Model Hamiltonians parametrized by Kohn-Sham density functional theory

We have developed a semiempirical method using a model Hamiltonian based on the Energy Weighted Maximum Overlap (EWMO) formalism. We introduced adjustable parameters in to the EWMO formula and fitted them to MO energies calculated by Kohn-Sham Density Functional Theory (KS-DFT). Our goal is to reproduce the molecular orbital (MO) energies of KS-DFT at a small fraction of the KS-DFT computational cost. The only integrals that we calculate are overlap integrals and the most time-consuming step in our calculation is to do a single diagonalization of a valence-only Hamiltonian matrix.; This method was applied to small silicon clusters Si_n, n = 10 to 16 and polysilanes H₃Si-(SiH₂)_n-SIH ₃. We evaluated the performance of the method by analyzing the HOMO-LUMO gap and density of states (DOS). For Si₁₀, the HOMO-LUMO gap calculated by the semiempirical method was reproduced with a root mean square (RMS) deviation of 0.29 eV compared to KS-DFT. For the Si₁₁ to Si₁₆ clusters, the gap was reproduced with an average (RMS) error of 0.24 eV. For polysilane, we investigated the effect of chain length, backbone conformation, substituents and removal of hydrogens on the HOMO-LUMO gap and DOS using both KS-DFT and the semiempirical method. In each case, the model was able to reproduce the KS-DFT HOMO-LUMO gaps relatively well. The semiempirical method was also used to simulate the effect of dopants and of an electric field on the polysilane chain to demonstrate possible future applications.