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

Abstract

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.

Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: Acrolein in water

“…To implement this idea, further methodological developments are needed and, in particular, we have to devise a different strategy to build the solute wave function when more solvent molecules are included in the system treated at the QMC level. An interesting opportunity in this regard comes from the work of Fracchia et al, 47 where the construction of the wave function is based on the use of localized orbitals and on a modular scheme which allows to treat different parts of the molecular system at different levels. In our case, we need in fact to perform a multiconfiguration calculation on the solute to describe both ground and excited states and maintain an active space of the same size also when explicit solvent molecules are added.…”

Optimized Structure and Vibrational Properties by Error Affected Potential Energy Surfaces

“…Zen et al Page 25 (5) 1628 (3) 7.50e-04 1612 (15) 1618 (7) 1633 (6) 1.00e-03 1662 (41) 1643 (11) 1630 (7) 1 1.00e-10 3795(0) 3795(0) 3796 (0) 5.00e-04 3805 (11) 3801 (6) 3798 (4) 7.50e-04 3815 (22) 3790 (8) 3796 (5) 1.00e-03 3823 (33) 3803 (11) 3787 (6) 3 1.00e-10 3897(0) 3898(0) 3898 (0) 5.00e-04 3920 (12) 3890 (6) 3899 (4) 7.50e-04 3894 (16) 3911 (9) 3891 (6) 1.00e-03 3902 (20) 3915 (13) 3907 (8) a Harmonic frequencies (in cm −1 ) for different mesh types (see description in the text) vs stochastic noise magnitude. Similarly to Figures 1 and 2, each reported frequency value is a single representative case, not the average frequency for the corresponding standard deviation.…”

“…Recent wave function developments include the Jastrowantisymmetrized geminal power (J-AGP), 36 the Pfaffian, 37,38 the backflow, 39 and other multideterminant-Jastrow functions. 40,41 Other QMC schemes beyond the variational ansatz are often based on projection methods. Although they are usually more accurate, they are computationally more demanding.…”

Low-lying Adiabatic Electronic States of NO: a QMC Study

“…al in their study, 18 is the leading term in such a CI expansion. In order to construct the energy curve we have varied the internuclear distance between 0.8 and 3.0 Å including completely the potential well and reaching the dissociation limit.…”

“…Finally, the resulting VMC wave function has been used as the trial wave function for the DMC calculation. Although not precisely the same, this recipe for the construction of the DMC trial wave function for NO ground state is very similar to the QMC generalized valence bond scheme recently introduced by Fracchia et al 18 in their J-LGVB3 form. The J-LGVBn theory is based on a new class of multideterminantal Jastrow-Slater wave functions constructed with localized orbitals.…”