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. 2 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. 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 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 S mN Fermi-contact induces electron spin-density in the metal atom The spin-density is transferred through the bond to the ligand atom. 5 Nonrelativistic Fermi-contact contribution Fermi-contact operator h FC 2ge (rN ) m N 3c Nonrelativistic Fermi-contact contribution K ( A, B)iiFC 4ge 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 6 Scalar relativistic correction scheme I and II Scalar relativistic correction I K ( A, B)iiFC ,SRI 4ge 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 4ge 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 7 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). 8 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(CH 3)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 Molecule Method K K 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]. 10 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). 11 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 K Ex p K SRII /K NR /K NR Figure 1 Comparison between the experimental and calculated relativistic increase in coupling constants 2 NR or K SRII /K NR 3 /K tPtCl P K Exp 2 cPtCl am 2 1 Ptam 2+ cPtCl P 2 2 tPtCl am Pt(PF ) 2 2 2 2 cPtH P 2 2 tPtH P 3 4 2 4 0 13 2 cPtCl P 4 tPtCl P 4 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. 14 Trans influence and spin-spin coupling constants B * 3u 2A * z 1 g y 2 1A * g 3 6p x 4 x 6s 5dx2-y2 4-2 2+4 1+3 B 3u 2A g Metal orbitals 1A g Ligand orbitals Figure 2 The MO scheme for a trans planar complex with symmetry D 2h 15 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. 16 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. 17