E. Buendía

Correlated Monte Carlo electron-pair density for the atoms helium to neon

The Monte Carlo method to obtain the electron-pair density for the atoms helium to neon has been applied. The wave functions of Schmidt and Moskowitz [J. Chem. Phys. 93, 4172 (1990)] to take into account the dynamic correlation among the electrons have been used. For the atoms Be, B and C we have considered the nondynamic correlation due to the near degeneracy 2s−2p by means of a configuration interaction wave function and for Li and Be we have also varied the central part of the wave function. A study of the differences between the correlated and the Hartree–Fock results has been carried out. Finally we have also calculated the interelectronic moments, 〈r12n〉, and the value of the electron pair density at the coalescence point for all the atoms considered.

Correlated electron extracule densities in position and momentum spaces

Spherically averaged extracule densities in position, d(R), and momentum, d(P), spaces have been calculated for the atoms helium to neon starting from explicitly correlated wave functions. Correlated values for the electron–electron counterbalance density in position, d(0), and in momentum, d(0), spaces, and also for the expectation values 〈Rn〉 and 〈Pn〉 are reported. A systematic study of the electronic correlation has been performed by comparing the correlated results with the corresponding Hartree–Fock ones.

Atomic properties from energy-optimized wave functions

Most of the variational Monte Carlo applications on quantum chemistry problems rely on variance-optimized wave functions. Recently, M. Snajdr and S. M. Rothstein, [J. Chem. Phys. 112, 4935 (2000)] have concluded that energy optimization allows one to obtain wave functions that provide better values for a wide variety of ground state properties. In this work we study the quality of energy-optimized wave functions obtained by using the methodology of Lin, Zhang, and Rappe [J. Chem. Phys. 112, 2650 (2000)], as compared with variance-optimized ones for He to Ne atoms. In order to assess this problem we calculate the energy and some other selected properties. The accuracy and performance of the energy-optimization method is studied. A comparison of properties calculated with energy-optimized wave functions to those existing in the literature and obtained by means of variance-optimized wave functions shows a better performance of the former.

A parametrized optimized effective potential for atoms

The optimized effective potential equations for atoms have been solved by parametrizing the potential. The expansion is tailored to match the known asymptotic behaviour of the effective potential at both short and long distances. Both single configuration and multi-configuration trial wavefunctions are implemented. Applications to several atomic systems are presented, improving on previous works. The results obtained here are very close to those calculated in either the Hartree–Fock (HF) or the multi-configurational HF framework.

CORRELATED TWO-ELECTRON MOMENTUM PROPERTIES FOR HELIUM TO NEON ATOMS

Two-electron properties in momentum space for the atoms helium to neon have been calculated starting from explicitly correlated wave functions. The different integrals involved in the calculation have been evaluated by using the Monte Carlo algorithm. In particular, the spherically averaged interelectronic momentum distribution, γ(2)(p12),its radial moments 〈p12n〉, with n=−2 to +3, the expectation value 〈p1⋅p2〉, and both the electron–electron coalescence, γ(2)(0), and counterbalance, Γ(2)(0), densities have been calculated. A systematic study of the electronic correlation has been performed by comparing the correlated results with the corresponding Hartree–Fock ones. Finally an analysis of the structure of the interelectronic momentum distribution in terms of its parallel and antiparallel components has been carried out.

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

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 〈δ(r)〉, 〈rn〉, 〈δ(r12)〉, 〈r12n〉, 〈δ(R)〉, and 〈Rn〉, where r, r12, 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 one- and two-electron densities of low-lying S-states in helium-like atoms

From high-quality, Pekeris-type electronic wavefunctions we calculate the single-particle density rho (r) and the intracule density h(s) of some low-lying S-states of two-electron atoms, obtaining very accurate values for the energies, the cusp-condition ratios and some radial expectation values. The effect of electron correlation on both densities for these states is also Studied by comparison with Hartree-Fock results. Some local important differences appear not only for the ground state, but also for the excited ones. Our results agree with some features previously found, such as the non-monotonic decrease of rho (r) for the excited states. We also find that the Coulomb hole of singlet excited states is strongly dependent on the procedure used for the Hartree-Fock calculations.

A variational Monte Carlo study of the 2s-2p near degeneracy in beryllium, boron, and carbon atoms

We apply the variational Monte Carlo method to study the beryllium, boron, and carbon atoms. An explicitly correlated wave function is used in order to include the dynamic correlation among the electrons. The nondynamic correlation due to the 2s-2p near degeneracy effect present in these atoms is taken into account by using a multideterminant wave function.

Correlated one-body momentum density for helium to neon atoms

Starting from explicitly correlated wavefunctions, the one-body momentum density, (), and the expectation values () and pn, with n = -2 to +3, have been obtained for the atoms helium to neon. All the calculations have been carried out by using the Monte Carlo algorithm. An analysis of the numerical accuracy of the method has been performed within the Hartree-Fock framework. The effects of the electronic correlations have been systematically studied by comparing the correlated results with the corresponding Hartree-Fock ones.

Single-particle and electron-pair densities at the origin in the ground state of helium-like ions

Here we study the single-particle and the electron-pair densities for the ground state of two-electron atomic systems using the wavefunctions which provide the best values for the energy known up to now. Special attention is paid to the convergence of some properties of the densities when we increase the dimension of the basis used. With these functions we have increased significantly the precision in the determination of the single-particle and the electron-pair densities at the origin and, therefore, of Katos cusp conditions.