PATH-INTEGRAL MONTE-CARLO SIMULATIONS OF ALUMINUM ATOMS EMBEDDED IN SOLID PARA-HYDROGEN AND IN HELIUM CLUSTERS

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2005-05-27

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Abstract

In this dissertation we use a path-integral Monte Carlo (PIMC) simulation method to study an open-shell atomic Al impurity doped in two kinds of low temperature condensed media.

We first use the Multilevel Metropolis PIMC method to study the arrangement of He atoms around a single Al atom doped in a He cluster. We use these results to simulate the Al electronic excitation spectrum in the cluster. Our accurate ab initio Al-He pair potentials and the Balling and Wright pairwise Hamiltonian model are used to describe the full potential and the electronic asymmetry arising from the open-shell character of the Al atom in its ground and excited electronic states.

To extend our investigation to more than one impurity atom, we develop a novel approach to the determination of the interaction between two atoms, each in a 2P electronic state, embedded in a cluster of spherical atoms. The model transforms accurate ab initio potential energy curves for all the 36 molecular orbital states of the M-M system into a set of 36 Cartesian states that correspond to assigning the two 3p electrons to Cartesian orbitals centered on each atom. In this Cartesian state basis, the matrix elements corresponding to the interaction of each 2P atom with any number of surrounding spherical ligands can be determined. The lowest eigenvalue of the resulting 36× 36 matrix defines, in an adiabatic approximation, the potential governing the motion of the atoms.

We use PIMC simulations to study the structural properties of pure solid para-hydrogen (pH2) and Al atoms embedded in solid pH2. For a single impurity Al atom, we predict the 3p electron density to be distributed mainly along one particular direction. This lowers the static lattice energy. For two Al atoms embedded in solid pH2 / oD2, we found that if the initial substitution sites are within a distance of ~ 13 Bohr, the Al atoms will significantly distort the lattice structure to allow recombination, with an accompanying release of energy during the process. For substitution distances longer than 14 bohr, the dispersion of Al atoms is shown to be metastable.

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