The Experts below are selected from a list of 3513 Experts worldwide ranked by ideXlab platform
Eric Neuscamman - One of the best experts on this subject based on the ideXlab platform.
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complementary first and second derivative methods for ansatz optimization in Variational Monte Carlo
Physical Chemistry Chemical Physics, 2019Co-Authors: Leon Otis, Eric NeuscammanAbstract:We present a comparison between a number of recently introduced low-memory wave function optimization methods for Variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors.
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Reduced scaling Hilbert space Variational Monte Carlo.
Journal of Chemical Physics, 2018Co-Authors: Eric NeuscammanAbstract:We show that for both single-Slater-Jastrow and Jastrow geminal power wave functions the formal cost scaling of Hilbert space Variational Monte Carlo can be reduced from fifth to fourth order in the system size, thus bringing it in line with the long-standing scaling of its real space counterpart. While traditional quantum chemistry methods can reduce costs related to the two-electron integral tensor through various tensor decomposition methods, we show that such approaches are ineffective in the presence of Hilbert space Jastrow factors. Instead, we develop a simple semi-stochastic approach that can take similar advantage of the near-sparsity of this four-index tensor. Through demonstrations on alkanes of increasing length, we show that accuracy and overall statistical uncertainty are not meaningfully affected and that a total cost crossover is reached as early as 50 electrons when using a minimal basis. Further study will be needed to assess where the crossover occurs in more compact molecular geometries and larger basis sets and to explore how in that context the crossover can be accelerated.
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reduced scaling hilbert space Variational Monte Carlo
Journal of Chemical Physics, 2018Co-Authors: Eric NeuscammanAbstract:We show that for both single-Slater-Jastrow and Jastrow geminal power wave functions the formal cost scaling of Hilbert space Variational Monte Carlo can be reduced from fifth to fourth order in the system size, thus bringing it in line with the long-standing scaling of its real space counterpart. While traditional quantum chemistry methods can reduce costs related to the two-electron integral tensor through various tensor decomposition methods, we show that such approaches are ineffective in the presence of Hilbert space Jastrow factors. Instead, we develop a simple semi-stochastic approach that can take similar advantage of the near-sparsity of this four-index tensor. Through demonstrations on alkanes of increasing length, we show that accuracy and overall statistical uncertainty are not meaningfully affected and that a total cost crossover is reached as early as 50 electrons when using a minimal basis. Further study will be needed to assess where the crossover occurs in more compact molecular geometries and larger basis sets and to explore how in that context the crossover can be accelerated.We show that for both single-Slater-Jastrow and Jastrow geminal power wave functions the formal cost scaling of Hilbert space Variational Monte Carlo can be reduced from fifth to fourth order in the system size, thus bringing it in line with the long-standing scaling of its real space counterpart. While traditional quantum chemistry methods can reduce costs related to the two-electron integral tensor through various tensor decomposition methods, we show that such approaches are ineffective in the presence of Hilbert space Jastrow factors. Instead, we develop a simple semi-stochastic approach that can take similar advantage of the near-sparsity of this four-index tensor. Through demonstrations on alkanes of increasing length, we show that accuracy and overall statistical uncertainty are not meaningfully affected and that a total cost crossover is reached as early as 50 electrons when using a minimal basis. Further study will be needed to assess where the crossover occurs in more compact molecular geometrie...
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excitation variance matching with limited configuration interaction expansions in Variational Monte Carlo
Journal of Chemical Physics, 2017Co-Authors: Paul J Robinson, Sergio Pineda D Flores, Eric NeuscammanAbstract:In the regime where traditional approaches to electronic structure cannot afford to achieve accurate energy differences via exhaustive wave function flexibility, rigorous approaches to balancing different states’ accuracies become desirable. As a direct measure of a wave function’s accuracy, the energy variance offers one route to achieving such a balance. Here, we develop and test a variance matching approach for predicting excitation energies within the context of Variational Monte Carlo and selective configuration interaction. In a series of tests on small but difficult molecules, we demonstrate that the approach is effective at delivering accurate excitation energies when the wave function is far from the exhaustive flexibility limit. Results in C3, where we combine this approach with Variational Monte Carlo orbital optimization, are especially encouraging.
Masatoshi Imada - One of the best experts on this subject based on the ideXlab platform.
