6.8
715
850
706
II.0
6.5
9.1
2604
2605
2572
2574
2568
1975
14.7
14.7
II.1
II.4
II.0
20.7
a25
726
715
704
707
4.9
10.6
7.0
8.0
7.7
a'
bl
297 b2
708
1968
10.6
20.8
918
881
878
--
14.0
12.8
II.3
1473
1467
1461
16.1
15.9
15.7
940
920
R32 0.0
2518
1904
5.2
14.7
II93
a'
7.8
1175
1065
4.7
6.3
a
904
u
bl
781
1461
1461
1456
15.7
15.7
15.5
902
887
a72
--
aIT
4.5
846
726
727
7.6
I.4
1.3
1850
1902
1897
1849
10.2
13.7
14.1
10.0
II89
II89
1189
1188
832
b g
7.6
b
"
6.9
b,
'g
782
13.7
b2
1961
a'
21.0
b
7.2
7.0
738 13.4
15.2
25.3
1.7
a2 00 -----A-
a'
822
1.7
6.5
II91
8.0
g
4.5 261
2560
bk
2u
0.0
10.9
a
703
b
272
2562
1968 20.9
a'
699 14.8
0.1
281
II.0
0 0
al
0.1
2565
830
5.3 283
14.3
6.4
733 u
7.1 b2g
11.4
0.2
2597
a'#
b
--
0.3
0.3
I.8
g
286
0.4
bl
b
a2
--
913
6.5
311
3u
I.1 =g
7.0
4.9
784
6.0
b
a'
1072
5.2
all
=I
1070
1179
a2 L
a
II79
1184
1290
b3e L-
211
1509
1291
bl"
t
%D4"2
1293
b2u
t
*2D3H3
6.3
1296
b2g
cist
1511 2.7 =g
as-
t
t
1450 15.3
b l"
722 4.7 728
Ab3g
0 0 1840 8.6 II86
b 3u
6.6
898
1062
1067
a97
a74
15.6
4.8
7.3
15.3
5.9
This does not preclude the possibility, however, that large Fermi resonance perturbations may occur in any isotopic diborane due to close coincidences between appropriate unperturbed vibration levels coupled by a large anharmonic resonance
SPECTROSCOPIC
PARAMETERS
FOR
75
DIBORANE
TABLE VIII-Continued
b
da2
b2
a2
al
bl
b2
t
b
D2
B2H3D
Cs(aC)
C,(C)
t D::
b B2H3D
t
B2D4"
D2
Cs(bd
b
bt H
B2D5H C2"(C)
Cl
2524
2521
2518
1894
1900
1843
6.4
5.8
5.9
13.5
13.1
9.5
9.5
2018
2022
2023
2027
2028
2028
2029 6.2
4.5
5.5
5.3
6.4
6.5
6.3
1180
1180
1085
1079
900
5.R
5.9
5.9
7.4
7.0
15.8
786
747
742
721
774
712
707
30.7
13.6
18.9
15.6
17.8
9.1
15.7
a
1
av~
a
a
v
1841
1185
=I
915 19.5
833
693
678
645
645
623
00
4.6
I.0
1.8
5.5
1.5
1695
1692
1689
1689
89 1689
1687
4.3
4.2
4.0
4.1
4.1
3.8
860
849
712
723
850
714
701
13.7
9.1
12.1
6.5
9.3
II.6
13.4
2613
2605
2605
2570
2572
2566
1975
15.0
14.7
14.7
11.1
11.4
II.0
20.8
826 bl
B2H3D
C1
C,“(C)
iil
b
B H DbDt 24
B2H5D
a'
b
78'3
a
593 a2
0.0 ,684
b2
3.5
798
752
3.1
19.3
5.7
II.0
6.7
10.6
338
319
306
303
301
288
275
0.1
0.2
0.3
0.1
0.0
0.1
0.0
2597
2565
1968
2562
2560
1968
1961
14.3
II.0
20.9
II.0
11 10.6
20.9
21.0
918
873
867
823
781
778
14.0
12.2
8.7
25.5
13.9
14.7
13.4
1486
1482
1478
1478
1479
1474
1470
10.8
10.5
t 10.1
10.2
10.2
9.8
956
930
914
912
844
839
3.1
4.3
8.1
2.7
10.0
6.2
a
a
a
(7
a
a'
a
a
t
711
a
722
989
977
968
946
963
941
I.5
2.0
2.6
2.4
2.2
2.3
2518
1899
1843
1904
1899
1899
at1
713 b'
a2
2.9
738
9.5 al
732 5.9 906
bl
I.2 1845
5.3
13.7
4.9
1234
1233
t 1231
6.6
6.7
6.6
6.8
6.8
6.7
6.7
1175
1078
899
1070
1076
1077
876
6.1
6.5
15.1
5.6
6.1
6.5
6.6
a
b
14.0
14.4
13.8
1231
all 1231
1228
9.5 b2
1227
parameter. The predicted unperturbed anharmonic fundamental vibration frequencies, and boron isotopic frequency shifts, for all deuterated diboranes are collected in Table VIII. In addition to being of assistance to any future infrared or Raman
76
J. L. DUNCAN
studies on these species, the data in Table VIII should be valuable for estimating the contributions to the microwave spectra from lower-lying vibrational levels which will be populated at ambient temperatures. RECEIVED:
February
26, 1985 REFERENCES
1. E. HAMILTONAND J. L. DUNCAN,J. Mol. Spectrosc. 90, 129-138 (1981). 2. E. HAMILTONANDJ. L. DUNCAN,J. Mol. Spectrosc. 90, 517-530 (1981). 3. J. HARPERANDJ. L. DUNCAN,J. Mol. Spectrosc. 100, 343-357 (1983). 4. J. L. DUNCAN, D. C. MCKEAN, I. TORTO, AND G. D. NIVELLINI,J. Mol. Spectrosc. 85, 16-39 (1981). 5. J. L. DUNCAN,J. HARPER,E. HAMILTON,AND G. D. NIVELLINI,J. Mol. Spectrosc. 102, 416-440 (1983). 6. C. E. BLOMAND A. MULLER,J. Chem. Phys. 69, 3397-3402 (1978). 7. D. G. LISTER,G. D. NIVELLINI,AND P. PALMIERI, J. Mol. Struct. 85, 279-283 (1981). 8. J. L. DUNCANANDJ. HARPER,Mol. Phys. 51, 371-380 (1984). 9. E. HIROTA,Y. ENDO, S. SAITO,ANDJ. L. DUNCAN,J. Mol. Spectrosc. 89, 285-295 (1981). JO. E. HIROTA,Y. ENDO, S. SAITO,K. YOSHIDA,I. YAMAGUCHI,AND K. MACHIDA,J. Mol. Spectrosc. 89,223-231 (1981). JJ. J. L. DUNCAN,Mol. Phys. 28, 1177-1191 (1974). J2. J. L. DUNCAN,D. C. MCI&AN, ANDA. J. BRUCE,J. Mol. Spectrosc. 74, 361-374 (1979). 13. F. HERLEMONT,M. LYSZYK, J. LEMAIRE,C. LAMBEAU,M. DE VLEESCHOUWER, AND A. FAYT, J. Mol. Spectrosc. 94, 309-3 15 ( 1982). 14. M. DE VLEESCHOUWER, C. LAMBEAU,D. VAN LERBERGHE, E. JANSSENS, AND A. FAYT, J. Mol. Spectrosc. 90, 273-286 (1981). IS. J. L. DUNCAN, E. HAMILTON,A. FAYT, D. VAN LERBERGHE, AND F. HEGELUND,Mol. Phys. 43, 737-752 (1981). 16. F. HEGELUNDAND F. M. NICOLAISEN, Mol. Phys.. in press. 17. Y. VERBIST-SUEUR, C. P. COURTOY,A. FAYT, AND D. VAN LERBERGHE, Ann. Sot. Sci. Bruxelles 90, 317-336 (1976). 18. M. DE VLEESCHOUWER AND A. FAYT, Privatecommunication. 19. T. OKA AND Y. MORINO,J. Mol. Spectrosc. 6, 472-482 (1961); Y. MORINO,K. KUCHITSU,AND T. OKA, J. Chem. Phys. 36, 1108-l 109 (1962); K. KUCHITSU,J. Chem. Phys. 49,4456-4462 (1968). 20. K, KUCHISTSUAND S. J. CYVIN, in “Molecular Structures and Vibrations” (S. J. Cyvin, Ed.), Ch.
