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Relativistic Methods in Computational Quantum Chemistry

  • Paweł TecmerEmail author
  • Katharina BoguslawskiEmail author
  • Dariusz KędzieraEmail author
Reference work entry

Abstract

In this chapter, we briefly discuss the theoretical foundations of relativistic two-component methods used in quantum chemistry calculations. Specifically, we focus on two groups of methods. These are (i) methods based on the elimination of the small component, such as the zeroth-order regular approximation (ZORA), the first-order regular approximation (FORA), and the normalized elimination of small component (NESC) formalisms, and (ii) approaches that use a unitary transformation to decouple the electronic and positronic states such as the Douglas–Kroll–Hess (DKH) and the infinite-order two-component (IOTC) Hamiltonians. Furthermore, we describe the algebraic approach to IOTC and scrutinize pure algebraic schemes that paved the way to the eXact 2-Component (X2C) Hamiltonians taking advantage of the nonsymmetric algebraic Riccati equation (nARE). Finally, we assess the accuracy of the aforementioned methods in calculating core and valence properties of heavy-element compounds and discuss some challenging examples of computational actinide chemistry.

Keywords

Dirac Equation Unitary Transformation Small Component Orbit Coupling Nonrelativistic Quantum Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We gratefully acknowledge the financial support from the National Science Center Poland, Grants No. DEC-2012/07/B/ST4/01347 and No. DEC-2013/11/B/ST4/00771. K.B. acknowledges financial support from a SONATA BIS grant of the National Science Centre, Poland (no. 2015/18/E/ST4/00584). We had many helpful discussions with Prof. Markus Reiher and Prof. Lucas Visscher.

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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Institute of Physics, Faculty of Physics, Astronomy and InformaticsNicolaus Copernicus UniversityToruńPoland
  2. 2.Department of Chemistry and Photochemistry of Polymers, Faculty of ChemistryNicolaus Copernicus UniversityToruńPoland

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