Cumulants and the Contracted Schrödinger Equation

Abstract

The quantum-mechanical wave function of an N-electron system contains much more information than is required to compute the expectation values for most observables. Because the interactions between electrons are pairwise within the Hamiltonian, the energy may be determined exactly through a knowledge of the two-particle reduced density matrix (2-RDM) [1, 2]. Unlike the unknown dependence of the energy on the one-particle density in density functional theory (DFT) [3], the dependence of the energy on the 2-RDM is linear. The 2-RDM, however, has not replaced the wave function as the fundamental parameter for many-body calculations because not every 2-particle density matrix is derivable from an N-particle wave function. The need for a simple set of necessary and sufficient conditions for ensuring that the 2-RDM may be represented by an N-particle wave function is known as the N-representability problem [4, 5]. Recent theoretical and computational results with the contracted Schrödinger equation (CSE), also known as the density equation, indicate that the CSE offers an accurate, versatile method for generating the 2-RDM without the wave function [6–17]. In the present article we will review the foundations of the CSE method.KeywordsWave FunctionSchrodinger EquationCouple ClusterGrassmann AlgebraReconstruction FormulaThese 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.