Analysis of self-consistent extended Hückel theory (SC-EHT): a new look at the old method

We present an extensive analysis of the self-consistent extended Hückel theory (SC-EHT) and discuss the possibilities of constructing accurate and efficient semiempirical methods on its basis. We describe the mapping approach to derive a self-consistency correction to the effective 1-electron Hamiltonian (Fock) operator that is utilized in electronic structure calculations and that variationally minimizes the total energy in the SC-EHT method. We show that the SC-EHT Hamiltonian can play the role of the 1-electron operator by definition, in which case no self-consistency correction is needed. Then, the SC-EHT method can be derived from the Hartree–Fock theory by approximation of the Fock matrix. Therefore, the SC-EHT based methods have rigorous foundations that may be utilized to develop a family of successively accurate model Hamiltonians. We analyze the underlying approximation and discuss it in the light of existing formulations of the EHT method. We indicate two major deficiencies of the existing formulations of the EHT method—neglect of exchange integrals and incorrect asymptotic behavior of the Coulomb integrals. The SC-EHT is compared to the charge equilibration scheme and to the DFTB family of approximations. We show that an improved version of the SC-EHT method can be connected to both of them, indicating relation of the SC-EHT derived approximations to the fundamental DFT origins and their potential for efficient computations on large-scale systems.