Transcript Relativistic Effects on NMR Spin

Relativistic Effects on the
Heavy Metal-ligand NMR
Spin-spin Couplings
Jana Khandogin and Tom Ziegler
Department of Chemistry
The University of Calgary
May, 1999
Copyright, 1996 © Dale Carnegie & Associates, Inc.
Abstract
The one-bond nuclear spin-spin coupling is particularly sensitive to
relativistic effects because the contraction of the s orbitals can significantly
alter the Fermi-contact contribution. The relativistic effects on the NMR
coupling constant can be to the first order modeled by adding corrections
on top of the non-relativistic nuclear coupling formulation. Here, we
present two different relativistic correction schemes. The first scheme
involves the Pauli Hamiltonian in the Quasi-relativistic approach[3]. In the
second scheme, use is of made of the non-relativistic molecular Kohn-Sham
orbitals where non-relativistic s-orbitals are replaced by relativistic sorbitals in the evaluation of the Fermi-contact term, without changing
orbital expansion coefficients. These schemes are applied to the calculation
of metal-ligand coupling constants involving heavy main-group and
transition metals. It is shown that the latter method gives a surprisingly
good agreement with experiment.
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Introduction
 There are four terms contributing to the indirect nuclear
spin-spin coupling constant in the nonrelativistic theory:
the Fermi contact and spin dipolar (SD) terms arising from
the spin of the electron, and the para- and diamagnetic
spin-orbit terms originating from the orbital motion of the
electron[1, 2].
 The FC operator takes effect whenever there is a finite
electron density (s orbitals) at one nucleus and creates
a net spin density (in a close-shell molecule), which then
interacts with the magnetic dipole of the second nucleus.
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Introduction
 The FC term gives in most cases the dominant contribution and is
particularly sensitive to relativistic effects as a result of orbital and
bond length contractions. The bond length shortening can be taken
into account by making use of the experimental geometries in the
calculation. The remaining relativistic effect on the FC term could
be to the first order dealt with by the presented scalar relativistic
correction schemes: SRI and SRII.
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Nuclear spin-spin coupling
through Fermi-contact
S
mN
Fermi-contact
induces electron spin-density
in the metal atom
The spin-density is transferred through
the bond to the ligand atom.
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Nonrelativistic Fermi-contact
contribution
 Fermi-contact operator
h FC 
2ge
 
 (rN )  m N
3c
 Nonrelativistic Fermi-contact contribution
K ( A, B)iiFC
4ge OccVir A,i 0

U kl k  (rB )ˆ i l0

3c k l
Unperturbed Kohn-Sham orbitals
U-matrix: the first-order expansion coefficient matrix for spin orbitals perturbed by
hFC of nucleus A, in the basis of the unperturbed orbitals
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Scalar relativistic correction
scheme I and II
 Scalar relativistic correction I
K ( A, B)iiFC ,SRI
4ge OccVir A,i ,QR 0,QR

U kl
k  (rB )ˆ i l0,QR

3c k l
Quasirelativistic U-matrix
QR Kohn-Sham orbital
 Scalar relativistic correction II
K ( A, B)iiFC ,SRII
4ge OccVir L,i , NR AO 's AO's 0, NR QR

