Experimental and Theoretical Study of the Spin-Spin Coupling Tensors in Methylsilane

Article abstract of DOI:10.1021/jp9920491

The experimental and theoretical ¹³C-²⁹Si spin-spin coupling tensors, ¹J_CSi, are reported for methylsilane, ¹³CH₃²⁹SiH₃. The experiments are performed by applying the liquid crystal NMR (LC NMR) method. The data obtained by dissolving CH₃SiH₃ in nematic phases of two LC's is analyzed by taking into account harmonic and anharmonic vibrations, internal rotation, and solvent-induced anisotropic deformation of the molecule. The necessary parameters describing the relaxation of the molecular geometry during the internal rotation, as well as the harmonic force field, are produced theoretically with semiempirical (AM1 and PM3) and ab initio (MP2) calculations. A quantum mechanical approach has been taken to treat the effects arising from internal rotation. All the J tensors are determined theoretically by ab initio MCSCF linear response calculations. The theoretical and experimental J coupling anisotropies, Δ¹J_CSi = -59.3 Hz and -89 ± 10 Hz, respectively, are in fair mutual agreement. These results indicate that the indirect contribution has to be taken into account when experimental ¹D_CSi^exp couplings are to be applied to the determination of molecular geometry and orientation. The theoretically determined J tensors are found to be qualitatively similar to what was found in our previous calculations for ethane, which suggests that the indirect contributions can be partially corrected for by transferring the corresponding J tensors from a model molecule to another.

Full text of DOI:10.1021/jp9920491

J. Phys. Chem. A 1999, 103, 9669-9677
9669
Experimental and Theoretical Study of the Spin-Spin Coupling Tensors in Methylsilane
†
‡
Jaakko Kaski, Perttu Lantto, Tapio T. Rantala, Jyrki Schroderus, Juha Vaara, and
Jukka Jokisaari*
Department of Physical Sciences, UniVersity of Oulu, P.O. Box 3000, FIN-90401 Oulu, Finland
ReceiVed: June 21, 1999; In Final Form: September 13, 1999
1
3
29
1
The experimental and theoretical C- Si spin-spin coupling tensors, JCSi, are reported for methylsilane,
13
29
CH
3
SiH
3
. The experiments are performed by applying the liquid crystal NMR (LC NMR) method. The
SiH in nematic phases of two LC’s is analyzed by taking into account
data obtained by dissolving CH
3
3
harmonic and anharmonic vibrations, internal rotation, and solvent-induced anisotropic deformation of the
molecule. The necessary parameters describing the relaxation of the molecular geometry during the internal
rotation, as well as the harmonic force field, are produced theoretically with semiempirical (AM1 and PM3)
and ab initio (MP2) calculations. A quantum mechanical approach has been taken to treat the effects arising
from internal rotation. All the J tensors are determined theoretically by ab initio MCSCF linear response
1
calculations. The theoretical and experimental J coupling anisotropies, ∆ JCSi ) -59.3 Hz and -89 ( 10
Hz, respectively, are in fair mutual agreement. These results indicate that the indirect contribution has to be
1
exp
taken into account when experimental DCSi couplings are to be applied to the determination of molecular
geometry and orientation. The theoretically determined J tensors are found to be qualitatively similar to what
was found in our previous calculations for ethane, which suggests that the indirect contributions can be partially
corrected for by transferring the corresponding J tensors from a model molecule to another.
Introduction
dependent indirect contribution, Janiso. In the case of experi-
mental HH and CH couplings, the indirect contributions to the
The spin-spin coupling tensor, Jij, between the nuclei i and
j of a molecule is a second-order tensor property formed by the
response of the electron system to perturbing nuclear magnetic
moments. The isotropic spin-spin coupling constant, Jij, is the
average of the diagonal terms of Jij, i.e., one-third of the trace
of the tensor. It is usually easy to determine experimentally using
nuclear magnetic resonance (NMR) spectroscopy, as it appears
in the ordinary isotropic liquid (or gas) phase.
corresponding experimental Dij couplings are less than 1%.1
exp
There may be exceptions to this, if the direct part of the
4
experimental coupling vanishes. However, a large relative
1
aniso
exp
contribution, /2Jij /Dij , due to vanishing or small denomi-
nator does not lead to serious errors, if the analysis of the
5
molecular properties is overdetermined. Based on experience
gained in studies of several model systems, if the maximum
acceptable errors are 0.5% in the internuclear distances and 0.5°
in bond angles, the indirect contributions can safely be ignored
Establishing the anisotropy of the J tensor, ∆J ) Jzz -
1/
2(Jxx + Jyy), with respect to a suitably chosen z-axis, is a
1
,5-7
in the experimental HH, CH, CC, and HF couplings.
The
demanding task that is experimentally possible by applying
1
2
4,5
situation is similar for JCF and JFF, whereas in the cases of
JCF, JCF, JCF, and JFF, the indirect contribution to the
corresponding D coupling may be significant. This depends
on the molecular orientation, because the direct and indirect
coupling tensors do not possess the same principal axis system
in general.
1,2
either the liquid crystal (LC) NMR or solid-state NMR
2
3
4
5
3
method. The former is the most applicable in the case of
exp
relatively small spin-spin coupling anisotropies, as the informa-
tion is easily masked by broad lines in the latter. In either NMR
method, the experimentally observable anisotropic coupling,
exp
D
, contains contributions from the direct dipolar coupling,
Recently, the utility of residual dipolar couplings in the
derivation of structural information on weakly aligned bio-
macromolecules has been recognized and the field is gaining
D, which contains information on the internuclear distances and
the orientation of the internuclear vector with respect to the
magnetic field, and the indirect spin-spin coupling. Thus, the
experimental determination of molecular geometry parameters
and orientation from the experimental NMR data requires that
the number of free parameters is equal to or smaller than the
number of couplings for which the indirect contribution is small
or known. This information can be used to calculate the direct
part of the remaining couplings. The difference between the
experimental and calculated coupling gives the orientation-
8
growing interest. The reliable use of the NMR data, however,
necessitates consideration of various contributions, such as
9
molecular vibrations, correlation of vibrational and reorienta-
tional motions (the so-called orientation-dependent deformation
1
0
effects), and spin-spin coupling tensor, in the experimental
exp
dipolar couplings, D , as seen below. Applications of the LC
NMR method to large molecules are often limited by the
availability of at least the harmonic force field (FF), which is
necessary for performing both the vibrational and deformational
corrections. This paper deals with the spin-spin coupling tensors
in methylsilane, but we also investigate the significance of the
quality of the harmonic FF by applying the results of both
semiempirical and ab initio electronic structure methods. They
*
Author for correspondence. Fax: +358-8-553 1287. Tel: +358-8-
5
53 1308. E-mail: Jukka.Jokisaari@oulu.fi.
†
Present address: Oulu Polytechnic, Raahe Institute of Computer
Engineering, P.O. Box 82, FIN-92101 Raahe, Finland.
‡
Present address: Max-Planck-Institut f u¨ r Festk o¨ rperforschung, Heisen-
bergstrasse 1, D-70569 Stuttgart, Germany.