12, Elsevier, Amsterdam, 1972. 21. H. S. PEISER,N. E. HOLDEN,P.
DE
BI~VRE,AND 1. L. BARNES,Pure Appl. Chem. 56, 695-768
( 1984). 22. M. NAKATA, S. YAMAMOTO, T. FUKUYAMA, AND K. KUCHITSU,J. Mol. Struct. 100, 143-159
(1983). 23. T. 0~ AND Y. MORINO,J. Mol. Spectrosc. 6,472-482 (1961). 24. 1. M. MILLS,in “Molecular Spectroscopy-Modem Research” (K. Narahari Rao and C. W. Mathews, Eds.), Vol. I, Ch. 3, Academic Press, New York, 1972. 25. J. L. DUNCANAND D. C. MCKEAN, J. Mol. Spectrosc. 107, 301-305 (1984). 26. J. K. G. WATSON,J. Mol. Spectrosc. 65, 123-133 (1977).
OF MOLECULAR
SPECTROSCOPY
113, 63-76 (1985)
Ground State Rotational Parameters and Fundamental Vibration Frequencies for Isotopically Substituted Diboranes J. L. DUNCAN Department sf Chemistry University of Aberdeen, Meston Walk. Old Aberdeen .4B9 2lJE. Scotland The present spectroscopic structural information on diborane derives from infrared studies of B2H6 and B2D6 species only. Due to the impossibility of selective isotopic substitution in diborane, and the consequent coexistence of a number of isotopic species in any partially deuterated sample, the most probable source of further structural information of quality will be from microwave studies of asymmetrically deuterated species. To assist in the assignment of the overlapping spectra that will occur, accurate rotation and quartic distortion constants are presented for the ground states of all isotopic diboranes in terms of existing zero-point average structural parameters and isotopic changes in these calculated through the harmonic potential function. Sets of fundamental anharmonic vibration frequencies are calculated in order that interference from low-lying vibrations with significant populations at ambient temperatures may be anticipated. 0 1985 Academic Press. Inc. 1. INTRODUCTION
Over the past few years we have made a concerted spectroscopic study of the diborane molecule through the isotopically pure “B2H6, “B2H6, “B2D6, and “B2D6 species. High-resolution rovibration assignment and analysis of a number of isolated bands in the spectrum of each species has enabled rather precise sets of ground state rotational and quartic centrifugal distortion constants to be determined from large basis sets of ground state rotational level combination differences (1-3). As a result of lengthy examination of the infrared and Raman spectra, fairly clear pictures of the major resonance perturbations have been constructed, and the positions of a number of previously uncertain fundamentals have been established, for each isotopic molecule (4). Sets of unperturbed fundamental vibration frequencies which obey closely the Teller-Redlich product rule have then been used to determine for the first time a physically realistic and accurately determined set of harmonic force constants (5), which are completely substantiated by the results of two independent ab initio calculations at the 4-31G level (6, 7). The harmonic potential function has then been used in conjunction with the 12 observed ground state inertial constants to determine the ground state average structure parameters, and their isotopic dependences, for the molecule (8). While this structure appears to be rather precisely defined, not all parameters could be allowed to refine independently, and one of two structural dependences on deuteration had to be constrained to the value predicted using the potential function. The apparent quality of the structure stemmed from the fact that, when either constraint was imposed, the other parameter refined to a value very close to that predicted. In essence, two almost identical sets
63
QO22-2852185$3.00 Copyright 0 1985 by Academic Press. Inc All rights of reproduction in any form reserved.
