Infrared and Raman spectra of trimethoxyborane isotopomers and quantum-chemical studies of structure and force field

Article abstract of DOI:10.1016/j.molstruc.2010.02.073

Infrared and Raman spectra in the gas phase are reported for trimethoxyborane, B(OCH₃)₃, and its ¹³C₃ and d₉ isotopomers. Some liquid phase Raman data were also obtained. Quantum-chemical (QC) studies of structure and force field have been made with B3LYP and MP2 models. These studies highlight the change in configuration of the methyl groups with change in basis set, within the C_3h point group. Scaled QC force fields together with the new spectra enable assignments of fundamental bands to be improved. A Fermi resonance involving ν₁₂ is examined. The difference in strength between the two types of C-H bond in each methyl group is reckoned to be rather less than that deduced earlier from IR spectra of B(OCHD₂)₃. This conclusion is supported by QC data for dimethylether. MP2 estimates of certain interaction force constants are superior to those from B3LYP calculations. Abnormal scale factors for the torsional motion involving the O-B-O-C system identify deficiencies in the QC models employed.

Full text of DOI:10.1016/j.molstruc.2010.02.073

Journal of Molecular Structure 976 (2010) 360–370
Contents lists available at ScienceDirect
Journal of Molecular Structure
journal homepage: www.elsevier.com/locate/molstruc
Infrared and Raman spectra of trimethoxyborane isotopomers
and quantum-chemical studies of structure and force field
c
c,1
Alison M. Coats a, Donald C. McKean b, , Howell G.M. Edwards , Victor A. Fawcett
*
a Department of Chemistry, University of Aberdeen, Aberdeen AB24 3UE, UK
b School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, UK
c Department of Chemistry, University of Bradford, Bradford, BD, UK
a r t i c l e i n f o
a b s t r a c t
Infrared and Raman spectra in the gas phase are reported for trimethoxyborane, B(OCH3)3, and its 13C3
and d9 isotopomers. Some liquid phase Raman data were also obtained. Quantum-chemical (QC) studies
of structure and force field have been made with B3LYP and MP2 models. These studies highlight the
change in configuration of the methyl groups with change in basis set, within the C3h point group. Scaled
QC force fields together with the new spectra enable assignments of fundamental bands to be improved.
A Fermi resonance involving m12 is examined. The difference in strength between the two types of C–H
bond in each methyl group is reckoned to be rather less than that deduced earlier from IR spectra of
B(OCHD2)3. This conclusion is supported by QC data for dimethylether.
Article history:
Received 5 February 2010
Received in revised form 26 February 2010
Accepted 26 February 2010
Available online 6 March 2010
Keywords:
Trimethoxyborane
Vibrational spectra
Isotopomers
QC studies
MP2 estimates of certain interaction force constants are superior to those from B3LYP calculations.
Abnormal scale factors for the torsional motion involving the O–B–O–C system identify deficiencies in
the QC models employed.
Structure
Force fields
Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction
the C3h structure from the HF/3-21G calculation, the in-plane C–
Hs bond was oriented cis relative to the boron atom. This structure
The molecule of trimethoxyborane (TMB) has been the subject
of a number of structural and spectroscopic studies [1–9]. Planarity
of the heavy atom skeleton is expected on chemical grounds and
has been verified in gas phase electron diffraction (ED) studies
[1,2]. However, the orientation of the methyl groups has been
the subject of dispute. In the ED study, these groups were consid-
ered to be twisted in such a way that the overall symmetry of the
molecule was C3, in contrast to the C3h point group which would be
expected if an equivalent CH bond in each group lay in the skeletal
plane. Earlier vibrational spectra were interpreted on the basis of
such a C3h structure [3]. Non-equivalence of the CH bonds in each
methyl group has been demonstrated in two ways, firstly by mea-
suring the infrared spectra of the partially substituted species
B(OCHD2)3 in the gas phase [4] and secondly, by a study of the
CH stretching overtones of the parent molecule [5]. The latter
study also included a calculation of the equilibrium geometry by
a quantum-chemical (QC) HF/3-21G calculation. Both of these
studies indicated the presence of two types of C–H bond, a single
strong one lying in the skeletal plane (CHs) and two weak ones
positioned symmetrically above and below this plane (CHa). In
contrasted with an earlier theoretical calculation which yielded a
C3 point group [6]. Accompanying a reinvestigation of the Raman
and infrared spectra of the parent molecule, a wider Hartree–Fock
study was made of the various possible conformations using the
basis sets, 3-21G, 4-21G and 6-31Gꢀ [7]. With the 3-21G basis,
the lowest energy was again obtained with the C3h (C–Hs cis to
B) structure. However with the 4-21G and 6-31Gꢀ basis sets the
trans structure became the stable form. This structure is illustrated
in Fig. 1.
Ab initio force constants from the HF/3-21G calculation were
then used in [7] in conjunction with a crude scaling procedure to
interpret the observed spectra and suggest locations of unobserved
fundamental frequencies.
The change of structure in the molecule of TMB has also been
explored in an unpublished study by Willetts [8]. Using a double
zeta basis, Willetts found that insertion of a polarisation function
onto each oxygen atom was enough to produce the stability switch
from cis to trans. At the same time there was a marked decrease of
ꢁ4° to 5° in the BOC angles in both forms. This led to the sugges-
tion that the erroneously large \BOC in the cis form found when
the polarisation function was absent, was enough to relieve a
repulsion between the Hs hydrogen atom and the neighbouring
oxygen which, when present, rendered the trans form more stable.
A double zeta MP2 calculation with polarisation functions on the
oxygen atoms gave the same result [8].
* Corresponding author. Tel.: +44 1316504822; fax: +44 1316506453.
E-mail address: dmckean@staffmail.ed.ac.uk (D.C. McKean).
1
Deceased.
0022-2860/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2010.02.073

A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
361
2400 cmꢂ1, of d9 is available as Figure S1 in the Supplementary
Data.
3. Theoretical
Hartree–Fock (HF), MP2 and B3LYP calculations were per-
formed using the Gaussian programs G98 or G03 [12]. The geome-
try was studied using basis sets varying from 3-21G to 6-311++Gꢀꢀ
and cc-pVTZ. This last basis set was used only in conjunction with
the B3LYP model. Three calculations of the vibrational force field
were made, using respectively B3LYP/6-311++Gꢀꢀ, B3LYP/cc-pVTZ
and MP2/6-311++Gꢀꢀ models.
For convenience in the tables below, 6-311Gꢀꢀ, 6-311++Gꢀꢀ and
cc-pVTZ are abbreviated to, tz (triple zeta), tz+ and cct respectively.
The prefix m or d then indicates the method used, MP2 or
DFT(B3LYP).
Fig. 1. Trans-C3h structure of B(OCH3)3 as obtained from the MP2/6-311++Gꢀꢀ
model.
Convergence in the prior geometry optimizations was con-
trolled by the ‘‘tight” option. For the density functional calculations
a grid of 99 shells, each containing 302 points, was employed.
Repetition of a given calculation from differing starting geome-
tries gave frequencies agreeing within 0.05 cmꢂ1. Bond lengths
were similarly reproduced to within about 0.00002 Å. This repro-
ducibility is relevant to our interest in the small differences in
properties exhibited by the two types of C–H bond.
Calculations were performed either on a DEC Alpha 1000 work
station or using the resources of the EPSRC National Service for
Computational Chemistry Software, on Columbus, a cluster of six
HP ES40 computers, each of which has four 833 MHz EV68 CPUs
and 8 Gbytes of memory.
For the calculation of force constants on a symmetry coordinate
basis and subsequent scaling, the Gaussian output of Cartesian-
based force constants was input into the program ASYM40 [13].
In order to avoid the use of complex symmetry coordinates in
the doubly degenerate E0 and E00 classes, the procedure devised
by Cyvin et al. was followed which uses only real coordinates
[3,14]. Our symmetry coordinates were identical in form (though
not in numbering) to those listed by Stampf et al. [7] with two
exceptions. Our A0 and E0 CH stretching coordinates were com-
posed of motions of one type of bond only, either CHs or CHa, while
More recently, DFT calculations with a larger basis set (B3LYP/
6-311G++(d,p), performed to underpin a study of the crystal struc-
ture by X-ray and neutron diffraction techniques, has confirmed
that in an isolated molecule the CHs bond lies trans to boron [9].
However, in the crystal, the X-ray diffraction evidence pointed to
the presence of orientational disorder among the methyl groups.
The present investigation is both theoretical and experimental.
In the theoretical part, HF, B3LYP and MP2 methods were used
with a variety of basis sets to provide further evidence for the sta-
bility of the trans-C3h structure and also to provide harmonic force
fields. The latter were then used after careful scaling to observed
frequencies to improve the interpretation of the vibrational spectra
and the prediction of unobserved fundamental frequencies. This
process was aided by accompanying QC calculations of infrared
and Raman intensities.
