Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom

Abstract

Explicitly correlated Gaussian functions are applied to extensive variational calculations of the 'S ground state of the beryllium atom. The convergence of the energy with respect to the basis-set expansion length is investigated. The nonrelativistic clamped-nuclei energy computed from a 1200-term wave function equals -14.667 355 hartree and is in error by about 1 cm '. This is the lowest variational upper bound to the beryllium ground-state energy reported to date and it shows that recent empirical estimates of the nonrelativistic energy of the Be atom lie slightly too high. Several expectation values, including powers of interparticle distances and the Dirac 6 function, are computed. The nuclear magnetic shielding constant, the magnetic susceptibility, the specific mass shifts, the transition isotope shift, and the electron density at the nucleus position are evaluated.PACS number(s): 31.15. Ar, 31.25.v

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

“…The results are summarized and compared with the literature values 9,10,17-23 in Table I, where the columns are arranged in the decreasing order of the total energies of the parent wave functions. When the intracule moments ͗u n ͘ are compared, the present values show satisfactory agreements with those of Komasa et al 19 with the lowest total energy. Except for ͗u Ϫ2 ͘ and ͗u Ϫ1 ͘, the correlated Monte Carlo results of Gálvez et al 22 have a larger deviation from Komasa et al values than the present, though their total energy is lower.…”

“…Our MCHF total energy E is Ϫ14.662 53 hartrees, which recovers 94.9% of the correlation energy in the Be atom. 19 The deviation in the virial ratio ϪE/T from unity is 1ϫ10 Ϫ9 , where T is the electronic kinetic energy. All the electron-pair densities and moments were then calculated by the procedure described in Ref.…”

“…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.…”

Stability of few-charge systems in quantum mechanics

“…The main advantage of the VMC is that while it is not necessarily the most precise method for small systems its applicable to larger systems with favorable scaling properties. [267] 1200 −14.6673 SVM [254] 500 −14.6673…”

Statistical angular correlation coefficients and second electron-pair moments for atoms

“…[30][31][32][33][34][35] In Table I, the angular correlation coefficients ͓r͔ from the explicitly correlated wave functions are compared with those from the Hartree-Fock limit wave functions and with those from density-functional 8 and configuration interaction 9,36 calculations. When we go beyond the Hartree-Fock approximation, all the atoms, including He-Be, have negative correlation coefficients and the so-called electron correlation effect works to increase the magnitudes of negative angular correlations.…”