Clean and Convenient Tessellations for Number Counting Jastrow Factors

Abstract

We introduce a basis of counting functions that, by cleanly tessellating three dimensional space, allows real space number counting Jastrow factors to be straightforwardly applied to general molecular situations. By exerting direct control over electron populations in local regions of space and encoding pairwise correlations between these populations, these Jastrow factors allow even very simple reference wave functions to adopt nodal surfaces well suited to many strongly correlated settings. Being trivially compatible with traditional Jastrow factors and diffusion Monte Carlo and having the same cubic per-sample cost scaling as a single determinant trial function, these Jastrow factors thus offer a powerful new route to the simultaneous capture of weak and strong electron correlation effects in a wide variety of molecular and materials settings. In multiple strongly correlated molecular examples, we show that even when paired with the simplest possible single determinant reference, these Jastrow factors allow quantum Monte Carlo to out-perform coupled cluster theory and approach the accuracy of traditional multi-reference methods. arXiv:1811.03191v1 [cond-mat.str-el]

A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states

“…31 If the minimum has indeed disappeared, then the only remedy is to improve the ansatz quality, as no amount of statistical precision will allow an optimization to find a minima that is not present. On the bright side, advances in VMC trial functions [60][61][62][63][64][65][66][67][68] offer a strong toolkit for improving ansatz quality, albeit one whose use can increase optimization difficulty by increasing the number of variational parameters. If anything, this reality further motivates the development of optimizers, like the hybrid approach tested here, that are designed to handle large, challenging trial functions.…”

“…Number-counting Jastrow factors are a recently developed 62,63 ansatz component and can be thought of as a many-body Jastrow factor in real space that aims to recover both strong and weak correlation. They are based on a Voronoi partitioning of space, where the population of electrons in each region, N I , is given by a sum of local counting functions C I at each electron coordinate.…”

“…The F IJ and G K are variational parameters though the latter is in practice eliminated with a basis transformation of the region populations and so we only optimize F IJ . 63 State-specific orbital optimization is useful for obtaining accurate VMC results on par-ticular excited state phenomena including charge transfer 44 and core excitations 43 and can avoid some of the pitfalls of state-averaged approaches. 76 Recent work 64,65 with the table method has enabled the efficient calculation of orbital parameter derivatives in MSJ wave functions even for large expansions and we refer the reader to the original publications for details.…”

“…The NCJF was produced using a set of 16 counting regions composed of 8 octants for each carbon atom. 63 Figure 3 shows the predicted excitation energy achieved by the LM and the hybrid method on both the simpler MSJ ansatzes and on all parameter wave functions that include the NCJF and orbital rotations. It is reassuring to find that the hybrid method's results agree with the LM's to within statistical uncertainty.…”

A Promising Intersection of Excited-State-Specific Methods from Quantum Chemistry and Quantum Monte Carlo

“…In pursuit of this challenge, we adopt an approach that combines the advantages of excited-state-specific quantum chemistry, sCI, and variational Monte Carlo (VMC). The combination [57][58][59][60][61][62][63] of sCI and QMC can be especially effective thanks to the determinant expansions' leveraging of wave function sparsity and the efficacy of Jastrow factors [64][65][66][67][68][69][70][71][72][73][74][75][76] for addressing weak correlation effects that sCI is less efficient for. While excited state VMC approaches in this area that use state-averaging are highly effective in many systems, 62,[77][78][79][80][81][82] we choose to employ state-specific formulations of VMC 64,83,84 in order to avoid the same challenges that state-averaged CASPT2 faces in charge transfer states.…”