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Linear-scaling local wave functions for ground and excited states in quantum Monte Carlo: A route to large biomolecules

Habiburrahman Zulfikri, C. Amovilli, Claudia Filippi

Published Jun 8, 2015• 0 citations
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We investigate here the performance of our recently developed linear-scaling Jastrow-generalized-valence-bond (J-LGVB) wave functions based on localized orbitals, for the quantum Monte Carlo (QMC) calculation of the barrier heights and reaction energies of five prototypical chemical reactions. Using the geometrical parameters from the Minnesota database collection, we consider three hydrogen-exchanges, one heavy-atom exchange, and one association reaction and compare our results with the best available experimental and theoretical data. For the three hydrogen-exchange reactions, we find that the J-LGVB wave functions yield excellent QMC results, with average deviations from the reference values below 0.5 kcal/mol. For the heavy-atom exchange and association reactions, additional resonance structures are important, and we therefore extend our original formulation to include multiple coupling schemes characterized by different sets of localized orbitals. We denote these wave functions as J-MC-LGVB, where MC indicates the multiconfiguration generalization, and show that such a form leads to very accurate barrier heights and reaction energies also for the last two reactions. We can therefore conclude that the J-LGVB theory for constructing QMC wave functions, with its multiconfiguration generalization, is valid for the study of large portions of ground-state potential energy surfaces including, in particular, the region of transition states.

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Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.

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Bryan K. Clark, Miguel A. Morales, Jeremy McMinis +2 more

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.

arXiv:1106.2456•The Journal of Chemical Physics•Dec 27, 2011•71 citations
We investigate here the performance of our recently developed linear-scaling Jastrow-generalized-valence-bond (J-LGVB) wave functions based on localized orbitals, for the quantum Monte Carlo (QMC) calculation of the barrier heights and reaction energies of five prototypical chemical reactions. Using the geometrical parameters from the Minnesota database collection, we consider three hydrogen-exchanges, one heavy-atom exchange, and one association reaction and compare our results with the best available experimental and theoretical data. For the three hydrogen-exchange reactions, we find that the J-LGVB wave functions yield excellent QMC results, with average deviations from the reference values below 0.5 kcal/mol. For the heavy-atom exchange and association reactions, additional resonance structures are important, and we therefore extend our original formulation to include multiple coupling schemes characterized by different sets of localized orbitals. We denote these wave functions as J-MC-LGVB, where MC indicates the multiconfiguration generalization, and show that such a form leads to very accurate barrier heights and reaction energies also for the last two reactions. We can therefore conclude that the J-LGVB theory for constructing QMC wave functions, with its multiconfiguration generalization, is valid for the study of large portions of ground-state potential energy surfaces including, in particular, the region of transition states.
Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.
Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.