Dipole moment derivatives and vibrational intensities of BCl3
Roy E. Bruns and Paul M. Kuznesof
Citation: The Journal of Chemical Physics 59, 4362 (1973); doi: 10.1063/1.1680634
View online: http://dx.doi.org/10.1063/1.1680634
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THE JOURNAL OF CHEMICAL PHYSICS
VOLUME 59, NUMBER 8
15
OCTOBER 197:3
Dipole moment derivatives and vibrational intensities of BCl3
Roy E. Bruns and Paul M. Kuznesof
Instituto de Quimica, Universidade Estadual de Campinas, 13100-Campinas-S.P., Brasil
(Received 15 March 1973)
The CNDO approximate molecular wave functions for Bel 3 have been applied to the calculation of the
derivatives of the dipole moment with respect to the symmetry coordinates. New experimental derivatives
calculated from previously published intensity data are presented. The set of experimental derivatives with
respect to internal coordinates definitely preferred by these calculations is that with all signs negative.
Inclusion of the d orbitals of chlorine in the atomic orbital basis set markedly influences the magnitudes of
the derivatives as well as improves the agreement with the experimental in-plane and out-of-plane bending
derivatives. The pd polarization terms appear to play an important role. Our results for BCl] are compared
with those previously obtained for BF].
INTRODUCTION
Recent studies of the dipole moment derivatives
of the X2Cyl,2 (X=F and Cl, and Y=O and S) molecules suggest that the experimental derivatives of
one of these molecules can be calculated from the
corresponding derivatives of the others. The differences in these CF and CCl stretching and bending derivatives appear to be independent of the oxygen or the sulfur substituent. The determination
of the dipole moment derivatives of trifluoroborane,
BFs, and trichloroborane, BCls, allows an extension of the investigation of these substituent effects.
The infrared intensities of the two haloboranes
have been measured previously. S,4 However, the
interpretation of the experimental data is complicated by the well-known sign ambiguity which
arises in the data reduction and results in multiple
sets of solutions for the experimental dipole moment derivatives. Approximate CNDO (complete
neglect of differential overlap) molecular orbital
calculations 5 have been used successfully for selecting unique preferred sets of derivatives from experimental data for various molecules 6 including
trifluoroborane. 6d Application of the CNDO method
to trichloroborane also provides the opportunity for
assessing the importance of d atomic orbitals in
the CNDO estimation of dipole moment derivatives.
In the process of comparing the calculated results with the experimental data we discovered several errors in the original transformation of the
trichloroborane intensity data into dipole moment
derivatives. These are discussed and corrected
in the Appendix.
CALCULATIONS
The experimental dipole moment derivatives with
respect to the symmetry coordinates, the ep/es J,
as amended in the Appendix for trichloroborane are
reproduced in Table I along with those calculated
by CNDO. The latter were determined using defi-
nitions of the symmetry coordinates and their relationships to the Cartesian coordinate system
identical to those given in Refs. 3 and 6(d). Calculations were performed as described previously6
using an IBM 360-44 computer with a modification
of the CNINDO program from QCPE. 7 The spd set
was obtained from a calculation involving 3s, 3p,
and 3d atomic orbitals of chlorine with Santry's
parametrization. 8 The sp set of calculations refers to the one obtained with an identical set of
parameters for the 3s and 3p orbitals, but in the
absence of the 3d orbitals. The B-Cl bond length
of 1. 72 A used here is identical to that employed in
the experimental analysis. 4
The equations relating the ep/es J to the ep/er;,
derivatives of the total dipole moment with respect
TABLE I. Comparison of the ep/es j values calculated
for BCIs with the experimental values.
E' Symmetry species a
8p/8S S (D/A)
Exptl.b
(± ±)C
Exptl. b (± +)
CNDO (spr1J
CNDO (sp)
Ai'
8p/8S4 (D/rad)
±3.30
±0.91
±4.04
-6.27
-5.72
±0.06
-1.45
-2.41
Symmetry species
8p/8S2 (D/rad)d
Exptl.b
(±)
±0.46
CNDO
CNDO
(spd)
(sp)
+2.95
+4.93
arhe calculated results for 8p/8S3a and 8p/8S4a are
identical to those for 8p/883b and 8p/884b • For this reason the letter subscript is not included below.
bJ'he experimental results of Ref. 4 as corrected in
the appendix.
