The density matrix form of Hartree-Foek perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H2, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.

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