Infinite-order two-component theory for relativistic quantum chemistry

Abstract

A method for the iterative algebraic generation of the numerically accurate two-component Hamiltonian for the use in relativistic quantum chemistry is presented. The separation of the electronic and positronic states of the Dirac Hamiltonian is accomplished by the algebraic solution for the Foldy–Wouthuysen transformation. This leads to the two-component formalism whose accuracy is primarily limited by the choice of basis functions. Its performance is tested in calculations of the most sensitive 1s1/2 energy for increasing values of the nuclear charge. These calculations show that the electronic part of the Dirac eigenspectrum can be obtained from the two-component theory to arbitrarily high accuracy. Moreover, if needed, the positronic states can be separately determined in a similar way. Thus the present method can be also used for the evaluation of quantum electrodynamic corrections in the finite basis set approximation.

Exact decoupling of the relativistic Fock operator

“…This idea was first proposed by Barysz et al [45] and is therefore know as the BSS approach although it has later been called by Barysz and Sadlej the infinite-order twocomponent (IOTC) method [46]. Their transformation U 1 0 is a U X -like operator…”

“…[75] for calculations on PbO. The scheme is usually called the ''BSS approach'' [4,45,46], but later Barysz et al preferred the abbreviation ''IOTC''. Other names for their approach, which have been used, are IOFW (infinite-order Foldy-Wouthuysen) [76,77] and IODK (infinite-order Douglas-Kroll) [43,78].…”

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.…”

Implementation of Efficient Two-component Relativistic Method Using Local Unitary Transformation to GAMESS Program

“…actually, most quantum chemical packages contain various 2c relativistic schemes. For example, the GameSS program package [1] implements the normalized elimination of the small component scheme [2], the relativistic elimination of the small component scheme [3], the first-to third-order Douglas-Kroll-Hess scheme [4][5][6], and the infinite-order two-component (IOTC) scheme [7]. Especially, iotc gives equivalent results to the four-component (4c) relativistic calculations in one-electron systems.…”