Ensemble Hartree-Fock and Kohn-Sham Schemes for Excited States

Abstract

Ground state Hartree Fock (HF) theory not only has proven a valuable tool to calculate the ground state properties of electronic systems, but has also served as a starting point for more sophisticated approaches which deal with correlation, like configuration interaction methods and density functional theory (DFT). Ground state HF theory is based on the Rayleigh-Ritz variational principle, which states that, the expectation value of the Hamiltonian of the N-electron system (atomic units)

$$H = \sum\limits_i {[ - \frac{\nabla }{2} + {U_{ext}}(r) + \frac{1}{2}\sum\limits_{j \ne i} {\frac{1}{{{r_{ij}}}}} ]}$$