Analytic and Variational Xα in the Slater−Roothaan Method

An analytic and mathematically variational linear-combination-of-atomic-orbitals density-functional method that allows arbitrary scaling of the Slater−Gáspár−Kohn−Sham exchange-correlation potential about each atom is described. The method can be made exact in the separated-atom limit. It is based on robust and variational fitting, which is reviewed and extended to fast-multipole methods. The Slater−Roothaan method requires four basis sets and delivers a total energy that is independent of all fitting errors through first order. A database of atomic Gaussian basis sets is used to construct inputs for a standard set of 56 molecules. That database contains our basis sets as well as the DGauss DZVP2 double-ζ and 6-311G triple-ζ polarized Gaussian basis sets for fitting molecular orbitals. Another two subdatabases contain the s- and non-s-type basis sets for fitting the charge density and the exchange-correlation potentials, which are related to the cube root of a partitioned density and its square. A bond-centered basis function can be added to all fitting bases via software. Eight different fitting basis sets are studied. Using the Hartree−Fock values of α, these molecules are overbound on average, but using a uniform α = 0.7, these molecules are underbound on average, independent of fitting basis. Mixing exact exchange will not obviously improve the method.