1
0.1021/jp9920491 CCC: $18.00 © 1999 American Chemical Society
Published on Web 11/12/1999

9670 J. Phys. Chem. A, Vol. 103, No. 48, 1999
Kaski et al.
are compared with the results obtained by using a scaled
Hartree-Fock level FF taken from ref 11. This test gives useful
information on the applicability of the semiempirical methods,
which are fast and, thus, usable also for quite large molecules.
thy comparison data in the case of the anisotropic properties of
the J tensor.
In the present study we investigate the methylsilane molecule
using LC NMR experiments and ab initio MCSCF linear
response calculations. Experimentally, we have fitted the
The spin-spin coupling anisotropies of methylsilane are
fundamentally interesting as they serve as an opportunity to
expand the general view on J tensors by examining their change
when carbon is substituted with silicon, which belongs to the
same column in the periodic table of elements. Molecules
containing similar structural units have related isotropic spin-
spin coupling constants, but an important question is whether
the anisotropic properties of J have similarities as well. In the
present study, we obtain some information for answering to this.
However, reliable sets of J tensors are available for quite few
molecules. The experimental and theoretical results are in good
mutual agreement for some model systems (HCN, HNC, CH3-
1
molecular geometry and ∆ JCSi to the LC NMR data. The
contributions arising from the molecular rovibrational motion
exp
to the D couplings are taken into account in the analysis.
The harmonic force field, used in the derivation of the motional
contributions, is produced using different methods in order to
obtain insight to the applicability of the semiempirical methods
for this purpose. Experimental information on J tensors is
compared with the ab initio MCSCF results, and the transfer-
ability of the tensors to other molecules is discussed.
The analysis of the experimental data of methylsilane is
relatively complicated due to the internal rotation of the
3
cis
3
trans
CN, and CH3NC,1 C6H6, C2H6, C2H4, and C2H2, CH3F,
2
6
7
molecule, which averages the DHH and DHH
couplings
5
4
between the methyl and silyl groups. In our previous investiga-
CH2F2, and CHF3, and 1,4-C6H4F2 ) containing light atoms.
This implies that the theoretical J tensors are reliable at least
for small molecules consisting of fluorine and other first-row
7
tion of the related ethane molecule, all relevant effects due to
the internal rotation were taken into account. In that case, the
analysis of the LC NMR data was relatively laborious as it
involved a description of the various contributions to the direct
couplings in terms of Fourier expansion as a function of the
rotation angle, necessitating a systematic scan of the coupling
parameters. In the present case, we have developed the data
analysis method to be more automatic.
main group atoms. Thus, the theoretical J tensors of, e.g.
formamide,13 for which experimental data are not available, are
most likely reliable. These theoretical calculations encompass
also couplings to oxygen. In systems containing heavier nuclei,
from the third row of the periodic table on, relativistic effects
1
4-16
on spin-spin coupling tensors become more important.
Although the performance of ab initio methods is not yet at a
satisfactory level, the DFT method has proved to be capable of
producing J tensors with reasonable degree of accuracy for this
kind of systems.17
Theory
NMR Observables. The NMR spin Hamiltonian in frequency
units as appropriate for spin- /2 nuclei in molecules partially
oriented in uniaxial LC solvents can be written, in the high field
approximation, as
1
In the theoretical calculations, the spin-spin coupling tensor
is obtained from the terms of the perturbation Hamiltonian that
are bilinear in the nuclear spins Ii and Ij, or (in the second order)
linear in one of these. Consequently, there are five different
contributions at the nonrelativistic level that, in the language
of the response theory,18 can be expressed as linear response
functions. Exception to this is the diamagnetic spin-orbit tensor
Hˆ ) -B /(2π) γ (1 - σ ) ˆI + J Iˆ ‚ Iˆ +
0
∑i
i
i
iz′
∑
i<j
1
ij i
j
aniso
ij
(D + / J )(3 ˆI ˆI - Iˆ ‚ Iˆ ) (1)
∑
ij
2
iz′ jz′
i
j
i<j
(DSO) that is a ground-state expectation value and hence easy
where B0 is the magnetic field of the spectrometer (in the z′
direction), γi, Iˆ i, and σi are the gyromagnetic ratio, dimensionless
spin operator, and nuclear shielding (sum of the isotropic and
anisotropic contributions), of nucleus i, respectively. The direct
dipolar coupling Dij is defined as
to calculate. The paramagnetic spin-orbit mechanism (PSO)
couples the ground state with singlet excited states, necessitating
solution of three linear response equations for each nucleus.
The main computational challenge is the many triplet linear
response calculations needed for accounting for the spin-dipolar
(
SD), the fully isotropic Fermi contact (FC), and the fully
µ pγ γ s
0
i
j
ij
anisotropic spin-dipolar/Fermi contact cross (SD/FC) mecha-
nisms. Particularly, the SD contribution is laborious to calculate,
as one is obliged to solve nine (six if the symmetry is
considered) linear response equations for each nucleus. The
triplet response functions require the use of a reference state
that is stable against triplet excitations. These can be obtained
using correlated MCSCF or coupled cluster (CC) methods.
When using the MCSCF linear response method, large restricted
active space (RAS) wave functions are usually required in order
to take electron correlation effects sufficiently into account. In
addition to this, the spin-spin coupling necessitates sufficient
flexibility from the basis set in core regions as the recently
reported systematic investigation also ascertained. The high
requirements for the quality of the description of the electronic
structure make these calculations especially demanding among
molecular properties. As a result, reliable J tensors and
sufficiently precise self-supporting data have been obtainable
only during recent years. Currently, the quality of the theoretical
results makes them good starting values for the analysis of the
experimental data. Similarly, calculations can provide trustwor-
D ) -
(2)
ij
2
3
〈
〉
8
π
rij
where the time averaging is indicated by the angular brackets
and µ0 and p have their usual meanings. The orientational order
parameter, Sij, of the internuclear rij vector is closely related to
1
2
the eq 2 by Sij ) 〈sij〉 ) /2〈3 cos θij,B - 1〉, where θij,B is the
0
0
angle between the rij vector and the direction of the external
3
magnetic field B0. One should note that 〈sij/rij 〉 is not equal to
Sij/〈rij 〉 due to the orientation-dependent deformation of the
* rij). Thus, the experimental
couplings of a molecule in a LC solvent can be expressed as a
sum of several contributions:
3
-
3 -1/3
solute (similarly, 〈rij
〉
19
exp
1
aniso
Dij ) D + / J
2 ij
)
ij
eq
ah
h
d
1
aniso
Dij + Dij + Dij + Dij + / J
(3)
2
ij
where Dijeq is the coupling corresponding to the equilibrium
ah
structure of the molecule, Dij arises from the anharmonicity
2
0
h
of the vibrational potential, Dij is the contribution from the

Spin-Spin Coupling Tensors in Methylsilane
J. Phys. Chem. A, Vol. 103, No. 48, 1999 9671
The function p(φ) that describes the probability of finding
the torsional oscillator at a given torsional angle was calculated
by using the torsional wave functions obtained using the
vibrational-torsional Hamiltonian
di
1
2
Hˆ vtr
)
ω V +
+ F pˆ + V (1 - cos 3φ) (7)
∑i
i
(
i
)
3
2
2
where ωi is the vibrational frequency, Vi is the vibrational
quantum number, and di is the degeneracy of the vibrational
mode i. The last two terms belong to the pure torsional
Hamiltonian, where F is the reduced rotational constant and V3
is the first term in the Fourier expansion of the torsional barrier
height. Operator pˆ is the torsional angular momentum and 1/2V3-
(1 - cos 3φ) is the torsional potential term. The last two terms
in operator (7) were used to set up the torsional matrix in the
free rotor basis. As a result, the following eigenfunctions are
obtained:
Figure 1. Methylsilane and the principal axis systems of its spin-
spin coupling tensors. The x axis is in the HCSiH plane, where the
protons are the ones for which the PAS of the JCH and JHH(a) tensors
1
3
10
V6
3k+τ
are shown (in the respective order).
