One- and two-body densities for the beryllium isoelectronic series

Abstract

One-and two-body densities in position 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 ͗␦(r)͘, ͗r n ͘, ͗␦(r 12 )͘, ͗r 12 n ͘, ͗␦(R)͘, and ͗R n ͘, where r, r 12 , and R stand for the electron-nucleus, interelectronic, and two electron center of mass coordinates, respectively, 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

“…1͑a͒; ⌬H(u) is positive in the regions 0.50ϽuϽ1.09 and 3.44ϽuϽ7.87, whereas ⌬H(u) is negative mainly in the regions 0ϽuϽ0.50 and 1.09ϽuϽ3.44, where the symbol ⌬ stands for the correlated quantity subtracted by the corresponding Hartree-Fock quantity. Analogous correlation effects in ⌬H(u) were reported by Banyard et al 17,18 and by Gálvez et al, 21 but the first positive region is missing in the result of the latter authors.…”

“…1͑b͒. Gálvez et al 21,23 reported similar behavior for ⌬D(R). The electron correlation in the Be atom reduces the average center-ofmass radius ͗R͘ of electron pairs.…”

“…The four sets of the correlated extracule moments ͗R n ͘ in Table I are not very different, but we expect that the present MCHF values will be more reliable than the Monte Carlo results [21][22][23] in view of the accuracy observed in the partner intracule moments. The correlated moments ͗R n ͘ with nϽ0 are larger, while those with nϾ0 are smaller than their Hartree-Fock values.…”

“…The vanishing ␦ pos value in the present and Hartree-Fock 9,10 calculations shows that the intracule and extracule properties are consistently obtained. However, we find nonzero ␦ pos for the Monte Carlo results, [20][21][22][23] though the value is within the sum of the statistical errors in the three relevant moments.…”

“…At the correlated level, however, the electron-pair properties were not known in a consistent manner except for the He 15 and Li 16 atoms. 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.…”