Generalization of the periodic LCAO approach in the CRYSTAL code to g-type orbitals

Abstract

The Linear Combination of Atomic Orbitals approach implemented into the public Crystal program for quantum-chemical simulations of n-dimensional periodic systems ( $$n = 0,1,2,3$$ ) is here extended to g-type basis functions. A general algorithmic procedure is devised for the calculation of the coefficients needed for the analytical evaluation of one- and two-electron integrals for energy and forces within the recursive McMurchie–Davidson strategy, up to arbitrarily high quantum numbers. Explicit routines are generated for the calculation of all the coefficients needed for g-type functions, which ensure a very high computational efficiency. The code has been generalized in many respects so as to allow for the use of g-type functions for: (1) Hartree–Fock energy and forces; (2) density functional theory energy and forces (in either a local density, generalized gradient, meta-GGA or various hybrid approximations); (3) all-electron and pseudo-potential basis sets; (4) spin-restricted and unrestricted calculations; (5) coupled-perturbed Hartree–Fock/Kohn–Sham (hyper)-polarizability calculations; (6) projected density-of-states. The g-type basis functions are expected to play an important role in (1) the description of the electronic structure of heavy elements and in particular of lanthanides and actinides with occupied 4f and 5f bands, respectively, where they represent the first polarization, (2) those calculations requiring an accurate description of the electronic polarization.