The symmetry of reduced density matrices. II. Spin-free quantum chemistry and point group symmetry

2009 ◽  
Vol 4 (S3B) ◽  
pp. 675-688
Author(s):  
D. J. Klein
Keyword(s):  
Quantum Chemistry ◽  
Point Group ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Reduced Density

Relativistic Symmetry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Group Theory ◽  
Quantum Chemistry ◽  
Relativistic Quantum ◽  
Point Group ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Finite Point ◽  
Theoretical Concepts ◽  
Relativistic Quantum Chemistry ◽  
Unifying Principles

Symmetry is one of the great unifying principles of physics and chemistry. Symmetry governs the geometry of molecules, as well as their spectra and the shapes of their crystals. The symmetry of a system provides fingerprints that show up under various probes of the system. Knowledge of the symmetry of a system provides us with valuable information about its properties and behavior, and symmetry may also be used to simplify quantum chemical calculations on the system. All this—provided we have the theory and tools to extract this information. The purpose of this chapter is to provide some of the tools to deal with the symmetries of relativistic quantum chemistry and examine the symmetries of the Dirac equation. Most chemists have a good working knowledge of the finite point group symmetry of molecules. Crystallographers and solid state chemists are also familiar with the symmetries of extended and infinite systems. This is usually accompanied by some knowledge of the mathematical discipline of group theory, which provides a powerful tool for the theoretical treatment of symmetry. Group theory in itself is a vast subject, and only a small fraction of it is actively used in physics, and even less in chemistry. For this presentation our selection will be aimed at those aspects of group theory immediately connected to relativistic quantum chemistry either as a foundation for the theory or in its application and interpretation.We will assume that the reader has a solid background in the finite point group symmetry of nonrelativistic quantum chemistry, as well as a familiarity with group theory at the level of a good advanced undergraduate course (e.g., Atkins and Friedman 1997). For completeness and ease of reference, some of the basic features of group theory commonly encountered by chemists are reviewed in appendix C. Group theoretical concepts beyond this level will be introduced in the text as they are needed. In this chapter, we start with a qualitative introduction of double groups and relativistic molecular symmetries, connecting to the more or less phenomenological introduction this subject is frequently accorded in quantum chemistry. The aim is to provide the necessary insight for those who only need an operational familiarity with double groups.

Reduced Density Matrices

2000 ◽  
Author(s):  
A. John Coleman ◽  
Vyacheslav I. Yukalov
Keyword(s):  
Density Matrices ◽  
Reduced Density Matrices ◽  
Reduced Density
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