Ideas of relativistic quantum chemistry

Abstract

The basic ideas of relativistic quantum chemistry are highlighted, with the most important ingredients summarised as follows. (1) The restricted kinetic balance (RKB) condition, being both necessary and sufficient, serves as the cornerstone for the matrix representation of the Dirac-based Hamiltonian. (2) The concept of matrix transformation plays the key role in formulating two-component relativistic theories. Some popular ones, albeit presented as operators, are de facto matrix formulations in terms implicitly of the RKB condition. They merely make simple things complicated as a one-step block-diagonalization of the matrix Dirac equation can do the whole job. (3) The computational efficiency for both four- and two-component relativistic theories can be gained by means of the simple chemical idea of ‘from atoms to molecule’ without recourse to mathematical tricks. The two branches of relativistic theories have thus been made fully equivalent in all the aspects of simplicity, accuracy, and efficiency. It is concluded that the best relativistic electrons-only Hamiltonian has been found, which can be combined with any know-how correlation methods for electronic structure calculations of all the atoms in the Periodic Table. Most amazingly, the new quantum mechanical equation serves as a seamless bridge between the Schrödinger and Dirac equations. In short, the ‘relativity problem’ in chemistry has been solved.

Keywords:

• relativistic quantum chemistry
• kinetic balance
• matrix transformation
• exact two-component Hamiltonian
• ‘from atoms to molecule’

Acknowledgments and dedication

The research of this work was supported by grants from the National Natural Science Foundation of China (Project Nos. 20625311 and 20773003) and from MOST of China (Project Nos. 2006CB601103 and 2006AA01A119)). The author is also grateful to the Alexander-von-Humboldt Foundation for a F.W. Bessel fellowship.

Notes

Note

1. The total number of effective equations, 314, coincides by chance with the birthday, March 14, 1879, of Albert Einstein, the founder of special theory of relativity.