64
J. L. DUNCAN
of parameters resulted. Nevertheless, at the moment insufficient inertial constant data of quality are available to enable an unequivocal set of structure parameters to be determined for the diborane molecule. 2. FURTHER
PROGRESS
Due to the impossibility of selective deuteration of the molecule at the bridge and terminal positions, a mixture of isotopic species results on partial deuteration of the diborane molecule. This renders detailed spectroscopic studies from either infrared or Raman spectra extremely difficult, to say the least, due to the overlapping of rovibration bands from a minimum of two, and often more, major isotopic species present in the sample. It seems that the most fruitful studies would be those undertaken in the microwave region, where only asymmetrically deuterated species would give rise to absorptions through the small permanent dipole moment introduced by the isotopic substitution. Comparable studies on partially deuterated ethanes (9) and ethylenes (IO) have proven to be highly successful, as well as highly accurate. The problem of blending of absorptions arising from different isotopic species generally does not arise in the microwave experiment. However, assignment work is very much simplified in such cases (and sometimes only possible) when the approximate relative positions of rotational transitions for different isotopic species are known, and when the relative populations of low-lying fundamental vibrations, and hence interference from “hot” transitions, can be predicted. These require, respectively, a prior knowledge with reasonable assurance of (a) the ground state rotational (or inertial) constants and centrifugal distortion constants, and (b) the fundamental vibration frequencies of the isotopic modifications concerned. We have at our disposal the means for predicting these spectroscopic phenomenological parameters to high accuracy for any isotopic modification of the diborane molecule. In this paper we list the appropriate data for all isotopic forms of diborane which contain either the i”B or “B nuclides. Calculations for “mixed” “B”B species have not been made because of their very large number, and because preparation prior to effective study would always be made in terms of an isotopically pure starting material. Calculations of this kind, carried out previously for isotopic species of ethylene (1 I) and ethane (12), have proven of great value to subsequent spectroscopic investigations on new isotopic species (9, 13-l@, ground state rotational constants being predicted to within 0.05% and centrifugal distortion constants generally being reliable to much better than 5%. Table I compares the ground state phenomenological parameters for isotopic ethylenes predicted in 1974 (II) with the experimental values which have been determined subsequently through infrared or microwave studies, to give some idea of the quality of prediction which is possible. 3. CALCULATIONAL
PROCEDURE
AND RESULTS
(a) Ground State Rotational Constants The harmonic potential function may be used to correct ground state rotational constants, B$, for the effects of averaging over the harmonic atomic displacements in the ground vibrational state, and for the very much smaller centrifugal distortion effects, to yield zero-point average constants, B; (19). No corrections for electronic
SPECTROSCOPIC
PARAMETERS
65
FOR DIBORANE
TABLE I Comparison of Ground State Phenomenological Parameters (in cm-‘) for Isotopic Ethylenes Predicted in 1974a with Experimental Values Determined Subsequently 13 ‘2”4 Pred.
Exp.(l8)
Pred.
IR
Exp. ( 16) IR
3.4860
3.48608
0.95067
0.91654
0.9163250
0.84798
0.8478267
0.83324
0.83297
0.79331
0.74406
0.7437726
0.67401
0.6737685
0.67091
0.67063
0.95068 0.79342
IO’ . A”R
Pred.
Mw 3.324541
Ro
A’,
Exp.(lO)
3.3256
Co
IO6 . AoJK
Pred.
ml 4.005888
4.86452
,06.
Exp.(lO)
4.0068
4.8656
A0
t~XWC2H2D2
cis-C2H2D4
‘ZH3’
1.31
I .332
1.27
1.3019
I. 16
1.20
1.05
1.089
9.94
9.659
6. I8
6.0174
3.82
3.90
3.04
2.85
48.66
54. I
55.21
82.1
82.05
66.8
70.595
45.6
I06 . 60J
0.234
0.2354
0.275
0.2803
0.280
0.2884
0.241
0.257
106 . 60K
8.97
8.97
7.60
8.132
6. I3
6.558
5.45
6.5
a Ref.
(II)
contributions to the moments of inertia, and hence rotational constants, are necessary for diborane, since there are neither lone pairs of electrons nor multiple bonds to give off-axis inertial contributions. The B; constants are compatible within any single isotopic molecular species (although isotopic dependences still remain), and enable one to calculate average structure parameters and the major isotopic dependences of these. Minor isotopic dependences, e.g., on substituting “B for “B, are small, but important to the overall quality and reliability of the determined parameters. These are estimated through the harmonic potential using a simple diatomic approximation to enable the anharmonic contribution to be calculated (20). Through the reverse calculation, starting with the average structure parameters and allowing for the particular isotopic dependences calculated through the potential function, a set of ground state rotational constants may be estimated for any isotopic modification desired. The set of harmonic force constants used are listed in Table V of Ref. (5) where the symmetry coordinates and molecular geometry to which they refer are also defined. The average structure parameters used are essentially those of Ref. (8) but are modified very slightly here due to a recent update of isotopic atomic masses (21). The recalculated average structure parameters for diborane are listed in Table II. Isotopic changes were calculated for these zero-point average distance parameters between bonded nuclei according to the relation (18) 6r, = s(Ar),
- X,,,
where (A$,, is the average displacement of the bonded distance, and 6Ko is a correction for the effect of nuclear displacements perpendicular to the bond. The subscript zero refers to 0 K, since the ground state is being considered. By treating
66
J. L. DUNCAN TABLE II Zero-Point Average Structural Parameters for the Diborane Molecule” Parameter
Value
rZ(“BHt)
1.1939’;1
0.001’3
+“BHb)
1.327238
0.00046
LZ(Ht’o~~t) LZ(Hb’O~Hb)
121.5Y”
0.19
96.42’
0.04
6rz(‘o~~t
- ‘OmJ
0.00’808
Gr=(“B”b
- “BDb)
0.003732
0.00038
0. ‘50
0.05
6LZ(Ht”BHt “8H
6’&(Hb 6r
z
(“BH
6rZ(loBHb
a See
Table
due
to
The
number
Constrained function, a(BHb)
t
-Dt”BDt)
b
-D
=
“BD,)
b
-“8H
t
-0.
)
- “BHb)
7 of
Ref.
a recent
consistency b
Uncertainty
of
(8).
update decimal
in
the
to
values
using 0-I 1.8A
6rL .
‘3O
0.04
0.000’2;1
constrainedb
0.00008;;
constrainedb
Individual of
isotopic
places
constrainedb
values atomic
quoted
are
are
slightly
masses.
required
See for
changed text.
internal
calculations. estimated = 3a&&2>0 See
through -
the
6Ko with
harmonic a(BHt)
potential 0-l = 2.5A and
text.
bonded distances in the diatomic approximation (equivalent to considering only the cubic stretching force constant for the bond in the light of its dominance over all others), the anharmonic contribution (Ar),, may be approximated to 3a(Az2)0/2. Here (Az2),-, is the mean square parallel amplitude of vibration, and a is the cubic anharmonicity constant for the bond in question, arising from the potential energy expansion for a diatomic molecule, I/ = $(Az2 - aAz3 + - - - ). On the basis of our structural calculations, supported by ab initio calculations, values of a(BH’) = 2.5 A-’ and a(BHb) = 1.8 A-’ were chosen for diborane (8) and are used here. The changes to the zero-point average BH distances may then be estimated for any isotopic substitution by calculation of the mean square parallel and perpendicular amplitudes through the harmonic potential function and application of the equation 6r, = 3a6(Az2j0/2 - 6K0. The zero-point average isotopic structural changes thus estimated for isotopic diboranes are collected in Table III. The numbering used for the atoms is given in Fig. 1.
