Barrier Heights in Quantum Monte Carlo with Linear-Scaling Generalized-Valence-Bond Wave Functions

We investigate here the performance of our recently developed linear-scaling Jastrow-generalized-valence-bond (J-LGVB) wave functions based on localized orbitals, for the quantum Monte Carlo (QMC) calculation of the barrier heights and reaction energies of five prototypical chemical reactions. Using the geometrical parameters from the Minnesota database collection, we consider three hydrogen-exchanges, one heavy-atom exchange, and one association reaction and compare our results with the best available experimental and theoretical data. For the three hydrogen-exchange reactions, we find that the J-LGVB wave functions yield excellent QMC results, with average deviations from the reference values below 0.5 kcal/mol. For the heavy-atom exchange and association reactions, additional resonance structures are important, and we therefore extend our original formulation to include multiple coupling schemes characterized by different sets of localized orbitals. We denote these wave functions as J-MC-LGVB, where MC indicates the multiconfiguration generalization, and show that such a form leads to very accurate barrier heights and reaction energies also for the last two reactions. We can therefore conclude that the J-LGVB theory for constructing QMC wave functions, with its multiconfiguration generalization, is valid for the study of large portions of ground-state potential energy surfaces including, in particular, the region of transition states

Size-Extensive Wave Functions for Quantum Monte Carlo: A Linear Scaling Generalized Valence Bond Approach

We propose a new class of multideterminantal Jastrow–Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a coupling scheme between electron pairs which progressively includes new classes of excitations in the determinantal component of the wave function. In this scheme, we exploit the local nature of the orbitals to construct wave functions which have increasing complexity but scale linearly. The resulting wave functions are compact, can correlate all valence electrons, and are size extensive. We assess the performance of our wave functions in QMC calculations of the homolytic fragmentation of N–N, N–O, C–O, and C–N bonds, very common in molecules of biological interest. We find excellent agreement with experiments, and, even with the simplest forms of our wave functions, we satisfy chemical accuracy and obtain dissociation energies of equivalent quality to the CCSD­(T) results computed with the large cc-pV5Z basis set