The experimental part involved new spectra of the parent (d0),
B(O13CH3)3(13C) and B(OCD3)3 (d9) substituted isotopomers. Some
of the infrared spectra of d0 and d9 involved have previously been re-
ported and some assignments made [4]. However, their detailed
interpretation had earlier proved impossible, when only empirical
force fields had been available. The addition of Raman spectra, ob-
tained in both gas and liquid phases, and of data for the 13C isotopo-
mer, together with our QC calculations has enabled a deeper though
still incomplete understanding of the spectra to be obtained.
the sCH3 and sOBOC torsions were defined with a larger number of
dihedral angles. Our set of symmetry coordinates, in the form input
into ASYM40, is included in Table S1 of the Supplementary Data.
2. Experimental
4. Results: QC predictions of structure and vibrational
properties
Samples of TMB were prepared by reacting BCl3 with a slight
excess of the appropriately labelled methanol, as described by Wi-
berg and Sütterlin [10]. Traces of methanol proved hard to remove
by fractional condensation, but their residual bands were readily
identified. The presence of a further impurity was indicated by
the observation of very weak, polarised Raman bands in both
phases, seen in the gas at 774 and 451 cmꢂ1 (d0), 767 and
Table 3 shows the relative energies and BOC angles of the cis
and trans-C3h structures found from the HF, B3LYP and MP2 models
with various basis sets. All three methods yield a stable cis struc-
ture only with the 3-21G basis set. For all the larger sets the trans
structure has the lower energy. Sample calculations found imagi-
nary frequencies for the less stable form, which means that there
was no evidence for an additional minimum on the potential sur-
face. However, a more comprehensive study would be needed to
establish firmly the absence of such minima. Trial calculations with
a C3 structure and methyl twist angle of 31.6°, as found from the
ED study [2], failed to converge and this conformation was not
investigated further.
446 cmꢂ1 13C) and 736 cmꢂ1 (d9). A likely source of these bands
(
is the compound (HO)B(OMe)2, for which a Raman band at
773.8 cmꢂ1 has been reported [11].
Infrared spectra were recorded in the 4000–400 cmꢂ1 region on
a Nicolet 7199 FTIR spectrometer at a resolution of 0.5 cmꢂ1. Be-
tween 650 and 50 cmꢂ1 a Nicolet 20F bench was employed, the
resolution then being 0.7 cmꢂ1
.
Gas and liquid phase Raman spectra were recorded on a Spex
1401 double monochromator equipped with an argon-ion laser.
Spectra were calibrated against emission lines from a neon lamp.
Polarisation information was obtained in the usual way by com-
paring I\ and I|| spectral intensities.
The marked influence of the inclusion of polarisation functions
into the basis set, noted by Willetts [8], is clearly visible. However,
there is little sign of any consistent change in BOC angle with mod-
el or basis which might affect the repulsion between an in-plane Hs
atom and the neighbouring non-bonded oxygen. It seems more
likely that the stable comformation is dictated by changes in the
The band frequencies obtained in this work are given in Tables 1
(d0) and 2 (d9) respectively. An infrared survey spectrum, 400 to
p
electron system.

362
A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
Table 1
Infrared and Raman frequencies (cmꢂ1) and 13C frequency shifts observed in B(O12CH3)3 and B(O13CH3)3.
IR(gas)
12C)
R(gas)
12C)
R(liq)
12C)
Assignmenta
m
(
ꢂDm
(
13C)b
m
(
ꢂD
m(
13C)b
m
(
3240 vw, bd
3030 sh
8(8)
7(2)
m
asCH3 + sCH3 ?
2999 vw, dp
2978 m, p
10(7)
2(1)
m1 (a0), m15 (e0), m24 (e00) FR
m9 (a00)
2980.2 sh, q
2964 s, bd
10.8(7)
6(3)
2966
2
m18 (A0) FR
m3 +
m18 (E0) FR
2949 s p
2911 m, p
0(1)
4(1)
2937
2899
2
2
m3 (A0) FR
m4 (A0) FR
2882 s, bd
2(2)
m16 (e0) FR
2874 s, p
2853 w, p
2841 w, p
2828 w, p
4(1)
1(1)
1(2)
2(2)
2862
m2 (a0) FR
m18
?
m18
2
2
m18
m6
m18
m4
+
+
m19 (A0, E0) 10B ?
m19 (A0, E0) 11B ?
2838
2810
2775 vw, sh
2721 w
9(3)
10(1)
5(2)
16(5)
21(2)
24(7)
29(4)
–
m19 (A0, E0) 10B
m
19 (A0, E0) 11B
m26 (A00, E00) ?
2622 vw
2591 vw
2524 vw
2485 vvw
2400 vw
2264 vw
2238 sh
2219 w
2151 w
2091 mw
2081 w
1915 sh
1888 vw
1763 w
1676 w
1641 w
1542 sh
1510 sh
1493.8 s
1484.9 s
+
+
m10 (A00)
+
m21 (A0, E0)
+
m21 (E0)
m11
+
m21
+
m23 (A00, E00)
m5
m7
m7
m6
m7
+
m21 (E0)
7(3)
+
+
+
+
m17 (E0) 10B
m17 (E0) 11B
m21 (E0)
10(1)
36(2)
10(1)
38(2)
10(6)
12(2)
23(1)
–
19(1)
5(3)
3(2)
3.3(4)
2.5(4)
m19 (E0)
2m
21 (A0, E0)
m19
m19
m7
m18
+
+
m22 (E0) 10B
m22 (E0) 11B
+
m21 (E0)
+
m23 (E0) ?
m6
m10
+
m22 (E0)
1534 w, bd, dp
8(8)
1537
+
m28 (E0) ?
m17 (e0) 10B
m17 (e0) 11B
m18 (e0)
1471 w, bd, dp
1453 m, sp, p
1(5)
5(1)
1466
1445
m3 (a0)
m4 (a0)
1393 sh
1384 sh
1363 vs
6(1)
5(7)
6(1)
m19 (e0) 10B
1378 sh
1340
m12
+
m22
+
m23 (A0) FR
m19 (e0) 11B
1339 w, sh, bd
2
m12 (A0) FR ? m21
+
m28 (A00, E00) ?
1249 sh
1200 m
1167 sh
13(1)
10(2)
m7
+
m22 (E0)
m20 (e0)
1173 w, bd, dp
1132vw, p
1121.4 w, p
5(7)
m11 (a00) ?
Impurity?
m6 (a0)
20(3)
1098
1112 vw, sh
1042 s
m21 +
m28 (A00, E00) ?
1074 vw, p
1047 w, bd dp
1036 m, p
5(4)
23(6)
21(2)
MeOH
18.0(7)
m21 (e0)
MeOH
997 vw, p
Impurity?
935, 924 w
869 vw
835 vw
4.7(7)
18(1)
9(1)
m7
m21
+
m23 (E0)
ꢂ
m27 (A00, E00)c
m8
m7
+
m22 (E0), m7
+
m14 (A00)
+
m13 (A00)
780 vvw
774 vw, p
753 vvw, p
731 vs, p
711 w, p
7(3)
769
B(OH)(OCH3)2
Impurity?
m7 (a0)
7.3(8)
9(5)
722
693
m22
m22
m22
+
+
+
m23 (A0, E0)
711.4 w, q
699.8 w, q
667.4 m, q
524.7 m
3(1)
5(1)
0.8(6)
5(1)
m27 (A00, E00) 10B FR
m27 (A00, E00) 11D FR
m12 (a00),11B FR
m22 (e0)
524 vw, bd, dp
379 vvw, bd, p
331 vw, sh, p
520
350
2
m23 (A0, E0)
7(4)
6(1)
2
m27 (A0, E0)
318 vw
273 vw
1(1)
1(3)
Impurity?
m8 (a0)
311 vs, p
321
264 vvw,p
Impurity?
m13 +
m27 (E0)
235 vvw, p
184 s, bd, dp
Impurity?
190 w, bd
0(3)
3(3)
m23 (e0)
102.8 m, sp
1.6(2)
m13 (a00)
a
b
c
Bands not appearing in earlier spectra [3] are labeled ‘‘impurity?” or identified as ‘‘B(OH)(OCH3)2” or ‘‘MeOH”.
In parentheses, the combined uncertainties from the two data subtracted.
27 = 173 cmꢂ1
This assignment yields m .

A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
363
Table 2
Table 4
Infrared and Raman frequencies (cmꢂ1) observed in B(OCD3)3.
Comparison of Observed and QC-calculated geometries for the trans-C3h structure of
trimethoxyborane.