SPECTROSCOPIC
PARAMETERS
67
FOR DIBORANE
TABLE III Calculated Zero-Point Average Structural Changes from “B2H6 for Isotopic Diboranes (negative and positive signs denote bond shortenings and lengthenings, respectively) Isotopic substitution
1lB 2 Dl DlDZ DlD8 D1D7 DlDZD7 DlD2D7D8 DqD5 DlD4D5 DlD2D4D5 DDDD 1458 DlD4D5D7 DDDDD 12457 DlD2D4D5D7D8 D4 DlD4 D1D2D4 DlD4D8 DlD4D7 DlD2D4D7 DlD2D4D7D8
5%
B"4
BHg
B"7
B%
10-4x
10-4x
10-4%
ld4R
10-4x
lO-48
-1.2
-1.2
-0.8
-0.8
-1.2
-1.2
-9
+2
-1
-1
-5
-6
-8
-8
-2
-2
-11
-11
-15
-2
-4
-4
-2
-15
-13
-4
-4
-4
-13
-4
-12
-13
-5
-5
-18
-7
-17
-17
-7
-7
-17
-17
-3
-3
-32
-32
-3
-3
-12
0
-33
-33
-7
-8
-11
-11
-34
-34
-11
-11
-16
-4
-36
-36
-4
-16
-15
-5
-36
-36
-15
-5
-14
-15
-36
-36
-20
-8
-18
-18
-38
-38
-18
-18
-2
-2
-27
-7
-2
-2
-11
+1
-28
-6
-6
-7
-10
-10
-33
-6
-11
-11
-16
-3
-32
-9
-3
-16
-14
-5
-32
-9
-14
-5
-13
-14
-33
-8
-19
-8
-17
-17
-36
-10
-17
-17
For interbond angles no comparable calculations can be made. Isotopic changes were assumed pro rata with respect to those experimentally determined on deuteration, and listed in Table II, with no changes on boron substitution. Some form of check on the validity of these last simplistic assumptions could be made by calculating the resulting nonbonded distance changes on partial deuteration and comparing these with values calculated using Eqn. (39) of Nakata et al. (22), derived for XY2 molecules as a development of the diatomic approximation. Using averages of their (approximately constant) estimates for the appropriate anharmonic constants, good agreement for H--H nonbonded distance changes on deuteration was observed. Consequently, our simple method for estimating isotopic angle changes was assumed to be a reasonable one.
68
J. L. DUNCAN c
I-
a
b
t
a
FIG. 1. Numbering of atoms and orientation of inertial axes for the diborane molecule.
Application of the structural data in Tables II and III enables the zero-point average inertial constants, Z;, to be calculated for any isotopic diborane, as listed in Table IV. Through application of the harmonic potential function and use of the relevant perturbation expressions (8, 23, 24), the zero-point harmonic vibrational (AZ&) and centrifugal distortion (AZ&,) contributions to the ground state I$ constants may be calculated, as listed in Table V. These enable zero-point average and ground state inertial constants to be interconverted for any isotopic diborane according to the relation
The data of Tables IV and V may finally be combined through this relation to predict the appropriate ground state rotational constants for any deuterated diborane, using the conversion B*/MHz = 505 379.0 pA2/Za. These constants are collected in Table VI. From our previous experiences, and from the quality of the empirical data used in their estimation, it is considered that these ground state rotational parameters should be reliable to considerably better than 1 part in 2000 in any predictive or comparative spectroscopic capacity. (b) Centrifusal Distortion Constants The quartic distortion constants are functions of the harmonic potential function and may be used to assist in its determination. Accordingly, values may be predicted for any isotopic modification through a reliably determined potential function. Strictly, these are hypothetical values at the equilibrium configuration rather than ground state values. Since the vibrational dependences of the constants are not known, the two are normally equated. It is our experience that differences are seldom greater than 5% in these small constants (see Table I), although in exceptional cases differences of 10% appear to be possible (25). Calculated quartic distortion constants consistent with a Z’A axis representation (A, B, C - z, x, y) are collected in Table VII for all deuterated diboranes.
SPECTROSCOPIC
PARAMETERS
69
FOR DIBORANE
TABLE IV Calculated Zero-Point Average Inertial Constants (in pA2) for Deuterated Diboranes from the Parameters of Tables II and III as-
BZ”6
'lB
"B
t
t
B2"5D
B2"4D2
"B
B2"4D2
t
t B2"3D3
B2H2D4t 10.68199
6.35090
7.30065
8.51935
8.12611
0.37229
I;
27.87255
30.05830
31.91115
32.58303
32.19284
34.38669
36.51320
I= z
30.27651
33.41236
36.48450
36.76433
36.62032
39.90739
43.25216
Ia z
6.35202
7.29261
a.52090
a.10100
8.36362
9.45706
10.68397
I;
26.31714
28.50471
30.33635
31.05608
30.63917
32.83599
34.96096
IC z
28.72175
31.85025
34.91077
35.21180
35.05751
38.34836
41.70143
trans-
cis-
B2D3"3
as-
t
B2D4"2t
B2D4"2
t B2D4"2
t B2D5"
B2D6
Ia z
a.30801
9.25960
10.47593
10.08152
10.33792
11.42318
12.63831
I;
29.66518
31.84024
33.70474
34.35900
33.96702
36.15995
38.27312
IC z
30.10694
33.23468
36.31669
36.57926
36.44372
39.72192
43.05280
8.30936
9.25205
10.47773
10.05663
10.33069
11.41595
12.64055
I;
28.12181
30.29950
32.14487
32.84372
32.42519
34.62131
36.73214
IC z
28.56448
31.68607
34.75829
35.03843
34.89395
38.17534
41.51317
trans-
cis-
b B2"5D
B H DbDt 24
B H DbD t 23 2
bt B2"3D D2
bt B2"3D D2
bt B2D4H H
b B2D5"
as-
"B
B*"4D*t
I:
B2D2"4t
"B
cis-
9.46493
t
1lB
trans-
1:
7.29374
a.24574
9.46287
9.32183
10.41173
11.62909
Ib z
28.72693
30.91701
32.76736
33.43457
33.04250
35.23985
37.35912
I= z
30.18489
33.32620
36.39447
36.66643
36.53048
39.81415
43.15099
Ia z
7.29250
8.23562
9.46233
9.04307
9.31168
10.40214
11.62927
I;
27.17653
29.36818
31.19732
31.91134
31.49239
33.69304
35.81061
c
28.63753
31.77139
34.82736
35.12163
34.97420
38.26119
41.60578
(c) Fundamental
9.07025
Vibration Frequencies
The determination of the molecular harmonic potential function requires that observed (anharmonic), unperturbed fundamental frequencies are “harmonized” so as to obey the product rule predictions as well as possible. In the absence of experimental anharmonicity constants, we have used a simple Dennison’s Rule approach with the original data on “B2H6, “B2H6, “BzD6, and “B2D6 (4). By
-0.14(-0.14)
0.23(0.23)
103.AI&
103.AIc;nt
-O.Ol(-0.01)
103.AIv;b
a cent
-71.00(-68.66)
-29.65(-27.66)
I03.AIvbib
103.AI
-3.85(-4.36)
B2H5D
b
0.17(0.16)
-O.ll(-0.10)
-O.Ol(-0.01)
-31.28(-29.27)
-67.73(-65.54)
-3.98(-4.57)
0.28(0.27)
-0.16(-O.
