Robust and variational fitting

Fitting used to simplify various approximations to the molecular Schrodinger equation is discussed. Robust fits correct the target function to first order in the error made due to fitting. Variational fits are compatible with the variational principle. A full variation of the fitted energy is used to generate the Fock matrix. Robust and variational fitting of the electric and magnetic fields of the electrons is defined. Robust-fitted MP2 (RF-MP2) methods are defined. Independent of how the charge distributions are fit, robust-fitted errors are quadratic in the difference between the fits and fitted quantities. Analytic, robust and variational fits of various fractional powers of electronic densities and other linear-combination-of-atomic-orbitals (LCAO) objects are described.