IR
Raman
Gas
Assignment
Parametera
QC model
dtz
obsdb
Gas
Liquid
dtz+
dcct
mtz
mtz+
2282 sh
2245 ms, br 2245 w, dp
2235.3 ms, q
masCD3 + sCD3
m1 (a0), m15 (e0), m24 (e000
m9 (a00)
)
rB–O
1.3661
1.4252
1.0936
1.0906
0.0029
0.0020
120.5
107.4
111.2
109.3
108.4
1.3671
1.4268
1.0931
1.0904
0.0027
0.0018
120.9
107.2
111.1
109.4
108.6
1.3670
1.4232
1.0910
1.0883
0.0027
–
121.0
107.4
111.2
109.3
108.5
180.0
1.3682
1.4246
1.0932
1.0906
0.0026
0.0020
117 8
107.1
111.1
109.5
108.5
180.0
1.3699
1.4272
1.0930
1.0907
0.0023
–
118.3
106.6
110.9
109.6
108.8
180.0
1.368(2)
1.424(2)
1.106(3)
1.106
rC–O
2223 sh
rC–Haa
rC–Hs
2183 vw, dp
2146 w, p
2087 vs, p
2 ꢃ dasCD3
2145 m
2085 ms
1994 vw
1938 vvw
1894 vvw
1805 vw
1670 w
1613 vw
1578 v
1490 sh
1449 vs
1403 vs
1333 w
1283 w
2 ꢃ dasCD3
D
D
rC–Ha-s
1.106
m2 (a0), m16 (e0)
rC–Ha–s(cis)
?
?
?
\BOC
121.0(2)
109.0(5)
109.0
109.9(5)
109.9
\OCHs
\OCHa
a
\HaCHs
\HaCHa
\BOCHs
?
?
?
?
180.0
180.0
31.6
Bond lengths in Å, angles in °. The Hs atom in each methyl group lies in the
skeletal plane in each C3h QC structure, but is out of this plane in the C3 electron
diffraction structure.
rC–Ha–s from the cis structure is included for three models.
a
m17 (e0) 10B
m17 (e0) 11B
D
b
C3 structure from [2], assuming C3v local symmetry for the methyl group.
0
?
1176.3 w, p
1165 w, p
m3 (a0)
0
sistently 2–3° larger than the MP2 ones and closer to that ob-
served, which, however carries an uncertainty of two degrees.
The QC-calculated vibrational frequencies and their associated
infrared and Raman intensities are listed in Table 5 for the
11B(O12CH3)3 and 11B(O12CD3)3 isotopomers. Modes are numbered
in order of descending frequency.
1175 sh
1122 s
?
1120 w, br, dp 1114 w, dp
1087 sh, p?
1067 w, br, dp 1067 m, dp
m18 (e0)
m4 (a0)
1066 w
1030 vw, q
1001 m
m5 (a0), 10 (a00), m19 (e0), 25 (e00)
m m
m6 +
m14 (A00)
1000 m, dp
996 vs, dp
m20 (e0)
985 vvw
CD3OH
943 w, sh, p
935 w, p
?
In order to evaluate the earlier experimental work on the IR
spectrum of B(OCHD2)3 (d6) [4], we used the mtz+ model to calcu-
late all the harmonic C–H stretching frequencies and some of the
associated IR intensities for all the conformers possible with this
species. The results are shown in Table 6. We observe firstly an al-
932 m, p
m6 (a0)
919 w, br
m21 (e0)
908 m, dp
m26 (e00)
m11 (a00)
m6 (a0)
908.7 sh, q
901 w, p
861 vvw
851 vvw
CD3OH
CD3OH
most complete independence of each
sition of the hydrogen atoms in neighbouring methyl groups. This
demonstrates that the coupling between CH motions in different
mCH frequency on the dispo-
736 vw, p
684.7 vs, p
729 vw, p
685 vs, p
B(OH)(OCD3)2
m12 (a00) 10B FR
m7 (a0)
?
m
702.0 m, q
methyl groups is essentially zero. This lack of coupling is also re-
flected in the virtual degeneracies visible in the A0, A00, E0 and
678.0 m, q
648 w, br
494 w
m12 (a00) 11FR
m22 +
m27 (A00, E00) FR
E
00mCH3 frequencies in Table 5. The
mCH and mCD frequencies can
492 w, dp
283 s, p
495 w, dp
289 m, p
m22 (e0)
m8 (a0)
be therefore regarded as effectively those of a single methyl group.
(A similar virtual degeneracy is found with the out-of-plane
methyl rocking modes in the A00 and E00 classes, near 1178 cmꢂ1
in d0, and 919 cmꢂ1 in d9.)
245 w
168 m
m14 +
m26 (e0)
164 m, bd, dp 177 m, bd, dp m23 (e0), m26 (e00)
156 sh
?
92.7 m, q
m14 (a00)
The second feature worthy of comment in Table 6 are the com-
puted infrared intensities associated with the unique m
isCH transi-
tion in a conformer which has only one C–Hs or C–Ha bond present.
These show only a modest variation with orientation. However, the
third and critical feature of Table 6 is the change in frequency with
orientation. This averages to 29.0 cmꢂ1 from the mtz+ treatment
(corresponding dtz+ value 32.5 cmꢂ1). This is substantially less
than the previous experimental value of about 62 cmꢂ1 for
Table 4 compares parameters of five of the trans-QC structures
with the larger bases with those from the ED experiment [1,2].
Agreement on the B–O and C–O lengths is generally good. There
is close agreement between the two models on the difference in
the two C–H bond lengths, the in-plane C–Hs bond being 0.002–
0.003 Å shorter than the out-of-plane C–Ha bond. A similar but
slightly smaller difference is computed for the corresponding cis-
C3h structures, see Table 4. B3LYP values of the BOC angle are con-
m
isCHs –
This discrepancy prompted us to test the validity of these QC
predictions for the CH bonds in TMB by making similar QC calcula-
m
isCHa [4].
Table 3
Relative energies and BOC angles for the cis- and trans-C3h structures of trimethoxyborane, from HF, B3LYP and MP2 models.
Basis
D
E(cis–trans) (kJ molꢂ1
)
\BOC (°)
trans
cis
trans
cis
trans
cis
HF
B3LYP
MP2
HF
HF
B3LYP
B3LYP
MP2
MP2
3-21G
6-31G
ꢂ1.80
1.11
5.92
5.30
6.07
–
ꢂ5.17
ꢂ
ꢂ4.19
ꢂ
122.9
125.1
121.6
121.8
–
124.2
126.4
124.0
124.1
–
120.0
–
120.4
120.5
120.9
121.0
121.2
–
122.4
122.4
122.7
123.0
119.0
–
118.2
117.8
117.8
–
120.4
–
120.8
120.4
120.9
–
6-31Gꢀ
1.24
0.97
2.45
2.49
3.98
4.54
5.28
–
6-311Gꢀꢀ
6-311++Gꢀꢀ
cc-pVTZ
–
–

364
A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
Table 5
Comparison of frequency data from QC calculations, experiment and refinement fit for the d0 and d9 isotopomers.
