Reduced Density Matrices in Quantum Chemistry

The articles in this special issue of the International Jouhal of Quantum Chemistry are on reduced density matrix theory.This issue, together with six articles in two previous issues, form the proceedings of a conference on reduced density matrices

John E. Harriman

Jerzy Ciosłowski

An explicit expression relating the magnitude of the fifth-order off-diagonal cusp in the real part of the one-electron reduced density matrix to the “on-top” two-electron density is derived in a rigorous manner from the behavior of the underlying electronic wavefunction at the electron–electron coalescence. The implications of the presence of this cusp upon electronic structure calculations of quantum chemistry and solid-state physics, including the limits imposed upon their accuracy, are elucidated. In particular, the power-law decay of the occupation numbers of the natural orbitals is demonstrated for 1S states of systems composed of arbitrary even numbers of electrons. The practical importance of analogous off-diagonal cusps in many-electron reduced density matrices is briefly discussed.

Adam E. Rothman

Hinne Hettema

Charles‐Émile Fecteau, Hubert Fortin, Samuel Cloutier +1 more

Eigenvectors of the reduced Bardeen–Cooper–Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this contribution, we report optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson–Gaudin pairs. Physical basis expressions were originally reported by Gorohovsky and Bettelheim [Phys. Rev. B 84, 224503 (2011)]. In each case, the expressions scale like O(N4), with the most expensive step being the solution of linear equations. Analytic gradients are also reported in the physical basis. These expressions are an important step toward practical mean-field methods to treat strongly correlated electrons.