U kl
P   (rM ) QR (rM ),



3c k l


Nonrelativistic U-matrix
QR atomic orbital value at the metal center
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Couplings involving maingroup metals
 Test of the scalar relativistic correction schemes on group 2 and 16
compounds: SR II gives overall better results than the scheme I in
comparison with experimental values (see Table 1).
 Quality of the nonrelativistic DFT based method: individual contributions
closely resemble the ones obtained by MCSCF approach (see Table 2). The
MCSCF result does not leave any room for relativistic corrections
whereas DFT does.
 Dependence on the density functional form: with respect to the values
obtained with BP86 functional, LDA shifts all coupling constants down
by roughly 10%, whereas other GGA functionals yield very similar
values (see Table 2).
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Couplings involving maingroup metals
Table 1. Calculated reduced coupling constants using
nonrelativistic method and SR I and II schemes.
Molecule
Coupling
KExp
KNR
KSRI
KSRII
SiH4
GeH4
SnH4
PbH4
Ge(CH3) 4
Sn(CH3) 4
Pb(CH3)4
Zn(CH3)2
Cd(CH3) 2
Hg(CH3) 2
[Zn(CN) 4]2[Cd(CN)4] 2
[Hg(CN)4] 2-
K(Si-H)
K(Ge-H)
K(Sn-H)
K(Pb-H)
K(Ge-C)
K(Sn-C)
K(Pb-C)
K(Zn-C)
K(Cd-C)
K(Hg-C)
K(Zn-C)
K(Cd-C)
K(Hg-C)
84.79
232
431
923
302
396
797
1263
465
855
2832
9
88
188
294
501
86
195
72
299
485
666
405
648
1039
87
207
304
629
89
187
-147
309
488
460
449
794
1471
89
217
293
851
108
201
207
349
634
1309
458
821
1857
Couplings involving maingroup metals
Table 2. Comparison of DFT and CAS B a calculations for
coupling constants in group 4 tetrahydrides.
K
K
K
Molecule Method K
SiH4
BP86
88.3
-0.170 0.013
84.79
LDA
75.9
-0.144 0.014
CAS B 78.21
GeH4
BP86
189.0
-0.482 0.019
232
LDA
170.0
-0.362 0.016
CAS B 232.7
-0.500 0.024
SnH4
BP86
295.5
-1.221 0.013
431
LDA
266.7
-1.074 0.013
CAS B 421.7
-1.227 0.007
PbH4
BP86
504.3
-2.81
0.010
923
LDA
442.1
-2.54
0.010
CAS B NR
FC
a
NR
PSO
NR
DSO
Exp
CAS B refers to the correlated results using the MCSCF wavefunction[5].
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Couplings involving platinum
 SRII correction is able to recover the relativistic increase with an
average error of approximately 25%, whereas the SRI method
fails completely (see Table 3).
 The SRII is superior to the hydrogen-like relativistic correction of
Pyykkö[4], where a multiplicative factor assigned for each heavy metal
is applied on the nonrelativistically calculated total coupling constants:
The comparison of KSRII/KNR with KEXP/KNR shows that SRII can reproduce
the trends of relativistic effect on spin-spin coupling in different chemical
environment (see Figure 1).
 Both the nonrelativistic and SRII corrected calculations are able to
reproduce the experimental trend in trans influence(see Table 3).
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Couplings involving platinum
Table 3. Calculated reduced coupling constants for some
platinum complexes.
Molecule
Coupling
KExp
KNR
KSRI
KSRII
[Pt(NH3)4] 2+
c-PtCl2(NH3) 2
t-PtCl2(NH3) 2
Pt(PF3)4
c-PtCl2(PMe3)2
t-PtCl2(PMe3)2
c-PtH2(PMe3)2
t-PtH2(PMe3)2
c-PtCl4(PEt3)2
t-PtCl4(PEt3)2
K(Pt-N)
K(Pt-N)
K(Pt-N)
K(Pt-P)
K(Pt-P)
K(Pt-P)
K(Pt-P)
K(Pt-P)
K(Pt-P)
K(Pt-P)
1089
1154
1059
6215
3316
2267
1786
2472
1976
1386
12
605
411
496
3542
1487
867
685
1200
946
695
599
150
368
3596
1609
892
430
839
978
626
999
730
891
5433
2286
1433
1192
1832
1602
1131
Couplings involving platinum
Exp
NR
K /K
KSRII/KNR
Figure 1 Comparison between the experimental and
calculated relativistic increase in coupling constants
K Exp/K NR or K SRII/K NR
3
2
tPt Cl P
2
cPt Cl am
2
1
Ptam
2+
cPt Cl P
2
2
tPt Cl am Pt(PF )
2
2
2
2
cPt H2P 2
tPt H P
3 4
2
4
0
13
2
cPt Cl P
4
tPt Cl4P 2
2
Trans influence and spin-spin
coupling constants
 The thermodynamic trans influence is defined as the extent to which a
ligand labilizes the bond opposite to itself in the ground state.
 Our calculation shows that the effect of trans influence on the coupling
constant can not be ascribed to the change in the metal-ligand bond
distance.
 An explanation can be found by examining the -type interaction between
the metal 6s5dx2-y2 hybrid orbitals and the ligand -orbitals. According to
the MO scheme (Figure 2) for a trans planar complex with symmetry D2h,
the metal-ligand -type interactions give rise to three orbitals, from which
two are of Ag symmetry and therefore contribute to the coupling. When L2
has a higher -donor ability, M-L2 gains more contribution from L2 at the
expense of M-L4. Since the s-character of phosphorus is proportional to the
-contribution of phosphine, this also means that M-L2 gains s-character
from L2 at the expense of M-L4 when L2 has a higher trans influence. As a
result, M-L2 shows a larger spin-spin coupling constant.
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Trans influence and spin-spin
coupling constants
B * 3u
z
2A * g
1
y
2
1A * g
3
6p x
4
x
6s
5dx2-y2
4-2
2+4
1+3
B 3u
2A g
Metal orbitals
Figure 2 The MO scheme for a
symmetry D 2h
1A g
Ligand orbitals
trans planar complex with
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References
[1] Dickson, R. M.; Ziegler, T. J. Phys. Chem. 1996, 100, 5286.
[2] Khandogin, J.; Ziegler, T. Spectrochim. Acta 1999, 55, 607.
[3] Ziegler, T.; Tschinke, V.; Baerends, E. J.; Snijders, J. G.; Ravenek, W. J.
Phys. Chem. 1989, 93, 3050.
[4] Pyykkö, P.; Pajanne, E.; Inokuti, M. Int. J. Quant. Chem. 1973, 7, 785.
[5] Kirpekar, S.; Jensen, H. J. A.; Oddershede, J. Theor. Chim. Acta 1997,
95, 35.
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Acknowledgement
 Financial support by NOVA and NSERC.
 One of us J. K. would like to thank Dr. Steven Wolff
and Dr. S. Patchkovskii for interesting discussions
about relativity and quantum chemistry.
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