"The first column corresponds to the sign of 8p/8Qs
and the second to that of 8P/8Q4'
"The values for 8p/aS2 refer to the definition S2
=3- 1 / 2 (1'1 + 1'2 + I's)·
4362
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DIP 0 L E MOM E N T DE R I V A T IV E S 0 F B C 13
to generalized internal coordinates, are identical
to those of Ref. 6(d}. The derivatives resulting from
the application of these equations to the values in
Table I are given in Table II. If the bond moment
hypothesis were valid for trichloroborane, negative
signs for the derivatives with respect to changes in
the B-Cl bond distance, the in-plane angles, and
the out-of-plane angles (ap/ ad, ap/ aa, and ap/ ay,
respectively) would represent charge separations
(or increases in charge separations with increases
in bond lengths) of direction B+C1 -.
RESULTS
4363
- 0.84 - -187D/rad found 1 ,2 for the CCI bending
derivatives of dichlorocarbonyl and dichlorothiocarbonyl. As these values may be expected to
parallel those of the analogous fluorine containing
molecules, we note that the preferred experimental
value of ap/aa for trifluoroborane (- 2. 61 D/rad)
lies within the range found for the CF bending derivatives of the difluorocarbonyl and difluorothiocarbonyl (- 0.76 - - 2. 79 D/rad).
A choice of the (-+) set of derivatives leads to
a value of ap/a(JI of - O. 08 D/rad. This is more
positive than the preferred value of ap/ay in the
symmetry species. The contrary is found for
trifluoroborane and the carbonyl and thiocarbonyl
halides reinforcing our preferred choice of the
(- -) set.
A;
E' Symmetry Species
As there are two infrared active in-plane normal
coordinates Q3a and Q4a (or the equivalent Q3b or
Q4b), four sets of values for dipole moment derivatives ap/aSSa and ap/as4a are obtained, all consistent with the magnitude of the experimental values
of ap/aQsa and ap/aQ4a' The four possible experimental sets are listed in Table I together with the
sets of values calculated from the CNDO method
using a sp and a spd basis set. All the experimental alternative sets of derivatives have values
of ap/aSSa and ap/as4a with identical signs. The
calculated values from both the sp and spd basis
sets have neg~tive signs. The calculated magnitudes from either the sp or spd basis set are much
larger than any of the experimental values. The
best agreement occurs between the spd calculated
value of ap/as4 and its experimental magnitude in
the (- -) set. This experimental value rephrased
as ap/ aa (- 1. 29 D/rad) falls in the range of
TABLE II. Comparison of the apl&r;a values calculated for BCl 3 with the experimental values
A:; Symmetry Species
There is only one vibration in this class; hence,
only the Sign of ap/as 2 is uncertain. Both calculated derivatives are positive suggesting that ap/
as 2 =+0. 46 D/rad is the preferred experimental
value. This necessitates a negative sign for ap/ay
and implies the same direction of charge separation
B+ -cr as found for the in-plane bend. Both calculated absolute magnitudes are much larger than the
experimental magnitude. The value of ap/ ay from
the spd basis set is 1. 1 D/rad more negative than
the experimental value. In trifluoroborane the
calculated dipole moment derivative for the out-ofplane B-F bend is 1. 0 D/rad more negative than
the experimental value. Differences of 1.4 D/rad
between the calculated and experimental out-ofplane derivatives of the carbonyl and thiocarbonyl
chlorides have been found and discussed previously.1,2,9 The calculated magnitude of ap/ay using
the sp basis set appears to be much too large.
DISCUSSION
E' Symmetry species
aplad
aplaa (D/rad)
(D/A)
Exptl. (± ±)b
±2.69
±1. 29
Exptl. (± +)
CNDO (spd)
CNDO (sp)
±3.30
-5.12
-4.67
±0.08
-2.05
-3.41
A;' Symmetry species
apia" (D/rad)
Exptl. (±)
CNDO
CNDO
(spd)
(sp)
±0.27
-1. 70
-2.85
aThe r; are the generalized internal coordinates. d
represents a change in the B-CI internuclear distance,
a is a change in the CI-B-Cl in-plane angle, and" is a
change in the angle between a B-Cl bond and the eqUilibrium BCl 3 plane.
bSe e Footnotes band c of Table I.
