Erratum: Calculation of nuclear magnetic shieldings. X. Relativistic effects [J. Chem. Phys. 105, 3175 (1996)]

Formal relations connecting different approaches to calculate relativistic effects on molecular magnetic properties

“…This decomposition is therefore fully consistent with the one carried out in the four-component linear-response calculations 1,2 which considers separately the contributions from electronic and positronic states to a given positive-energy fourcomponent spinor in order to define the paramagnetic and diamagnetic components. The Breit-Pauli approach, in which the magnetic vector potential A is added to the canonical momentum in the Breit-Pauli Hamiltonian, was first investigated by Fukui et al, 17,18 and later expanded and completed by Manninen et al 8 and Fukui et al 18 However, it is interesting to remark the following point. It seems natural to identify the paramagnetic contribution as that originating in operators linear in A, and to identify the diamagnetic one with operators quadratic in A.…”

“…8,17,21,22 As a consequence, relativistic effects on magnetic properties within the Breit-Pauli approximation can be expressed as first-, second-, and third-order RSPT corrections to the Schrödinger molecular energy.…”

Relativistic effects on the nuclear magnetic shielding tensor

“…4,10 Relativistic spin-orbit ͑SO͒ effects on magnetic molecular properties were thought to be the most important ones until recent calculations of Visscher et al 4 Numerical results for nuclear magnetic shieldings obtained by four-component calculations and their counterpart from RayleighSchrödinger perturbation theory ͑RSPT͒ only match each other for the shielding of heavy atoms X in HX compounds when a new term different from SO is included. The so called mass-correction ͑MC͒ term was proposed for the first time by Fukui et al 6 It was obtained within a formalism in which the external magnetic field is explicitly included in the Breit-Pauli Hamiltonian in order to get a gauge-invariant scheme up to order c Ϫ4 . The MC term is a second order expression containing the Fermi contact ͑FC͒ and the kinetic energy (p 2 ) operators.…”

“…In the last few years an ever increasing number of new formalisms and calculations for the evaluation of relativistic effects on molecular properties from four-, two-, or onecomponent response schemes or perturbation theory approaches have been published. [1][2][3][4][5][6][7][8][9][10][11] It was shown that the inclusion of such effects in the calculation of some molecular properties is mandatory when one wants to reproduce experimental trends. 4,10 Relativistic spin-orbit ͑SO͒ effects on magnetic molecular properties were thought to be the most important ones until recent calculations of Visscher et al 4 Numerical results for nuclear magnetic shieldings obtained by four-component calculations and their counterpart from RayleighSchrödinger perturbation theory ͑RSPT͒ only match each other for the shielding of heavy atoms X in HX compounds when a new term different from SO is included.…”

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

“…Several approaches can be found in the literature incorporating relativistic effects in the calculation of NMR parameters. [8][9][10][11][12][13][14][15] Most of these works are focused on NMSs, while those reporting calculations of SSCs are less abundant. Full fourcomponent calculations were carried out by Visscher et al in the hydrogen halides HX ͑X = F, Cl, Br, and I͒ 13 and by Enevoldsen et al in the tetrahydrides series XH 4 ͑X = C, Si, Ge, Sn, and Pb͒ 9 using the Dirac-Hartree-Fock ͑DHF͒ formalism.…”