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Application of Laguerre Polynomials to Evaluation of Two-Center, Two- and Three-Electron Integrals in the Basis of Slater-Type Orbitals - Algorithm and Numerical Results

100%
Budziński J., Firszt M., Woźnicki W.
Acta Physica Polonica A
|
1994
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vol. 86
|
issue 6
883-894
EN
Numerical verification of the algorithm for evaluation of the two-center, two- and three-electron integrals with the correlation factors of the type r^{k}_{12}, elaborated by us previously is presented. The influence of different parameters on the accuracy of the expressions for evaluating the integrals is discussed on the basis of the numerical results obtained.
2
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n the Fixed-Node Importance-Sampling Quantum Monte Carlo Method: Performance Analysis on Model Systems

100%
Chłobowski A.
Acta Physica Polonica A
|
1991
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vol. 79
|
issue 6
775-787
EN
Performance of Importance-Sampling Quantum Monte Carlo process is considered on simple, model systems, such as: multi-dimensional oscillator, hydrogen-like ions, and "helium oscillator" (quadratic-potential analog of helium atom). A mean and standard deviation of that process is numerically determined and also, in the first two cases, calculated analytically together with the distribution of the process values. Results are presented to show how a mean value precision and necessary computational time depend on an importance function quality and dimensionality of the case. Distributions are shown to be highly asymmetrical which questions the value of variance-based estimators of precision. However, a variance is proposed to be the good estimate of the importance function quality. Finally, effects of fixed-node approximation on the second excited state of oscillator are presented to explain the meaning of the differences between exact and approximate solutions.
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Closed Relation Between Single-Particle Kinetic Energy and Electron Density in One-Dimensional Two-Level Systems

51%
Kozłowski P., March N.
Acta Physica Polonica A
|
1992
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vol. 82
|
issue 3
421-424
EN
For a two-level problem in one dimension, an implicit relation is derived relating the kinetic energy density t_{s}(x) to the electron density ρ(x) plus its first and second derivatives. As an example, the harmonic oscillator potential is used to make this relation explicit.
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