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mvmc open source software for many variable Variational Monte Carlo method
Computer Physics Communications, 2019Co-Authors: Takahiro Misawa, Masatoshi Imada, Satoshi Morita, Kazuyoshi Yoshimi, Mitsuaki Kawamura, Yuichi Motoyama, Takahiro Ohgoe, Takeo KatoAbstract:Abstract mVMC (many-variable Variational Monte Carlo) is an open-source software package based on the Variational Monte Carlo method applicable for a wide range of Hamiltonians for interacting fermion systems. In mVMC, we introduce more than ten thousands Variational parameters and simultaneously optimize them by using the stochastic reconfiguration (SR) method. In this paper, we explain basics and user interfaces of mVMC. By using mVMC, users can perform the calculation by preparing only one input file of about ten lines for widely studied quantum lattice models, and can also perform it for general Hamiltonians by preparing several additional input files. We show the benchmark results of mVMC for the Hubbard model, the Heisenberg model, and the Kondo-lattice model. These benchmark results demonstrate that mVMC provides ground-state and low-energy-excited-state wave functions for interacting fermion systems with high accuracy. Program summary Program title: mVMC Program Files doi: http://dx.doi.org/10.17632/xhgyp6ncvt.1 Licensing provisions: GNU General Public License version 3 Programming language: C External routines/libraries: MPI, BLAS, LAPACK, Pfapack, ScaLAPACK (optional) Nature of problem: Physical properties (such as the charge/spin structure factors) of strongly correlated electrons at zero temperature. Solution method: Application software based on the Variational Monte Carlo method for quantum lattice model such as the Hubbard model, the Heisenberg model and the Kondo model. Unusual features: It is possible to perform the highly-accurate calculations for ground states in a wide range of theoretical Hamiltonians in quantum many-body systems. In addition to the conventional orders such as magnetic and/or charge orders, user can treat the anisotropic superconductivities within the same framework. This flexibility is the main advantage of mVMC.
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mVMC—Open-source software for many-variable Variational Monte Carlo method
Computer Physics Communications, 2019Co-Authors: Takahiro Misawa, Masatoshi Imada, Satoshi Morita, Kazuyoshi Yoshimi, Mitsuaki Kawamura, Yuichi Motoyama, Takahiro Ohgoe, Takeo KatoAbstract:Abstract mVMC (many-variable Variational Monte Carlo) is an open-source software package based on the Variational Monte Carlo method applicable for a wide range of Hamiltonians for interacting fermion systems. In mVMC, we introduce more than ten thousands Variational parameters and simultaneously optimize them by using the stochastic reconfiguration (SR) method. In this paper, we explain basics and user interfaces of mVMC. By using mVMC, users can perform the calculation by preparing only one input file of about ten lines for widely studied quantum lattice models, and can also perform it for general Hamiltonians by preparing several additional input files. We show the benchmark results of mVMC for the Hubbard model, the Heisenberg model, and the Kondo-lattice model. These benchmark results demonstrate that mVMC provides ground-state and low-energy-excited-state wave functions for interacting fermion systems with high accuracy. Program summary Program title: mVMC Program Files doi: http://dx.doi.org/10.17632/xhgyp6ncvt.1 Licensing provisions: GNU General Public License version 3 Programming language: C External routines/libraries: MPI, BLAS, LAPACK, Pfapack, ScaLAPACK (optional) Nature of problem: Physical properties (such as the charge/spin structure factors) of strongly correlated electrons at zero temperature. Solution method: Application software based on the Variational Monte Carlo method for quantum lattice model such as the Hubbard model, the Heisenberg model and the Kondo model. Unusual features: It is possible to perform the highly-accurate calculations for ground states in a wide range of theoretical Hamiltonians in quantum many-body systems. In addition to the conventional orders such as magnetic and/or charge orders, user can treat the anisotropic superconductivities within the same framework. This flexibility is the main advantage of mVMC.
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Finite-Temperature Variational Monte Carlo Method for Strongly Correlated Electron Systems
Journal of the Physical Society of Japan, 2016Co-Authors: Kensaku Takai, Takahiro Misawa, Youhei Yamaji, Masatoshi ImadaAbstract:A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the Variational Monte Carlo method originally developed for the ground state. ...
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Variational Monte Carlo method for electron phonon coupled systems
Physical Review B, 2014Co-Authors: Takahiro Ohgoe, Masatoshi ImadaAbstract:We develop a Variational Monte Carlo (VMC) method for electron-phonon coupled systems. The VMC method has been extensively used for investigating strongly correlated electrons over the last decades. However, its applications to electron-phonon coupled systems have been severely restricted because of its large Hilbert space. Here, we propose a Variational wave function with a large number of Variational parameters which is suitable and tractable for systems with electron-phonon coupling. In the proposed wave function, we implement an unexplored electron-phonon correlation factor which takes into account the effect of the entanglement between electrons and phonons. The method is applied to systems with diagonal electron-phonon interactions, i.e. interactions between charge densities and lattice displacements (phonons). As benchmarks, we compare VMC results with previous results obtained by the exact diagonalization, the Green function Monte Carlo and the density matrix renormalization group for the Holstein and Holstein-Hubbard model. From these benchmarks, we show that the present method offers an efficient way to treat strongly coupled electron-phonon systems.