Ψ(V ,τ,φ) )
A
exp[iφ(3k + τ)]
(8)
6
∑
k)-10
9
d
harmonic vibrations, and Dij is the deformational contribu-
tion.10 The anisotropic contribution due to the J tensor is given
In eq 8, V6 is the torsional principal quantum number, τ is a
label for the torsional sublevels, and k is the free rotor quantum
number. The probability density of the torsional oscillator can
by
aniso
D
2
J
) (2/3)P (cos θ) S J
(4)
be calculated as |Ψ| .
2
∑
Râ Râ
Râ
In order to obtain a probability distribution to describe the
statistical ensemble of torsional oscillators, the energy manifold
given by the eigenvalues of the operator (7) was used. The
energy level structure consists of various combinations of all
the fundamental vibrations including the stack of torsional levels
D
Râ
where S are the elements of the Saupe orientation tensor
with respect to the LC director n, expressed in a molecule-
fixed frame (x, y, z). P2 is the second-order Legendre polyno-
mial, δRâ is the Kronecker delta, and θ the angle between B0
and n. In the present case of C3V molecular point group
symmetry, eq 4 is expressed as
-1
and sublevels. The energies beyond 3000 cm do not give any
statistically significant contribution to the population, and they
were neglected from the total probability density. The torsional
parameters F and V3 were assumed to be independent of the
vibrational states.
aniso
D
zz
J
) (2/3)P (cos θ)S ∆J
(5)
2
The normalized probability distribution function is
The orientation tensor is calculated from the traceless solvent-
solute interaction tensors, A,1 assigned to the chemical bonds
of a molecule. In the present case, the fitted interaction tensors
are ACH, ASiH, and ACSi, which were assumed to be cylindrically
symmetric in the corresponding bond directions. The use of
interaction tensors has been documented in detail in ref 10c.
0c
2
d exp{-E(V,V ,τ)/k T}|Ψ(V ,τ,φ)|
∑
V
6
B
6
V,V ,τ
6
p(φ) )
(9)
d exp{-E(V,V ,τ)/k T}
∑
V
6
B
V,V6,τ
2
1
Internal Rotation. We used the program MASTER to
eq
h
d
calculate the molecular orientation and D , D , and D couplings
see eq 3) from the molecular geometry, harmonic force field,
where kB is the Boltzmann constant and T is the temperature. E
is the eigenvalue of operator (7) and V represents the combina-
tion (V1, V2, ..., V5, V7, ..., V12) of the vibrational quantum
numbers, i.e., the total vibrational quantum number. The quantity
dV is the degeneracy of the corresponding state, and the
denominator is the partition function at temperature T. The
experimental values for the vibrational frequencies were taken
(
and the interaction tensors. Anharmonic vibrations are taken
into account by using the AVIBR program20 for other than the
torsional degree of freedom that causes the averaging of the
3
exp
DHH . The effect arising from the torsional motion is
calculated numerically with the equation
-
1
from ref 22 and the torsional parameters F ) 8.207 14 cm
π/3
-1
12
28
and V3 ) 603 cm for CH3 SiH3 were taken from ref 23.
〈
D〉 )
∫
D(φ)p(φ) dφ
(6)
0
Experiments and Computational Details
where D(φ) is the direct coupling (including all contributions)
as a function of the internal rotation angle and p(φ) is the
corresponding normalized probability distribution function at a
given temperature. The changes of the geometrical parameters
as function of the internal rotation are taken into account on
the basis of semiempirical and ab initio electronic structure
calculations that are used to produce also the harmonic force
field as a function of φ. In Figure 1, the molecule and the
molecule-fixed coordinate frame used are shown. In the figure,
the molecule is in the equilibrium geometry, where φ ) 0.
13
29
Experiment. Methylsilane ( C and Si in natural abundance)
was prepared by reacting methylsilyl trichloride with LiAlH4.24
The LC solvents Merck ZLI 1167 and ZLI 2806 were placed
into NMR sample tubes (Wilmad) of 10 mm outer diameter
and 1.5 mm wall thickness, and degassed before methylsilane
was condensed into them. Then the tubes were sealed with
flame. The gas pressures were approximately 12 atm at room
temperature. The NMR spectra were recorded on a Bruker
Avance DSX 300 spectrometer. For the determination of the

9
672 J. Phys. Chem. A, Vol. 103, No. 48, 1999
Kaski et al.
TABLE 1: Basis Sets Used in the Ab Initio Calculationsa
isotropic spin-spin coupling constants for each sample, H, 13C,
1
2
9
13
1
Si, and C-{ H} spectra were measured at temperatures
basis
HII
element
Gaussians
slightly above the nematic-isotropic phase transition. The
sufficient signal-to-noise ratio was reached after 64, 2000, 800,
and 4000 scans, respectively. The isotropic C- Si spin-spin
coupling constant was extracted from the 13C-{ H} spectrum
by applying total-line-shape (T) mode in the iterative PERCH
H
C
Si
H
C
[5s1p/3s1p]
[9s5p1d/5s4p1d]
[11s7p2d/7s6p2d]
[6s2p/4s2p]
[10s7p2d/7s6p2d]
[12s8p3d/8s7p3d]
13
29
1
HIII
25
Si
program. The other Jij couplings were analyzed by incorporat-
1
13
29
a
ing the H, C, and Si spectra of a sample to the same analysis
and by using the T mode. The values were fixed to those
obtained at temperatures where the samples are in the isotropic
phase. For determination of the complete set of Dij couplings,
Spherical Gaussians are used throughout. Only the innermost
primitives of a given type are contracted.
allowed from the occupied (in the SCF picture) valence
molecular orbitals (MOs) belonging to the RAS2 subspace to
the virtual MOs in RAS3. We kept six core MOs consisting of
the 1s AO of the carbon atom and 1s, 2s, and 2p AOs of the
silicon atom inactive. The active spaces in the RAS-I and RAS-
II wave functions consist of orbitals containing 71.7% and
only the 1 C-{ H} spectrum with Si satellites and the H
3
1
29
1
1
3
29
spectrum with C and Si satellites were needed. The proton
irradiation of the 13C-{1H} experiment tends to heat the sample,
which forced us to use short accumulation (irradiation) time of
0.38 s and long relaxation delay of 2.0 s with gated decoupling.
9
4.4% of all virtual MP2 particles and the number of the Slater
The power used in the proton irradiation was set to as low as
determinants was 7956 and 40 669, respectively. All the
nonrelativistic terms were determined at each level of calcula-
tion.
