Partial Separability of the Schrödinger Equation Combined with a Jastrow Factor.

Describing the Coulomb interactions between electrons in atomic or molecular systems is an important step to help us obtain accurate results for the different observables in the system. One convenient approach is to separate the dynamic electronic correlation, i.e., Coulomb electron-electron repulsion, from the motion of the electrons in the nucleus electric field. The wave function is written as the product of two terms, one accounting for the electron-electron interactions, which is symmetric under identical particle exchange, and the other is antisymmetric and represents the dynamics and exchange of electrons within the nuclear electric field. In this work, we present a novel computational scheme based on this idea that leads to an expression of the energy as the sum of two terms. To illustrate the method, we look into few-body Coulombic systems, H2, H3+, and Li(1s2,2s), and discuss the possible extension to larger systems. A simple correlation factor, based on the Jastrow exponential term, is employed to represent the dynamics of the electron pairs, leading to simple analytical forms and accurate results. We also present and illustrate a different approach with the Li atom based on the partial separability applied to a portion of the atom.

An off-center endohedrally confined hydrogen molecule.

In this study, we address the problem of a C60 endohedrally confined hydrogen molecule through a configuration-interaction approach to electronic dynamics. Modeling the confinement by means of a combination of two Woods-Saxon potentials, we analyze the stability of the system as a function of the nuclei position through the behavior of the electronic spectrum. After studying the convergence of two different partial wave expansions, one related to the molecular Coulomb centers and the other related to the off-centering of the C60 well, we found that the second approach provides a more accurate description of the system. Furthermore, we observed that the inter-atomic distance changes based on the position of the atoms inside the cavity. Thus, to obtain the most favourable energetic configuration for the molecule, it should be positioned inside the cavity next to the structure, where its size decreases.

Isotopic Effects on Covalent Bond Confined in a Penetrable Sphere.

A model of confinement of the covalent bond by a finite potential beyond the Born-Oppenheimer approximation is presented. A two-electron molecule is located at the center of a penetrable spherical cavity. The Schrödinger equation has been solved by using the diffusion Monte Carlo method. Total energies, internuclear distances, and vibrational frequencies of the confined molecular system have been obtained. Even for confining potentials of a few electronvolts, a noticeable increase in the bond energy and the nuclear vibrational frequency is observed, and the internuclear distance is lowered. The gap between the zero point energy of different molecular isotopes increases with confinement. The confinement of the electron pair might play a role in chemical reactivity, providing an alternative explanation for the tunnel effect, when large values of primary kinetic isotopic effect are observed. The Swain-Schaad relation is still verified when confinement changes the zero point energy. A semiquantitative illustration is proposed using the data relative to an hydrogen transfer involving a C-H cleavage catalyzed by the bovine serum amine oxidase. Changes on the confining conditions, corresponding to a confinement/deconfinement process, result in a significant decrease in the activation energy of the chemical transformation. It is proposed that confinement/deconfinement of the electron-pair bonding by external electrostatic forces inside the active pocket of an enzyme could be one of the basic mechanisms of the enzyme catalysis.

Variational Monte Carlo Method with Dirichlet Boundary Conditions: Application to the Study of Confined Systems by Impenetrable Surfaces with Different Symmetries.

Variational Monte Carlo method is a powerful tool to determine approximate wave functions of atoms, molecules, and solids up to relatively large systems. In the present work, we extend the variational Monte Carlo approach to study confined systems. Important properties of the atoms, such as the spatial distribution of the electronic charge, the energy levels, or the filling of electronic shells, are modified under confinement. An expression of the energy very similar to the estimator used for free systems is derived. This opens the possibility to study confined systems with little changes in the solution of the corresponding free systems. This is illustrated by the study of helium atom in its ground state (1)S and the first (3)S excited state confined by spherical, cylindrical, and plane impenetrable surfaces. The average interelectronic distances are also calculated. They decrease in general when the confinement is stronger; however, it is seen that they present a minimum for excited states under confinement by open surfaces (cylindrical, planes) around the radii values corresponding to ionization. The ground (2)S and the first (2)P and (2)D excited states of the lithium atom are calculated under spherical constraints for different confinement radii. A crossing between the (2)S and (2)P states is observed around rc = 3 atomic units, illustrating the modification of the atomic energy level under confinement. Finally the carbon atom is studied in the spherical symmetry by using both variational and diffusion Monte Carlo methods. It is shown that the hybridized state sp(3) becomes lower in energy than the ground state (3)P due to a modification and a mixing of the atomic orbitals s, p under strong confinement. This result suggests a model, at least of pedagogical interest, to interpret the basic properties of carbon atom in chemistry.

