Alternative perspective on density-functional perturbation theory

Perturbation theory is examined in analytic density-functional theory (ADFT), for which V representability means slightly more than in conventional density-functional theory because the potential is fitted. There is synergism between variationality and V representability. Together they redirect the object of perturbation theory from the set of occupied virtual orbital rotations to the change in the fit to the Kohn-Sham potential, which is called the Sambe-Felton potential. This reduces the dimensionality of perturbation theory from order N-2 to order N, where N is the number of basis functions. With variational fitting, no fractional or negative powers of the density appear when using the Slater exchange kernel, which is proportional to the cube root of the spin density. Requiring the Fock matrix and density matrix to commute through each order of perturbation theory determines the role of fractional occupation numbers in density-functional perturbation theory, which are treated via the corresponding nonintegral differences between the occupation numbers of orbitals. This theory is tested by removing a tenth or twentieth of an electron from the highest occupied molecular orbital for a standard set of small molecules, in which case the first- and second-order perturbed energies are accurate to 70%, when compared to the energy difference of the two corresponding self-consistent-field (SCF) calculations. For an all-electron ADFT calculation on a C-4v-symmetric Zr6O12 cluster, the timing for all SCF coupled perturbed iterations is not significant compared to the single required N-4 sum over occupied and virtual orbitals.