arXiv:2003.01831 · The Journal of Chemical Physics
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo
P. R. C. Kent, Abdulgani Annaberdiyev, Anouar Benali, M. Chandler Bennett, Edgar Josué Landinez Borda, Peter Doak, Hongxia Hao, Kenneth D. Jordan, Jaron T. Krogel, Ilkka Kylänpää, Joonho Lee, Ye Luo, Fionn D. Malone, Cody Melton, Luboš Mitáš, Miguel A. Morales, Eric Neuscamman, Fernando Agustín Reboredo, Brenda M. Rubenstein, Kayahan Saritas, Shiv Upadhyay, Guangming Wang, Shuai Zhang, Luning Zhao
We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing the accuracy. Advances in real space methods include techniques for accurate computation of bandgaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods, including GW and density functional based techniques. To provide an improved foundation for these calculations, we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.
We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing the accuracy. Advances in real space methods include techniques for accurate computation of bandgaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods, including GW and density functional based techniques. To provide an improved foundation for these calculations, we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.
QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.
The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here, we introduce the theory and algorithm of the method specialized for real materials and present several recent developments. We give a systematic exposition of the key steps of AFQMC, closely tracking the framework of a modern software library we are developing. The building of a Monte Carlo Hamiltonian, projecting to the ground state, sampling two-body operators, phaseless approximation, and measuring ground state properties are discussed in detail. An advanced implementation for multi-determinant trial wave functions is described, which dramatically speeds up the algorithm and reduces the memory cost. We propose a self-consistent constraint for real materials, and discuss two flavors for its realization, either by coupling the AFQMC calculation to an effective independent-electron calculation or via the natural orbitals of the computed one-body density matrix.
Electronic structure quantum Monte Carlo Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. The QMC approaches combine analytical insights with stochastic computational techniques for efficient solution of several classes of important many-body problems such as the stationary Schrödinger equation. QMC methods of various flavors have been applied to a great variety of systems spanning continuous and lattice quantum models, molecular and condensed systems, BEC-BCS ultracold condensates, nuclei, etc. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion Hamiltonians. Some of the key QMC achievements include direct treatment of electron correlation, accuracy in predicting energy differences and favorable scaling in the system size. Calculations of atoms, molecules, clusters and solids have demonstrated QMC applicability to real systems with hundreds of electrons while providing 90-95% of the correlation energy and energy differences typically within a few percent of experiments. Advances in accuracy beyond these limits are hampered by the so-called fixed-node approximation which is used to circumvent the notorious fermion sign problem. Many-body nodes of fermion states and their properties have therefore become one of the important topics for further progress in predictive power and efficiency of QMC calculations. Some of our recent results on the wave function nodes and related nodal domain topologies will be briefly reviewed. This includes analysis of few-electron systems and descriptions of exact and approximate nodes using transformations and projections of the highly-dimensional nodal hypersurfaces into the 3D space. Studies of fermion nodes offer new insights into topological properties of eigenstates such as explicit demonstrations that generic fermionic ground states exhibit the minimal number of two nodal domains. Recently proposed trial wave functions based on Pfaffians with pairing orbitals are presented and their nodal properties are tested in calculations of first row atoms and molecules. Finally, backflow "dressed" coordinates are introduced as another possibility for capturing correlation effects and for decreasing the fixed-node bias.
to develop quantum Monte Carlo (QMC) approaches for excited states and for more systematic and accurate treatment of ground states of strongly correlated sytems and heavier elements. We use the auxiliary-field quantum Monte Carlo (AFQMC) framework, which is a many-body total energy method that looks like many coupled mean-field calculations. I will discuss this method’s relations and dierences with traditional density-functional and quantum chemistry methods, and with other forms of QMC. The AFQMC method uses importance-sampled random walks in the space of nonorthogonal Slater determinants to project out the many-body ground state, or excited state. The random walks are constrained by a trial wave function (TWF) to remove the so-called sign problem, giving approximate (but non-perturbative) results. With singledeterminant TWFs from Hartree-Fock or density-functional theory (DFT), this approach can be thought of as a post-DFT method with no parameter. In this form, the accuracy is typically comparable to the quantum chemistry coupled-cluster CCSD(T) method near equilibrium geometries, and better than CCSD(T) when bonds are stretched. The computational cost of AFQMC scales as N 3 with characteristic size of the system. Its accuracy can be further improved at the cost of increased computing (releasing the constraint) or better TWF. With AFQMC, we can systematically target selected orbitals to correlate. This allows many-body calculations in solids with a frozen core, with down-folded Hamiltonians, or possibly embeded in a DFT calculations to extend scales. Results from a few on-going applications will be presented, including band structures in simple solids, magnetic phases in MnO, and Cobalt adsoption on graphene.
auxiliary-field quantum Monte Carlo (AFQMC) is a systematically improvable many-body method, but its application to extended solids has been severely limited by unfavorable computational scaling and memory requirements that obstruct rigorous access to the thermodynamic and complete-basis-set limits. By combining tensor hypercontraction with k -point symmetry, we reduce the computational and memory scaling of AFQMC for solids to O ( N 3 ) and O ( N 2 ) , respectively, with an arbitrary basis, comparable to diffusion Monte Carlo. This enables simultaneous, controlled extrapolation of full-system AFQMC calculations to the thermodynamic and complete-basis-set limits across insulating, metallic, and strongly correlated solids, without embedding, local approximations, empirical finite-size corrections, or composite schemes. Our results establish AFQMC as a general-purpose, systematically improvable alternative to diffusion Monte Carlo and coupled-cluster methods for predictive simulations of solids, enabling accurate energies and magnetic observables within a unified framework.
The auxiliary‐field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time‐independent Schrödinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of nonorthogonal Slater determinants, the method resembles an ensemble of density‐functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low‐power of system size, similar to the corresponding independent‐electron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high‐performance computing platforms and numerical libraries. In this review, we provide a self‐contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure of molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Materials Science Computer and Information Science > Computer Algorithms and Programming