Calculating atomic and molecular properties using Variational Monte Carlo methods

Alexander, S. A.; Coldwell, R. L.; Aissing, Gerrard; Thakkar, Ajit J.

doi:10.1002/qua.560440819

Cited by 20 publications

(13 citation statements)

References 39 publications

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“…However, the bias that the minimization of the root-mean-square local energy deviation introduces (see Table I) is such that our results, using only six terms of the Koga's expansion, are better than those obtained by VMC simulations including 50 terms [16].…”

Section: Wave-function Optimizationcontrasting

confidence: 56%

Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

Bianchi¹,

Bressanini²,

Cremaschi³

et al. 1996

Int. J. Quantum Chem.

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mThe sampling of the exact solution of the Schrodinger equation by quantum Monte Carlo methods allows one to solve the problem of the optimization of linear and nonlinear parameters of a trial wave function by minimization of the distance to the exact wave function in Hilbert space even for those systems whose exact wave function is unknown. The overlap integrals between the basis functions and the exact wave function can be easily estimated within the quantum Monte Carlo formalism. Several observables of the helium atom ground state, computed both within the orbital approximation and by an explicitly correlated basis set, evidence the overall goodness of the wave function optimized according to this criterion.

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Section: Wave-function Optimizationcontrasting

confidence: 56%

Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

Bianchi¹,

Bressanini²,

Cremaschi³

et al. 1996

Int. J. Quantum Chem.

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Here ⌿ i ϭ⌿ t (x i ) is the value of the trial wave function at the Monte Carlo integration point x i and w i ϭw(x i ) is the relative probability of choosing this point. Because no analytic integrals need be determined, even complicated operators acting on highly nonlinear wave function forms are usually easy to evaluate.…”

Section: Introductionmentioning

confidence: 99%

Calculating atomic properties using variational Monte Carlo

Alexander

Coldwell

1995

The Journal of Chemical Physics

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Monte Carlo calculations of the properties of sputtered atoms at a substrate surface in a magnetron discharge Using variational Monte Carlo and the explicitly-correlated wave function forms optimized by Schmidt and Moskowitz, we compute a number of properties for the atoms He-Ne. The expectation value of the Hamiltonian using these wave functions contains between 70.0% and 99.8% of the correlation energy for the neutral atoms ͑17 parameters͒, 60.8% and 99.1% for selected cations ͑9 parameters͒, and 73.9% and 89.4% for selected anions ͑17 parameters͒. For those properties which sample the valence region, our results are in good agreement with previous calculations ͑where available͒. Because of a defect in the wave function form, a substantial error is found in those properties which two electrons that are in close proximity.

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“…As in Ref. [14] the energy differences in Eq. (7) are computed over the same Monte Carlo integration points to substantially reduce the statistical error in these calculations.…”

Section: Calculating Derivativesmentioning

confidence: 88%

Spectroscopic constants of H₂ using Monte Carlo methods

Alexander

Coldwell

2004

Int J of Quantum Chemistry

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ABSTRACT:We have computed the spectroscopic constants w e , w e x e , ␣ e , and B e of the ground state of H 2 using two methods. In the first method, a highly accurate potential energy surface was generated using explicitly correlated wave functions and variational Monte Carlo techniques. We calculated the vibrational-rotational energies from this surface and then obtained the spectroscopic constants by fitting these energies to a simple equation. In the second method, the spectroscopic constants were determined from local derivatives of the energy with respect to the internuclear distance. These derivatives have also been calculated using variational Monte Carlo techniques. For this system we find that the first method yields spectroscopic constants that are in excellent agreement with experiment. We also find that the second method, although slightly less accurate, is extremely well suited to Monte Carlo calculations.

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Calculating atomic and molecular properties using Variational Monte Carlo methods

Cited by 20 publications

References 39 publications

Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

Calculating atomic properties using variational Monte Carlo

Spectroscopic constants of H₂ using Monte Carlo methods

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Calculating atomic and molecular properties using Variational Monte Carlo methods

Cited by 20 publications

References 39 publications

Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

Calculating atomic properties using variational Monte Carlo

Spectroscopic constants of H2 using Monte Carlo methods

Contact Info

Product

Resources

About

Spectroscopic constants of H₂ using Monte Carlo methods