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.
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.
TurboRVB is a computational package for {\it 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. The electronic wave function (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 product with spin-singlet pairing, or as a Pfaffian, including both singlet and triplet correlations. This wave function can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) ansatz, first proposed by L. Pauling and P. W. Anderson in quantum chemistry and condensed matter physics, 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. 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 is made possible thanks to state-of-the-art stochastic algorithms for energy minimization. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, that is also an ideal environment for exploiting the computational power of modern GPU accelerators.
With the ability to solve the many-body Schrödinger equation accurately, in principle all physics and chemistry could be derived from first principles. However, exact wave functions of realistic and interesting systems are in general unavailable because they are non-deterministic polynomial-hard to compute (Troyer, 2005). This implies that we need to rely on approximations. The variational Monte Carlo (VMC) method is widely used for ground state studies, but requires a trial wave function ansatz which must trade off between efficiency and accuracy. The method also has many common features with machine learning algorithms, and as neural networks have shown impressive power as function approximators, the idea is to use a neural network as the trial wave function guess. For fermionic systems, like electronic structure systems, the wave function needs to obey Fermi-Dirac statistics. This is typically achieved using a Slater determinant. As a neural network hardly can model this feature, our approach is to replace the single-particle functions in the Slater determinant with restricted Boltzmann machines, getting the RBM ansatz. In addition, we add further correlations via so-called Jastrow factors (Drummond, 2004). The de facto standard trial wave function ansatz for electronic structure calculations is the Slater-Jastrow ansatz, which was implemented as a reference. Our primary focus is on closed-shell circular quantum dots, where we compute the ground state energy and electron density of two-dimensional systems with up to 90 electrons and three-dimensional systems with up to 70 electrons. The energy obtained by the RBM ansatz was reasonably close to experimental results, and it gradually became closer as we added more complex correlation factors. For our most complicated Jastrow factor, the energy was found to be lower than the energy provided by the Slater-Jastrow ansatz for small dots, but for larger dots it was slightly higher. However, the one-body density profile reveals that the RBM ansatz gives more distinctly located electrons compared to the Slater-Jastrow ansatz. This can be explained by the way the RBM ansatz models the correlations. From the two-body density profile, we also observe that the repulsive interactions get more significant as we add a Jastrow factor. Based on the electron densities and the energy distribution between kinetic and potential energy, it is certain that the various methods provide different electron configurations. For low-frequency dots, the electron density becomes more localized with an additional radial peak compared to high-frequency dots. This is reminiscent of what is known as Wigner localization (Ghosal, 2007). The computational time consumption was found to be favorable for the RBM ansatz for small systems and the Slater-Jastrow ansatz for large systems. This can be explained by the exploding number of variational parameters in the RBM ansatz as the system sizes increase. The RBM ansatz with Jastrow factors were notably more computationally intensive than the other ansätze, and evidently, there is no reason to use the simplest Jastrow factor when more complicated Jastrow factors are available.
We present the first open access version of the QMeCha (Quantum MeCha) code, a quantum Monte Carlo (QMC) package developed to study many-body interactions between different types of quantum particles, with a modular and easy-to-expand structure. The present code has been built to solve the Hamiltonian of a system that can include nuclei and fermions of different mass and charge, e.g. electrons and positrons, embedded in an environment of classical charges and quantum Drude oscillators. To approximate the ground state of this many-particle operator, the code features different wavefunctions. For the fermionic particles, beyond the traditional Slater determinant, QMeCha also includes Geminal functions such as the Pfaffian, and presents different types of explicit correlation terms in the Jastrow factors. The classical point charges and quantum Drude oscillators, described through different variational ansätze, are used to model a molecular environment capable of explicitly describing dispersion, polarization, and electrostatic effects experienced by the nuclear and fermionic subsystem. To integrate these wavefunctions, efficient variational Monte Carlo and diffusion Monte Carlo protocols have been developed, together with a robust wavefunction optimization procedure that features correlated sampling.
