Scalar-relativistic LCGTO DFT calculations for atoms using the Douglas-Kroll transformation

Abstract

ABSTRACT:Haberlen and Rosch HR demonstrated Chem. Phys. Lett. 199, 491Ž.x Ž . 1992 the feasibility of performing scalar-relativistic, density functional theory DFT Ž . linear combination of Gaussian-type orbitals᎐fitting function LCGTO-FF calculations on clusters of atoms using an ''incomplete'' Douglas᎐Kroll transformation. Some of the approximations used in their multiatom calculations have not yet been fully explored for isolated atoms, especially the neglect of matrix elements involving vector products of the momentum and the use of fitting functions. In this investigation, scalar-relativistic Ž . LCGTO calculations without fitting functions were carried out at four levels of approximation, including that employed by HR, for four atoms: Ce, Au, Pb, and Pu. The results of these calculations suggest that the HR approximation should be applicable to atoms through the light actinides, so long as spin᎐orbit effects are unimportant. A comparison of very large basis-set results with results obtained using ordinary-size basis Ž . sets indicates that the valence bonding states from scalar-relativistic LCGTO-FF calculations should be no more sensitive to the orbital basis-set size than are their nonrelativistic counterparts.

Spin–orbit interaction in the Douglas–Kroll approach to relativistic density functional theory: the screened nuclear potential approximation for molecules

“…The separation into SO and SR terms is clear for E 1 ½m eff , but not for E 2 ½m eff [17]. The first-order SO operator in E 1 ½m eff is…”

A Scalar Relativistic Full-Potential LCAO Method

“…So far, the scalar relativistic method has been implemented in several methods: the augmented-plane-wave (APW) method, 3) the linearized muffin-tin-orbital (LMTO) method, 4) the Korringa-Kohn-Rostoker (KKR) method, 5) and the linear-combination-of-atomic-orbitals (LCAO) method. [6][7][8][9][10][11][12][13][14][15][16][17][18] In particular, the usefulness of the scalar relativistic formulation given by Koelling and Harmon 19) for the APW, LMTO, and KKR method has been established in the last two decades. On the contrary, there are no standard scalar relativistic formulations for the LCAO method; it is difficult to apply directly the Koelling-Harmon formulation to the LCAO method because this method uses fixed basis sets in contrast to the APW, LMTO, and KKR methods.…”

“…Although this approach encountered a difficulty due to singular behavior of the resultant terms near nuclei, the frozen core approximation has circumvented this difficulty. 11) Another approach [13][14][15][16][17] is to use Douglas-Kroll-Hess (DKH) transformation, [20][21][22] which generates no singular terms in contrast to the case of the FWT transformation. Also, there is an alternative approach which uses pseudopotential for simulating the scalar relativistic effects.…”

Relativistic effects on the structural phase stability of molybdenum

“…Throughout the remainder of this work, it will be assumed that all of the spin-orbit coupling terms in equation ( 3) are neglected to obtain the scalar-relativistic EFP approximation. (A detailed discussion of the separation of the relativistic corrections into scalar-relativistic and spin-orbit coupling terms has been presented elsewhere [23] and will not be repeated here.) Analytical evaluation of the GTO matrix elements for the momentum-space operators in equation ( 3) has not proven to be practical thus far.…”

“…Häberlen and Rösch [5] achieve a further reduction in the resources required for their calculations by dropping all terms in the nuclear-only EFP equation that require p × v n p; this is the HR approximation. A recent series of test calculations on isolated atoms [23] found that the HR approximation produces one-electron eigenvalues for the chemically active valence states that differ little from those obtained with the complete scalar-relativistic Douglas-Kroll-Hess transformation. This then is the version of scalar relativity implemented in GTOFF.…”