The domain Green’s function Monte Carlo (GFMC) method with the fixed-node approximation is used to calculate the binding energies and correlation energies of most of the first row diatomic molecules. Our results show that the many-electron correlations are significant and that GFMC corrections to Hartree–Fock wave functions produce 80% to 90% of the correlation energy. Our GFMC calculations have an accuracy comparable to or better than standard methods in quantum chemistry.
The domain Green’s function Monte Carlo (GFMC) method with the fixed-node approximation is used to calculate the binding energies and correlation energies of most of the first row diatomic molecules. Our results show that the many-electron correlations are significant and that GFMC corrections to Hartree–Fock wave functions produce 80% to 90% of the correlation energy. Our GFMC calculations have an accuracy comparable to or better than standard methods in quantum chemistry.
Quantum Monte Carlo (QMC) methods have received considerable attention over past decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with the number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multideterminant expansions in QMC and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems.Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations.In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult.In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set.We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions.When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them.In fact, only the explicitly-correlated CCSD(T) method with a large basis set produces more accurate results.Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.
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.
The initiator full configuration interaction quantum Monte Carlo (i-FCIQMC) method has recently been developed as a highly accurate stochastic electronic structure technique. It has been shown to calculate the exact basis-set ground state energy of small molecules, to within modest stochastic error bars, using tractable computational cost. Here, we use this technique to elucidate an often troublesome series of first-row diatomics consisting of Be2, C2, CN, CO, N2, NO, O2, and F2. Using i-FCIQMC, the dissociation energies of these molecules are obtained almost entirely to within chemical accuracy of experimental results. Furthermore, the i-FCIQMC calculations are performed in a relatively black-box manner, without any a priori knowledge or specification of the wave function. The size consistency of i-FCIQMC is also demonstrated with regards to these diatomics at their more multiconfigurational stretched geometries. The clear and simple i-FCIQMC wave functions obtained for these systems are then compared and investigated to demonstrate the dynamic identification of the dominant determinants contributing to significant static correlation. The appearance and nature of such determinants is shown to provide insight into both the i-FCIQMC algorithm and the diatomics themselves.
We investigate the accuracy of trial wave functions for quantum Monte Carlo based on Pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-Pfaffian pairing wave functions. We show that a small number of Pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that Pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.
We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.