Basis set convergence was studied with the larger active space
by using two basis sets, HII and HIII, originally adopted from
possible. The temperature-dependent orientation of the solute
molecules during the 13C-{1H} accumulation was checked and
1
found unchanged by measuring the H spectrum with one scan
1
2
28
(enough for the CH3 SiH3 isotopomer) immediately after the
13
1
end of the irradiation experiment. The C-{ H} spectrum was
analyzed with the T mode, whereas the H spectrum, consisting
of spectra of three isotopomers, was analyzed with peak-top-fit
3
4
35
1
Huzinaga and modified by Kutzelnigg and co-workers. As
noticed earlier, the latter set provides well-converged spin-
spin couplings with a fairly small number of basis functions.1
The basis sets are listed in Table 1. The experimental r0
9,36
13
28
mode, assuming the same orientations for CH3 SiH3 and
1
2
29
CH3 SiH3 isotopomers.
3
7
geometry was used in the calculations.
Molecular Vibrational Potential. To assess the effects
arising from molecular vibration to the observed NMR param-
eters, the harmonic force field of the molecule was calculated
Results
26
using the Gaussian software at the semiempirical level with
Experimental Spin-Spin Coupling Tensors. Some of the
isotropic spin-spin coupling constants and their signs of
methylsilane are reported in the literature. For example, JSiH
2
7
28
two parametrizations AM1 and PM3, and at the ab initio
(
2
9
1
MP2) level. The force fields from different methods serve in
3
8
finding trends (and hopefully convergence) as the level of
sophistication of the method of calculation is improved.
Three different conformations were considered. The calcula-
tions of the harmonic force fields and relaxed molecular
geometries were performed at the internal rotation angles of
is negative and values of (-)194.3 and (-)193.0 Hz are
1
reported in ref 39. JCSi is most likely negative because the
similar coupling in the TMS molecule is about -50 Hz.3 JSiH
9 2
38
is known to be positive and in the range from 3 to 10 Hz.
1
This information, combined with the fact that JCH is positive,
enables us to determine each observable J coupling of meth-
ylsilane with their signs from the NMR spectra taken from
isotropic and anisotropic phases. The experimental Jij couplings
in LC’s ZLI 1167 and ZLI 2806 are given in Table 2 and the
sets of the experimental Dij couplings are given in Table 3.
In the analysis of the data by applying eq 6, the relaxation of
a geometrical parameter was scaled with the same ratio as the
theoretical parameter by using
0°, 30°, and 60°. Due to the C3V symmetry, this range determines
the full 360° rotation. The force constants representing the
torsional vibration were ignored in MASTER, but they were
taken into account when applying eq 6.
In the semiempirical calculations, only the outermost s and
p electrons of each atom are treated explicitly, amounting to
total of 14 valence electrons in the molecular orbitals of CH3-
SiH3. At the MP2 level, all-electron calculations were carried
out and the basis set was enlarged until sufficient convergence
was found at the 6-311+G(d,p) level.
P(φ) ) (P /P )[a + a cos(nφ) + a cos(2nφ)] (10)
iter theor
0
1
2
Ab initio Calculations of J Tensors. The spin-spin coupling
tensors were calculated with the MCSCF linear response
Here n ) 3 due to the symmetry and P(φ) is a geometrical
parameter (bond length or angle) as function of the internal
rotation φ. (One should point out that D(φ) in eq 6 is a function
30
31
method implemented in the Dalton software. For details, we
refer to the original paper and a recent review.32
exp
of P’s.) Piter is obtained from the fit to D couplings, while
Two restricted active space (RAS) MCSCF wave functions
were chosen on the basis of natural orbital occupation num-
bers obtained from MP2 analysis. Using the nomenclature
Ptheor, corresponding to the torsional angle φ ) 0, is given by
semiempirical or ab initio calculations. The coefficients a0, a1,
and a2 are fitted a priori to describe the theoretical molecular
geometry at 0°, 30°, and 60° of internal rotation angle and these
values are used to calculate the theoretical geometrical param-
eters at any φ. The a’s are given in Table 4.
inactive
RAS2
RAS3
RAS
adopted from ref 33, the smaller RAS-I wave
function is 51RAS1 and the larger RAS-II wave function is
52
0;5
5
1
52
RAS21;13. The numbers in each category express the orbitals
belonging to A′ and A′′ irreps of the Abelian Cs point group
and in the SCF wave function these symmetries contain 10 and
The harmonic force field was given by the theoretical
calculations in Cartesian coordinates, but the force constants
change significantly as functions of the torsional angle and the
systematics of the functions is complicated. Therefore, the
interpolation of the FF to a given φ would have been difficult.
The easiest way to avoid this problem was to use the FF in the
3
occupied orbitals. Both RAS wave functions were of the
single-reference type, as static correlation is expected to be
relatively unimportant in this kind of singly bonded system (at
the equilibrium geometry). Single and double excitations were

Spin-Spin Coupling Tensors in Methylsilane
J. Phys. Chem. A, Vol. 103, No. 48, 1999 9673
TABLE 2: Experimental and Theoretical Isotropic Jij Coupling Constants of Methyl Silane in LC Solventsa
solvent
1JCSi
1JCH
1JSiH
2JCH
2JSiH
3JHH(av)
ZLI 1167
ZLI 2806
ab initio
-51.59(3)
-51.55(2)
-60.50
122.514(12)
122.42(2)
115.74
-194.449(11)
-194.670(5)
-182.88
4.552(11)
4.63(3)
3.40
7.962(12)
7.989(12)
9.68
4.62(2)
4.629(2)
b
3.80
a
Values in Hz. The experimental values are measured at 350 K, where the liquid crystal is in the isotropic state, and the theoretical ab initio
results are taken from the present RAS-II/HIII calculation. b (av) subscript means average coupling over two gauche- and one trans-position.
TABLE 3: Experimental Dij Couplings (in Hz) of Methylsilane in Thermotropic Liquid Crystals ZLI 2806 and ZLI 1167
solvent T/K
ZLI 2806 315
ZLI 2806 305
ZLI 2806 298
ZLI 1167 310
ZLI 1167 300
1
D
D
D
D
D
D
D
D
CH
SiH
CSi
-98.10(4)
32.93(3)
-13.55(4)
-157.588(11)
-63.266(11)
13.18(5)
-117.89(3)
39.68(2)
-16.40(2)
-189.487(7)
-76.147(7)
15.85(3)
-127.13(5)
42.94(3)
-17.66(2)
-204.51(2)
-82.22(2)
17.27(5)
-115.18(3)
37.93(3)
-15.86(8)
-184.141(8)
-74.206(10)
15.43(3)
-124.22(2)
40.83(2)
-17.12(4)
-197.809(7)
-79.725(6)
16.47(2)
1
1
2
2
2
2
3
a
HH
HH
CH
b
SiH
HH
-17.45(3)
37.154(9)
-20.99(2)
44.631(6)
-22.80(4)
48.136(11)
-20.50(3)
43.435(7)
-22.02(2)
46.621(5)
a
2
group. b The DHH coupling within the SiH
2
The DHH coupling within the CH
3
3
group.