Ab initio quantum Monte Carlo (QMC) methods are state-of-the-art electronic structure calculations based on highly parallelizable stochastic frameworks for accurate solutions of the many-body Schrödinger equation, suitable for modern many-core supercomputer architectures. Despite its potential, one of the major drawbacks that still hinders QMC applications, especially when targeting dynamical properties of large systems or extensive datasets, is the lack of an affordable method to compute atomic forces that are consistent with the corresponding potential energy surfaces (PESs), also known as unbiased atomic forces. Recently, one of the authors in the present paper proposed a way to obtain unbiased forces with the Jastrow-correlated Slater determinant Ansatz, where the determinant part is frozen to the values obtained by a mean-field method, such as density functional theory [K. Nakano, M. Casula, and G. Tenti, Phys. Rev. B 109, 205151 (2024)]. However, the proposed method has a significant drawback for its applications: for a system with N nuclei, one requires 6N additional density functional theory (DFT) calculations to get unbiased forces, which is not negligible as the system size increases. This paper presents a way to replace the 6N DFT calculations with a single coupled-perturbed Kohn-Sham calculation, following the so-called Lagrangian technique established in quantum chemistry. This improves the computational cost and scalability of the method. We also demonstrate that the developed unbiased variational Monte Carlo (VMC) force calculation improves not only the consistency with PESs but also its accuracy, by investigating three molecules from the rMD17 benchmark set, and comparing the unbiased VMC forces with those obtained by the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] calculations. We found that the bare VMC forces are biased from the CCSD(T) ones, while the unbiased ones give values closer to those of the CCSD(T) ones. Our benchmark test also reveals that the unbiased VMC forces yield very consistent values with hybrid and meta generalized gradient approximations (e.g., ωB97X-D3BJ and ωB97M-D3BJ), but do not necessarily yield values that are very close to those of CCSD(T). Our finding paves the way to generate machine learning interatomic potentials based on VMC forces more efficiently and accurately.
Variational quantum Monte Carlo (VMC) method applied to interacting electron systems has played a pivotal role for the studies of electronic states of atoms, molecules and condensed matters. First, the many-body wave functions optimized by the VMC method provide good guiding functions in more accurate, diffusion quantum Monte Carlo (DMC) calculations for identical systems. Second, the VMC calculations themselves can give a good upper bound for the exact ground-state energy of many-electron systems when an appropriate form for the variational wave function is employed. In addition to a conventional form for the variational wave function that is expressed by the product of the Jastrow factor and the single Slater determinant, recent investigations have found that the expression in terms of many Slater determinants can provide a very accurate description of electronic states, especially for intrinsically multi-reference systems, which corresponds to the configuration interaction (CI) expansion method in conventional quantum chemistry. Although the CI method needs an extremely large number of expansion coefficients as variational parameters, the number of parameters can be reduced efficiently by using an idea of (molecular) orbital pair correlations. The purpose of the present paper is to examine the feasibility and usefulness of this idea within the framework of VMC method with the Jastrow–Slater wave function, where the ground state of a water molecule is investigated as a test case. In this study we rely on a variational wave function composed of a product of the Jastrow and Slater parts as 1⁄4 J S; ð1Þ
We present jQMC, a Python-based computational package for {\it ab initio} Quantum Monte Carlo (QMC) simulations, designed for modern GPU-accelerated computing environments. jQMC implements two well-established QMC algorithms: Variational Monte Carlo (VMC) and the lattice-regularized variant of Diffusion Monte Carlo (LRDMC). The employed wave function is a Jastrow factor combined with the antisymmetrized geminal power with spin-singlet and spin-triplet pairings, which contains the single Slater determinant as its special lowest-rank case. The wave function can be initialized from external Hartree-Fock/Density Functional Theory calculations through the TREX-IO library (a common wave-function format across electronic-structure packages) and optimized by stochastic reconfiguration and linear-method energy minimization. One of the prominent features of jQMC is its use of JAX, which enables automatic differentiation for wave function optimization and atomic force calculations, and allows the main QMC algorithms to be Just-In-Time (JIT) compiled and portable across CPU and GPU. jQMC is vectorized over walkers at the top level of the QMC algorithms, providing efficient intra-GPU~(CPU) vectorization. The multi-GPU~(CPU) parallelization is also supported through MPI and JAX sharding. To assess the practical performance of this implementation, we benchmarked jQMC performance on NVIDIA GPUs (A100 and H100) and analyzed CUDA kernels. For the test cases analyzed here, with system sizes up to 160 electrons, the current version of jQMC is faster than TurboRVB, a Fortran90 code implementing the same algorithms and wave functions, once jQMC is run on GPUs. In terms of wall-time, the gain can reach an order of magnitude for VMC, while it is more moderate for LRDMC.