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Analytic expressions for the derivatives of the total molecular energy with respect to external electric field are derived within the regular approximation to the full four-component relativistic Hamiltonian and presented in matrix form suitable for implementation in standard quantum-chemical codes. Results of benchmark calculations using the infinite-order regular approximation with modified metric method are presented and discussed. The static electric dipole polarizabilities of group VIII metal tetroxides MO[SUB4] for M = Ru, Os, Hs (Z5108) are studied with the help of second-order Møller-Plesset perturbation theory using the infinite-order regular approximation with modified metric Hamiltonian. The polarizabilities obtained vary in the sequence RuO[SUB4] > OsO[SUB4] > HsO[SUB4], which is different from those obtained in other studies. However, it is in line with calculated [SUP1]T[SUB2] ← [SUP1]A[SUB1] excitation energies of the group VIII tetroxides, which provide a measure for the magnitude of their polarizabilities. [ABSTRACT FROM AUTHOR]