-O.Ol{-0.01) 15) 0.38(0.37)
-O.Zl(-0.20)
-O.OZ(-0.02)
-24.08(-22.41)
b
-82.75(-80.44)
-8.94(-9.51)
B2H3D
as-
-27.18(-25.42)
bc D
-76.89(-74.44)
-6.59(-7.08)
B2H4D
0.29(0.28)
-0.17(-O.
-0.13(-0.12)
0.21(0.20)
-O.OZ(-0.02)
-25.74(-24.16)
-O.Ol(-0.01)
-79.37(-77.14)
-7.99(-8.60)
-28.89(-27.15)
l7(-6.74)
B2D4H2
-73.46(-71.25)
-6.
B2D3H3
as-
B2D2H4t
t
-0.02(-0.02)
-O.Ol(-0.01)
0.33(0.32)
103.AIv\b
103.AI
=
= Cent
b. vrb
103.AIc;nf
103.AI
lo3.AI”~b
103.AI
103.AIv;b
103.AIr;nr
-20.24(-18.60)
-23.05(-21.31)
0.50(0.49)
18)
-86.52(-83.97)
-80.62(-78.98)
-0.26(-0.25)
-0.19(-O.
103.AIc;nt
t
t
16)
D2
t
-9.55(-10.10)
B2H4D2
0.38(0.37)
-O.Ol(-0.01)
V
t
13)
t
b
H
t
0.27(0.26)
-0.15(-O.
-O.Ol(-0.01)
0.30(0.29)
-0.16(-O.
-O.Ol(-0.01)
0.34(0.33)
-0.18(-O.
-0.02(-0.02) 17)
0.33(0.32)
-0.17(-O.
-O.OZ(-0.02)
-18.70(-17.38)
-10.69(-11.28)
B2D5H
-87.85(-85.73)
-9.90(-10.45)
B2D4H
-21.66(-20.26)
16)
D2
-85.35(-83.06)
b
-24.82(-23.26)
-8.89(-9.41)
B2H3D
-82.83(-80.64)
14)
D2
cis-
0.26(0.26)
-0.14(-O.
-24.76(-23.23)
b
0.26(0.25)
-0.02(-0.02)
-79.17(-76.82)
-7.83(-8.28)
B2H3D
trans-
0.20(0.20)
t
-0.13(-O.
-0.12(-O.
-0.15(-0.14)
-O.Ol(-0.01)
-O.Ol(-0.01)
0.23(0.22)
-O.Ol(-0.01)
-26.46(-24.91)
b
ll(-18.80)
-84.71(-82.65)
-26.42(-24.90)
-75.89(-73.68)
-20.
-79.43(-77.41)
B2D6 -9.16(-9.78)
-82.04(-79.89)
-8.68(-9.28)
B2D5Ht
-8.08(-8.67)
cis-
0.41(0.40)
-23.30(-21.87)
-7.04(-7.56)
B2D4H2
tra”S-
12)
-0.20(-O.
0.43(0.42)
-O.Zl(-0.21)
19)
-0.20(-O.
-0.19(-O. 0.40(0.39)
-O.OZ(-0.02)
-0.02(-0.02)
-O.Ol(-0.01)
0.3610.35)
-15.46(-14.17)
-l8.17(-16.69)
-21.12(-19.50)
-9l.l2(-88.83)
-O.Ol(-0.01)
-ll.97(-12.52)
B2H2D4
-20.79(-19.22)
18)
t
-88.81(-86.48)
-10.81(-11.32)
B2H3D3
-86.49(-84.12)
t
-82.84(-80.29)
B2H4D2
cis-
-9.30(-9.77)
t
-8.23(-8.63)
B2H4D2
tl-C%lS?
and Centrifugal Contributions (in rAZ) to Ground State Inertial “B Diboranes (values for ‘“B diboranes in parentheses)
-O.Zl(-0.20)
-25.32(-23.27)
‘. vlb
103.AI
-74.87(-72.32)
-6.53(-6.98)
-3.11(-3.58)
103. AIctnt
103.AIvbib
I03.Alv~.
BZH5D
t
Harmonic Vibrational Constants for Deuterated
B2"6
Calculated
TABLE
16)
13)
19)
t
71
SPECTROSCOPIC PARAMETERS FOR DIBORANE TABLE VI Predicted Ground State Rotational Constants (in MHz) for Deuterated Diboranes as-
11B
"B
trans-
cis-
B2H6=
t BZ"5D
t B2"4D2
B2H4D2t
B2H4D2t
t B2"3D3
t B2H2D4
A0
79 615
69 286
59 388
62 255
60 430
53 456
47 364
B 0
18 181
16 859
15 880
15 550
15 741
14 735
13 876
C 0
16 706
15 136
13 859
13 754
13 808
12 669
11 689
A
79 607
69 367
59 381
62 451
60 496
53 503
47 358
B.
