Momentum space densities for the beryllium isoelectronic series

Abstract

Articles you may be interested inOne-and two-body densities of carbon isoelectronic series in their low-lying multiplet states from explicitly correlated wave functions Electron correlation and noninteracting v -representability in density functional theory: The Be isoelectronic series One-and two-body densities in momentum space have been calculated for the atomic beryllium isoelectronic series starting from explicitly correlated multideterminant wave functions. The effects of electronic correlations have been systematically studied by comparing the correlated results with the corresponding Hartree-Fock ones. Some expectation values such as ͗␦(p ជ )͘, ͗p n ͘, ͗␦(p ជ 12 )͘, ͗p 12 n ͘, ͗␦(P ជ )͘, and ͗P n ͘, where p ជ , p ជ 12 , and P ជ stand for the electron-nucleus, interelectronic, and two-electron center-of-mass momentum coordinates, respectively, and the angular correlation coefficient have been obtained. All the calculations have been carried out by using the Monte Carlo algorithm.

Correlated electron-pair properties of the Be atom in position and momentum spaces

“…The difference ⌬H ( ) is positive at 0Ͻ Ͻ0.80 and 1.79Ͻ Ͻ7.37, whereas it is negative at 0.80Ͻ Ͻ1.79 and Ͼ7.37. An analogous correlation effect was previously observed by Gálvez et al 25 The predominant contribution of the electron correlation is the density shift from a large-to a small-region, in accord with the change in the intracule moments ͗ n ͘ discussed previously. The electron correlation effect works to reduce the average distance ͗ ͘ of two electrons in momentum space; an opposite result observed for ͗u͘ in position space.…”

“…When the consistency of the momentum-space intracule and extracule properties is checked by means of ␦ mom ͓Eq. ͑5b͔͒, we find that ␦ mom is zero for the present and Hartree-Fock results, whereas it is nonzero for the results of Sarsa et al 23,24 and of Gálvez et al 25 The statistical uncertainty was not reported for the electron-pair moments in momentum space. Judging from the total energies, virial errors, and ␦ mom values, we consider that the present MCHF results are most accurate among the three sets of available data summarized in Table II.…”

“…2͑b͒, which shows that the extracule density mainly migrates from a small-P (0Ͻ PϽ0.40) to a large-P (0. [23][24][25] are analogous, when available. When the consistency of the momentum-space intracule and extracule properties is checked by means of ␦ mom ͓Eq.…”

“…In the case of the Be atom, several correlated calculations were reported for the intracule [17][18][19][20][21][22] and extracule [21][22][23] properties in position space. On the other hand, correlated studies are extremely limited in momentum space: Only Sarsa et al [23][24][25] published correlated electron-pair data of the Be atom based on Monte Carlo calculations. However, a closer examination shows that the results of Sarsa et al are insufficiently accurate in that the statistical uncertainty is large in the sum rule, the total energy of the parent wave function is rather poor, and the virial error is nontrivial.…”

Momentum space properties for the atoms helium to neon from energy‐optimized explicitly correlated wave functions

“…The variational Monte Carlo (VMC) method constitutes an efficient alternative to obtain both accurate trial wave functions and atomic properties 24. In general, the calculation is carried out in position space but the Monte Carlo can be extended to calculate local and global momentum space properties 25–28. For most of the VMC applications to quantum chemistry the trial wave functions are obtained by minimizing the variance of the local energy instead of the energy itself.…”