Structure of the exact wave function

Abstract

We investigate the structure of the exact wave function as a solution of the Schrödinger equation, aiming the singles and doubles description of the exact wave function. The basis is that the Hamiltonian involves only one and two body operators. We first present two theorems that indicate a possibility of the singles and doubles description of the exact wave function. We then examine the exponential ansatz, as this theorem implies it to be a possible structure of the exact wave function. Variational CCS (singles) wave function is shown to be certainly exact for one particle Hamiltonian. Thouless transformation plays an important role in the formulation. The conventional CCSD (singles and doubles) function is restrictive, even if it is solved variationally. A wider coupled cluster function with general singles and doubles substitution operators (CCGSD) is also not exact for the existence of noncommuting operators. We then analyze some formal properties of the full CI wave function, and finally, we propose an ansatz of the exact wave function and describe the method of solution. It involves successive solutions of the secular equations of the order of singles and doubles. It is variational and we can calculate both ground and excited states.