19 256
17 778
16 705
16 315
16 540
15 432
14 481
Co
17 610
15 878
14 404
14 360
14 424
13 184
12 123
trans-
cis-
0
as-
t
"B
"B
B2D2H4t
B2D3"3t
B2D4H2
B2D4H2t
t B2D4H2
t B2D5"
B2D6a
A0
60 860
54 615
48 278
50 164
48 923
44 276
40 017
B 0
17 075
15 910
15 030
14 742
14 913
14 008
13 234
Co
16 805
15 219
13 926
13 826
13 878
12 730
11 744
A0
60 854
54 663
48 273
50 291
48 961
44 306
40 012
B0
18 013
16 719
15 760
15 422
15 623
14 631
13 790
Co
17 711
15 963
14 550
14 434
14 494
13 246
12 179
trans-
cis-
asb
B2H5D
"B
"B
a
bt B2H4D D
bt B2H3D D2
bt B2H3D D2
bt B2H3D D2
bt B2D4H H
b B2D5H
A0
69 326
61 339
53 457
55 766
54 266
48 586
43 498
B 0
17 635
16 387
15 462
15 151
15 333
14 376
13 559
Co
16 758
15 176
13 895
13 792
13 844
12 700
11 717
A0
69 343
61 418
53 463
55 937
54 328
48 633
43 500
B0
18 643
17 252
16 241
15 875
16 089
15 037
14 146
Co
17 644
15 919
14 520
14 399
14 460
13 216
12 152
me
fit (observed - calculated) to the spectroscopic rotational constants A,, Bo, C 0
in MHz for B2H6 and B2D6 species are: 11B2H6 (0,2,1), 1°B2H6 (O,-2,-2), "B2D6
(-3,-3,-l), 1°B2D6 (1.0,2).
using the same procedure in reverse, the predicted unperturbed anharmonic fundamental frequencies for any isotopic modification may be calculated through the potential function. The predicted values are considered to be reliable to within 10
72
J. L. DUNCAN TABLE VII Quartic Centrifugal Distortion Constants (in kHz) for Deuterated “B diboranes in the I’A Representation (z, x, y - A, B, C) (values for “B diboranes in parentheses)
B2H6 t B2”5D t
as-B2H4D2
t
tram-B2H4D2 t
cis-B2R4D2 t B2H3D3 t B2H2D4 t B2D2H4 t B2D3H3 t
as-B2D4H2
t
tram-B2D4H2
t B2D5H B2D6 b B2H5D b
B2H4D D
t
as-B2H3D
t D2 b
trans-B2H3D cis-B2H3D
b
D2
t D2 t
a
If
a IrS
molecules, values
2.28(2.66)
27.OC29.4)
42.9C42.6)
500(498)
2.82C3.27)
22.2C24.0)
74.7C77.6)
292(287)
2.82C3.23)
50.4(53.
21.7C23.4)
30.2C28.9)
411(411)
2.59C2.95)
31.3C32.2)
24.2(26.4)
12.2C8.8)
461(462)
3.4lC3.95)
42.OC44.2)
18.9C20.4)
37.7C37.5)
274(272)
2.82C3.20)
41.5C43.5)
15.8Cl6.9)
32.9C32.5)
190(189)
2.6OC2.92)
36.5C38.0)
27.4C29.6)
33.8C37.8)
297(292)
0.04(0.
23.2C25.0)
23.2C24.3)
279(277)
0.95(1.14)
-llV(-129)
lV.l(20.5)
43.2C45.5)
168(164)
l.30(1.50)
-38.9(-42.4)
relations
1.35(0.28) 31.4C32.5)
IO)
228(227)
l.lS(l.32)
-55.7(-61.1)
3.76C2.26)
270(271)
I .76(2.06)
-40.4(-43.9)
16.4(17.6)
22.OC22.4)
162(161)
1.56Cl.79)
-15.5(-17.3)
13.7C14.6)
20.5C20.7)
ll5(114)
l.57Cl.78)
29.6C32.0)
47.4C51.7)
395(388)
1.10(1.31)
-151(-165) -53.9(-58.8)
17.8(18.
I)
I)
32.8C33.5)
376(374)
I .86(2.17)
20.6C22.2)
57.6C60.3)
222(218)
2.03C2.33)
20.2C21.7)
24.2C24.0)
307(307)
I .84(2,
I)
-3.02(-3.70)
-6.71(-8.00) IO)
-24.6(-27.6) -10.7(-12.1)
354(356)
2.57(2.99)
17.6(19.0)
29.5C29.7)
21 l(2lO)
2.17(2.47)
3.62(3.
14.7Cl5.8)
26.5C26.6)
148(147)
2.07C2.33)
l0.1(10.1)
7.99C5.75)
representation
this in
is
preferred
corresponding table
Table
and I
of
constants the
Ref.
rotational
for
these DJ,
nearly
prolate
. . . . d2 may be
constants
in
Table
I)
-463(-504)
20.8(22.5)
the in
6K
503(497)
22.4(24.4)
B D HbHt 2 4 b B2D5H
J
61.5C65.4)
25.0(27. b
6
31.9C34.7)
18.8(20.
t
cis-B2D4H2
A K
A JK
AJ
asymetric
calculated VI,
using
18)
top from
the
the
(a).
cm-’ or 1% (whichever is smaller) at worst, but most should be reliable to within 5 cm-‘.’ It must be emphasized here that the values are free from all effects of Fermi resonance, which does not exist within the harmonic model. In B2H6 and BzD6 species, Fermi resonance perturbations of up to 50 cm-’ have been observed ’ The standard deviation of the overall fit for B2H6 is 4.2 cm-r on frequencies and 0.4 cm-’ on “‘B isotopic shifts; for B2D6, 4.5 cm-’ on frequencies and 0.4 cm-’ on “‘B isotopic shifts.