TABLE 4: Fitted Coefficients of Eq 10 Determining the
Geometry Parameters as Functions of Internal Rotation
the present case. rR(T) is defined by the thermal average
positions of the atoms at the temperature T. At T ) 0 K, the
system is in the vibrational ground state and the average
Pa
a
a
b
a
2
c
0
1
4
1
d
geometry, rR(0 K), is equal to the rz geometry. The latter is
also an internally consistent geometry that is determinable
especially with microwave and infrared spectroscopic methods.
In LC NMR, rR is the geometry corresponding to the dipolar
couplings after corrections for harmonic vibrations and solvent-
induced deformations. Usually it is very close to rz, because at
room temperature the occupancy of vibrational states other than
the ground state is typically small.
r
r
r
∠
CH
1.1149
0.0057
0.0105
0.0315
-0.123
-0.215
-0.494
-0.0073
0.0010
-0.0002
-3.43
-0.0167
-0.225
-0.0100
-0.200
-0.550
-0.178
-0.0167
0
-0.0175
18.2
-1.08
-17.3
12.8
1
1
.0945
.0931
CSi
SiH
1.8079
1
1
.8656
.8819
1.4630
1
1
.4932
.4780
HCSi
111.771
In the present case, the changes, δDah ) D (T) - D (300
ah
ah
1
1
11.676
11.149
-3.10
K), in the anharmonic corrections to dipolar couplings are small
-10.2
(as seen in Table 5, where an example case of this and other
∠
CSiH
110.922
-10.1
corrections to the experimental anisotropic couplings is given),
1
1
10.753
10.572
-10.3
-8.89
-23.3
ah
-16.1
so that possible error in δD as large as 20% is meaningless in
the present case. In fact, this is the expected result, because at
the small range of the present temperatures, the average
geometries are close to each other.
a
The geometrical parameters in eq 10 corresponding to the equi-
librium geometry are defined as Ptheor ) a + a + a . Piter’s are given
later in Table 6 (including also the fixed bond lengths, which are given
0
1
2
b
c
in footnote b of the table). Multiplied by 100. Multiplied by 10 000.
The top values are for AM1, in the middle for PM3, and the lowest
for ab initio/MP2 calculation.
The final optimization of the anisotropies (∆Aij) of the
d
10
interaction tensors acting on the CH, CSi, and SiH bonds, as
well as that of the molecular geometry, was performed using
the MASTER program as a Fortran-extension in the Matlab
internal (curvilinear) coordinate basis, where the interpolation
was easy. In the internal coordinate basis, the force constants
as a function of φ are given by
4
2
3
software. The average DHH coupling was calculated as the
3
mean of three DHH couplings at a given angle of internal
rotation. The indirect contributions, except for CSi coupling,
were very small as examplified in Table 5.
h(φ) ) h + h cos(nφ) + h cos(2nφ)
(11)
0
1
2
In the iteration procedure, we had to fix the rCSi bond length
for scaling the size of the system, as well as rCH, because there
was not enough information in the NMR data to obtain this
parameter. The fixed values 1.864 and 1.095 Å, respectively,
taken from ref 37 were obtained by “rigid rotor analysis” using
rotational constants of the vibrational ground state, which means
that the resulting geometry is of the r0 type. Unfortunately, this
geometry may differ slightly from rR. Therefore, we give the
where h(φ) is a harmonic force constant. h0, h1, and h2 were
fitted to conform to the theoretical force constants at the
calculated torsional angles. The period-dependent n has the value
1
for each parameter that corresponds to correlation between
given CH and SiH vibrations. Otherwise n ) 3 due to symmetry.
In the case of FF taken from ref 11, we used our ab initio (MP2)
results for relaxation of the geometry and for changes in FF
1
(scaled with the adopted constants) during the internal rotation.
relation between ∆ JCSi and rCH in Table 6 (changes in rCSi cause
The anharmonic contributions were calculated with the
only new scaling of each parameter). The resulting rR geometries
are also given in the table and they are very close to each other
when determined using different methods. However, the iterated
geometrical parameters depend on the fixed values and, thus,
their accuracy should not be overemphasized.
20
AVIBR program on the basis of diagonal cubic anharmonic
stretching force constants that were estimated from the harmonic
-
1 40
force field with frrr ) -3afrr, where a ) 2 Å . This method
is able to only partially correct for anharmonic effects and, thus,
we do not give the experimental re geometry. We choose instead
to make very small corrections in order to transform the
corresponding rR(T ) 298, 305, 310, and 315 K) to the rR(300
K) geometry, where T ) 300 K is the reference temperature in
The results for the iterated geometry parameters and the
anisotropy of JCSi tensor are given in Table 6. The average
1
∆ JCSi changes by -10.7% between the semiempirical AM1
and PM3 methods. From PM3 to ab initio MP2 basis the change

9674 J. Phys. Chem. A, Vol. 103, No. 48, 1999
Kaski et al.
TABLE 5: Example of Contributions to the Experimental Couplingsa
coupling
Da
Dh
δDah
Dd
1/
2
Janiso
0.018
Dcalc
Dexp
diffb
1/
2
Janiso/DRc
3
D
D
D
D
D
D
D
D
HH
-85.909
389.415
148.303
-30.780
256.964
-74.194
41.554
-0.508
-12.809
-3.106
0.237
0.002
0.105
0.033
-0.002
-0.023
0.005
-0.395
-8.316
3.230
-0.351
-9.392
-5.496
-0.471
-0.030
e
-86.794
368.195
148.395
-30.889
230.322
-76.036
41.019
-86.869
368.282
148.411
-30.860
230.365
-75.859
40.994
-0.077
-0.019
-0.017
0.030
0.066
0.172
-0.02
-0.02
-0.02
-0.02
0.04
-0.09
0.09
2
2
2
1
1
2
1
HH(C)
HH(Si)
CH
-0.095
-0.033
0.005
0.101
0.069
0.038
-1.077
e
CH
-17.351
SiH
3.584
SiH
-0.102
0.114
-0.001
-0.004
-0.025
-0.123
CSi
32.847
32.931
31.728
-3.28
d
e
S
CSi ) 0.036087; ∆ACH ) 1.91; ∆ASiH ) -5.77; ∆ACSi ) 3.86
a
R
h
Values in Hz for methylsilane, dissolved in liquid crystal ZLI 1167 at 310 K. D is the dipolar coupling in the r
R
geometry at 300 K, D is due
ah
1
aniso
to harmonic vibrations, and δD is the difference of the anharmonic contributions at 300 and 310 K. The indirect part ( /
basis of ab initio results except for the CSi coupling it is based on the current experimental results.
are given in percent. The term defines the orientational parameter of the symmetry axis that is parallel with the CSi bond. The anisotropies of
the interaction tensors are given in 10 J.