Speciesa
Mode
xmtz+
xdtz+
xdcct
Rdtz+
mobsd
m
,ꢀmtz+
m
,ꢀdtz+
m,
ꢀdcct
Motion
a
a
a
b
c
d
d
d
A0
d0
m1
m2
m3
m4
m5
m6
m7
m8
3189
3080
1528
1505
1252
1149
752
3114
3026
1502
1481
1235
1129
734
3109
3025
1506
1485
1241
1135
737
95
475
2
1
0.4
4
–
–
1471
3001.8
2899.1
ꢂ7.5
3005.2
2919.9
ꢂ5.0
3005.3
2923.6
ꢂ4.1
m
m
CHs
sCHa2
dasCH3
dsCH3
q
m
m
1453
ꢂ1.9
ꢂ0.7
ꢂ0.4
1208
1121.4
731.4
311.0
1217.1
ꢂ1.9
1225.3
ꢂ0.9
1227.5
ꢂ0.9
CH3,
CO,
BO,
m
CO
CH3
CO
q
m
10
2
ꢂ0.8
ꢂ0.4
ꢂ0.2
311
297
298
ꢂ0.8
ꢂ0.8
ꢂ0.9
dBOC
d9
m1
m2
m3
m4
m5
m6
m7
m8
2368
2207
1203
1119
1099
960
2311
2168
1184
1106
1081
941
2308
2167
1189
1110
1085
994
43
241
2
0.2
2
4
8
2
–
–
2253.5
2100.2
1.7
3.6
3.3
1.0
0.2
0.7
2255.5
2114.6
0.1
2255.3
2117.3
0.5
m
m
m
CDs
sCDa2
CO, dsCD3, mBO
1176.3
1087
1067
935
684.7
283
ꢂ1.2
ꢂ1.7
dsCD3,
dasCD3
mBO
4.9
4.4
0.4
0.7
0.8
0.5
0.4
0.8
q
CD3,
BO,
dBOC
mCO
704
281
688
270
690
270
m
mCO,
qCD3
a
a
a
e
c
d
d
d
Species
Mode
xmtz+
xdtz+
xdcct
Adtz+
mobsd
m
,
ꢀmtz+
m,
ꢀdtz+
m,
ꢀdcct
Motion
A00
d0
m9
3167
1515
1199
682
100
42
3088
1495
1178
681
106
51
3083
1499
1184
676
105
61
102
20
2
57
14
0
2980.2
–
0.0
0.0
0.0
m
asCHa2
m10
m11
m12
m13
m14
1477.2
1176.2
ꢂ0.1
1477.4
1174.5
ꢂ0.3
1476.8
1174.3
ꢂ0.4
dasCH3
q00CH3
dBO3
s
s
–
673f
102.8
49
ꢂ2.0
ꢂ0.4
ꢂ0.4
OBOC,
sCH3
0.6
0.0
0.0
CH3, OBOC
s
d9
m9
2350
1094
926
680
88
2292
1079
911
678
95
2288
1083
915
673
94
62
8
8
53
11
0
2235.3
1066
908.7
671f
92.7
–
2236.8
0.0
2236.5
0.0
0.0
0.3
0.5
34.7
2236.4
0.0
0.0
0.3
0.5
34.7
m
asCDa2
m10
m11
m12
m13
m14
dasCD3
q00CD3
dBO3
s
s
ꢂ0.1
0.3
1.9
35.3
OBOC,
CD3,
sCD3
OBOC
30
36
43
s
a
a
a
e
b
c
d
d
d
Species
Mode
xmtz+
xdtz+
xdcct
Adtz+
Rdtz+
mobsd
m
,ꢀmtz+
m
,
ꢀdtz+
m
,
ꢀdcct
Motion
E0
d0
CHs,
sCHa2,
m
m
sCHa2
m15
m16
m17
m18
m19
m20
m21
m22
m23
3189
3080
1534
1524
1393
1213
1071
530
3114
3025
1512
1498
1369
1194
042
3109
3024
1519
1502
1378
1200
1047
523
96
148
0.1
2
21
2
9
6
2
0.8
3001.7
2898.4
0.8
4.0
0.4
3005.0
2918.9
0.7
2.6
9.9
3005.3
2922.5
-1.0
3.2
11.0
8.1
m
m
CHs
BO
dasCH3, dsCH3
BO, dsCH3
CH3
CO
175
264
14
1167
30
156
25
9
1494
1485
1363
1200
1042.4
524.7
190
dsCH3.
m
m
q
m
7.5
2.8
8.8
9.0
8.7
522
173
ꢂ5.6
ꢂ21.7
ꢂ21.3
dOBO, dBOC
dBOC, dOBO
197
173
1.8
6.0
5.8
d9
m15
m16
m17
m18
m19
m20
m21
m22
m23
Mode
2368
2206
1426
1161
1099
1026
942
2311
2166
1406
1135
1081
1004
927
2307
2165
1420
1137
1085
1007
930
61
76
0.6
0.1
1
5
14
3
2245
2082
1403
1122.3
1066
1001
919
2253.7
2099.2
4.1
ꢂ3.2
ꢂ1.5
0.8
2255.7
2113.4
14.3
2255.5
2116.1
14.3
m
m
m
CDs,
m
sCDa2
m
117
1334
192
5
63
17
sCDa
,
2
CDs
BO, dOBO
0.6
1.2
dsCD3,
dasCD3
mCO
ꢂ3.8
ꢂ2.1
ꢂ3.3
ꢂ19.7
5.3
ꢂ4.5
ꢂ2.4
ꢂ2.9
ꢂ19.4
5.1
mCO
ꢂ5.6
ꢂ5.6
1.3
q
CD3
500
166
493
153
494
153
18
2
494
dOBO, dBOC
dBOC, dOBO
Motion
7
0.6
168
mobsd
a
a
a
b
c
d
d
d
Species
xmtz+
xdtz+
xdcct
Rdtz+
mmtz+
mdtz+
mdcct
E00
d0
m24
m25
m26
m27
m28
3166
1515
1200
175
3088
1495
1177
183
3082
1498
1184
185
171
32
8
0.2
0.7
–
–
–
2979.7
1477.4
1177.4
179.7
65.9
2979.5
1477.2
1174.2
178.2
50.8
2979.5
1475.7
1174.3
175.8
49.1
m
asCH3
dasCH3
CH3
OBOC
CH3
q
s
s
173g
–
55
53
60
d9
m24
m25
m26
m27
m28
2350
1095
927
163
40
2291
1080
910
171
38
2287
1083
915
170
43
90
12
8
0.3
0.4
–
–
–
–
–
2236.5
1067.0
910.2
166.5
47.3
2235.9
1066.9
908.3
166.1
36.3
2235.6
1066.7
908.2
164.0
35.0
m
asCD3
dasCD3
CD3
q
s
s
OBOC
CD3
a
b
c
Unscaled harmonic frequency (cmꢂ1) from G03.
Raman intensity (amu Åꢂ4) from G03.
Observed frequency (cmꢂ1), where identified. In italics, data used to scale the QC force fields.
d
Calculated scaled frequency (
m
) or frequency fit (
ꢀ) from scaled model force field. Calculated mCD values have been premultiplied by 1.011 to compensate for the differing effects of
anharmonicity on
m
CH and
m
CD stretching frequencies.
e
G03 calculated infrared intensity (km molꢂ1).
Corrected for Fermi resonance: see text.
f
g
From a likely difference band at 869 cmꢂ1 (1042 ꢂ 869 = 173).

A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
365
Table 6
As well as the assistance from the calculated IR and R intensities
in Table 5, substantial help in assigning bands was derived from
our measured isotopic frequency shifts. Values for the 12C–13C,
11B–10B and 11B12C–10B13C frequency shifts calculated from the
‘‘Unsealed” MP2/6–311++Gꢀꢀ CH stretching frequencies and infrared intensities in
11B(OCHD2)3 conformers.
Conformera
Point group
x
CH (cmꢂ1
)
A (km molꢂ1
)
b
c
scaled mtz+ force field are listed together with observed 12C–13
shifts in Table 8.
C
sss
ssa
sa1a1
sa1a2
a1a1a1
ala1a2
C3h
C1
C1
C1
C3
C1
3168.1(a0), 3167.2 (e0)
3167.8, 3167.2, 3138.5
3167.5, 3138.5, 3138.4
3167.5, 3138.6, 3138.3
3138.6(a), 3138.4(e)
3138.7, 3138.4, 3138.3
31.5 (Ha)
38.5 (Hs)
38.5 (Hs)
5.1. mCH and mCD regions
a
Hydrogen atoms ‘‘Hs” are in the skeletal plane; ‘‘Hai”, ‘‘Ha2” are above and below
Analysis of these regions in a methyl-containing compound is
normally difficult due to the universal Fermi resonances (FRs)
occurring between the fundamental levels and those of overtones
and combinations of methyl deformations. These resonances are
particularly marked in Me–O compounds due to the high frequen-
cies of the dasMe and dsMe modes in such molecules [16]. An addi-
this plane respectively. Differences in CH for a given type of bond in any one
x
conformer are indicative of the small degree of coupling between the motions of the
two like C–H bonds concerned.
b
Double degeneracy is found only with the sss and a1a1a1 conformers. In italics,
the frequency for which the IR intensity is given in column four.
c
Infrared intensity for the stretching of the unique C–Ha or C–Hs bond present in
this conformer.
tional complicating factor in TMB is the mixing of masBO3 motion
into the E0 modes in the 1450–1500 cmꢂ1 region of d0. This could
tions for dimethylether (DME), for whose
m
isCH bands both fre-
lead to differing effects of FR on the A0 and E0 fundamental bands
quency and IR intensity data are available from experiment. [15].
The DME results, seen in Table 7, show that a fair agreement is ob-
tained between theory and experiment, bearing in mind the small
differences expected between harmonic and anharmonic data.
in the mCH region. Apart from this possible effect, the lack of cou-
pling between CH stretching motions in different methyl groups
Table 8
(The fall in
29.5 cmꢂ1 in TMB gives an indication of the extent to which the
electrons on the oxygen atoms in TMB have been delocalized.)