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Variational Monte Carlo method combined with quantum number projection and multi variable optimization
Journal of the Physical Society of Japan, 2008Co-Authors: Daisuke Tahara, Masatoshi ImadaAbstract:Variational wave functions used in the Variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed Variational form of the wave functions. We construct a highly generalized Variational form by introducing a large number of Variational parameters to the Gutzwiller–Jastrow factor as well as to the one-body part. Moreover, the projection operator to restore the symmetry of the wave function is introduced. These improvements enable to treat fluctuations with long-ranged as well as short-ranged correlations. A highly generalized wave function is implemented by the Pfaffians introduced by Bouchaud et al. , together with the stochastic reconfiguration method introduced by Sorella for the parameter optimization. Our framework offers much higher accuracy for strongly correlated electron systems than the conventional Variational Monte Carlo methods.
Naoto Umezawa - One of the best experts on this subject based on the ideXlab platform.
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quantum Monte Carlo study of first row atoms using transcorrelated Variational Monte Carlo trial functions
Journal of Chemical Physics, 2007Co-Authors: Rajendra Prasad, Naoto Umezawa, Dominik Domin, Romelia Salomonferrer, William A. LesterAbstract:The effect of using the transcorrelated Variational Monte Carlo (TC-VMC) approach to construct a trial function for fixed node diffusion Monte Carlo (DMC) energy calculations has been investigated for the first-row atoms, Li to Ne. The computed energies are compared with fixed node DMC energies obtained using trial functions constructed from Hartree-Fock and density functional levels of theory. Despite major VMC energy improvement with TC-VMC trial functions, no improvement in DMC energy was observed using these trial functions for the first-row atoms studied. The implications of these results on the nodes of the trial wave functions are discussed.
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Excited electronic state calculations by the transcorrelated Variational Monte Carlo method: application to a helium atom.
Journal of Chemical Physics, 2004Co-Authors: Naoto Umezawa, Shinji TsuneyukiAbstract:We have implemented the excited electronic state calculations for a helium atom by the transcorrelated Variational Monte Carlo (TC-VMC) method. In this method, Jastrow-Slater-type wave function is efficiently optimized not only for the Jastrow factor but also for the Slater determinant. Since the formalism for the TC-VMC method is based on the variance minimization, excited states as well as the ground state calculations are feasible. It is found that both the first and the second excitation energies given by TC-VMC are much closer to the experimental data than those given by the Variational Monte Carlo method with using the Hartree–Fock orbitals. The successful results in the TC-VMC method are considered to be due to the nodal optimization of the wave functions.
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transcorrelated method for electronic systems coupled with Variational Monte Carlo calculation
Journal of Chemical Physics, 2003Co-Authors: Naoto Umezawa, Shinji TsuneyukiAbstract:A Jastrow–Slater-type wave function is often used as a trial function for precise calculations of the total energy of electronic systems, where the correlation effect is taken into account by the Jastrow factor that directly depends on the distance between electrons. Since many-body integrals are inevitable there, the calculation totally depends on Monte Carlo sampling, and so, except for very simple cases, it is very difficult to optimize one-body wave functions in the Slater determinant which determine the nodal surfaces of the total wave function. Here we propose and demonstrate that the total wave function is efficiently optimized by coupling an ordinary Variational Monte Carlo (VMC) technique with the transcorrelated method, in which the one-body wave functions are definitely obtained by solving Hartree–Fock-type self-consistent-field (SCF) equations derived from the similarity-transformed Hamiltonian. It is shown that the present method reproduces about 90% of the correlation energy for helium-like ...
William A. Lester - One of the best experts on this subject based on the ideXlab platform.
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quantum Monte Carlo study of first row atoms using transcorrelated Variational Monte Carlo trial functions
Journal of Chemical Physics, 2007Co-Authors: Rajendra Prasad, Naoto Umezawa, Dominik Domin, Romelia Salomonferrer, William A. LesterAbstract:The effect of using the transcorrelated Variational Monte Carlo (TC-VMC) approach to construct a trial function for fixed node diffusion Monte Carlo (DMC) energy calculations has been investigated for the first-row atoms, Li to Ne. The computed energies are compared with fixed node DMC energies obtained using trial functions constructed from Hartree-Fock and density functional levels of theory. Despite major VMC energy improvement with TC-VMC trial functions, no improvement in DMC energy was observed using these trial functions for the first-row atoms studied. The implications of these results on the nodes of the trial wave functions are discussed.