2
J
) is calculated on the
. The relative indirect contributions
b
calc
exp c
D
- D
d
e
-
22
TABLE 6: Molecular r
r
Geometry at 300 K and the
given in Table 7. The correlation convergence of the spin-
spin coupling tensors can be investigated by comparing the
RAS-I and RAS-II wave function levels. A substantial improve-
ment in correlation treatment from RAS-I to RAS-II calculation
produces typically relative changes up to 4% in the properties
of J tensors. The coupling between two protons in silyl group,
Anisotropy of Carbon-Silicon Spin-Spin Coupling in
Methylsilane
force
field
r
SiH
/
HCSi/ CSiH/
deg deg
∆1JCSi
Hz
/
d∆1JCSi
drCHa
/
LC
Å
ZLI 1167b AM1 1.514 110.69 111.20 -108
c
-22
-22
-15
-12
-9
-12
-13
-9
-12
-11
c
PM3
MP2
MP2
1.514 110.71 111.21 -100
1.520 110.81 111.30 -102
2
JHH(Si), is particularly sensitive to the correlation treatment as
c
2
its sign changes. Although the relative changes also in ∆ JCH
d
1.516 110.85 111.21
1.514 110.83 111.15
-95
-89
-98
-86
-88
-88
-89
3
e
and JHH(a) are of the order of 10%, the absolute changes are
SCF
ZLI 2806b AM1 1.511 110.81 110.99
c
maximally 4 Hz in all the mentioned parameters. These results
indicate reasonably good correlation convergence of the pa-
rameters.
c
PM3
MP2
SCF
1.508 110.86 110.94
1.514 110.95 111.02
1.515 110.92 111.03
d
e
averagef
ab initio
a
The basis set convergence of the spin-spin coupling tensors
was examined at the RAS-II level. When using the HIII basis
set instead of the more modest HII, the properties of J tensors
change typically less than 10%. Although the tensor anisotropies
g
-59.32
The dependence of the fitted anisotropy on the fixed rCH bond length
b
is given in Hz/0.01 Å. Basis for the indicated, iterated molecular
2
geometry parameters: rCH ) 1.095 Å and rCSi ) 1.864 Å.37 ∆1JCSi is
and the JHH(Si) show larger relative changes than the other
constrained to be the same at different temperatures in a given LC.
coupling constants, the order of magnitude of the absolute
c
1
The corrections due to anharmonic vibrations and the indirect
changes is 1 Hz in all cases except in the quite large JCSi, which
d
contributions (except for CSi coupling) are ignored. All contributions
alters by 4 Hz. This is consistent with the previous application
e
are taken into account. The experimentally scaled harmonic force field
19
calculations and the recent systematic study and supports the
in the equilibrium geometry is taken from ref 11, and other information
from our MP2 calculations. Mean of the results in the LC solvents,
given by the force field denoted with e. RAS-II/HIII calculation using
0
r geometry, given in ref 37.
argument that HIII basis set provides reasonably good J tensors.
f
g
The FC mechanism gives the most significant contribution
to the coupling constants, although in smaller constants this is
due to the cancellation of DSO and PSO contributions. The SD
is -2.0% and the “best” result using the scaled ab initio force
1
1
1
contribution is generally very small, but in JCSi it is of the same
field (giving the best compatibility with the experimental
harmonic frequencies) changes by further -2.8%. The signifi-
cance of the other possible approximations (not included in the
order as DSO and PSO contributions. The typical dominance
of SD/FC contribution in anisotropies is valid in the cases of
1
1
1
∆ JCSi and ∆ JCH. However, in other anisotropies also the DSO
and PSO contributions are at least equally important, though
they partially cancel each other in several cases. There is a slight
presented results) to ∆ JCSi are as follows: (1) classical
calculation of the probability distribution as a function of the
internal rotation angle (instead of a quantum mechanical one),
7
difference in comparison with the case of ethane, where the
+
4.4%; (2) ignoring the relaxation of the geometry during
internal rotation, -1.1%. These values imply that in the present
dominance of the SD/FC contribution was more obvious.
case the internal rotation is described with the classical treatment
Compared with the experiment, the best (RAS-II/HIII)
7
2
to a reasonable accuracy and, contrary to ethane, the relaxation
calculation underestimates JCH about 5.5%. The two-bond
2
2
of the geometry as a function of φ gives only small contribution
couplings JCH and JSiH are considerably smaller than one-bond
couplings and therefore they actually differ less (1.7 Hz in
maximum) than one-bond coupling from the experimental
couplings. This is satisfactory, particularly as the two-bond
couplings are known to be difficult to calculate reliably. In the
exp
to the D couplings.
1
The theoretical result (discussed below), ∆ JCSi ) -59.3 Hz,
is 33% smaller than the best experimental value, -89 Hz. The
difference is slightly larger than in the experimentally very
1
exp
1
theor
3
accurate isotropic values ( JCSi ) -51.6 Hz and JCSi
)
average HH coupling between methyl and silyl groups, JHH(av),
-
60.5 Hz, see Table 2) where the difference is 17%. The reliable
error limit estimation for the experimental value of ∆ JCSi is
the underestimation is only about 1 Hz compared to experi-
mental coupling. As expected, the most difficult object to
1
1
very complicated, but if we use an estimated error of 0.01 Å
calculate is, however, the JCSi tensor, because the 17.3%
for the fixed rR,CH, we obtain the change of about 10 Hz in
overestimation in coupling constant implies that a better
description of either or both orbital and configuration spaces
would be necessary. In the present system it seems that the
improvement of both the basis set and the valence region
1
∆
JCSi. This is most probably the dominant source of error.
Ab Initio Spin-Spin Coupling Tensors. The calculated
spin-spin coupling constants and the tensor anisotropies are

Spin-Spin Coupling Tensors in Methylsilane
J. Phys. Chem. A, Vol. 103, No. 48, 1999 9675
TABLE 7: Results of the MCSCF Calculations for the Spin-Spin Coupling Tensors in Methylsilanea
propertyb
RAS-I/HIIc
RAS-II/HIId
RAS-II/HIIIe
DSO
PSO
SD
FC
SD/FC
1JCSi
∆
-66.95
-59.97
118.40
8.37
-186.50
5.77
-64.52
-60.23
116.89
8.12
-182.88
5.75
3.36
0.44
10.76
3.14
-16.57
-7.83
1.52
-2.70
0.62
1.44
9.43
1.56
3.56
1.48
-60.50
-59.32
115.74
7.10
-182.88
5.81
3.40
0.41
9.68
2.56
-15.24
-7.33
2.52
-1.96
0.66
1.04
10.06
1.61
3.80
1.23
-0.04
-3.17
0.56
-6.52
-0.12
6.41
-0.31
1.31
0.21
-3.53
-2.68
-7.77
-2.11
-4.41
-0.66
2.98
1.55
-0.99
1.53
4.08
0.58
-2.55
0.24
-0.66
0.03
1.33
2.94
5.18
1.77
3.20
0.56
-1.35
-2.14
-0.10
0.22
0.12
-0.14
0.01
-60.66
1JCSi
-53.02
9.31
1
J
CH
1JCH
113.75
-183.45
3.47
∆
1
J
SiH
∆
1JSiH
2.09
2
J
CH
3.36
0.40
∆
2JCH
0.01
-0.25
4.91
2
J
SiH
11.01
3.14
-17.29
-7.92
-0.29
-2.77
0.69
1.45
9.41
1.57
3.60
-0.16
-0.15
0.37
-0.41
0.06
-0.01
0.03
0.02
0.00
-0.04
9.60
∆
2JSiH
2
J
HH(C)
-15.87
2.80
∆
2JHH(C)
-4.33
-0.73
0.23
2
J
HH(Si)
∆
2JHH(Si)
3
J
HH(a)
0.74
∆
3JHH(a)
-2.19
2.32
-0.43
3
J
HH(b)
-2.53
0.74
10.27
∆
3JHH(b)
1.34
3
J
HH(av)
∆
3JHH(av)
1.49
a
Results in Hz. Calculations performed at the r
geometry: rCH ) 1.095 Å, rCSi ) 1.864 Å, ∠ HCSi ) 110.88°, and ∠ CSiH ) 110.41°.37 The
0
1
anisotropy is defined as ∆ J ) Jzz - / (Jxx + Jyy) with the CSi bond at the z direction. The contributions of the different physical mechanisms to
b
2
the calculated tensors are indicated for the RAS-II/HIII calculation. (a) and (b) subscripts denote coupling between hydrogens belonging to
methyl and silyl groups at gauche- and trans-position to each other, respectively. (av) subscript means average coupling over two gauche- and one
trans-position. Total energy -330.483 116 Ha. Total energy -330.557 097 Ha. e Total energy -330.593 950 Ha.