This confirmation of the reliability of QC estimates points to a con-
Dx
isCH from about 108 cmꢂ1 (mtz+) in DME to
Isotope frequency shifts Dm
(cmꢂ1) from the 11B(O12CH3)3 species to the tsotopomers
11B(O13CH3)3, 10B(O12CH3)3 and 10B(O13CH3)3, as calculated from the scaled mtz+
force field.
p
A0
flict between the QC and the earlier
discussed further in detail below.
m
isCH evidence which will be
Mode
ꢂ
D
m
(
13C)
Motion
calc
obsd
Among other types of motion, consistent features of all the QC
predictions of vibration frequency are the low methyl torsional fre-
quencies, which lie in the range 40–61 cmꢂ1 for the d0 species (see
Table 5). This feature makes it very likely that at room tempera-
tures there will be significant populations of molecules in excited
torsional states, including those above the barrier to methyl tor-
sion. To this state of affairs we attribute some of the breadth and
lack of characteristic structure observed in most of the gas phase
band contours.
m1
m2
m3
m4
m5
m6
m7
m8
11.2
2.7
2.2
–
–
m
m
CHs
sCHa
2
1(5)
5(1)
–
20(3)
–
dasCH3
dsCH3
q0CH3,
5.5
10.0
13.9
6.0
m
CO
CH3
CO
mCO,
q
m
mBO,
5.8
6(1)
dBOC
A00
Mode
ꢂ
calc
D
m
(
13C)
D
m
(
10B)
calc
D
m
(
10B13C)
Motion
obsd
calc
5. Results: Assignments of observed spectra and force field scale
factors
m9
11.2
1.9
8.3
0.0
1.2
0.1
10.8(7)
–
–
FR
1.6(2)
–
0.0
0.0
0.0
26.6
0.4
0.0
ꢂ11.2
ꢂ1.9
ꢂ8.3
26.6
m
asCHa2
m10
m11
m12
m13
m14
dasCH3
q00CH3
d\BO3
The 28 normal modes of the molecule, together with their spec-
tral activity, infrared (IR) or Raman (R), are distributed as follows: 8
A0 (R,pol.); 6 A00 (IR); 9 E0 (IR, R,dp); 5 E00 (R,dp). The A00 infrared
bands should in the gas phase exhibit the contour of a parallel band
of an oblate symmetric top, with a prominent narrow central Q
branch. However, the gas phase contours of the E0 infrared bands
are expected to be variable in nature. No attempt was made to
interpret gas phase Raman band contours.
ꢂ0.8
s
s
OBOC,
CH3,
s
CH3
ꢂ0.1
s
OBOC
E0
Mode
ꢂ
D
m
(
13C)
D
m
(
10B)
calc
D
m(
10B13C)
Motion
calc
obsd
calc
m
m
CHs,
sCHa2,
m
sCHa2
CHs
mBO
m15
m16
m17
m18
m19
m20
m21
m22
m23
E00
11.2
2.6
2.7
2.5
4.1
8.9
16.8
4.3
4.3
FR
FR
0.0
0.0
16.0
0.4
29.2
2.1
4.2
ꢂ11.2
ꢂ2.6
13.9
m
3.3(4)
2.5(4)
6(1)
10(2)
18.0(7)
5(1)
dsCH3.
dasCH3, dsCH3
BO, dsCH3
q0CH3
CO
Table 7
ꢂ1.7
Computed harmonic frequency
(CHD2)(CD3)O.
x and infrared intensity A for C–H stretching bands in
24.5
m
ꢂ7.0
ꢂ12.9
ꢂ2.6
ꢂ4.0
m
Parameter
dtz+
dcct
mtz+
mcct
Obsd.a
1.6
0.3
dOBO, dBOC
dBOC, dOBO
x
x
D
CHs (cmꢂ1
CHa (cmꢂ1
xs–a (cmꢂ1
)
)
)
3106.3
2990.3
116.0
29.3
67.8
38.5
3100.0
2986.7
113.3
30.3
64.9
34.6
3174.0
3066.0
108.0
25.9
57.1
31.2
3170.8
3064.2
106.6
24.4
51.8
27.4
2985
2883
102
3(3)
Mode
ꢂ
D
m(
13C)
Motion
ACHs (km molꢂ1
ACHa (km molꢂ1
Aa–s (km molꢂ1
)
)
)
25.8b
47.5b
21.7b
calc
m
asCHa2
D
m24
m25
m26
m27
m28
11.1
2.0
8.3
0.8
0.1
dasCH3
q00CH3
s
s
a
Observed anharmonic frequency and IR intensity data for the species (CHD2)2O
from reference [15].
OBOC
CH3
b
Partial overlap between the two m
isCH bands leads to some uncertainty in the
division of intensity between each.

366
A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
mentioned above means that interpretation of frequencies may be
carried out as for a single methyl group.
A third difficulty is the possibility of error in the QC calculations
of the interaction force constants which couple the motions of indi-
vidual C–H bonds to produce the stretching vibrations in a CH2 or
CH3 system. Such interaction force constants are typically smaller
from MP2 model calculations than they from DFT based ones.
[20–24] Evidence suggests that the MP2 constants are to be pre-
ferred to DFT ones [20,21]. For this reason we will confine our dis-
In the past, successful interpretations of the
containing molecules have depended on experimental data for
CHD2-substituted compounds which yield
isCH values [17]. The
effect of the two lone pairs on the oxygen atom is to lower
isCHa
relative to
isCHs. The degeneracy of the E vibrations of a methyl
group of C3v local symmetry is thereby lifted, resulting in the fre-
quency sequence
asCH3(a0) > asCH3(a00) > sCH3(a0) [17]. Here the
mCH regions of MeO
m
m
m
cussion of the mCH region to results from the mtz+ model.
m
m
m
Faced with the varying estimates given above of the relative
subscripts ‘‘s” and ‘‘as” have lost some of their original significance.
Delocalisation of the oxygen lone pairs to the boron atom will of
course lessen this effective loss of symmetry by reducing the dif-
ference in C–H bond strength.
strengths (in cmꢂ1) of the two kinds of CH bond, it is natural to
ask if there is alternative evidence bearing on mCH scale factors
to be found in the spectra of the normal (d0) or fully deuterated
(d9) species. The only such datum to be found, which might be use-
In the case of TMB, the IR spectrum of B(OCHD2)3 (hereafter, d6)
is complex [4]. The main, low frequency band has a sharp low fre-
quency cut-off leading to a Q branch at 2950.4 cmꢂ1. This is fol-
lowed by two more Q branches at 2953 and 2956 cmꢂ1 which
merge into broad absorption on which there is a prominent shoul-
der at 3012 cmꢂ1. A plausible interpretation of this spectrum is
that the lowest Q branch comes from transitions involving stretch-
ing of the CHa bond in the ground torsional state of the molecule
while the higher Q branches derive from progressively higher ex-
cited torsional states. In the latter the mean orientation of the C–
Ha bond should progressively approach closer to the skeletal plane,
thereby increasing its strength. This interpretation is to be pre-
ferred to the alternative one in which the three Q branches are as-
cribed to different d6 conformers, since the QC evidence, as seen in
ful in determining a mCH scale factor, is the frequency of m
9 (a00). The
parallel-type band due to this mode is readily identified by means
of the narrow Q branch seen at 2980.2 cmꢂ1 in d0 and at 2235 cmꢂ1
in d9. The d0 band exhibits a 13C shift of 10.8 cmꢂ1 in good agree-
ment with that predicted for this mode from our QC models. Evi-
dence from other methyl-containing molecules points to FR
effects on asymmetric stretching vibration band frequencies s to
be much smaller or even negligible compared with those operating
on msCH3 levels [17]. m9, otherwise represented as m
asCHa2, involves
motions of the CHa bonds only and the frequency of m9 therefore
provides directly a scale factor for the stretching of the latter bond.
In Table 9 we explore four different ways of scaling the stretch-
ing force constants of the two kinds of CH bond and the effect these
have on the prediction of all the CH and CD frequencies in the d0, d9
and d6 species. The data used to define scale factors are given in
bold.
Table 6, indicates that these should yield identical
cies, rather than ones differing by 2–3 cmꢂ1
With the previous ascription of the shoulder in the d6 spectrum
m
CHa frequen-
.
First, a word of caution is needed. In attempting to account for
at 3012 cmꢂ1
m
isCHs, the resulting difference in
m
isCH becomes
both
stants, we need to remove as far as possible the effects of the dif-
fering anharmonicities affecting CH and CD vibrational
mCH and mCD frequencies with a single set of scaled force con-
3012 ꢂ 2950.4 = 61.6 cmꢂ1
.
