Relativistic calculation of indirect NMR spin-spin couplings using the Douglas-Kroll-Hess approximation

Abstract

Articles you may be interested inTheoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes J. Chem. Phys. 140, 144303 (2014) We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides CH 4 , SiH 4 , GeH 4 , and SnH 4 . Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data.

Perspective: Relativistic effects

“…115 The subsequent introduction of magnetic-field dependent terms in the DKH method in a rigorous way has taken a rather long time and the efforts of several research groups. 57,[118][119][120][121][122] At the DKH1 level, the expression for the magnetic perturbation operator is relatively compact and may be written as 120…”

Relativistic calculations of magnetic resonance parameters: background and some recent developments

“…The expressions in second order (DKH2) are not particularly compact and therefore are not repeated here. The reader is referred to references [129,[139][140][141][142][143][144][145][146] for details. The formalism has recently been extended to infinite order [147], whereby a recursive equation is solved for the decoupling operator following the free-particle FW transformation ( §5).…”

“…This is also true in higher orders of the DKH expansion. A diamagnetic operator appears at the DKH2 level [141]. The developments for constructions of formally exactly decoupled two-component Hamiltonians (X2C) have led to formulations of how to construct X2C magnetic-field perturbed operator matrices, along with a pilot application to NMR shielding [149,150].…”

“…As the DKH transformations involve operators that contain functions of p 2 , the transformations should in principle include the vector potential from the onset [148] (because of (7.1)). At the DKH1 level [141], an expression has been given for the one-electron magnetic perturbation operator that structurally resembles that of the ZORA framework:…”

Exact two-component relativistic theory for nuclear magnetic resonance parameters

“…As such, NMR parameters such as nuclear magnetic shielding ͑NMS͒ and indirect spin-spin coupling ͑SSC͒ tensors are intrinsically all-electron relativistic properties. Various quasirelativistic methods have been developed in the past, including first order perturbation approaches, 1,2 zeroth order regular approximation, [3][4][5] Douglas-Kroll-Hess type approximation, [6][7][8][9][10][11][12] and second order regular approximation [13][14][15] to the normalized elimination of the small component ͑NESC͒. 16 While such approximate methods are very useful for elucidating the various physical contributions and meanwhile work well for chemical shifts, they cannot provide accurate absolute NMS and SSC scales for heavy elements, as the inherent approximations therein arise solely from the atomic cores, precisely the regions sampled by the parameters.…”