c
d
TABLE 8: Theoretical Principal Values and the Orientation
correlation description has an effect in the same direction and
therefore there is no possibility to utilize error cancellation. The
apparent relative similarity of the results from our two active
spaces (differing in the treatment of electron correlation in the
of the Principal Axis System of the J Tensors in Methyl
a
3 3
Silane (CH SiH )
couplingb
J
J
J
∆Jijc
33
22
11
1
1
1
2
2
2
2
3
3
d
J
J
J
J
J
J
J
J
J
CSi
-100.05
125.63
-195.16
3.84
-40.73
124.85
-176.97
3.58
11.41
-9.73
3.69
-40.73
96.73
-176.50
2.79
5.56
-9.50
0.15
-59.32
14.84
-18.42
0.65
valence region) and two basis sets seems to point to an earlier
e
suggestion43 that the neglect of core correlation (in the Si atom
CH
f
SiH
in the present system) may be largely responsible for the error.
In addition, comparison of ab initio and LC NMR results is
fully justified only when the former are performed at the rR
geometry, and not at the r0 geometry as done presently (nor at
the re geometry as often done). As previously noted, also the
g
CH
h
SiH
12.06
3.58
i
HH(C)
-26.49
-16.88
j
HH(Si)
3.72
1.80
k
l
HH(a)
1.45
11.26
0.60
9.80
-0.06
9.13
1.19
1.80
1
HH(b)
experimental determination of ∆ JCSi involves many approxima-
a
tions. However, it is justified to state that the calculated results
are at least satisfactory for all couplings.
To our knowledge, there are only few first principles
Principal values in Hz. The principal values have been ordered
according to |J11| e |J22| e |J33|. The principal axis systems are shown
in Figure 1. b (a) and (b) subscripts denote coupling between hydro-
gens belonging to methyl and silyl groups at gauche- and trans-
calculations of J tensors for methylsilane. The first article was
c
position to each other, respectively. Anisotropy is defined as ∆Jij
)
44
published by Fronzoni and Galasso, who used the EOM
J33
are in the HCSi plane and J11 makes an angle of 2.4° with the CH
bond toward the Si atom J33 makes an angle of 0.9° with the SiH
-
1
/2(J11 + J ).
d
J33 is directed along the CSi bond.
e
J11 and J
22
22
1
method and obtained the values JSiH ) -193.63 Hz and
1
f
JCSi ) -54.63 Hz, which are close to the experimental values.
bond toward the C atom in the CSiH plane. J22 is also in this plane.
The small 6-31G** basis set used in the calculations allows
g
2
Coupling is to the proton where the PAS of the JHH(Si) tensor is shown.
4
3
speculation about possible error cancellation. Malkina et al.
J
33 makes an angle of 22.6° with the CH direction away from silane
applied their DFT method45 to the determination of different
atom in the CSiH plane. J22 is in the same plane. h
J
22 makes an angle
silicon spin-spin coupling constants and they give the result
of 20.8° with SiH direction away from Si atom in the HCSi plane.
1
i
JSiH ) -196.94 Hz for methylsilane, which is in excellent
Also J11 is in this plane. J11 is directed along the HH direction in the
j
agreement with the experiment. Whereas the DFT method has
severe problems for couplings involving centers with lone
HCH plane and J33 is practically perpendicular with this plane. J33 is
directed along the HH direction in the HSiH plane and J22 makes an
k
4
3,45
angle of 3.4° with this plane toward the methyl group. Coupling is to
pairs,
it has been shown to perform extremely well for
2
the proton where the PAS of the JSiH is located. J33 makes an angle of
couplings between the nuclei of group 14 atoms and/or
hydrogen, as in the present case. Neither of the two earlier papers
reported the tensorial properties of the couplings, which form
our main topic in the present contribution.
9
.6° with the HH direction and an angle of 10.0° with the HSiC plane.
l
For J11, the same angles are 80.4° and 39.1°, respectively. Coupling
is to the proton where the PAS of the J tensor is shown. J33 is of
2
SiH
24.2° from the HH direction toward the carbon atom in the HSiCH
plane. Also J22 is in this plane.
The principal values of the principal axis system (PAS) for
all the theoretical J tensors in methylsilane are listed in Table
the electronic coupling regardless of the gyromagnetic ratios
of the coupled nuclei, the comparison has to be carried out using
reduced spin-spin couplings, Kij, which are related to the Jij
through
8
. The orientations of the principal axis are described in the
footnote. The principal axes are plotted at one of the coupled
nuclei in Figure 1.
When comparing the J tensor properties between molecules
having different symmetry, one is generally forced to use the
PAS of the tensors. Moreover, if the object of interest is purely
J ) (1/2π)pγ γ K
ij
(12)
ij
i
j

9676 J. Phys. Chem. A, Vol. 103, No. 48, 1999
Kaski et al.
in AM1, 201 cm- in PM3, and 528 cm in MP2, whereas the
1
-1
TABLE 9: Reduced Spin-Spin Coupling Constants and
Anisotropies in the Principal Axis Systema
-1 23
experimental value used is 603 cm . At least in the present
K
ij
∆Kijc
case, this implies that semiempirical methods may not be reliable
in the case of properties concerning large-amplitude motions
or for structural energetics far from the equilibrium geometry.