SPECTROSCOPIC
PARAMETERS
13
FOR DIBORANE
TABLE VIII Anharmonic Fundamental Frequencies (in cm-‘) for all Deuterated “B Diboranes (associated upward “B isotopic shift below each frequency) tran.s-
ast
t B2H6
t
t
t
B2H4D2
B2H4D2
B2H5D
cis-
t B2H4D2
B2H3D3
B2H2D4 D2h
D2h 2526
2521
2521
1898
1842
6.6
5.9
5.9
13.3
12.9
9.2
8.5
2096
2102
2105
2108
2109
2112
2114
1.8
0.8 a
a
g
u
1187
b2u
Ig
b l"
b3g A
b 3u
1.9 a~
II81
3.0
2.9 a
g 1086
al
1083
3.0 a
1080
3.1 ag
917
6.3
6.3
7.7
7.2
6.8
788
761
744
721
753
718
708
31.1
21.1
19.1
15.6
21.0
13.4
13.6
833
709
648
646
624
0.0
5.0
2.0
5.7
1.8
704 fa2
a
00
"
vt 1754
1752
1752
4.2
4.3
4.4
4.4
860
850
13.9
9.2
2613 15.0
a
1752
a
a
593 "
11 1750
0.0 1747
4.5
770
850
716
13.3
14.0
9.4
14.9
2606
2605
2570
2574
2568
1975
14.7
14.7
II.1
II.4
II.0
20.8
951
940
940
880
865
4.3
7.1
7.0
II.4
4.9
343
326
323
320
0.3
0.2
0.0
al
bl
b2
b
717
g
a2
20.0
4.4
367
b
II81
6.2
1756
b2g
a
1837
867
b u
5.0
al
a'
4.6 b2g
703 16.1
860
b 2u
3.6
306
291
0.1
0.1
0.0
0.0
2597
2566
1968
2564
2560
1968
1961
14.3
II.1
20.9
11.0
10.6
20.8
21.0
918
836
796
781
771
14.0
19.5
10.5
25.9
14.0
15.1
13.4
1924
1922
1920
1920
1920
1918
1916
10.7
10.6
10.5
10.5
10.5
10.4
924
834
974
a
88 942
bl
a g
a
924
u
bl
b Ig
738
10.3
b
11 839
I11 744
5.0
6.2
7.2
997
1012
985
0.9
0.8
0.9
a
4.7
4.2
1023
1015
0 0
0.4
2518
1899
1842
1905
1900
1899
5.3
13.7
9.2
14.2
14.6
13.9
10.0
1615
' 1612
1608
1609
1609
1 1605
1601
a
7.8
824
998 La2
=I
3.9 b g
00
4.5
4.2
1175
1080
901
6.4
6.7
16.8
3.5
b u
3.8
b2
bl
a
b A 3g
943 00 1847
b 3"
2.5
3.8
3.2
1073
1077
903
878
5.5
6.5
16.9
7.1
(4), the largest associated with the bridge deformation vibration, v13. It seems likely that this resonance will persist through many isotopic diboranes. Other identified resonance perturbations in B2H6 and BzD6 species were not greater than 20 cm-‘.
74
J. L. DUNCAN TABLE VIII-Continued
B2D2"4 D2h 2523
~-
a"
tra”St %D4"2
BzD4"2
BzD5"
B2D6
Cs(a,b)
C*"(a)
C2h(C)
C2"(b)
Cs(ab)
D
2520
2520
1906
1'112
1905
1858
5.7
5.8
15.7
15.4
15.0
II.8
1506
1506
1506
1504
1501
2.3
I.8
I.9
I.9
1.4
a
'
=I
g
1084
5.6
6.2
720
792
719
706
18.9
15.7
23.9
12.8
13.7
664
643
644
621
I.6
5.2
I.3
1291
4.7
794
741
30.5
24.0
833
682
0.0
3.8
no
="
6.6
6.6
6.6
860
a52
____~ 13.6
9.7
2605 15.0
a
0,
18.9
a
593 u
1288
0.0 1286
6.8
715
850
706
II.0
6.5
9.1
2604
2605
2572
2574
2568
1975
14.7
14.7
II.1
II.4
II.0
20.7
a25
726
715
704
707
4.9
10.6
7.0
8.0
7.7
a'
bl
297 b2
708
1968
10.6
20.8
918
881
878
--
14.0
12.8
II.3
1473
1467
1461
16.1
15.9
15.7
940
920
R32 0.0
2518
1904
5.2
14.7
II93
a'
7.8
1175
1065
4.7
6.3
a
904
u
bl
781
1461
1461
1456
15.7
15.7
15.5
902
887
a72
--
aIT
4.5
846
726
727
7.6
I.4
1.3
1850
1902
1897
1849
10.2
13.7
14.1
10.0
II89
II89
1189
1188
832
b g
7.6
b
"
6.9
b,
'g
782
13.7
b2
1961
a'
21.0
b
7.2
7.0
738 13.4
15.2
25.3
1.7
a2 00 -----A-
a'
822
1.7
6.5
II91
8.0
g
4.5 261
2560
bk
2u
0.0
10.9
a
703
b
272
2562
1968 20.9
a'
699 14.8
0.1
281
II.0
0 0
al
0.1
2565
830
5.3 283
14.3
6.4
733 u
7.1 b2g
11.4
0.2
2597
a'#
b
--
0.3
0.3
I.8
g
286
0.4
bl
b
a2
--
913
6.5
311
3u
I.1 =g
7.0
4.9
784
6.0
b
a'
1072
5.2
all
=I
1070
1179
a2 L
a
II79
1184
1290
b3e L-
211
1509
1291
bl"
t
%D4"2
1293
b2u
t
*2D3H3
6.3
1296
b2g
cist
1511 2.7 =g
as-
t
t
1450 15.3
b l"
722 4.7 728
Ab3g
0 0 1840 8.6 II86
b 3u
6.6
898
1062
1067
a97
a74
15.6
4.8
7.3
15.3
5.9
This does not preclude the possibility, however, that large Fermi resonance perturbations may occur in any isotopic diborane due to close coincidences between appropriate unperturbed vibration levels coupled by a large anharmonic resonance
SPECTROSCOPIC
PARAMETERS
FOR
75
DIBORANE
TABLE VIII-Continued
b
da2
b2
a2
al
bl
b2
t
b
D2
B2H3D
Cs(aC)
C,(C)
t D::
b B2H3D
t
B2D4"
D2
Cs(bd
b
bt H
B2D5H C2"(C)
Cl
2524
2521
2518
1894
1900
1843
6.4
5.8
5.9
13.5
13.1
9.5
9.5
2018
2022
2023
2027
2028
2028
2029 6.2
4.5
5.5
5.3
6.4
6.5
6.3
1180
1180
1085
1079
900
5.R
5.9
5.9
7.4
7.0
15.8
786
747
742
721
774
712
707
30.7