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CHARACTERISTICS OF ELECTRON MOVEMENT IN Variational Monte Carlo SIMULATIONS
Journal of Chemical Physics, 1994Co-Authors: M.m. Soto, William A. LesterAbstract:Improving the efficiency of quantum Monte Carlo (QMC) to make possible the study of large molecules poses a great challenge. Evaluating the efficiency of Monte Carlo sampling, however, is at a rudimentary level and in need of new algorithms. Instead of the autocorrelation time as an efficiency measure for Monte Carlo simulations, we propose a direct method to characterize the movement of electrons in atoms or molecules during Variational Monte Carlo computations. Further, the approach makes possible an efficient diagnostic tool to understand objectively many interesting issues in QMC. The usefulness of the method is demonstrated by comparisons among improved Metropolis algorithms and the original Metropolis algorithm. We also present an optimization method for choosing step sizes for Monte Carlo walkers. These step sizes are governed by the acceptance ratio of the electrons closest to the heaviest nucleus. Step sizes obtained for Ne and Ar are consistent with those obtained by the autocorrelation approach...
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Quantum and Variational Monte Carlo interaction potentials for Li2 (X 1Σ+g)
Chemical Physics Letters, 1992Co-Authors: R. N. Barnett, William A. LesterAbstract:Abstract Optimized trial functions are used in quantum Monte Carlo and Variational Monte Carlo calculations of the Li 2 (X 1 Σ + g ) potential curve. The trial functions used are a product of a Slater determinant of molecular orbitals multiplied by correlation functions of electron—nuclear and electron—electron separation. The parameters of the determinant and correlation functions are optimized simultaneously by reducing the deviations of the local energy E L ( E L Ψ −1 T H Ψ T , where Ψ T denotes a trial function) over a fixed sample. At the equilibrium separation, the Variational Monte Carlo and quantum Monte Carlo methods recover 68% and 98% of the correlation energy, respectively. At other points on the curves, these methods yield similar accuracies.
Shinji Tsuneyuki - One of the best experts on this subject based on the ideXlab platform.
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Excited electronic state calculations by the transcorrelated Variational Monte Carlo method: application to a helium atom.
Journal of Chemical Physics, 2004Co-Authors: Naoto Umezawa, Shinji TsuneyukiAbstract:We have implemented the excited electronic state calculations for a helium atom by the transcorrelated Variational Monte Carlo (TC-VMC) method. In this method, Jastrow-Slater-type wave function is efficiently optimized not only for the Jastrow factor but also for the Slater determinant. Since the formalism for the TC-VMC method is based on the variance minimization, excited states as well as the ground state calculations are feasible. It is found that both the first and the second excitation energies given by TC-VMC are much closer to the experimental data than those given by the Variational Monte Carlo method with using the Hartree–Fock orbitals. The successful results in the TC-VMC method are considered to be due to the nodal optimization of the wave functions.
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transcorrelated method for electronic systems coupled with Variational Monte Carlo calculation
Journal of Chemical Physics, 2003Co-Authors: Naoto Umezawa, Shinji TsuneyukiAbstract:A Jastrow–Slater-type wave function is often used as a trial function for precise calculations of the total energy of electronic systems, where the correlation effect is taken into account by the Jastrow factor that directly depends on the distance between electrons. Since many-body integrals are inevitable there, the calculation totally depends on Monte Carlo sampling, and so, except for very simple cases, it is very difficult to optimize one-body wave functions in the Slater determinant which determine the nodal surfaces of the total wave function. Here we propose and demonstrate that the total wave function is efficiently optimized by coupling an ordinary Variational Monte Carlo (VMC) technique with the transcorrelated method, in which the one-body wave functions are definitely obtained by solving Hartree–Fock-type self-consistent-field (SCF) equations derived from the similarity-transformed Hamiltonian. It is shown that the present method reproduces about 90% of the correlation energy for helium-like ...
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Variational Monte Carlo study of isotope effect on hydrogen bonded materials
Solid State Communications, 1995Co-Authors: Yuji Suwa, Shinji TsuneyukiAbstract:Abstract A Variational Monte Carlo calculation is performed to investigate the origin of large isotope effects in ferroelectric or antiferroelectric phase transitions of hydrogen bonded materials. Non-adiabatic coupling between an electron and a nucleus is especially considered in the Variational wavefunction. A characteristic feature of the hydrogen bond is that, in a certain range of oxygen-oxygen distance, two stable states for a hydrogen (deuteron) nucleus, i.e., a localized state and a tunneling state, is energetically in subtle balance with each other. It is demonstrated that the balance is strongly affected by isotope substitution. This can easily lead to the large isotope effect. However, the difference of the charge state between H and D reported by an x-ray experiment cannot be explained even by including the non-adiabatic effect.
