TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo

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.

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

“…In non-covalent interactions, the challenge for FN-DMC is to provide precise and accurate evaluations of the interaction energy E int , despite E int being a tiny fraction of the total energy, e.g., it is circa 1/10 4 of the total energy in the C 60 @ [6]CPPA complex. Precision is achieved by exploiting the almost perfect scaling of DMC on modern supercomputer facilities [42][43][44] and thanks to recent algorithmic improvements which reduced the time-step bias and made DMC up to 100 times more efficient 40 . The FN-DMC setup here employed has been used and validated against experiments and CCSD(T) a number of times, for instance in refs.…”

Candidate structure for the H$_2$-PRE phase of solid hydrogen

“…Therefore, we rely in DFT methods to obtain geometry and phonons in this work. We note that, to our knowledge, there is only one example of FNDMC phonon calculation for diamond [49] using TurboRVB [50].…”

Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo

“…[46] This means that the quality of our solution will depend on the nodal surface resulting from the choice of the functions that form the Slater determinant. The possibility to go beyond the fixed-node approximation and recover even more static electron correlation using a single Slater determinant only by means of the backflow transformation, [17,18,25,47] shadow wave function, [5,6,[48][49][50] or resonating valence bond approach, [51][52][53] is to be underlined and will be presented elsewhere.…”