On the physical meaning of the ZORA Hamiltonian

Abstract

By expanding the Foldy-Wouthuysen representation of the Dirac equation near the free-particle solution it is shown that the Hamiltonian of the zeroth-order regular approximation (ZORA) leads to an infinite summation of the leading relativistic corrections to the free-particle, non-relativistic energy. The analysis of the perturbation expansion of the ZORA Hamiltonian reveals that the ZORA Hamiltonian recovers all terms of the Breit-Pauli theory to second order. This result is general and applies not only to hydrogen-like atomic ions (as was demonstrated before) but also to a wide variety of physical problems. ZORA is analogous to the random phase approximation in many-body theory in the sense that both methods include an infinite-order summation of the asymptotically non-vanishing terms. This highlights the difference between ZORA and the Douglas-Kroll method, with the latter being analogous to finite-order many-body perturbation theory. On the basis of this analysis the performance of ZORA when calculating various molecular properties is discussed.