The CNDO calculated dipole moment derivatives
may be conveniently discussed in terms of the various contributions 6b to the derivatives as presented
in Table III. In particular, the role of d orbitals
becomes more evident. Inclusion of the d orbitals
in the atomic orbital basis set for trichloroborane
decreases the absolute magnitudes of the in-plane
(t::..I1/ t::..r;, r; = a) and out-of-plane (t::..I1/ t::..r;, r; =y)
derivatives by 1.4 and 1. 2 D/rad, respectively,
improving agreement between the calculated (Column 6, Table III) and experimental (Column 7, Table III) derivatives. These decreases result from
a substantial cancellation of the sp polarization
contributions (t::..Jlst'! t::..r;, Column 3, Table III) by
the pd contributions (t::..l1pa/ t::..r;, Column 4, Table
III). We note that the contribution of the sp polarization term is essentially identical regardless of
basis set. Obviously, no pd polarization terms
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4364
R.
TABLE III.
E.
BRUNS AND P.
M. KUZNESOF
Contributions to the CNDO calculated dipole moment derivatives of BCl3 and BF3a.
tl./.lq b/tl.ri
(tl./.l/tl.ri) "
1
M
3a (ri=d)
BC13 (sp)
BC1 3 (spd)
BF3
-0.29
-0.25
-1.12
-4.43
-4.22
-3.00
0.01
-0.02
-0.72
-0.63
-0.50
-0.42
-1.45
-1. 06
-0.92
-0.47
-1. 85
-1. 84
-1. 06
+1.13
-0.50
-0.43
-1.45
0.00
0.00
0.00
-2.35
-2.33
-1.28
+1. 06
0.01
-0.65
- O. 72
-4.67
-5.12
-4.84
-1. 85
-0.71
-1. 06
-3.41
-2.05
-2.98
-2.35
-1.27
-1.28
-2.85
-1. 70
-2.73
-2.69
-3.95
tl.S 4a (rj =O!)
BC1 3 (sp)
BC1 3(spd)
BF3
-1. 29
-2.61
M 2 (ri =')1)
BC1 3(sp)
BCI 3 (spd)
BF3
-0.27
-1. 72
aThe entries in this table have units of D/P.. (M3a ) and D/rad (Moo and M 2).
bThe contribution arising from the movement of the nuclei bearing the equilibrium static charge.
cThe contribution resulting from rehybridization of the orbitals about the nuclei (intramolecular charge transfer).
dThe contribution arising from changes in sp polarization of the orbitals about the nuclei.
eThe contribution arising from changes in pd polarization of the orbitals about the nuclei.
f CNDO calculated total derivatives.
"Experimental derivatives: for BCI 3, Ref. 4 as corrected in the Appendix; for BF 3, Ref. 3.
are available for cancellation in the sp basis calculation.
Previous calculations1,2 on dichlorocarbonyl1 and
dichlorothiocarbonyl2 also yielded the same sign
alternation for the sp and pd polarizations contributing to the C-CI bending derivatives. For these
molecules the spd basis calculations also gave lower absolute values of the bending derivatives in
better agreement with the preferred experimental
values with only one exception: The asymmetric
bending derivative (tl./J./tl.0!) in dichlorothiocarbonyl
is slightly larger (0.27 D/rad) when d orbitals are
included. It is also worth noting that the sums of
the sp and pd polarization contributions [(tl./J.sP
+ tl./J.Pd)/ tl.rj, Column 5, Table III] for the bending
distortions in the carbonYls have values similar to
the corresponding sp polarization term (tl./J. s / tl.r j )
for trifluoroborane. Such polarization backpolarization effects are commonly seen in the calculation
of equilibrium dipole moments when d orbitals are
included in the atomic orbital basis set. Santry and
Segal 10 found that d orbitals are essential to the
CNDO estimation of reasonable static moments for
molecules containing second row atoms. In their
calculations the pd lone pair dipoles are directed in
an opposite sense to the sp dipoles. As lone pair
dipoles appear to be quite sensitive to changes in
intramolecular angles, we may anticipate that calculations of accurate bending derivatives would
depend on their proper conSideration. Calculation
of bending force constants, on the other hand, does
not appear to be as sensitive to the inclusion of d
orbitals as are dipole moments which may explain
why one basis set is not generally preferable to
the other. 10 We note that calculation 11 of the outof-plane bending force constant of trichloroborane
using the smaller sp basis set gives better agreement with experiment.
Intramolecular charge transfer contributions to
the in-plane bending derivative (tl./J.qz/ tl.0!, Column
2, Table III) for trichloroborane are Significantly
large. The charge rearrangement shown in Fig. 1
for S4<l indicates that electron transfer occurs away
from the Cl(z) -B-CI(3) angle as it becomes larger.
