Electronic Excitations in Crystalline Solids through the Maximum Overlap Method

The maximum overlap method (MOM) has emerged from molecular quantum chemistry as a convenient practical procedure for studying excited states. Unlike the Aufbau principle, during self-consistent field (SCF) iterations, the MOM forces orbital occupation to be maximally similar to that of a reference state. Although still within a single-particle framework, this approach allows for the evaluation of excitation energies (Δ-SCF) and geometry optimization of electronic configurations other than the ground state. In this work, we present an extension of the MOM to periodic crystalline solids, within the framework of an atom-centered Gaussian basis set. In order to obtain a realistic concentration of excited electrons, we allow excitation in only one-or a few-points of the Brillouin zone, leading to a fractional occupation of crystalline Kohn-Sham states. Since periodic SCF solution techniques involve an iteration between direct and reciprocal spaces, only totally symmetric excitations are allowed in our treatment, in order to preserve the translational symmetry: vertical Γ-point excitations or collective excitations in a sphere around Γ. Other types of excitations are accessible through folding of the Brillouin zone subsequent to the creation of a supercell. The features and performance of the method are presented through its application to prototypical solids such as bulk silicon, diamond, and lithium fluoride and comparing the results with the available experimental data. The demonstrative application to nickel oxide and solid CuI(piperazine)-a luminescent copper halide compound-highlights the promising potential of the MOM in solid-state quantum chemistry.