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The basis set polarization approach is applied to the generation of medium-size polarized GTO/CGTO basis sets for accurate calculations of molecular dipole moments and polarizabilities. The polarized basis sets determined in this paper for H and C through F are employed in SCF HF and MBPT calculations of dipole moments and polarizabilities of FH, H2O, NH3, and CH4. The excellent results obtained at both the SCF HF and MBPT(4) levels of approximation indicate that the present basis sets can be employed for the accurate high-level correlated studies of relatively large molecules The use of those basis sets in calculations of intermolecular interactions is also discussed.

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A method for the iterative algebraic generation of the numerically accurate two-component Hamiltonian for the use in relativistic quantum chemistry is presented. The separation of the electronic and positronic states of the Dirac Hamiltonian is accomplished by the algebraic solution for the Foldy–Wouthuysen transformation. This leads to the two-component formalism whose accuracy is primarily limited by the choice of basis functions. Its performance is tested in calculations of the most sensitive 1s1/2 energy for increasing values of the nuclear charge. These calculations show that the electronic part of the Dirac eigenspectrum can be obtained from the two-component theory to arbitrarily high accuracy. Moreover, if needed, the positronic states can be separately determined in a similar way. Thus the present method can be also used for the evaluation of quantum electrodynamic corrections in the finite basis set approximation.

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.