Relativistic effects on electric properties of many-electron systems in spin-averaged Douglas-Kroll and Pauli approximations

Relativistic effects and electron correlation effects on the dipole moments of the coinage metal hydrides are investigated and compared employing one-component (scalar) relativistic approximations based on the mass-velocity and Darwin operator and, alternatively, the Douglas-Kroll-transformed spin-averaged no-pair Hamiltonian. The former of the two operators is found to perform quite accurately for CuH and AgH. For AuH the limits of the Pauli approximation seem to be reached, as can be inferred from a comparison with the values obtained within the spin-averaged Douglas-Kroll no-pair formalism. The coupled cluster calculations in the Douglas-Kroll no-pair approximation for relativistic effects establish the dipole moment values of the coinage metal hydrides as equal to 1.05 a.u. for CuH, 1.14 a.u. for AgH and 0.52 for AuH. The corresponding non-relativistic results are 1.14 a.u., 1.36 a.u., and 1.22 a.u., respectively. Some formal problems arising in applications of the Douglas-Kroll no-pair approximation are discussed. It is shown that the Hellmann-Feynman theorem leads to a rather complicated form of the first-order energy change due to external perturbation. The usual expectation value formula is, however, valid through terms proportional to 1/c(4) and can be used in most applications. The invariance property with respect to a shift in the external potential is addressed for the Douglas-Kroll no-pair approximation in a finite basis set. (C) 1996 American Institute of Physics.