For the system at hand, the indirect contribution is very
significant as it gives the dominant correction to the experi-
propertyb
C
H
2 6
CH
3
SiH
3
C
2
H
6
3 3
CH SiH
1
K
K
K
K
K
K
K
K
K
K
CSi
100.73
98.75
1
1
1
2
2
2
2
3
3
CC
51.10
39.66
42.25
4.31
CH
38.31
76.57
1.13
-4.05
-1.27
0.21
4.91
7.71
0.22
-1.50
-1.40
0.15
1
SiH
mental CSi coupling (see Table 5). If the experimental DCSi is
CH
-1.76
-1.18
-0.81
-1.42
used in the study of orientational order parameter, SCSi, omitting
the correction due to indirect coupling contribution would lead
to an error of -3.3% (the ab initio result leads to -2.2%). When
determining the rCSi bond length, the corresponding error would
be +1.1%. Probably the situation remains in other molecules
that include CSi single bonds. The principal axis directions are
generally difficult to guess, but the J tensors in a molecule-
fixed frame appear to be directly transferable to other molecules
owing to the same local symmetry for the tensor. This is
indicated for example by a comparison of the ab initio JCH
tensors of C2H6, CH3F, and CH3SiH3. The ∆ JCH values in
the respective order are 6.0, 6.1, and 8.1 Hz (symmetry axis
used as the z axis in each molecule). The values for ∆ JHH(C)
are -8.3, -10.5, and -7.3 Hz in the same molecule-fixed
coordinate system. Especially, JCH is very close to being
cylindrically symmetric in the bond direction and, therefore,
the relative indirect contribution, /2 JCH / DCH , is nearly
orientation-independent. The ratio is nearly the same in different
molecules and, therefore, it may be used as an approximate a
priori correction for other molecules, for which JCH is otherwise
unknown. Correspondingly, in the case of the JCF tensor,
SiH
HH(C)
HH(Si)
HH(a)
HH(b)
0.29
1.22
0.06
0.84
0.14
0.27
0.10
0.15
a
Properties in 1019 T2 J-1. The reduced spin-spin coupling constants
and anisotropies of the methylsilane and ethane are derived from the
present RAS-II/HIII calculation and the best theoretical data in ref 7,
b
c
respectively. See footnote b in Table 8. Anisotropy is defined as
∆
K
ij ) K33 - 1/
ordered as |K33| g |K22| g |K11|.
2
(K11 + K22), where the principal values have been
1
7
5
1
h
eq
TABLE 10: Relative Harmonic Contributions D /D Given
2
by Different Force Fieldsa
coupling
AM1
PM3
MP2
ref 11b
1
3
D
D
D
D
D
D
D
D
HH
-0.26
-2.68
-2.49
-1.12
-5.41
-6.34
-0.28
0.41
-0.34
-2.95
-2.04
-0.78
-5.86
-5.06
-0.19
0.40
-0.59
-3.61
-2.29
-0.78
-6.85
-4.90
-0.25
0.33
-0.56
-3.38
-2.07
-0.77
-6.92
-4.45
-0.27
0.35
2
2
2
1
1
2
1
HH(C)
HH(Si)
CH
1
1
aniso 1
eq
CH
1
SiH
1
4,5
SiH
CSi
1
exp
the indirect contribution to DCF coupling is partially remov-
able by multiplying the DCF with 1.01 ( /2 JCF
00, compare with eq 3) in the analysis of the molecular
geometry and orientation. ∆ JCC appears between 26.5 and 47.5
a
1
eq
1
1
aniso
1
eq
In percent at the equilibrium value φ ) 0 of internal rotation.
≈ - DCF /
b
Scaled ab initio force constants.
1
1
The comparison of the Kij tensors between methylsilane and
Hz in the CC internuclear direction (in the case of planar
7
1
1
ethane is interesting as the electronic structure is expected to
be quite similar at least from the symmetry point of view. Table
molecules also J
- J
CC,yy
possesses a nonzero value, which
CC,xx
is systematically about -40 Hz, with z axis in the CC direction
and x axis in the molecular plane).
CC
is 32.1 Hz in ethane and 36.6 Hz in
acetonitrile, both possessing CC single bond. Therefore, most
probably also ∆ J
molecules with CSi single bond and it may be used as an a
priori correction to D
4,6,7
9
shows the coupling constants and anisotropies of the Kij
Especially, the theoretical
1
1
2
1
7
tensors in the PAS. The KCSi, KSiH, and KSiH couplings in
methylsilane are twice as large as the KCC, KCH, and KCH
result for ∆ J
1
1
2
12
1
aniso
couplings in ethane, respectively. As expected, the coupling
remains fairly constant in different
CSi
1
2
constants as well as the anisotropies of the KCH and KHH(C)
tensors are very similar between the molecules. It is also
noticeable that in the couplings over two bonds the sign changes
when the atom in the coupling path is silicon instead of carbon
1
exp
CSi
.
Conclusions
2
2
as one can see in both the KCH and the KHH couplings.
1
The spin-spin coupling tensor, JCSi, for methylsilane is
determined experimentally by utilizing liquid crystal NMR
method and, along with also all the other J coupling tensors of
the molecule, theoretically with ab initio MCSCF linear response
calculations. The best theoretical and experimental results are
in fair mutual agreement. The respective anisotropies of the
tensor are -89 ( 10 Hz and -59.3 Hz, whereas the values for
the J coupling constant are -51.6 and -60.5 Hz, respec-
tively. The anisotropic part of the indirect coupling, /2 JCSi
is found to contribute to the corresponding experimental
anisotropic coupling DCSi coupling significantly, by about
3%. In the analysis of the experimental data, the sensitivity of
the contributions due to harmonic vibrations to the method of
calculating the harmonic force field was tested by applying
semiempirical and ab initio methods. The nonscaled ab initio
MP2 calculation is found to give sufficient accuracy for the
harmonic force field, used in LC NMR, but also the semiem-
pirical FF corrects for most of the vibrational effects. However,
in the latter case the parameters associated with the large-
amplitude torsional motion are poorly determined. The present
Discussion
Comparing the different methods, there are no significant
differences between the geometries given by using different
harmonic force fields (see Table 6). Possibly the most clear
distinction is seen in the directly comparable relative harmonic
h
eq
1
contributions, D /D , given in Table 10.
CSi
1
1
aniso
For most couplings, the corrections given by our ab initio
MP2 calculation without scaling and most probably the best of
the current force fields, i.e., that given in ref 11 (scaled SCF
method), are in good mutual agreement, whereas the semiem-
pirical AM1 and PM3 results deviate from these. However, also
semiempirical force fields correct for most of the harmonic
vibrational effects and, consequently, it is much better to use
them than to ignore the vibrational contributions altogether. It
must be noted that with each set of analysis parameters, we
used the same probability distribution as a function of internal
rotation; i.e., the rotational barrier was not adopted from the
calculations. The theoretical barriers would have been 121 cm-
,
1
exp
1

Spin-Spin Coupling Tensors in Methylsilane
J. Phys. Chem. A, Vol. 103, No. 48, 1999 9677
results, together with earlier experience, suggest that the ab initio
MCSCF calculations are able to produce qualitatively correct
indirect contributions to the experimental dipolar couplings at
least for small probe molecules containing silicon. Explicit
treatment of core correlation in second-row atoms may be
necessary for quantitatively correct spin-spin couplings to these
nuclei when the MCSCF method is used. The J tensors are
found to be transferable from one molecule to another containing
the similar structural unit, and the necessary harmonic force
field can be determined with reasonable accuracy with fast
semiempirical calculations, although the ab initio method is
preferred. The transferability of the J tensors may be exploited
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Acknowledgment. The authors are grateful to the Academy
of Finland for financial support. J.K. expresses his gratitude to
the Finnish Cultural Foundation and Oulu University Foundation
for grants. P.L. acknowledges grants from the Finnish Cultural
Foundation and the Pohjois-Pohjanmaa Fund of the Finnish
Cultural Foundation. The computational resources were supplied
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