Charge transfer in the same direction was calculated for trifluoroborane and is consistent with the
expected changes in hybridization and hence with
the electronegativities of the boron orbitals. The
+0.00113
-'y
+0.00513
CI
*
Y
2
/-CI
CI 3
\\
-001010
+0.00513
t.S 3a =+0.02450
A
1----t>X
CI 2*
\1/-CI
-000"7
1--t>X
a 3 .......
+QOOll3
~S4a
= +0.04275 rad
FIG. 1. The in-plane motions S3a and Soo of trichloroborane, including the changes in charges on the chlorine
atoms, calculated using an spd basis set.
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DIPOLE MOMENT DERIVATIVES OF BCl s
charge transferred to Cl(l) (calculated using either
basis set) is about 1. 5 times smaller than that to
F (l) for an equivalent magnitude of distortion.
This may reflect the larger valence state ionization
potential and the smaller valence state electron affinity of the fluorine atom. 12 The relatively large
B-Cl bond length leads to a value of ilJl.J ilQl which
is about twice the corresponding contribution in
trifluoroborane. There is no contribution due to
charge rearrangement for the out-of-plane bending
derivatives. This has been found and previously
discussed for other molecules. 9
For the B-Cl stretching derivatives (ilJl/ ild,
Column 6 of Table III) both basis sets yield calculated values which are much higher than the experimental value (Column 7 of Table III). The spd
value is 0.45 D/A larger than the sp value. This
contrasts with the results for the carbonyls1,2
where the sp basis calculation provided the larger
values which were also in better accord with the
preferred experimental data. Apparently, d orbitals in the basis set effect the trichloroborane
stretching derivatives quite differently than the
corresponding C-Cl derivatives of the carbonyls.
The predominant contribution to the stretching derivative of trichloroborane arises from the intramolecular charge transfer term ilJl.2/ ild. This
contribution is rather insensitive to the alternative
basis sets; it is about 1. 3 D/A greater for trichloroborane than for trifluoroborane. However, the
large contribution of ilJl.d ild (Column 1 of Table
III) in trifluoroborane due to movement of the high
negative equilibrium charge of the fluorine atom
differs considerably from the smaller value (by
0.8 D/A) in trichloroborane. This yields calculated values of ilJl/ ild for the two halides which are
of Similar magnitude. Polarizations of atomic orbitals (Column 5, Table III) appear to be more
properly accounted for by the spd basis calculations
where this contribution is very similar to that calculated for the fluoride; a nearly zero value for
trichloroborane (sp basis) seems unreasonable.
The net electron populations calculated for the
chlorine atoms indicate that in the ground electronic state resonance structures of the type
Cl-, etc.,
become important as the atoms are distorted in
S3a' The form of this symmetry coordinate is illustrated in Fig. 1 with the amount of electronic
charge transferred to or from the chlorine atoms
4365
with reference to their equilibrium charges. The
O. OlOlOe (spd basis set) transferred to Cl m for a
distortion of ilS3a =+ 0.02450 A is very close to
that transferred to F (1) in trifluoroborane (0. 00953e)
for an equivalent magnitude of distortion. The
resonance structures appear of comparable importance for each molecule. The transfer of electronic charge through the relatively long B-Cl
bonds is the primary reason that ilJl.J ild is 1. 3
D/ A larger in trichloroborane than in trifluoroborane.
In summary, the calculations are in harmony
with our chemical intuition concerning the signs
of the dipole moment derivatives. Furthermore,
it is encouraging that the major contributions to
these derivatives (i. e., the intramolecular charge
transfer term for the stretch and the polarizations
for the bends) are the same for both haloboranes.
This same parallel is also found between C1 2CO, 1
C1 2CS, 2 and cis -C1 2C 2H2, 13 and their fluorine analogs. In all these comparisons, however, quantitative agreement between calculated and experimental results is Significantly better for the fluorides. In addition, it is clearly unsatisfactory that
neither the sp or spd basis set is superior in estimating the derivatives for all types of vibrations
involving chlorine atoms. This is not too surprising since, in general, the theory appears to be
more reliable for calculating properties of molecules containing only first row atoms. In part,
this weakness regarding calculations on molecules
with second row atoms stems from the provisionary parametrization for these atoms. 8, 10 The
spectral data and reference quantum mechanical
calculations needed to evaluate these constants
for the 3s and 3p orbitals are less well-determined than the corresponding data for the. first
row atoms. The parameters for the 3d orbitals
were obtained from data of even greater uncertainty. In view of the success of CNDO theory in
calculating dipole moment derivatives involving
only first row atoms, attempts to arrive at more
accurate second row atom parameters should be
encouraged.
