Two-component relativistic methods for the heaviest elements

Abstract

Different generalized Douglas-Kroll transformed Hamiltonians (DKn, n=1, 2,...,5) proposed recently by Hess et al. are investigated with respect to their performance in calculations of the spin-orbit splittings. The results are compared with those obtained in the exact infinite-order two-component (IOTC) formalism which is fully equivalent to the four-component Dirac approach. This is a comprehensive investigation of the ability of approximate DKn methods to correctly predict the spin-orbit splittings. On comparing the DKn results with the IOTC (Dirac) data one finds that the calculated spin-orbit splittings are systematically improved with the increasing order of the DK approximation. However, even the highest-order approximate two-component DK5 scheme shows certain deficiencies with respect to the treatment of the spin-orbit coupling terms in very heavy systems. The meaning of the removal of the spin-dependent terms in the so-called spin-free (scalar) relativistic methods for many-electron systems is discussed and a computational investigation of the performance of the spin-free DKn and IOTC methods for many-electron Hamiltonians is carried out. It is argued that the spin-free IOTC rather than the Dirac-Coulomb results give the appropriate reference for other spin-free schemes which are based on approximate two-component Hamiltonians. This is illustrated by calculations of spin-free DKn and IOTC total energies, r(-1) expectation values, ionization potentials, and electron affinities of heavy atomic systems.

Perspective: Relativistic effects

“…24 and 26. In this context, we also mention elimination schemes dubbed IOTC to construct two-component relativistic operators by Barysz and co-workers [78][79][80][81] and normalized elimination of the small component (NESC) methods 82,83 which have helped paving the way for the development of X2C. There is no closed-form expression available for the X2C one-electron Hamiltonian, but its approximate construction in matrix form utilizing a finite basis set can be summarized in a few algorithmic steps, none of which require the calculation of molecular integrals that are not already available in 4c codes.…”

The quadrupole moment of the As nucleus from molecular microwave data and calculated relativistic electric field gradients

“…For closed-shell systems with moderately heavy nuclei this contribution is dominated by scalar relativistic effects which can be easily accounted for by using finite-order Douglas-Kroll methods (DKH) [23][24][25][26] or the scalar approximation to the infinite-order two-component (IOTC) theory of Barysz et al [27][28][29][30]. The latter approach fully decouples the positive and negative spectra of the Dirac Hamiltonian and will be used in this study.…”

“…This can be in MOLCAS easily accounted for using the Douglas-Kroll method [22] in the implementation proposed by Hess (DKH) [23][24][25]. However, we took advantage of the infinite-order two-component (IOTC) approach of Barysz and co-workers [27][28][29] in the scalar implementation [30]. The IOTC method is essentially as demanding as the usual DKH approach but has an advantage in complete decoupling the electronic from the positronic states.…”

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

“…There have been other elimination schemes devised to construct formally exact twocomponent relativistic operators, for instance, infinite-order methods by Barysz and co-workers (BSS = Barysz-Sadlej-Snijders, IOTC = infinite-order two-component) [55][56][57][58] and normalized elimination of the small component (NESC) methods [59][60][61][62][63][64][65][66]. In its recent incarnations, the X2C technique rests on a representation of the four-component equation in an RKB basis.…”