Spin-Interactions and the Non-relativistic Limit of Electrodynamics

Abstract

Abstract This chapter discusses how to extinguish spin–orbit interactions and/or scalar relativistic effects from four-component relativistic molecular calculations in order to assess their importance on molecular properties. It is pointed out that standard non-relativistic calculations use the non-relativistic free-particle Hamiltonian H ˆ p , but the relativistic Hamiltonian H ˆ int which describes the interaction between particles and fields. In the strict non-relativistic limit, electrodynamics reduce to electrostatics, that is there are no effects of retardation and no magnetic interactions. It is, however, perfectly reasonable from a pragmatic point of view to introduce both scalar and vector potentials in a non-relativistic framework. Non-relativistic theory can perfectly well accommodate magnetic sources, including spin, but does not provide a mechanism for generating them. We demonstrate that the pragmatic approach leads to some inconsistencies in that non-relativistic theory cannot describe spin–same orbit interactions, but spin–other orbit interactions. We also emphasize that the distinction between spin–orbit interactions and other spin interactions is somewhat artificial and highly dependent on the chosen reference frame. In a previous paper [L. Visscher and T. Saue, J. Chem. Phys. , 2000, 113 , 3996] we demonstrated how to eliminate spin–orbit interaction from four-component relativistic calculations of spectroscopic constants by deleting the quaternion imaginary parts of matrix representations of the modified Dirac equation. In this chapter, we discuss the extension of this approach to second-order electric and magnetic properties. We will demonstrate the elimination of poles corresponding to spin-forbidden transitions from the dispersion of the dipole polarizability of the mercury atom. More care is needed when considering second-order magnetic properties in that the elimination of quaternion imaginary parts will extinguish all spin interactions. A procedure is developed which allows us to demonstrate important spin–orbit effects on the NMR shielding polarizabilities of the xenon atom. It is also possible to extinguish all spin interactions in relativistic calculations, but only within the framework of the Sternheim approximation, that is when calculating the diamagnetic contribution as an expectation value.