Theoretical Studies of Heavy-Atom NMR Spin- spin Coupling Constants With Applications to Solvent Effects in Heavy Atom NMR Jochen Autschbach & Tom Ziegler, University of Calgary, Dept. of Chemistry University Drive 2500, Calgary, Canada, T2N-1N4 1

What is interesting about Heavy Metal Compounds ? Spin-orbit coupling, scalar relativistic effects Relativistic theoretical treatment: sizeable effects on bonding for 6 th row elements (bond contractions, D e, e,IP, …) are already textbook knowledge (e.g. “Au maximum”) Simple estimates propose absolute (!) scalar relativistic effects of  100% for 6 th row elements for NMR spin-spin coupling constants Coordination by solvent molecules possible 2

Spin-spin coupling constants Nucleus A Spin magnetic moment creates magnetic field Direct coupling (vanishes for rapidly rotating molecules) Nucleus B Spin magnetic moment creates magnetic field Electrons with orbital- and spin- magnetic moments Indirect coupling Indirect coupling K (A,B) Methodology 3

we need to know including relativity including relativity Reduced spin-spin coupling tensor Coupling constants in Hz from the NMR spectrum Reduced coupling constant 4

The ZORA one-electron Hamiltonian Replacement to account for magnetic fields T nrel + relativistic corrections of T and V, spin-orbit coupling Magnetic field due to nuclear magnetic moments Molecular effective Kohn-Sham potential if used in DFT Variationally stable two-com- ponent relativistic Hamiltonian 5

Nuclei A and B, directions j and k, point-like magnetic dipoles The ZORA Hyperfine Terms Requires solution of 1 st -order pertur- bation equations 6

Description of the code Auxiliary program “CPL” for the program ADF (Amsterdam Density Functional, see Based on nonrelativistic, ZORA scalar or ZORA spinorbit 0 th order Kohn-Sham orbitals Analytic solution of the coupled 1 st order Kohn- Sham equations due to FC-, SD-, and PSO terms (instead of finite perturbation) Accelerated convergence for scalar relativistic calculations (< 10 iterations) Spin-dipole term implemented Currently no current-density dependence in V, X  or VWN approximation for 1 st order exchange potential 7

Results I : scalar ZORA One-bond metal ligand couplings Hg-C Pt-P W-C, W-H, W-P, W-F Pb-H,Pb-C, Pb-Cl FC + PSO + DSO terms included JCP 113 (2000),

Tungsten compounds W(CO) 6 W(CO) 5 PF 3 W(CO) 5 PCl 3 W(CO) 5 WI 3 cp-W(CO) 3 H WF 6 Lead compounds PbH 4 * Pb(CH 3 ) 2 H 2 Pb(CH 3 ) 3 H Pb(CH 3 ) 4 PbCl 4 ** * exp. extrapolated from Pb(CH 3 ) x H y ** not directly measured * ** 9

Platinum compounds Pt(PF 3 ) 4 PtX 2 (P(CH 3 ) 2 ) cis-PtCl 2 (P(CH 3 ) 3 ) 2 trans-PtCl 2 (P(CH 3 ) 3 ) 2 cis-PtH 2 (P(CH 3 ) 3 ) 2 trans-PtH 2 (P(CH 3 ) 3 ) 2 Pt(P(CH 3 ) 3 ) 4 Pt(PF 3 ) 4 Hg(CH 3 ) 2 CH 3 HgCl CH 3 HgBr CH 3 HgI Hg(CN) 2 [Hg(CN) 4 ] 2- Hg(CH 3 ) 2 (CH 3 )Hg-X [Hg(CN) 4 ] 2- Hg(CN) 2 Mercury compounds 10

