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 zThere 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]. zThe 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. 3

Introduction zThe 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. 4

Nuclear spin-spin coupling through Fermi-contact Fermi-contact induces electron spin-density in the metal atom S The spin-density is transferred through the bond to the ligand atom. NN 5

Nonrelativistic Fermi-contact contribution z Nonrelativistic Fermi-contact contribution U-matrix: the first-order expansion coefficient matrix for spin orbitals perturbed by h FC of nucleus A, in the basis of the unperturbed orbitals Unperturbed Kohn-Sham orbitals z Fermi-contact operator 6

Scalar relativistic correction scheme I and II z Scalar relativistic correction II 7 QR Kohn-Sham orbital QR atomic orbital value at the metal centerNonrelativistic U-matrix Quasirelativistic U-matrix z Scalar relativistic correction I

Couplings involving main- group metals zTest 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). zQuality 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. zDependence 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). 8

Couplings involving main- group metals 9

10

Couplings involving platinum zSRII correction is able to recover the relativistic increase with an average error of approximately 25%, whereas the SRI method fails completely (see Table 3). zThe 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 K SRII /K NR with K EXP /K NR shows that SRII can reproduce the trends of relativistic effect on spin-spin coupling in different chemical environment (see Figure 1). zBoth the nonrelativistic and SRII corrected calculations are able to reproduce the experimental trend in trans influence(see Table 3). 11

Couplings involving platinum 12

Couplings involving platinum 13

Trans influence and spin-spin coupling constants zThe thermodynamic trans influence is defined as the extent to which a ligand labilizes the bond opposite to itself in the ground state. zOur 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 6s5d x2-y2 hybrid orbitals and the ligand  -orbitals. According to the MO scheme (Figure 2) for a trans planar complex with symmetry D 2h, the metal-ligand  -type interactions give rise to three orbitals, from which two are of A g symmetry and therefore contribute to the coupling. When L 2 has a higher  -donor ability, M-L 2 gains more contribution from L 2 at the expense of M-L 4. Since the s-character of phosphorus is proportional to the  -contribution of phosphine, this also means that M-L 2 gains s-character from L 2 at the expense of M-L 4 when L 2 has a higher trans influence. As a result, M-L 2 shows a larger spin-spin coupling constant. 14

Trans influence and spin-spin coupling constants 15

References [1] Dickson, R. M.; Ziegler, T. J. Phys. Chem. 1996, 100, [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, [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,

Acknowledgement zFinancial support by NOVA and NSERC. zOne of us J. K. would like to thank Dr. Steven Wolff and Dr. S. Patchkovskiifor interesting discussions about relativity and quantum chemistry. 17