Alternative evidence for the difference in C–H bond strength has
come from the local mode study of Mananzares et al. [5]. In their
gas phase spectra these authors identified two individual broad
m
m
transitions. This we have done in Table 9 by the usual expedient
bands as arising from
Dv = 5 and 6 transitions respectively. These
broad bands by deconvolution each yielded two peaks, which
when fitted to a Birge–Sponer quadratic expression yielded values
Table 9
Variations in
model force field.
x
e of 3089 and 3051 cmꢂ1. While thus result must be considered
m
CH and
m
CD frequencies (cmꢂ1) with scale factor (sf) from the mtz+
(b)a (c)a
of
as preliminary, it may be significant that the difference of 38 cmꢂ1
values is larger than the ꢁ29 cmꢂ1 predicted by
Parameter (a)a
(d)
mobsd(IRgas
)
mobsd(Rgas)
between the two
x
the QC studies, though much less than the 61.6 cmꢂ1 derived from
the CHD2 study [4].
sfCHs
sfCHa
(0.8858)b 0.9039 0.9039 0.8898
0.8858
2981.7
2953.9
3001.8
2899.4
2253.5
2100.2
2980.2
2236.8
3001.7
2898.4
2253.7
2099.2
2979.7
2236.5
21.5
0.8858 0.8837 0.8837
m
m
isCHs
isCHa
3012.0 3012.0 2988.4c 3012.0?
In attempting to use QC evidence in analysing the mCH region
2953.9 2950.4 2950.4
3026.8 3026.3 3006.4
2904.4 2901.4 2897.7
2270.7 2270.1 2256.5
2105.4 2103.4 2099.6
2980.2 2976.7 2976.7
2236.8 2234.1 2234.2
3026.6 3026.0 3006.2
2903.9 2900.9 2897.1
2270.7 2270.1 2256.7
2104.5 2102.6 2098.6
2979.7 2976.1 2976.2
2236.5 2233.9 2233.9
2950.4?
?
FR
several kinds of difficulty are encountered. In large measure
these stem from the circumstance that we will be attempting
to interpret observed, anharmonic frequency data by the use of
QC based harmonic force fields. The latter will therefore require
scaling if observed frequency data are to be fitted. The first dif-
ficulty arises from the evidence that QC models at the level of
theory we are able to employ in this study may not reproduce
quantitatively the difference in CH bond strength to be encoun-
tered. Several instances of this are known [18,19]. Differing scale
factors therefore may well be needed for the stretching of each
of the two kinds of C–H bond present in TMB. This explains
the reason for our choice of CH stretching symmetry coordinates,
described above.
A0 d0 m1
m2
2999
FR
A0 d9 m1
m2
2245
2245
2106
*
d
*
d
2105
2980.2
2235
?
A00 d0 m9
A00 d9 m9
E0 d0 m15
m16
2999
FR
FR
E0 d9 m15
m16
2245
2105
2245
2106
?
*
d
*
d
E00 d0 m24
E00 d9 m24
?
e
(m15
–
m9
)
46.4
49.3
29.5
19?
10?
d0
e
(m15
–
m9
)
16.9
33.9
36.0
22.5
d9
A second difficulty arises from recent findings which suggest
that CH stretching anharmonicity can vary according to the type
of vibration involved, for instance, whether the stretching is sym-
metric or antisymmetric in nature [20,21]. A scale factor based
a
In bold, data used to fix the two mCH scale factors, All calculated mCD values
have been premultiplied by 1.011.
b
Constrained to value for sfCHa.
m
c
isCHa xs xa = 48 cmꢂ1 from the local mode study of
+ Dx. where Dx = –
on
the stretching motions of a CH3 group. Variation in anharmonicity
may also occur from one
isCH motion to another. However, explo-
m
isCH frequency data may then not be strictly applicable to
Manzanares et al. [5].
d
Deperturbed value from a rough estimate of FR.
These differences give a close measure of the splitting of the masCH3 modes into
e
m
A0 and A00 components in an individual methyl group. An alternative measure of this
ration of the effect of anharmonicity variation is beyond the scope
of the present study.
splitting, m15–m
24, is about 0.5 cmꢂ1 larger.

A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
367
of multiplying by 1.011 all
constants fitting observed
m
CD frequencies calculated from force
We were unable to assign
m
15 in the IR spectrum of d0 due to the
m
CH data [17].
diffuseness of the band contour in this region, but it can be discerned
Under (a) we use the d0 m9 frequency to define the scale factor
for the stretching of the CHa bond and assume this same factor
to apply to CHs bond stretching. The close prediction
at 2992 cmꢂ1 in CCl4 solution [3] and in the solid at 2999 [7].
If these analyses of the d0 and d9 spectra are correct, then m
isCHs
cannot be as large as 3012 cmꢂ1 as originally assigned [4]. We may
also expect that a more extended study of local mode spectra will
(2236.8 cmꢂ1) of the 9 band observed at 2235 cmꢂ1 in d9, is pleas-
m
ing as it suggests that the effects of FR on m9 are small, bearing in
revise the value of
5.2. Assignments: other fundamentals
A0 class. Apart from the
CH and mCD vibrations, discussed
Dx downwards.
mind the approximation involved in the 1.011 factor. m
isCHa is pre-
dicted at 2953.9 cmꢂ1 which is within 3.5 cmꢂ1 of the value of
2950.4 assigned from the d6 spectrum. The small difference be-
tween these two estimates for
small residual FR on m9 or from a difference in the intrinsic anhar-
monicities of the
isCHa2 and isCHa motions. There is therefore no
case at present for reinterpreting this part of the d6 spectrum, at
least. However, the value predicted for
isCHs, 2981.7 cmꢂ1, is con-
siderably less than the 3012 cmꢂ1assigned in [4].
Under (b) we use two scale factors, one for
isCHs based on the
3012 cmꢂ1 shoulder, the other, for isCHa based on
9. A substantial
difference of 0.018 appears in the resulting scale factors and the
values of
1 (A0) and 15 (E0) now differ significantly from their pre-
m
isCHa could easily derive from a
m
above, modes which give rise to difficulty in assignment are m3
m
m
and m5 in d0 and m4 in d9. m3 (d0) will certainly contribute to the
broad dCH3 band at 1470 cmꢂ1
. m5 has previously been assigned
m
to a weak Raman band in the solid state, either at 1183 cmꢂ1 [3]
or at 1208 cmꢂ1 [7]. Our scaled force field predicts this mode at
about 1217 cmꢂ1 in the gas, in fair agreement with the later esti-
mate. In d9, a weak, sharp shoulder in the Raman spectrum at
m
m
m
1087 cmꢂ1, possibly polarised, is a likely candidate for
m4., pre-
m
m
dicted at 1083 cmꢂ1
. m5 is presumed to contribute to the
dicted values under (a).
1067 cmꢂ1 band along with other dCD3 modes.
In the refinement under (c) we use the two d6 based
m
isCH val-
A00 class. The assignments in d0 of m12 (667.4 cmꢂ1 and m13
(102.8 cmꢂ1) are non-controversial and follow the earlier studies
[3,7]. However, as commented on earlier [4], there is clear evidence
ues, with very little change from the predictions made under (b).
Under (d) we utilise the local mode data by taking their
xis CH
difference of 38 cmꢂ1 to approximate a similar mis CH value and
D
D
for a Fermi resonance on m12, the out-of-plane BO3 bending mode,
from the IR spectra of both d0 and d9 isotopomers, illustrated in
adding the latter to our
m
isCHa of 2950.4 cmꢂ1, to give mis-
CHs = 2988.4 cmꢂ1, The resulting predictions of m1
, m15 etc. are then
Fig. 2.
fairly close to those under (a).
The 10B–11B frequency shift calculated for this mode is close to
27 cmꢂ1 (Table 8) in both d0 and d9 species, while the d0 to d9 shift
should be 2–3 cmꢂ1(Table 5). By contrast the 12C–13C shift is pre-
dicted to be zero.
Comparing the results from (a)–(d), we see only a modest vari-
ation of up to 7 cmꢂ1 in the predictions of
m2, but somewhat larger
variations of up to 25 cmꢂ1 in m1 in d0 and d9.
In comparing these predictions with experimental data, it is evi-
The IR Q branches at 702.0 and 678.0 cmꢂ1 in d9 are undoubt-
dent that little can be deduced from the observed values of m2
,
edly the 10B and 11B components of
m12, but their separation of
which are strongly affected by FR. This is particularly evident in
the Raman spectrum of d0 where there are no less than seven
polarised lines between 2978 and 2728 cmꢂ1 showing the small
24 cmꢂ1 is 3 cmꢂ1 less than expected, while the expected deutera-
tion shift on the 11B band is absent. However, an additional, broad-
er weak band appears at about 648 cmꢂ1
.
13C shifts expected from m2
,
m16 and associated overtone and com-
In the d0 spectrum where a single 10B band due to
m12 would be
bination levels. Suggestions for the latter are included in Table 1.
