Weighted nodal domain averages of eigenstates for quantum Monte Carlo and beyond

Abstract

We study the nodal properties of many-body eigenstates of stationary Schrödinger equation that affect the accuracy of real-space quantum Monte Carlo calculations. In particular, we introduce weighted nodal domain averages that provide a new probe of nodal surfaces beyond the usual expectations. Particular choices for the weight function reveal, for example, that the difference between two arbitrary fermionic eigenvalues is given by the nodal hypersurface integrals normalized by overlaps with the bosonic ground state of the given Hamiltonian. Noninteracting and fully interacting Be atom with corresponding almost exact and approximate wave functions are used to illustrate several aspects of these concepts. Variational formulations that employ different weights are proposed for prospective improvement of nodes in variational and fixed-node diffusion Monte Carlo calculations.

A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

“…In addition, the results show that areas which show higher node curvatures are also important to be described with sufficient accuracy. Note that due to the wave function continuity its behaviour at the node is one-to-one connected to the exact eigenvalue, see, for example, our recent work [42]. Once this is achieved and the crucial balance between kinetic and potential terms is maintained, the sensitivity to basis set becomes less pronounced.…”