Rovibrationally averaged properties of H<sub>2</sub> using Monte Carlo methods

Alexander, S. A.; Coldwell, R. L.

doi:10.1002/qua.21130

Cited by 11 publications

(6 citation statements)

References 27 publications

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“…This is in Reasonable agreement, in view of the nodal error, with the experimental value of -24.541246 atomic units. This visualizes the regression fit is Table-1 shows the final results of the energy using a very large of MC points together with the standard deviation given by equation (4) and equation (5). It is clear from Table-2 that, the obtained result is of good agreement with the recent experimental Hylleraas value.…”

Section: Resultssupporting

confidence: 62%

“…In most of its current applications the VMC method has become a valuable method because of a wide variety of wave function forms for which analytical integration would be impossible. The major advantage of this method is the possibility to freely choose the analytical form of the trial wave function which may contain highly sophisticated term in such a way that electron correlation is explicitly taken into account [4][5]. This is an important feature valid for quantum Monte Carlo methods, which are therefore extremely useful to study physical cases where the electron correlation plays a crucial role.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Boron Ground State Energy by Monte Carlo Simulation

Kabir¹

2015

AJAM

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Quantum Monte Carlo (QMC) method is a powerful computational tool for finding accurate approximation solutions of the quantum many body stationary Schrödinger equations for atoms, molecules, solids and a variety of model systems. Using Variational Monte Carlo method we have calculated the ground state energy of the Boron atom. Our calculations are based on using a modified five parameters trial wave function which leads to good result comparing with fewer parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Boron. Based on comparisons, the energy obtained in our simulation are in excellent agreement with experimental and other well established values.

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Section: Resultssupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Estimation of Boron Ground State Energy by Monte Carlo Simulation

Kabir¹

2015

AJAM

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“…All of these values were accurate to a microhartree or better. In a subsequent article, we used these same wavefunctions to calculate a wide variety of molecular properties 14.…”

Section: Calculating the Densitiesmentioning

confidence: 99%

Visualizing molecular wavefunctions using Monte Carlo methods

Alexander

Coldwell

2008

Int J of Quantum Chemistry

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Using explicitly correlated wavefunctions and variational Monte Carlowe calculate the electron density, the electron density difference, the intracule density, the extracule density, two forms of the kinetic energy density, the Laplacian of the electron density, the Laplacian of the intracule density, and the Laplacian of the extracule density on a dense grid of points for the ground state of the hydrogen molecule at three internuclear distances (0.6, 1.4, 8.0). With these values we construct a contour plot of each function and describe how it can be used to visualize the distribution of electrons in this molecule. We also examine the influence of electron correlation on each expectation value by calculating each function with a Hartree-Fock wavefunction and then comparing these values with our explicitly correlated values.

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“…The diamagnetic susceptibilities χ are presented in Table I along with selected reference values from the literature [4][5][6][7]9,[33][34][35][37][38][39]. The PIMC values are linearly extrapolated to zero time step, τ → 0, to control the estimator error that, unlike with energies, is significant.…”

Section: Validation Of Accuracymentioning

confidence: 99%

Diamagnetic susceptibility from a nonadiabatic path-integral simulation of few-electron systems

2022

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Diamagnetism is the response of dynamical compositions of charged particles, electrons, and nuclei, to an incident magnetic field. In this paper, we study how the finite temperature and finite nuclear masses affect the diamagnetic susceptibilities of selected small atoms and molecules, as limiting cases of dilute gas. We use nonrelativistic path-integral Monte Carlo simulation (PIMC), where both electrons and nuclei are treated on equal footing at finite temperatures in sampling exact Coulomb pair density matrices. The PIMC estimator of diamagnetic susceptibility has been briefly introduced in Ceperley [D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)], but here we present a comprehensive derivation, discussion of practical effects, and proof-of-concept results for selected few-body Coulomb systems. Our results are in perfect agreement with high-accuracy literature references, where available, but also demonstrate additional thermal effects of the diamagnetic response of low-mass systems.

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Rovibrationally averaged properties of H₂ using Monte Carlo methods

Cited by 11 publications

References 27 publications

Estimation of Boron Ground State Energy by Monte Carlo Simulation

Estimation of Boron Ground State Energy by Monte Carlo Simulation

Visualizing molecular wavefunctions using Monte Carlo methods

Diamagnetic susceptibility from a nonadiabatic path-integral simulation of few-electron systems

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Rovibrationally averaged properties of H2 using Monte Carlo methods

Cited by 11 publications

References 27 publications

Estimation of Boron Ground State Energy by Monte Carlo Simulation

Estimation of Boron Ground State Energy by Monte Carlo Simulation

Visualizing molecular wavefunctions using Monte Carlo methods

Diamagnetic susceptibility from a nonadiabatic path-integral simulation of few-electron systems

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Rovibrationally averaged properties of H₂ using Monte Carlo methods