Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants
This work addresses the need for more efficient wavefunction expansions in quantum chemistry, potentially improving accuracy for many-electron systems.
The authors present a method to approximate wavefunctions as unconstrained sums of Slater determinants, removing orthogonality or excitation constraints, with computational complexity competitive to current methods.
The wavefunction for the multiparticle Schrödinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions, and insight into the inherent structure of the wavefunction. 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. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.