ICCAS OpenIR
Matrix formulation of direct perturbation theory of relativistic effects in a kinetically balanced basis
Kutzelnigg, Werner1; Liu, Wenjian2,3
2008-06-16
Source PublicationCHEMICAL PHYSICS
ISSN0301-0104
Volume349Issue:1-3Pages:133-146
AbstractDirect perturbation theory (DPT) and its quasi-degenerate version (QD-DPT) in a matrix formulation, i.e. DPT-mat and QD-DPT-mat are derived from the matrix representation of the Dirac operator in a kinetically balanced basis, both in the intermediate and the unitary normalization. The results are compared with those of an earlier formulation in terms of operators and wave functions. In the wave function formulation it is imperative to describe the weak singularities of the wave function at the position of a point nucleus correctly and to satisfy the key relation between large and small components locally. This formulation is incompatible with an expansion in a regular basis. In a matrix formulation in a kinetically balanced basis both the large and the small component are expanded in regular basis sets and the key relation is only satisfied in the mean. DPT is essentially a theory at bispinor level. Although it is possible to eliminate the small component to arrive at a quasi-relativistic theory, this requires some care. A both compact and numerically stable formulation is in terms of the large and the small component. The generalization from a theory for one state to a quasi-degenerate formulation for a set of states, is very simple in the matrix formulation, but rather complicated and somewhat indirect at wave function level, where an intermediate quasi-relativistic step is needed. The advantage of the matrix formulation is particularly pronounced in the unitary normalization. (c) 2008 Elsevier B.V. All rights reserved.
KeywordDirect Perturbation Theory Relativistic Effects Kinetic Balance
DOI10.1016/j.chemphys.2008.01.056
Indexed BySCI
Language英语
WOS IDWOS:000257538300016
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.iccas.ac.cn/handle/121111/64552
Collection中国科学院化学研究所
Corresponding AuthorKutzelnigg, Werner
Affiliation1.Ruhr Univ Bochum, Lehrstuhl Theoret Chem, D-44780 Bochum, Germany
2.Peking Univ, Coll Chem & Mol Engn, State Key Lab Rare Earth Mat Chem & Applicat, Beijing Natl Lab Mol Sci,Inst Theoret & Computat, Beijing 100871, Peoples R China
3.Peking Univ, Ctr Computat Sci & Engn, Beijing 100871, Peoples R China
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Kutzelnigg, Werner,Liu, Wenjian. Matrix formulation of direct perturbation theory of relativistic effects in a kinetically balanced basis[J]. CHEMICAL PHYSICS,2008,349(1-3):133-146.
APA Kutzelnigg, Werner,&Liu, Wenjian.(2008).Matrix formulation of direct perturbation theory of relativistic effects in a kinetically balanced basis.CHEMICAL PHYSICS,349(1-3),133-146.
MLA Kutzelnigg, Werner,et al."Matrix formulation of direct perturbation theory of relativistic effects in a kinetically balanced basis".CHEMICAL PHYSICS 349.1-3(2008):133-146.
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