Symmetry Properties of Reduced Density Matrices and Natural p-States

Abstract

Publisher Summary This chapter discusses symmetry properties of reduced density matrices and natural p -states resulting from a given symmetry behavior of the wave functions, from which the density matrices are constructed. Symmetry properties of p- densities are defined as the diagonal elements of the corresponding density matrices. Reduced density matrices have received increasing interest in quantum-chemical investigations. On one hand, numerical first- and second-order density matrices (one- and two-particle density matrices) for certain states of simple atomic and molecular systems have been calculated starting from rather good approximate wave functions. These matrices are particularly useful for testing the validity of different wave functions of the same system. Different approximations are most conveniently compared in terms of the eigenstates of these matrices— that is, the natural spin-orbitals and natural spin-geminals as well as the corresponding eigenvalues, the occupation numbers. On the other hand, the general properties of these matrices and their eigenstates— that is, those properties that are independent of the nature of the wave functions used in their construction, are especially interesting and some effort has been spent on studying them.