A. Sarsa

A path integral ground state method

Ground state expectation values are obtained by using a path integral ground state Monte Carlo method. The method allows calculations of ground state expectation values without the extrapolations often used with Green’s function and diffusion Monte Carlo methods. We compare our results with those of Green’s function Monte Carlo by calculating some ground state properties of the van der Waals complex He2Cl2 as well as the infinite systems liquid and solid 4He. Advantages and disadvantages of the present method with respect to previous ones are discussed.

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.

Mg impurity in helium droplets

Within the diffusion Monte Carlo approach, we have determined the structure of isotopically pure and mixed helium droplets doped with one magnesium atom. For pure (4)He clusters, our results confirm those of Mella et al. [J. Chem. Phys. 123, 054328 (2005)] that the impurity experiences a transition from a surface to a bulk location as the number of helium atoms in the droplet increases. Contrarily, for pure (3)He clusters Mg resides in the bulk of the droplet due to the smaller surface tension of this isotope. Results for mixed droplets are presented. We have also obtained the absorption spectrum of Mg around the 3s3p (1)P(1) ← 3s(2) (1)S(0) transition.

Quadratic diffusion Monte Carlo and pure estimators for atoms

The implementation and reliability of a quadratic diffusion Monte Carlo method for the study of ground-state properties of atoms are discussed. We show in the simple yet nontrivial calculation of the binding energy of the Li atom that the method presented is effectively second-order in the time step. The fulfillment of the expected quadratic behavior relies on some basic requirements of the trial wave function used for importance sampling, in the context of the fixed-node approximation. Expectation values of radial operators are calculated by means of a pure estimation based on the forward walking methodology. It is shown that accurate results without extrapolation errors can be obtained with a pure algorithm, explicitely reported, that can be easily implemented in any previous diffusion Monte Carlo program.

Constraint dynamics for quantum Monte Carlo calculations

We describe how to apply classical constraint dynamics to problems in diffusion Monte Carlo. We apply the method to rigid and nonrigid water molecules with an internal rotational degree of freedom. The method is applicable to a wide variety of problems.