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 MO4 for M=Ru, Os, Hs (Z=108) are studied with the help of second-order Moller-Plesset perturbation theory using the infinite-order regular approximation with modified metric Hamiltonian. The polarizabilities obtained vary in the sequence RuO4>OsO4>HsO(4), which is different from those obtained in other studies. However, it is in line with calculated T-1(2)<--(1)A(1) excitation energies of the group VIII tetroxides, which provide a measure for the magnitude of their polarizabilities. (C) 2003 American Institute of Physics.