Assessment of relative stabilities of positional isomers of polyhedral heteronuclear clusters via a simplified method of bond energy calculations based on tight-binding approach and adjacent matrix method: applications to binary icosahedral clusters

A new and simple method for assessing the relative stabilities of various positional isomers of a given heteronuclear cluster is described. The method is based on a tight-binding approach in conjunction with an adjacent matrix methodology (TBAM). The usefulness of the method is illustrated by bond energy calculations of a number of binary icosahedral clusters, including noncentered icosahedral A(n)B(12)(-)n clusters comprising main-group elements B, C, N, and S as well as B- and A-centered icosahedral A(n)B(13)(-)n clusters that consist of transition metals, Au, Ag, Ni, and Pt atoms. The latter results are compared with the previously reported molecular mechanics calculations based on Lennard-Jones potential and with experimental results, whenever possible. The trends of the total bond energies obtained by the two methods are nearly parallel in all cases, indicating that the relative stabilities predicted by the two methods follow the same order. The TBAM approach provides a simple and efficient way of predicting the relative stabilities of various positional isomers of a given cluster, particularly for clusters where the number of positional isomers is so large that it cannot be handled manually. The total bond energies exhibit a stepwise progression. Each step is characterized by a set of A-A, B-B, and A-B bonds which uniquely determines the total bond energy and, hence, the stability. The step formation implies that positional isomers of a given cluster geometry can be categorized by sets of numbers of A-A, B-B, and A-B bonds, or simply the numbers of the minority (either A-A or B-B) bonds. Three site preference rules, the strong-bond rule, the heterobond rule, and the big-hole rule, were formulated based on these model calculations. These rules are useful in rationalizing and/or predicting the relative stabilities of various positional isomers of a given cluster geometry.