The band structure of silicon is calculated at the $\ensuremath{\Gamma}$, $X$ , and $L$ wave vectors using diffusion quantum Monte Carlo (DMC) methods. Excited states are formed by promoting an electron from the valence band into the conduction band. We obtain good agreement with experiment for states around the gap region, and demonstrate that the method works equally well for direct and indirect excitations, and that one can calculate many excited states at each wave vector. This work establishes the fixed-node DMC approach as an accurate method for calculating the energies of low-lying excitations in solids.The band structure of silicon is calculated at the $\ensuremath{\Gamma}$, $X$, and $L$ wave vectors using diffusion quantum Monte Carlo (DMC) methods. Excited states are formed by promoting an electron from the valence band into the conduction band. We obtain good agreement with experiment for states around the gap region, and demonstrate that the method works equally well for direct and indirect excitations, and that one can calculate many excited states at each wave vector. This work establishes the fixed-node DMC approach as an accurate method for calculating the energies of low-lying excitations in solids.

arXiv:cond-mat/9803207Physical review. B, Condensed matterMay 15, 199886 citations

Efficient computation of excited states with quantum Monte Carlo

Monika Dash, Claudia Filippi

Jan 1, 20180 citations

Excited states by quantum Monte Carlo method

D. Blume, Marius Lewerenz, K. Birgitta Whaley

Mathematics and Computers in SimulationAug 1, 199810 citations

Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions

Seiichiro L. Ten-no

Model space quantum Monte Carlo (MSQMC) is an extension of full configuration interaction QMC that allows us to calculate quasi-degenerate and excited electronic states by sampling the effective Hamiltonian in the model space. We introduce a novel algorithm based on the state-selective partitioning for the effective Hamiltonian using left eigenvectors to calculate several electronic states simultaneously at much less computational cost than the original MSQMC with the energy-dependent partitioning. The sampling of walkers in MSQMC is analyzed in the single reference limit using a stochastic algorithm for higher-order perturbation energies by the analogy of the deterministic case utilizing a full configuration interaction program. We further develop size-consistency corrections of the initiator adaptation (i-MSQMC) in three different ways, i.e., the coupled electron pair approximation, a posteriori, and second-order perturbative corrections. It is clearly demonstrated that most of the initiator error is originating from the deficiency of proper scaling of correlation energy due to its truncated CI nature of the initiator approximation and that the greater part of the error can be recovered by the size-consistency corrections developed in this work.Model space quantum Monte Carlo (MSQMC) is an extension of full configuration interaction QMC that allows us to calculate quasi-degenerate and excited electronic states by sampling the effective Hamiltonian in the model space. We introduce a novel algorithm based on the state-selective partitioning for the effective Hamiltonian using left eigenvectors to calculate several electronic states simultaneously at much less computational cost than the original MSQMC with the energy-dependent partitioning. The sampling of walkers in MSQMC is analyzed in the single reference limit using a stochastic algorithm for higher-order perturbation energies by the analogy of the deterministic case utilizing a full configuration interaction program. We further develop size-consistency corrections of the initiator adaptation (i-MSQMC) in three different ways, i.e., the coupled electron pair approximation, a posteriori, and second-order perturbative corrections. It is clearly demonstrated that most of the initiator error is originating from the deficiency of proper scaling of correlation energy due to its truncated CI nature of the initiator approximation and that the greater part of the error can be recovered by the size-consistency corrections developed in this work.

arXiv:1708.09498The Journal of Chemical PhysicsDec 26, 201729 citations

Quantum Monte Carlo calculations of energy gaps from first principles

R. J. Hunt, Marcin Szyniszewski, Genki I. Prayogo +2 more

We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC methods on atoms, molecules, and solids. We propose a finite-size-error correction scheme for bulk energy gaps calculated in finite cells subject to periodic boundary conditions. We show that finite-size effects are qualitatively different in two-dimensional materials, demonstrating the effect in a QMC calculation of the band gap and exciton binding energy of monolayer phosphorene. We investigate the fixed-node errors in diffusion Monte Carlo gaps evaluated with Slater-Jastrow trial wave functions by examining the effects of backflow transformations, and also by considering the formation of restricted multideterminant expansions for excited-state wave functions. For several molecules, we examine the importance of structural relaxation in the excited state in determining excited-state energies. We study the feasibility of using variational Monte Carlo with backflow correlations to obtain accurate excited-state energies at reduced computational cost, finding that this approach can be valid. We find that diffusion Monte Carlo gap calculations can be performed with much larger time steps than are typically required to converge the total energy, at significantly diminished computational expense, but that in order to alleviate fixed-node errors in calculations on solids the inclusion of backflow correlations is sometimes necessary.We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC methods on atoms, molecules, and solids. We propose a finite-size-error correction scheme for bulk energy gaps calculated in finite cells subject to periodic boundary conditions. We show that finite-size effects are qualitatively different in two-dimensional materials, demonstrating the effect in a QMC calculation of the band gap and exciton binding energy of monolayer phosphorene. We investigate the fixed-node errors in diffusion Monte Carlo gaps evaluated with Slater-Jastrow trial wave functions by examining the effects of backflow transformations, and also by considering the formation of restricted multideterminant expansions for excited-state wave functions. For several molecules, we examine the importance of structural relaxation in the excited state in determining excited-state energies. We study the feasibility of using variational Monte Carlo with backflow correlations to obtain accurate excited-state energies at reduced computational cost, finding that this approach can be valid. We find that diffusion Monte Carlo gap calculations can be performed with much larger time steps than are typically required to converge the total energy, at significantly diminished computational expense, but that in order to alleviate fixed-node errors in calculations on solids the inclusion of backflow correlations is sometimes necessary.

arXiv:1806.04750Physical review. B./Physical review. BAug 13, 201850 citations

Strategies for computing excited states of large molecules in quantum Monte Carlo

Habiburrahman Zulfikri, Claudia Filippi

Sep 11, 20160 citations

The band structure of silicon is calculated at the $\ensuremath{\Gamma}$,

X

, and

L

wave vectors using diffusion quantum Monte Carlo (DMC) methods. Excited states are formed by promoting an electron from the valence band into the conduction band. We obtain good agreement with experiment for states around the gap region, and demonstrate that the method works equally well for direct and indirect excitations, and that one can calculate many excited states at each wave vector. This work establishes the fixed-node DMC approach as an accurate method for calculating the energies of low-lying excitations in solids.