(HCl)2 and (HF)2 in small helium clusters: quantum solvation of hydrogen-bonded dimers.

We present a rigorous theoretical study of the solvation of (HCl)(2) and (HF)(2) by small ((4)He)(n) clusters, with n=1-14 and 30. Pairwise-additive potential-energy surfaces of He(n)(HX)(2) (X=Cl and F) clusters are constructed from highly accurate four-dimensional (rigid monomer) HX-HX and two-dimensional (rigid monomer) He-HX potentials and a one-dimensional He-He potential. The minimum-energy geometries of these clusters, for n=1-6 in the case of (HCl)(2) and n=1-5 for (HF)(2), correspond to the He atoms in a ring perpendicular to and bisecting the HX-HX axis. The quantum-mechanical ground-state energies and vibrationally averaged structures of He(n)(HCl)(2) (n=1-14 and 30) and He(n)(HF)(2) (n=1-10) clusters are calculated exactly using the diffusion Monte Carlo (DMC) method. In addition, the interchange-tunneling splittings of He(n)(HCl)(2) clusters with n=1-14 are determined using the fixed-node DMC approach, which was employed by us previously to calculate the tunneling splittings for He(n)(HF)(2) clusters, n=1-10 [A. Sarsa et al., Phys. Rev. Lett. 88, 123401 (2002)]. The vibrationally averaged structures of He(n)(HX)(2) clusters with n=1-6 for (HCl)(2) and n=1-5 for (HF)(2) have the helium density localized in an effectively one-dimensional ring, or doughnut, perpendicular to and at the midpoint of the HX-HX axis. The rigidity of the solvent ring varies with n and reaches its maximum for the cluster size at which the ring is filled, n=6 and n=5 for (HCl)(2) and (HF)(2), respectively. Once the equatorial ring is full, the helium density spreads along the HX-HX axis, eventually solvating the entire HX dimer. The interchange-tunneling splitting of He(n)(HCl)(2) clusters hardly varies at all over the cluster size range considered, n=1-14, and is virtually identical to that of the free HCl dimer. This absence of the solvent effect is in sharp contrast with our earlier results for He(n)(HF)(2) clusters, which show a approximately 30% reduction of the tunneling splitting for n=4. A tentative explanation for this difference is proposed. The implications of our results for the interchange-tunneling dynamics of (HCl)(2) in helium nanodroplets are discussed.

Structure, rotational dynamics, and superfluidity of small OCS-doped He clusters.

The structural and dynamical properties of carbonyl sulfide (OCS) molecules solvated in helium clusters are studied using reptation quantum Monte Carlo, for cluster sizes n=3-20 He atoms. Computer simulations allow us to establish a relation between the rotational spectrum of the solvated molecule and the structure of the He solvent, and of both with the onset of superfluidity. Our results agree with a recent spectroscopic study of this system and provide a more complex and detailed microscopic picture of this system than inferred from experiments.

HF dimer in small helium clusters: interchange-tunneling dynamics in a quantum environment.

We present diffusion quantum Monte Carlo calculations of the interchange tunneling splitting of (4)He(n)(HF)(2) clusters, n = 1-10. The tunneling splitting decreases rapidly for n = 1-4 clusters, and much more slowly for n>4. The decrease calculated for (4)He(n)(HF)(2) represents 74% of the reduction in the tunneling splitting measured recently for HF dimer in nanodroplets of more than 2000 He atoms. The first four He atoms quench the interchange tunneling very efficiently by virtue of occupying the equatorial ring which encircles the C(2h) transition state of the tunneling pathway.