Preliminary results on approximating a wavefunction as an unconstrained sum of Slater determinants

A multiparticle wavefunction, which is a solution of the multiparticle Schrödinger equation, satisfies the antisymmetry condition, thus making it natural to approximate it as a sum of Slater determinants. Many current methods do so but, in addition, they impose structural constraints on the Slater determinants, such as orthogonality between orbitals or a particular excitation pattern. By removing these constraints, we hope to obtain much more efficient expansions. We use an integral formulation of the problem, a Green’s function iteration, and a fitting procedure based on the computational paradigm of separated representations. For constructing and solving a matrix-integral system of equations derived from antisymmetric inner products, we develop new algorithms with computational complexity competitive with current methods. We describe preliminary numerical results and make some observations.