Abstract
TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.
Highlights
The solution of the many-body Schrödinger equation, which describes the interaction between electrons and ions at the quantum mechanical level, represents a fundamental challenge in computational chemistry, condensed matter, and materials science
An important application for Quantum Monte Carlo (QMC) is the description of systems interacting through weak van der Waals dispersive interactions, which are fundamental in supramolecular chemistry, layered and porous materials, molecular crystals, adsorption of molecules on surfaces, and so on. vdW interactions play a major role in non-covalent intra-molecular bonds, which result from the interplay of forces of different nature, including electrostatic contributions
TURBORVB with JDFT, Jastrow correlated SD (JSD), and JAGP guiding functions has been applied to several interesting systems, such as molecular hydrogen adsorbed on benzene,151 benzene dimers,43 graphite layers,152 water or methanol molecules adsorbed on a clay surface,153 and metallic clusters,154 and to evaluate the cohesive energies of B2O3 polymorphs
Summary
The solution of the many-body Schrödinger equation, which describes the interaction between electrons and ions at the quantum mechanical level, represents a fundamental challenge in computational chemistry, condensed matter, and materials science. This review is organized as follows: in Sec. II, we briefly explain the fundamental QMC algorithms implemented in TURBORVB, namely, the VMC and LRDMC; in Sec. III, we describe the RVB WF; in Sec. IV, we extend the WF to treat periodic systems; in Sec. V, we introduce the DFT algorithm efficiently implemented in TURBORVB; in Sec. VI, we describe the way energy derivatives are computed (e.g., atomic forces) by means of AAD; in Sec. VII, we list the TURBORVB steps to optimize a many-body WF; in Sec. VIII, we introduce the first and the second-order Langevin molecular dynamics implemented in TURBORVB; in Sec. IX, we summarize the typical QMC workflow from the WF generation to the final LRDMC calculation; in Sec. X, we show weak and strong scaling results of TURBORVB, measured on the Marconi/CINECA supercomputer; in Sec. XI, we list the physical properties that can be calculated by TURBORVB; in Sec. XII, we review the major TURBORVB applications done so far; and in Sec. XIII, we introduce a Python-based workflow system, named TURBO-GENIUS
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