Helium at zero temperature with hard-sphere and other forces

Kalos, M. H.; Levesque, D.; Verlet, Loup

doi:10.1103/physreva.9.2178

Cited by 562 publications

(307 citation statements)

References 28 publications

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“…The introduction of information on the system from another source is the essence of importance sampling [25,26], which improves convergence to the Ψ T Φ state of interest. In the DMC method the propagation of the distribution of walkers is achieved with the short-time approximation, which provides an analytical approximation to the Green's function [27].…”

Section: Methodsmentioning

confidence: 99%

Quantum Monte Carlo study of singlet–triplet transition in ethylene

Akramine

Kollias

Lester

2003

The Journal of Chemical Physics

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A theoretical study is reported of the transition between the ground state ( and the lowest triplet state( ) of ethylene based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using DMC trial functions constructed from Hartree-Fock, complete active space self-consistent field and multi-configuration self-consistent field wave functions, we have computed the atomization energy and the heat of formation of both states, and adiabatic and vertical energy differences between these states using both all-electron and effective core potential DMC. The ground state atomization energy and heat of formation are found to agree with experiment to within the error bounds of the computation and experiment.Predictions by DMC of the triplet state atomization energy and heat of formation are presented.The adiabatic singlet-triplet energy difference is found to differ by 5 kcal/mol from the value obtained in a recent photodissociation experiment.1

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Section: Methodsmentioning

confidence: 99%

Quantum Monte Carlo study of singlet–triplet transition in ethylene

Akramine

Kollias

Lester

2003

The Journal of Chemical Physics

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“…Green's function Monte Carlo (GFMC) methods eliminate any variational constraints by solving directly the Schrödinger equation for a N -body problem. The most advanced of these methods is domain GFMC, in which the corresponding Green's function is time-independent (Kalos, 1962;Kalos, Levesque, and Verlet, 1974;Ceperley et al, 1976;Schmidt and Kalos, 1984). A related method is diffusion Monte Carlo (DMC), which is time-dependent and nowadays widely used (Ceperley and Alder, 1980;Reynolds et al, 1982;Hammond, Lester, and Reynolds, 1994;Anderson, 2002).…”

Section: Diffusion Monte Carlomentioning

confidence: 99%

Simulation and understanding of atomic and molecular quantum crystals

2017

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Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases ( 4 He and Ne), molecular solids (H 2 and CH 4 ), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be only explained in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields like, for instance, planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals formed by atoms and small molecules, as well as the wide palette of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, structural properties, elasticity, crystalline defects and the effects of reduced dimensionality, are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are the simulation methods of choice, and other quantum simulation approaches (e. g., path-integral molecular dynamics and quantum thermal baths) is provided. The overarching objective of this article is twofold. First, to clarify in which crystals and physical situations the disregard of QNE may incur in important bias and erroneous interpretations. And second, to promote the study and appreciation of QNE, a topic that traditionally has been treated in the context of condensed matter physics, within the broad and interdisciplinary areas of materials science.

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“…The FNA has been found to provide accurate results for ground and excited states with trial functions constructed using various ab initio basis set methods. The introduction of information about the system from another source is the essence of importance sampling, 35 which improves convergence to the state of interest. In the DMC method the propagation walker distribution is achieved with the short-time approximation, which provides an analytical approximation to the Green's function.…”

Section: Qmc Methodologymentioning

confidence: 99%

Geometry optimization in quantum Monte Carlo with solution mapping: Application to formaldehyde

Schuetz

Frenklach

Kollias

et al. 2003

The Journal of Chemical Physics

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The solution mapping methodology is presented as a method of geometry optimization of molecules in the quantum Monte Carlo method. Applied to formaldehyde as a test system, this approach is found to yield optimized bond lengths and bond angle in the diffusion Monte Carlo method that lie within experimental error. The variational Monte Carlo optimized geometry also lies within experimental error, with the exception of the CH bond length, which is slightly underestimated. Additionally, the resulting quadratic representation of the potential energy surface in the region of the minimum is used to calculate three of the force constants and harmonic frequencies.2

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Helium at zero temperature with hard-sphere and other forces

Cited by 562 publications

References 28 publications

Quantum Monte Carlo study of singlet–triplet transition in ethylene

Quantum Monte Carlo study of singlet–triplet transition in ethylene

Simulation and understanding of atomic and molecular quantum crystals

Geometry optimization in quantum Monte Carlo with solution mapping: Application to formaldehyde

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