Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

Abstract

Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.

Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

“…[40,41] The Jastrow function can also be augmented by a linear combination of determinants. [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] In the transcorrelated method, a similarity transformation is performed on the Hamiltonian using an explicitly correlated function. [50,66,67] Explicit dependence on r 12 term in the wave function has been implemented in other methods such as MP2-R12, [68][69][70][71] and coupled cluster, [72][73][74][75][76][77] and geminal augmented MCSCF.…”

Fractional Charge by Fixed-Node Diffusion Monte Carlo Method

“…The total FNDMC energy is an upper bound to the exact energy 10 and the related FN bias goes quadratically with the nodal displacement error 4 . Ψ T can be well sophisticated so that the related FN bias becomes negligible 11,12 , nevertheless, practical FNDMC feasible for large systems requires simple and efficient ansätze like the popular Slater-Jastrow wave function 13 , Ψ T = Ψ S J, where Ψ S is a single Slater determinant and J is a positive-definite explicit correlation Jastrow term 14 .…”

Using local operator fluctuations to identify wave function improvements

“…Other states exist within the full orbital space, but their inclusion yields only small improvement to the final wave function and system energy. Because different methods of determinant selection produce significantly different rates of energy convergence [30], the covariance-based method we have described can yield interesting results even at the level of a multi-Slater-Jastrow ansatz. Our chief objective in this section is to show that the covariance technique can select the most significant determinants for a particular molecule before performing a variational optimization of the wave function.…”