Applications of Simulated Annealing in Electronic Structure Studies of Metallic Clusters

Abstract

With the advent of the density functional formalism¹, improved numerical schemes, and the steady increase in computational power, researchers are now confidently studying a wide variety of technologically important materials properties which in some cases are not amenable to laboratory observation. In this paper, we survey an all-electron, full potential computational algorithm which employs a compact basis set of Gaussian type function for such studies. In Sec. II, the computationally intensive steps of this problem and recent work-toward reducing the computational complexity, are briefly reviewed^2,3. By incorporating a simulated annealing algorithm we are able to simultaneously vary both the linear and nonlinear “electronic coordinates” and, when necessary, bypass the direct diagonalization step. With this formulation, the computational cost increases linearly with the number of atoms in the regime of tens to hundreds of non-identical atoms^3,4. This method enables the accurate evaluation of Hellmann-Feynman (HF) forces. In Sec. III through V we present static and dynamic simulations on a variety of lithium clusters ranging in size from two to twenty seven atoms. By way of these examples, we explicitly show how to predict vacancy formation energies, defect induced lattice relaxation, cohesive energies and vibrational phenomena in many-atom systems. In addition, by carrying out calculations on successively larger crystal fragments, we are able to simulate crystal growth and observe the transition from atomistic to bulk phenomena. The cohesive energies, bulk moduli and lattice constants are presented as a function of cluster size and are found to agree favorably with other theoretical and experimental perfect crystal results.