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.
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.
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 chemistry is a useful tool that provides insight into the properties and behavior of chemical systems. Modern software packages have made quantum chemistry methods more easily accessible, and the continued increase in available computational resources has allowed them to be applied to larger systems at higher levels of theory. Two significant problems that the field faces are the high computational complexity of high-level methods and the shift toward parallelism in high performance computing architectures. This work examines the treatment of weakly interacting molecular systems with the fixed-node diffusion Monte Carlo (DMC) method. DMC and other quantum Monte Carlo (QMC) methods offer a possible solution to both of the aforementioned problems: they can produce near-exact results with a lower scaling (with respect to problem size) than other similarly-accurate methods, and they are inherently parallel, so there is little additional cost associated with distributing the work of a single QMC calculation across a large number of processing units. The only error in DMC that is not systematically improvable is the constraint of a fixed nodal surface of the many-particle wave function of the system being studied. There are many cases in which a single Slater determinant trial function is sufficient to obtain accurate results, but there are others in which more sophisticated multi-determinant trial functions are necessary. Furthermore, it is non-trivial to generate nodal surfaces of similar quality for isolated and interacting molecules, so cancellation of errors is not guaranteed. We examine the use of different single- and multi-determinant trial functions in DMC calculations on small chemical systems with the goal of further understanding how to construct appropriate trial functions for molecules and clusters.
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.
Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.
Abstract In this paper Grossman reported pseudopotential fixed-node diffusion QMC calculations of atomization energies for the Gl set of 55 small molecules,0 a standard benchmark set for testing methods in quantum chemistry. To maintain the uniformity in the calculations, they were carried out with the same basis sets and orbital types for single-determinant trial functions and effective core potentials (with a few exceptions). Variational QMC was used to optimize the determinan Jastrow trial functions. The mean absolute deviation EMAD in atomization energy from the experimental values was found to be 2.9 kcal/mol, the maximum deviation was 14 kcal/mol (for SO2), and the next five largest deviations were 7-8 kcal/mol. A comparison with results from other methods tested with the Gl set shows the FN-DQMC method to be competitive. For EMAD the list is: FN-DQMC, 2.9 kcal/mol; DFT (LDA), 40 kcal/mol; DFT (B3LYP or B3PW91), 2.9 kcal/mol; CCSD(T)/aug-cc-pVQZ, 2.8 kcal/mol; CCSD(T)/extrapolated, 1.3 kcal/mol; semi-empirical G1 theory, 1.6 kcal/mol. Additional calculations with different trial functions indicated that node location errors could be significantly reduced with multi determinant trial functions. Computational effort was not compared, but linear scaling for FN-DQMC was mentioned as an important advantage for QMC. 0J. A. Pople, M. Head-Gordon, D. J. Fox, K. Raghavachari, and L. A. Curtiss, Gaussian-I theory - A general procedure for prediction of molecular energies, J. Chem. Phys. 90, 5622 (1989).
The fixed-node diffusion quantum Monte Carlo (DMC) method is the most accurate method known for calculating the energies of large many-particle quantum systems. The key element of the method is the development of accurate trial many-body wavefunctions which control the statistical efficiency of the calculations and the accuracy obtained. Accurate wavefunctions can be obtained by building correlation effects on top of mean field descriptions such as density functional theory. The wavefunctions can be improved by introducing multi-determinants, pairing functions, and backflow transformations. The calculations are expensive, but the method scales well with system size and calculations on 1000 particles are possible. Some recent applications of the DMC method to atoms, molecules and solids will be presented.