Results II : spinorbit coupling System *) K / kg/m -2 C -2 NrelScalarSOExpt. Tl-F  120  139  203  202 Tl-Cl  133  129  219  224 Tl-Br  217  132  315  361 Tl-I  288  115  382  474 *) VWN + Becke86 + Perdew 88 functional, Tl-X coupling constants Spin-orbit (SO) coupling causes cross terms between the spin-dependent ope- rators (FC,SD) and the orbital dependent ones (here: PSO). The differences between Scalar and SO in the table above is mainly caused by these cross terms, and by the SO effects on the PSO contribution itself. Tl-I is the first example where SO coupling was demonstrated to cause the major contributions to heavy atom spin-spin couplings. JCP 113 (2000),

Results III : solvent effects 12 Experimental results on pages 9 and 10 obtained from solution. The cases where results are unsatisfactory are marked red (linear Hg and square planar Pt complexes) SO coupling yields only minor corrections in all these cases! Is coordination of the heavy atoms by solvent molecules important? Some structures that were optimized, explicitly including a number of solvent molecules

Mercury compounds with solvents : K / kg/m -2 C -2 *) Hg(CN) 2 +2MeOH+4MeOHExpt.+4THFExpt. 443 (426) (561) HgMeCl+3CHCl 3 +4CHCl 3 Expt.+3DMSOExpt HgMeBr+2CHCl 3 +3CHCl 3 Expt.+3DMSOExpt HgMeI+2CHCl 3 +3CHCl 3 Expt.+3DMSOExpt HgMe 2 +2CHCl 3 +3CHCl 3 Expt.+3DMSOExpt *) Hg-C coupling, VWN functional, scalar ZORA (numbers in parentheses: ZORA spin-orbit) 13 JACS 123 (2001), 3341.

*) K / kg/m 2 C 2 Pt-P coupling, VWN functional. scalar ZORA (in parentheses: ZORA spin-orbit) cis- PtH 2 (PMe 3 ) 2 trans- PtH 2 (PMe 3 ) 2 no solvent *) 107 (97) acetone acetoneN/A169 (158)277 Expt Pt complexes

15 *) Optimized bond distances, experimental bond lengths in parentheses (in Å) **) J. Glaser et al., JACS 117 (1995), Experiment: **) 1 J (Tl-Pt) : 57 kHz 1 J (Tl-C B ) : 2.4 kHz 2 J (Tl-C A ) : 9.7 kHz 2 J (Tl-C C ) : 0.5 kHz 2.55 (2.60) 2.15 (2.13) *) 1.93 (2.01) Two heavy nuclei: A Pt-Tl cyano complex Results III : more solvent effects Two-bond coupling much larger than one-bond coupling Four water molecules can coordinate to Tl in aqueous solution (exp. confirmed) Complex I

16 Results III : more solvent effects Spin-spin couplings complex I, J / kHz Coupling nrelscalarScalar + 4H 2 O SO + 4H 2 O Exp. (in H 2 O) Pt-Tl Tl-C B  1.2  Tl-C A Tl-C C  0.2  0.5  The unintuitive experimental result 2 J(Tl-C A ) >> 1 J(Tl-C B ) questions the proposed structure with a direct Tl-Pt bond (page 15). However, our computations confirm the structure and the unusual coupling pattern. The solvent coordination effect on J(Pt-Tl) and the Tl-C cpouplings is remarkably large.

17 Results III : more solvent effects JACS 123 (2001), in press. free complex: both couplings are comparably large in magni- tude but of opposite sign inclusion of solvent molecules shifts both couplings. The one- bond coupling is – as expected – influenced much stronger. As a result, the two-bond coup- ling is much larger than the one- bond coupling Delocalized bonds along the C-Pt-Tl-C axis are responsible for the large magnitude of the two-bond Tl-C coupling in the free complex

Summary NMR shieldings and spin-spin couplings with ADF now available for light and heavy atom systems Based on the variationally stable two-component ZORA method Relativistic effects on spin-spin couplings are substantial and recovered by the ZORA method Spin-orbit effects are rather small for many cases, but dominant for Tl-X Coordination by solvent molecules has to be explicitly taken into account for coordinatively unsaturated systems. Saturating the first coordination shell yields satisfactory results in these cases. Further solvent contributions within the DFT error bars 18