Relativistic Effects on the Heavy Metal-ligand NMR

Spin-spin Couplings

Copyright, 1996 © Dale Carnegie & Associates, Inc.

Jana Khandogin and Tom Ziegler

Department of Chemistry

The University of Calgary

May, 1999

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 s-orbitals 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.

2

Introduction

There are four terms contributing to the indirect nuclearspin-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 theninteracts with the magnetic dipole of the second nucleus.

3

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 couldbe to the first order dealt with by the presented scalar relativistic correction schemes: SRI and SRII.

4

Nuclear spin-spin coupling through Fermi-contact

Fermi-contactinduces electron spin-densityin the metal atom

S

The spin-density is transferred through the bond to the ligand atom.

N

5

Nonrelativistic Fermi-contact contribution

Occ

k

Vir

lliBk

iAkl

eFCii rU

c

gBAK 00, ˆ)(

3

4),(

Nonrelativistic Fermi-contact contribution

U-matrix: the first-order expansion coefficient matrix for spin orbitals perturbed by

hFC of nucleus A, in the basis of the unperturbed orbitals

Unperturbed Kohn-Sham orbitals

NNeFC r

c

gh )(

3

2

Fermi-contact operator

6

Scalar relativistic correction scheme I and II

Occ

k

Vir

l

QRliB

QRk

QRiAkl

eSRIFCii rU

c

gBAK ,0,0,,, ˆ)(

3

4),(

Scalar relativistic correction II

,)()(3

4),(

' ',0,,,

Occ

k

Vir

l

sAO sAO

MQR

MQRNRNRiL

kleSRIIFC

ii rrPUc

gBAK

7

QR Kohn-Sham orbital

QR atomic orbital value at the metal centerNonrelativistic U-matrix

Quasirelativistic U-matrix

Scalar relativistic correction I

Couplings involving main-group metals

Test of the scalar relativistic correction schemes on group 2 and 16 compounds: SR II gives overall better results than the scheme I incomparison 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). TheMCSCF 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 downby roughly 10%, whereas other GGA functionals yield very similar

values (see Table 2).

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Couplings involving main-group metals

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Table 1. Calculated reduced coupling constants usingnonrelativistic method and SR I and II schemes.Molecule Coupling KExp KNR KSRI KSRII

SiH4 K(Si-H) 84.79 88 87 89GeH4 K(Ge-H) 232 188 207 217SnH4 K(Sn-H) 431 294 304 293PbH4 K(Pb-H) 923 501 629 851Ge(CH3)4 K(Ge-C) - 86 89 108Sn(CH3)4 K(Sn-C) 302 195 187 201Pb(CH3)4 K(Pb-C) 396 72 -147 207Zn(CH3)2 K(Zn-C) - 299 309 349Cd(CH3)2 K(Cd-C) 797 485 488 634Hg(CH3)2 K(Hg-C) 1263 666 460 1309[Zn(CN)4]

2- K(Zn-C) 465 405 449 458[Cd(CN)4]

2 K(Cd-C) 855 648 794 821[Hg(CN)4]

2- K(Hg-C) 2832 1039 1471 1857

Couplings involving main-group metals

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Table 2. Comparison of DFT and CAS B a calculations for coupling constants in group 4 tetrahydrides.Molecule Method NR

FCK NRPSOK NR

DSOK ExpK

SiH4 BP86LDACAS B

88.375.978.21

-0.170-0.144-

0.0130.014-

84.79

GeH4 BP86LDACAS B

189.0170.0232.7

-0.482-0.362-0.500

0.0190.0160.024

232

SnH4 BP86LDACAS B

295.5266.7421.7

-1.221-1.074-1.227

0.0130.0130.007

431

PbH4 BP86LDACAS B

504.3442.1-

-2.81-2.54-

0.0100.010-

923

a CAS B refers to the correlated results using the MCSCF wavefunction[5].

Couplings involving platinum

SRII correction is able to recover the relativistic increase with an average error of approximately 25%, whereas the SRI methodfails 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 metalis 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 toreproduce the experimental trend in trans influence(see Table 3).

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Couplings involving platinum

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Table 3. Calculated reduced coupling constants for someplatinum complexes.Molecule Coupling KExp KNR KSRI KSRII

[Pt(NH3)4]2+ K(Pt-N) 1089 605 599 999

c-PtCl2(NH3)2 K(Pt-N) 1154 411 150 730t-PtCl2(NH3)2 K(Pt-N) 1059 496 368 891Pt(PF3)4 K(Pt-P) 6215 3542 3596 5433c-PtCl2(PMe3)2 K(Pt-P) 3316 1487 1609 2286t-PtCl2(PMe3)2 K(Pt-P) 2267 867 892 1433c-PtH2(PMe3)2 K(Pt-P) 1786 685 430 1192t-PtH2(PMe3)2 K(Pt-P) 2472 1200 839 1832c-PtCl4(PEt3)2 K(Pt-P) 1976 946 978 1602t-PtCl4(PEt3)2 K(Pt-P) 1386 695 626 1131

Couplings involving platinum

13

0

1

2

3

Figure 1 Comparison between the experimental andKExp/KNR

KSRII/KNR calculated relativistic increase in coupling constants

Ptam4

2+

cPtCl2am

2

tPtCl2am

2Pt(PF

3)4

cPtCl2P

2

tPtCl2P

2

cPtH2P

2

cPtCl4P

2tPtH

2P

2

tPtCl4P

2KE

xp/K

NR o

r K

SR

II /KN

R

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

15

x

yz

1+3

2+4

4-2

5dx2-y2

6s

6p x

1Ag

2Ag

B3u

1A*g

2A*g

B*3u

Figure 2 The MO scheme for a trans planar complex with symmetry D 2h

Metal orbitals Ligand orbitals

2

3

1

4

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 discussionsabout relativity and quantum chemistry.

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