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Setting Limits on Supersymmetry Using Simplified Models
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Localization scheme for relativistic spinors.

J Ciupka1, M Hanrath, M Dolg

  • 1Institute for Theoretical Chemistry, University of Cologne, Cologne, Germany. ciupkaj@uni-koeln.de

The Journal of Chemical Physics
|January 10, 2012
PubMed
Summary
This summary is machine-generated.

A novel method introduces approximate joint diagonalization for calculating localized complex-valued orbitals, applicable to various electronic structures. This advance enables new local correlation methods in relativistic quantum chemistry.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Relativistic Quantum Mechanics

Background:

  • Accurate calculation of localized electron functions is crucial for understanding chemical bonding and electronic properties.
  • Existing methods for localizing orbitals face limitations with complex-valued and multi-component wavefunctions.

Purpose of the Study:

  • To develop a new, versatile method for determining localized complex-valued one-electron functions.
  • To enable the formulation of local correlation methods within a multi-component relativistic framework.

Main Methods:

  • The study employs approximate joint diagonalization (AJD) of Hermitian matrices, adapted from electronic signal processing.
  • A novel iterative 2x2 pair rotating basis is used to reformulate localization criteria for complex-valued spinors.
  • The method is applied to heavy and super-heavy element systems using Kramers-restricted self-consistent field and relativistic two-component pseudopotentials.

Main Results:

  • The method successfully calculates localized orbitals for one-component systems, yielding results consistent with standard quantum chemical software (e.g., Foster-Boys, Pipek-Mezey).
  • For multi-component systems, it generates complex-valued spinors that satisfy chosen localization criteria.
  • Demonstrates the feasibility of formulating local correlation methods in a multi-component relativistic context.

Conclusions:

  • The new AJD-based approach provides a robust and general method for orbital localization, particularly for complex-valued and relativistic systems.
  • This work opens avenues for advanced local correlation studies in heavy element chemistry, accounting for spin-orbit coupling effects.