Localization scheme for relativistic spinors

Ciupka, J.; Hanrath, M.; Dolg, M.

doi:doi:10.1063/1.3670415

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Communication: The reason why +c ZnO surface is less stable than −c ZnO surface: First-principles calculation

It has been experimentally shown that an O(−c)-polar ZnO surface is more stable than a Zn(+c)-polar surface in H2 ambient. We applied first-principles calculations to investigating the polarity dependence on the stability at the electronic level. The calculations revealed that the −c surface terminated with H atom was stable maintaining a wurtzite structure, whereas the +c surface was unstable due to the change of coordination numbers of Zn at the topmost surface from four (wurtzite) to six (roc...

Unambiguous optimization of effective potentials in finite basis sets

The optimization of effective potentials is of interest in density-functional theory (DFT) in two closely related contexts. First, the evaluation of the functional derivative of orbital-dependent exchange-correlation functionals requires the application of optimized effective potential methods. Second, the optimization of the effective local potential that yields a given electron density is important both for the development of improved approximate functionals and for the practical application o...

A new method to determine localized complex-valued one-electron functions in the occupied space is presented. The approach allows the calculation of localized orbitals regardless of their structure and of the entries in the spinor coefficient matrix, i.e., one-, two-, and four-component Kramers-restricted or unrestricted one-electron functions with real or complex expansion coefficients. The method is applicable to localization schemes that maximize (or minimize) a functional of the occupied spinors and that use a localization operator for which a matrix representation is available. The approach relies on the approximate joint diagonalization (AJD) of several Hermitian (symmetric) matrices which is utilized in electronic signal processing. The use of AJD in this approach has the advantage that it allows a reformulation of the localization criterion on an iterative 2 × 2 pair rotating basis in an analytical closed form which has not yet been described in the literature for multi-component (complex-valued) spinors. For the one-component case, the approach delivers the same Foster-Boys or Pipek-Mezey localized orbitals that one obtains from standard quantum chemical software, whereas in the multi-component case complex-valued spinors satisfying the selected localization criterion are obtained. These localized spinors allow the formulation of local correlation methods in a multi-component relativistic framework, which was not yet available. As an example, several heavy and super-heavy element systems are calculated using a Kramers-restricted self-consistent field and relativistic two-component pseudopotentials in order to investigate the effect of spin-orbit coupling on localization.

Article Outline

INTRODUCTION
NOTATION
AJD APPROACH TO RELATIVISTIC LOCALIZATION
1. The approximate joint diagonalization problem
2. Foster-Boys criterion
3. Pipek-Mezey criterion
4. AJD in Kramers-restricted framework
5. Convergence
6. CG AJD localization algorithm
APPLICATION TO EXEMPLARY SYSTEMS
DISCUSSION
CONCLUSION

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KEYWORDS and PACS

Keywords

chemistry computing, Hermitian matrices, pseudopotential methods, relativistic corrections, SCF calculations, spin-orbit interactions

PACS

31.30.J-

Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
31.15.xr

Self-consistent-field methods

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.3670415

PUBLICATION DATA

ISSN

0021-9606 (print)

1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef

American Institute of Physics

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