Optimized Jastrow–Slater wave functions for ground and excited states: Application to the lowest states of ethene

Abstract

A quantum Monte Carlo method is presented for determining multideterminantal Jastrow-Slater wave functions for which the energy is stationary with respect to the simultaneous optimization of orbitals and configuration interaction coefficients. The approach is within the framework of the so-called energy fluctuation potential method which minimizes the energy in an iterative fashion based on Monte Carlo sampling and a fitting of the local energy fluctuations. The optimization of the orbitals is combined with the optimization of the configuration interaction coefficients through the use of additional single excitations to a set of external orbitals. A new set of orbitals is then obtained from the natural orbitals of this enlarged configuration interaction expansion. For excited states, the approach is extended to treat the average of several states within the same irreducible representation of the pointgroup of the molecule. The relationship of our optimization method with the stochastic reconfiguration technique by Sorella et al. is examined. Finally, the performance of our approach is illustrated with the lowest states of ethene, in particular with the difficult case of the 1(1)B(1u) state.

Quantum Monte Carlo for noncovalent interactions: an efficient protocol attaining benchmark accuracy

“…Since the concept of error cancellation is not limited to one determinant, similar behaviour is expected in case of noncovalent interactions between open-shell systems where completeactive-space wave functions capturing multi-reference effects 41,42 may be used instead of Hartree-Fock/Kohn-Sham determinants.…”

Energy and Variance Optimization of Many-Body Wave Functions

“…The reason is that, for a sufficiently flexible variational wave function, it is possible to lower the energy on the finite set of Monte Carlo (MC) configurations on which the optimization is performed, while in fact raising the true expectation value of the energy. On the other hand, if the variance of the local energy is minimized, each term in the sum over MC configurations is bounded from below by zero and the problem is far less severe [5].Nevertheless, in recent years several clever methods have been invented that optimize the energy rather than the variance [6,7,8,9,10,11,12,13,14,15]. The motivations for this are four fold.…”

“…Nevertheless, in recent years several clever methods have been invented that optimize the energy rather than the variance [6,7,8,9,10,11,12,13,14,15]. The motivations for this are four fold.…”

“…The generalized eigenvalue method of Nightingale and Melik-Alaverdian [9] is the most efficient choice for optimizing linear parameters, but for nonlinear parameters they use variance minimization. The effective fluctuation potential method [10,11,12,13,14] is the most successful method for nonlinear parameters and has been applied to optimizing the orbitals [11,14] and the linear coefficients in a multideterminantal wave function [12,14], and, has been extended to excited states [14]. It is not straightforward to use this method to optimize Jastrow factors, but Prendergast, Bevan and Fahy [13] have formulated a version for periodic systems and have optimized an impressively large number of parameters.…”

“…However, the method is complex and needs to be reformulated for finite systems. The stochastic reconfiguration method [15] is related to the effective fluctuation potential method and is simpler but less efficient [14]. The Newton method as implemented in Ref.…”