However, in d9 there are only two polarised lines, at 2146 (IR:
2145) and 2087 (IR 2086) cmꢂ1. If the former is the overtone of
1067 cmꢂ1, its deperturbed position might be estimated to lie near
2 ꢃ 1067 ꢂ 7 = 2127 cmꢂ1, yielding a FR shift of about 19 cmꢂ1 and
placing mꢀ2 near 2106 cmꢂ1. Remembering that this estimate in-
cludes both FR and normal anharmonicity corrections, we can only
claim that all four estimates of the position of mꢀ2 (d9) are in the
right range.
expected, two bands appear at 711.4 and 699.8 cmꢂ1 which yield
separations of 44.0 and 32.4 cmꢂ1 from the 11B m12 frequency of
667.4 cmꢂ1. Moreover, both these higher bands carry significant
12C–13C frequency shifts, ꢁ3 and ꢁ5 cmꢂ1 respectively. A smaller
such shift can also be discerned in the 677.4 cmꢂ1 band. All these
features are explained by a FR involving the combination level
m
22(e0) +
m
27(e00) which is predicted to lie above m12
(
(
11B) in d0 but
below m12
11B) in d9. An exact reproduction of the observed fre-
quencies is not possible but rough calculations with an interaction
A more severe problem arises in attempting to assign
m
1 (a0) and
parameter W12,23,27 of about 13 cmꢂ1 suggest that the FR shift on
m15 (e0), which are expected to coincide. The splitting between
m12 (
11B) has been about 6 cmꢂ1 downwards, placing the deper-
either of these modes and m9 (a00), shown at the bottom of Table 9,
turbed mꢀ12 at about 673 cmꢂ1. By contrast, m12 in d9 has been dis-
represents the splitting mentioned above of the degenerate
m
asCH3
placed upwards, by about 7 cmꢂ1
(
11B) or ꢁ4 cmꢂ1
(
10B), yielding
values for the deperturbed m12 of ꢁ671 cmꢂ1. (11B) or 698 cmꢂ1
*
modes of a methyl group of C3v local symmetry, due to insertion of
the BO3 plane.
(
10B). The 699.8 (d0) and 648 cmꢂ1 (d9) bands are each assigned
In the spectra of d9 there is only one feature capable of assign-
as m22 +
m27 in he 11B species, which on the basis of a zero value
ment to either or both of m1 and
m
15, and that is the band at
of x22,27 yields values of m27 of 700 ꢂ 6 ꢂ 525 = 169 cmꢂ1 in d0,
and 648 + 7 ꢂ 494 = 161 cmꢂ1 in d9. (There is no boron isotope
shift in the E00 species.) The additional 10B band at 711.4 cmꢂ1 is as-
2245 cmꢂ1, seen in both the IR and Raman spectra. The splitting
from m9 at 2135 cmꢂ1 is then only 10 cmꢂ1, rather less than the
smallest separation shown in Table 9, that of ꢁ17 cmꢂ1 under op-
tion (a).
signed to a more strongly perturbed m22 + m27 level, perhaps a 50/50
mixture, with the other 10B component level lying at about
691 cmꢂ1 and so far unidentified in the complex absorption in this
region.
A similar situation is found in the spectra of d0. Here a definite
band with large appropriate 13C shift is seen in the Raman spec-
trum at 2999 cmꢂ1. Intensities calculated from the dtz+ model, Ta-
For the assignment of m
11, a Q branch is seen at 908.7 cmꢂ1 in d9,
ble 5, suggest that this band represents m15 more strongly than m1
.
but there is no corresponding gas phase feature in d0 at the ex-
pected value of ꢁ1175 cmꢂ1. The infrared intensity predicted for
the latter is very low, which provides a likely explanation for its
non-observance in the gas. However, m11 has previously been as-
signed to a solid state shoulder at 1184 cmꢂ1.[7] m10 (dasCH3) in
The splitting between this frequency and that of m
9 at 2980.2 cmꢂ1
is then only 19 cmꢂ1. However, this is now compatible with the
splitting of 21.5 cmꢂ1 predicted under (a), when the likely effects
of small resonances and experimental error are borne in mind.

368
A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
m23 in both d0 and d9. In the gas phase infrared spectrum of d0 the
13C shift of about 10 cmꢂ1 on the band at 1200 cmꢂ1 is compatible
with an assignment to 20, as in [7], but is incompatible with the
earlier choice of the combination m21
m28 (A00) [3], for which the
m
+
13C shift should be ꢁ18 cmꢂ1. However, the corresponding gas
phase Raman band is broad and rather lower in frequency. This
may be in part because it arises from both m20 (e0) and m27 (e00),
the latter predicted 13–16 cmꢂ1 below the former (Table 5). In
the Raman liquid spectrum of Stampf et al. [7] two depolarised
lines are resolved at 1171 and 1165 cmꢂ1 which fit quite well the
expected positions of these two fundamentals if there are signifi-
cant gas/liquid shifts. However, a value for the centre of m20 (d0)
in the gas near 1193 cmꢂ1 would be more commensurate with
the corresponding value of 1001 cmꢂ1 in d9.
A somewhat similar situation arises near 190 cmꢂ1 where the
infrared gas phase band due to m23 (d0) is observed at 190 cmꢂ1
,
slightly above the Raman band at 184 cmꢂ1 which can arise from
both m23 (e0) and m27 (e00), predicted to have similar intensities.
However, the 13C shift of about 4 cmꢂ1 on this Raman band is con-
sistent only with its assignment to
168 cmꢂ1 fits well with the position expected for m23
E00 class. The only d0 fundamental for whose position there is
significant evidence is 27. The analysis outlined above of the FR
affecting m12 placed m27 near 169 cmꢂ1. With m14 at 103 cmꢂ1
m
23 (e0). The d9 infrared band at
.
m
,
m14 + m
27 (E0) is predicted to be 272 cmꢂ1, providing an explanation
for the weak IR feature at 273 cmꢂ1. The weak, polarised Raman
line at 331 cmꢂ1 may at the same time be assigned as the first
overtone of m
27. A slightly higher value for m27 of 173 cmꢂ1 is ob-
tained from the infrared band at 869 cmꢂ1 if the latter is the differ-
ence m21
ꢂ
m27 (1042 ꢂ 173 = 869 cmꢂ1), as the large 18 cmꢂ1 13C
shift suggests. Transfer of the appropriate mtz+ scale factors from
the A00 class predicts m27 to be 180 cmꢂ1
The scaled mtz+ value of 1177 cmꢂ1 for
ible with one of the two liquid phase Raman lines 1171, 1165 cmꢂ1
.
m
26 (d0) may be compat-
,
observed by Stampf et al. [7], if there is a significant downwards
shift upon condensation. In a similar manner, the predicted value
for m
28 of 64 cmꢂ1 is compatible with the assignment of this mode
to the solid phase Raman frequency of 78 cmꢂ1 [7], since the up-
wards shift here of 14 cmꢂ1 is acceptable for the effect of conden-
sation on a methyl torsion.
Locating
appear to be currently feasible.
In d9,
26 is seen as a Raman line at 908 cmꢂ1 in the liquid, close
to its predicted value of 910 cmꢂ1
m24 and m
25, predicted at 2980 and 1477 cmꢂ1, does not
Fig. 2. Infrared spectra of TMB species in the region of m12, showing Fermi
resonating bands.
m
.
d0 could not be distinguished in the complex absorption in the
1450–1520 cmꢂ1 region and its dasCD3 counterpart is likely in the
same way to be part of the 1066 cmꢂ1 IR band in d9. Refining to
the latter value then predicts m10 in d0 near 1477 cmꢂ1. Neglect
of d0/d9 anharmonicity differences means that the d0 value is likely
to be lower still. The earlier assignment of m10 to 1509 cmꢂ1 [7]
therefore seems unlikely.
5.3. Overtone and combination bands
Some of the earlier assignments of Rogstad et al. for d0 are con-
firmed by the 13C shifts shown in Table 1 but not all. However, the
error in the measured shifts may be greater than those indicated in
this table, due to the breadth of the peaks measured. In particular
the shifts observed on the seven polarised Raman lines involved in
the m2 FR system, whose origin can hardly be doubted, are gener-
ally less than anticipated.
Finally, a plausible value of 49 cmꢂ1 is obtained for
very weak IR band at 780 cmꢂ1 if this is interpreted as the combi-
nation 731 (
7, A0) + 49 ( 14, A00) = 780 cmꢂ1, (A00). Torsional fre-
quencies are also expected to combine with antisymmetric CH3
stretching modes to give weak shoulders above asCH3 bands
[25] and such shoulders can in fact be seen (see Table 1).
