Development of a Semi-empirical Hamiltonian for Phosphorus for Quantum Mechanics Based Simulations of Phosphorous-based Nanostructures

We have developed a parameterized semi-empirical Hamiltonian for phosphorous for simulation studies of phosphorous-based nanostructures including phosphorous-doped silicon nanowires.This Hamiltonian models the environment-dependent electron-ion and ion-ion interactions and electron-electron correlations, by capturing the salient features of \textit{ab initio} Hamiltonians/\textit{ab initio} methods, ($e.g$., electron screening and charge self-consistency).Such a semi-empirical Hamiltonian has been shown to be successful in predicting the properties of intermediate-sized silicon, boron, and carbon clusters and extended structures of boron and silicon [1-4]. We optimized the parameters of our Hamiltonian for phosphorous by fitting the properties of bulk (black phosphorous) and small clusters (P$_{2}$ to P$_{10})$ as obtained by our method to \textit{ab initio} calculations. It is expected that such a Hamiltonian will have the predictive power to enable the study of larger phosphorous based nanostructures that are not possible via \textit{ab initio} studies. \\[4pt] [1] C. Leahy, et al, Phys. Rev. B 74,155408 (2006). [2 ]P. Tandy, et al, Bulletin of the APS,2009 APS March Meeting Vol. 54, Num.1, Sess. D26, [3] Ming Yu, et al, J. Chem. Phys. 130,184708 (2009). [4] Ming Yu, S.Y. Wu, and C.S. Jayanthi, Physica E 42, 1 (2009).