ACKNOWLEDGMENTS
We are pleased to mention that Dr. Mandirola
has confirmed our reanalysiS of her data. Free
computer time from the Instituto de Fisica, Universidade de Sao Paulo and partial financial support from the Funda~ao de Amparo a Pesquisa do
Estado de Sao Paulo are gratefully acknowledged.
APPENDIX
We have discovered two significant errors in th
original reduction4 of the trichloroborane intenSity
data to the derivatives of the dipole moment with
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R.
4366
E.
TABLE AI. Absorption intensities and
for trichloroborane.
Frequency
(cm-t)
A(IO B +l1 B )
(cm mole-I)
v2
455
475
14.99 x 104
v3
956
995
23.13 Xl OS
249
260
7.823 X 104
v4
BRUNS AND P.
ap/aQi values
M. KUZNESOF
TABLE All.
l1BCI 3•
The L -I matrix elements of IOBC1 3 and
ap/aQ
(cm3 / 2sec-1
± 14. 61
± 128.5
(L -1)11 = 2.731 X 10-12 a
(L -1)21 = - 4.953 X10.-12 a
(L -1)12 = 0.371 x 10-20 b
(L -1)22 = 5.601 X 10-20 b
(L"1)11=2.853X10-12a
(L- I )12 =0.378X10- 20b
(L- I )21 =-4. 951 X 10-12a
(L -1)22 =5. 687x10-20b
± 7.471
respect to the normal coordinates. First, the degeneracy factor gi had apparently been overlooked
in the equation
aUnits are gl /2.
bUnits are gl/2 em rad-I .
changes in the frequencies of BC13 upon changing
boron isotopes. The newly derived experimental
derivatives are presented in the tables in the main
portion of the text.
Ai =(Nrr/3C 2 ) g i (ap/aQ i )2.
For the E' species gj =2, and we obtain the values
of ap/aQj listed in Table AI which may be compared with Table 4 of Ref. 4.
Second, the L -I equations given by Mandirola for
the llBC13 isotopic molecule are not consistent
with her G matrix in that L L' is not equal to G.
We have redetermined the L- l matrix for both IOBC1 3
and nBC13 • These matrix elements are listed in
Table All. Our matrix elements for IOBC13 are in
agreement with those of Ref. 4 and are consistent
with L L' = G. Corresponding L- 1 matrix elements
for IOBC1 3 and " BC13 in Table All differ by 4% or
less relative to the values for IOBC1 3 • These percentage differences are comparable to those between the frequencies of these two isotopes (4%5%). Corresponding L-lmatrix elements given
in Ref. 4 differ by as much as 14%. These differences appear too large considering the small
IR. E. Bruns and R. K. Nair, J. Chern. Phys. 58, 1849 (1973).
'R E. Bruns, J. Chern. Phys. 58, 1855 (1973).
3D. C. McKean, J. Chern. Phys. 24, 1002 (1956).
40. Brieux de Mandirola, Spectrochim. Acta A 23,767 (1967).
5J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital
Theory (McGraw-HilI, New York, 1970).
6(a) D. C. McKean, R E. Bruns, W. B. Person, and G. A. Segal,
J. Chern. Phys. 55,2890 (1971); (b) G. A. Segal and M. L.
Klein, 1. Chern. Phys. 47, 4236 (1967); (c) L W. Levin and T P.
Lewis, J. Chern. Phys. 52, 1608 (1970); (d) R E. Bruns and W.
B. Person, J. Chern. Phys. 55, 5401 (1971).
7The program QCPE 141, CNINDO, by P. A. Dobosh has been
used for these calculations. This program was modified and
overlayed to meet a maximum storage requirement of 128 kbytes
for an IBM 360-44 computer.
3D. P. Santry, J. Am. Chern. Soc. 90, 3309 (1968).
9R. E. Bruns and W. B. Person, J. Chern. Phys. 58,2585 (1973).
IOD. P. Santry and G. A. Segal, J. Chern. Phys. 47, 158 (1967).
"D. F. Shriver and B. Swanson, Inorg. Chern. 10, 1354 (1971).
12J. Hinze and H. H. Jaffe, J. Am. Chern. Soc. 84, 540 (1962).
IJR E. Bruns (unpublished results).
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