E0 class. The assignment of
17 in d0, which in this isotopomer is a
coupled
BO/dsCH3 motion, to the IR bands at 1509 (10B) and
1494 cmꢂ1 11B) is strongly supported by its observation at 1448.7
10B) and 1403.5 cmꢂ1 11B) in d9. The force constant refinement re-
sults show how this large
B–O isotope shift of 45 cmꢂ1 in d9 is in d0
split between 17 and
19, the latter seen at 1363 cmꢂ1 11B).
m14 from the
m
m
The large 13C shift of 29 cmꢂ1 on the band at 2400 cmꢂ1 can
m
only be accounted for by the ternary combination m11
+ m21 + m23
(A00). The simpler alternatives of 2m20 or m19 m21 involve 13C shifts
+
of only 18 or 21 cmꢂ1
.
m
In the spectrum of d9, the absence of 13C shift data made it
impractical to list in Table 2 the many combination and overtone
permutations possible.
m
(
(
(
m
A final comment regarding the interpretation of the IR spectra is
that the problems presented by the breadth and diffuseness of the
bands would be greatly eased if spectra were to be obtained in liq-
uefied noble gas solution. [26] Such a study is greatly to be desired.
m
m
(
Elsewhere there are problems associated with assignment of
the methyl rocking frequency m20 in d0 and with the skeletal bend

A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
369
5.4. Force fields, scale factors and frequency fits
mtz+ model which is significantly larger from the E0 species than
it is from the A0. The mtz+ model also requires a
than that for any of the other methyl motions.
sCH3 factor larger
The scale factors for the three model force fields are shown in Ta-
ble 10, grouped according to the type of motion involved. With the
objective of testing each model force field for self consistency, we
setoutto determineasmanyindividualscalefactorsaspossible. This
might permit testing of the common practice of assuming identical
scale factors for a particular type of internal coordinate, for example,
all those involved in CH bending motions. In the event, the complex-
ity of bands in the 1400–1500 cmꢂ1 (d0) and 1000–1100 cmꢂ1 (d9)
regions made this difficult. We were therefore obliged to constrain
certain scale factors equal, for instance, in the case of the dsCH3
and d0asCH3 pairs in the A0 and E0 species. The same problem as it af-
Among the skeletal motions, the mtz+ model yields a better
agreement between the factors for symmetric and antisymmetric
BO stretches than do the dtz+ or dcct models, although the error
in the
masBO3 factor is large for the latter. This is associated with
a
smaller
mBO/m
BO constant, f0 (unscaled mtz + value of
0.6185 aJ Åꢂ2) than is found with the B3LYP models (f0 = 0.6646
(dtz+), f0 = 0.6714 (dcct). This repeats the pattern found for the
stretching of C–F and C–Cl bonds n 1,1-difluorocyclopropane [20]
and dichloromethane [21]. Stretch/stretch interaction force con-
stants f0 are smaller and the
mas and ms scale factors closer together
fected the
m
CHs and
m
CHa stretching force constants has been dis-
from MP2 models than they are from B3LYP ones. This has been
considered to be an advantage of the former [20,21].
Another difference between the MP2 and DFT models is seen
with the d||BO3 and d||BOC factors which are significantly larger
than average for the DFT ones.
cussed in detail above, see Table 9. Of the options in Table 9 we
selected for use in Table 10, that under (a) which employs a single
m
CH scale factor based on the value of
m9 in d0.
The frequency fits given by the three model force fields are in-
cluded in Table 5, while the preferred mtz+ scaled force field is gi-
ven in the Supplementary Data, Table 2.
Perhaps the most curious set of scale factors is that associated
with the sOBOC coordinate, S10. These vary from very large (1.48)
Two major anomalies can be seen in the frequency fit data. The
for the mtz+ model to very small (0.646) for the dcct one. By con-
trast the dtz+ value of 0.925 is almost average in value. A similar
large variation in scale factor was discovered in butadiene, associ-
ated with the out-of-plane bending modes [27]. However, in the
latter case, the source of the anomalous scale factors could be
attributed to the absence of f functions in the 6311++Gꢀꢀ basis
set [27] and the anomalies disappeared when the cc-pVTZ basis,
which employs such f functions, was used. Clearly a similar expla-
first is associated with the predictions of m2 and m16 which are up to
20 cmꢂ1 higher from the B3LYP models than they are from the MP2
model. This difference can only derive from a difference in calcu-
lated CH stretch/CH stretch interaction force constants, as found
previously in a number of instances [20–24]. If the rough FR correc-
tion applied above to m2 is correct, comparison with the m2 and m15
frequencies predicted in Table 5 strongly favours the MP2 result.
A more striking example of the superiority of the mtz+ force
field is seen in the failure of the B3LYP models to fit the E0 modes
nation cannot apply to the sOBOC factor in TMB. The marked var-
iability in this last scale factor points to a general need for caution
in utilising QC calculations for the estimation of out-of-plane bend-
ing motions of planar systems, particularly when these derive from
extended atomic arrays where long range interactions between
non-bonded atoms may be important.
m22 and m23. These vibrations are composed of strongly coupled
dOBO and dBOC motions and the failure of the two DFT models
to reproduce their frequencies, especially in the d9 isotopomer, is
readily traced to the lower DFT values of the interaction force con-
stant F16,18 linking the two motions: F16,18 = 0.1008 (mtz+), 0.0720
The full set of symmetry force constants from the scaled mtz+
model is available in the Supplementary Data, Table S2.
(dtz+), 0.0716 (dcct) aJ radꢂ2
.
It is also of interest to compare the scale factors (sf) from the
three models.
Within the uncertainties, often substantial, of the sf values for
the various methyl motions, there is little to indicate variation in
6. Conclusions
the dasCH3, dsCH3 or qCH3 factors with choice of origin. A possible
exception to this is the in-plane methyl rocking factor from the
1. New vibrational spectra of labelled trimethoxyborane species,
aided by scaled QC-based force fields, enable a more reliable
set of fundamental frequencies to be established for B(OCH3)3
and a new such set for B(OCD3)3.
Table 10
Scale factors for symmetrised QC force fields for trimethoxyborane.
2. The change in stability with basis set from cis- to trans-C3h
structure is demonstrated using HF, B3LYP and MP2 models.
3. A combined use of the QC results and IR spectra in the CH and
CD stretching regions indicates that the difference in C–H bond
strength between the two kinds of CH bond present is much
less than had been previously diagnosed from a B(OCHD2)3
spectrum, indicating the need for a reinterpretation of the lat-
ter. This conclusion is supported by similar data for
dimethylether.
Motion type
Symmetry
Scale factor
coordinatea
A0
A00 E0
E00 mtz+
dtz+
dcct
mCHs,
mCHa
4, 5 12 19,
26 0.886b
0.931b
0.934b
20
dsCH3,d0asCH3 6, 7
dsCH3,
0.936(3)
0.942(5)
0.964(4)
0.978(18)
0.959(3)
0.973(18)
21,
22
d0asCH3
CH3
00
13
27 0.950(39)
0.938(9)
0.975(9)
0.978(8)
0.993(28)
0.997(9)
0.945(6)
0.991(9)
0.956(30)
0.992(10)
0.970(30)
0.969(9)
0.975(8)
0.984(27)
0.984(9)
0.963(7)
0.989(8)
0.934(29)
0.976(10)
0.963((30)
d
as
q0CH3
q0CH3
q00CH3
8
4. A Fermi resonance involving m12 (a00) is identified and treated
approximately.
23
0.968(8)
14
11
28 0.965(40)
25 1.004(60)
0.941(8)
5. Evidence is found for the superiority of MP2-based force fields
over those from B3LYP models.
s
m
m
m
m
CH3
sBO3
asBO3
CO
1
2
15
0.957(9)
0.965(10)
0.934(9)
1.016(6)
0.961‘(29)
1.011(5)
6. Anomalous scale factors are found associated with the
torsional motion.
sOBOC
CO
17
16
d||BO3
d\BO3
d||BOC
1.138((21) 1.134(21)
0.980(6)
1.105(5)
9
1.001(7)
1.104(5)
0.646(12)
3
18
Acknowledgments
sJBOC
10
24 1.476(192) 0.925(17)
a
We are very grateful to Dr. A.J. Willetts for communicating his
unpublished calculations on the structure of TMB.
In italics, location of constrained scale factors.
b
Refined to give exact fit to m9 (A) = 2980.2 cmꢂ1 in TMB–d0.

370
A.M. Coats et al. / Journal of Molecular Structure 976 (2010) 360–370
[11] K.P. Steinfeldt, J. Heller, R. Baumert, Z. Naturforsch. 36B (1981) 691.
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[12] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman,
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National Service for Computational Software (admininstered by
the Department of Chemistry, Imperial College London, Kensing-
ton, London SW72, AZ), is thanked for computing time on Colum-
bus. Dr. D. Wann and Dr. S.G.D. Henderson are thanked for
assistance with the production of the figures.
Appendix A. Supplementary data
Symmetry coordinates for trimethoxyborane, Table S1; scaled
MP2/6-311++Gꢀꢀ symmetry force constants, Table S2; infrared
survey spectrum, 400 to 2400 cmꢂ1, of B(OCD3)3, Figure S1. Supple-
mentary data associated with this article can be found, in the on-
line version, at doi:10.1016/j.molstruc.2010.02.073.
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