13.6
18.9
15.6
17.8
9.1
15.7
a
1
av~
a
a
v
1841
1185
=I
915 19.5
833
693
678
645
645
623
00
4.6
I.0
1.8
5.5
1.5
1695
1692
1689
1689
89 1689
1687
4.3
4.2
4.0
4.1
4.1
3.8
860
849
712
723
850
714
701
13.7
9.1
12.1
6.5
9.3
II.6
13.4
2613
2605
2605
2570
2572
2566
1975
15.0
14.7
14.7
11.1
11.4
II.0
20.8
826 bl
B2H3D
C1
C,“(C)
iil
b
B H DbDt 24
B2H5D
a'
b
78'3
a
593 a2
0.0 ,684
b2
3.5
798
752
3.1
19.3
5.7
II.0
6.7
10.6
338
319
306
303
301
288
275
0.1
0.2
0.3
0.1
0.0
0.1
0.0
2597
2565
1968
2562
2560
1968
1961
14.3
II.0
20.9
II.0
11 10.6
20.9
21.0
918
873
867
823
781
778
14.0
12.2
8.7
25.5
13.9
14.7
13.4
1486
1482
1478
1478
1479
1474
1470
10.8
10.5
t 10.1
10.2
10.2
9.8
956
930
914
912
844
839
3.1
4.3
8.1
2.7
10.0
6.2
a
a
a
(7
a
a'
a
a
t
711
a
722
989
977
968
946
963
941
I.5
2.0
2.6
2.4
2.2
2.3
2518
1899
1843
1904
1899
1899
at1
713 b'
a2
2.9
738
9.5 al
732 5.9 906
bl
I.2 1845
5.3
13.7
4.9
1234
1233
t 1231
6.6
6.7
6.6
6.8
6.8
6.7
6.7
1175
1078
899
1070
1076
1077
876
6.1
6.5
15.1
5.6
6.1
6.5
6.6
a
b
14.0
14.4
13.8
1231
all 1231
1228
9.5 b2
1227
parameter. The predicted unperturbed anharmonic fundamental vibration frequencies, and boron isotopic frequency shifts, for all deuterated diboranes are collected in Table VIII. In addition to being of assistance to any future infrared or Raman
76
J. L. DUNCAN
studies on these species, the data in Table VIII should be valuable for estimating the contributions to the microwave spectra from lower-lying vibrational levels which will be populated at ambient temperatures. RECEIVED:
February
26, 1985 REFERENCES
1. E. HAMILTONAND J. L. DUNCAN,J. Mol. Spectrosc. 90, 129-138 (1981). 2. E. HAMILTONANDJ. L. DUNCAN,J. Mol. Spectrosc. 90, 517-530 (1981). 3. J. HARPERANDJ. L. DUNCAN,J. Mol. Spectrosc. 100, 343-357 (1983). 4. J. L. DUNCAN, D. C. MCKEAN, I. TORTO, AND G. D. NIVELLINI,J. Mol. Spectrosc. 85, 16-39 (1981). 5. J. L. DUNCAN,J. HARPER,E. HAMILTON,AND G. D. NIVELLINI,J. Mol. Spectrosc. 102, 416-440 (1983). 6. C. E. BLOMAND A. MULLER,J. Chem. Phys. 69, 3397-3402 (1978). 7. D. G. LISTER,G. D. NIVELLINI,AND P. PALMIERI, J. Mol. Struct. 85, 279-283 (1981). 8. J. L. DUNCANANDJ. HARPER,Mol. Phys. 51, 371-380 (1984). 9. E. HIROTA,Y. ENDO, S. SAITO,ANDJ. L. DUNCAN,J. Mol. Spectrosc. 89, 285-295 (1981). JO. E. HIROTA,Y. ENDO, S. SAITO,K. YOSHIDA,I. YAMAGUCHI,AND K. MACHIDA,J. Mol. Spectrosc. 89,223-231 (1981). JJ. J. L. DUNCAN,Mol. Phys. 28, 1177-1191 (1974). J2. J. L. DUNCAN,D. C. MCI&AN, ANDA. J. BRUCE,J. Mol. Spectrosc. 74, 361-374 (1979). 13. F. HERLEMONT,M. LYSZYK, J. LEMAIRE,C. LAMBEAU,M. DE VLEESCHOUWER, AND A. FAYT, J. Mol. Spectrosc. 94, 309-3 15 ( 1982). 14. M. DE VLEESCHOUWER, C. LAMBEAU,D. VAN LERBERGHE, E. JANSSENS, AND A. FAYT, J. Mol. Spectrosc. 90, 273-286 (1981). IS. J. L. DUNCAN, E. HAMILTON,A. FAYT, D. VAN LERBERGHE, AND F. HEGELUND,Mol. Phys. 43, 737-752 (1981). 16. F. HEGELUNDAND F. M. NICOLAISEN, Mol. Phys.. in press. 17. Y. VERBIST-SUEUR, C. P. COURTOY,A. FAYT, AND D. VAN LERBERGHE, Ann. Sot. Sci. Bruxelles 90, 317-336 (1976). 18. M. DE VLEESCHOUWER AND A. FAYT, Privatecommunication. 19. T. OKA AND Y. MORINO,J. Mol. Spectrosc. 6, 472-482 (1961); Y. MORINO,K. KUCHITSU,AND T. OKA, J. Chem. Phys. 36, 1108-l 109 (1962); K. KUCHITSU,J. Chem. Phys. 49,4456-4462 (1968). 20. K, KUCHISTSUAND S. J. CYVIN, in “Molecular Structures and Vibrations” (S. J. Cyvin, Ed.), Ch.
12, Elsevier, Amsterdam, 1972. 21. H. S. PEISER,N. E. HOLDEN,P.
DE
BI~VRE,AND 1. L. BARNES,Pure Appl. Chem. 56, 695-768
( 1984). 22. M. NAKATA, S. YAMAMOTO, T. FUKUYAMA, AND K. KUCHITSU,J. Mol. Struct. 100, 143-159
(1983). 23. T. 0~ AND Y. MORINO,J. Mol. Spectrosc. 6,472-482 (1961). 24. 1. M. MILLS,in “Molecular Spectroscopy-Modem Research” (K. Narahari Rao and C. W. Mathews, Eds.), Vol. I, Ch. 3, Academic Press, New York, 1972. 25. J. L. DUNCANAND D. C. MCKEAN, J. Mol. Spectrosc. 107, 301-305 (1984). 26. J. K. G. WATSON,J. Mol. Spectrosc. 65, 123-133 (1977).