Bertha — 4-Component Relativistic Molecular Quantum Mechanics

Abstract

The need to include relativistic effects in calculations of atomic structure and processes has been appreciated for many years. Although Dirac (1928) only considered the hydrogen atom, for which relativistic effects are tiny, his formalism showed that relativistic effects grow rapidly with atomic number Z, and Swirles (1935) was the first to formulate a relativistic self-consistent field formalism for many-electron atoms based on the Dirac hamiltonian. Little was done to apply this development until serious calculations on many-electron atoms became possible in the 1960s with the introduction of electronic computers, coinciding with a compact reformulation of the relativistic self-consistent field problem using Racah algebra (Grant 1961). Relativistic correlation effects were first studied in the 1970s, (Desclaux 1975, Grant et al., 1976) and relativistic electronic structure calculations can now be made for any open shell atom in the Periodic Table, limited only by the available computing power. Relativity profoundly affects the properties of matter. Although relativity cannot be switched off, it is a comforting fallacy to think that because an electron has a binding energy of only a few electron volts it exhibits no relativistic behaviour, and that perhaps relativistic effects can therefore be ignored. The analogy with a comet in a low energy solar orbit is instructive. The body accelerates in the solar gravitational field, reaching its maximum speed at perihelion, when it is closest to the sun. Similarly, a valence electron which probes the high potential regions near an atomic nucleus may move there with speeds approaching the velocity of light, even though its total energy is small. Quantitative radial density plots for hydrogen-like atoms were first made by Val Burke and myself (Burke et al., 1967) in the case of hydrogen-like mercury (Z = 80). Such density plots are all more compact than their nonrelativistic counterparts, and the orbital binding energies are correspondingly increased. Whereas Schrodinger states of hydrogenic atoms can be labelled by quantum numbers where is the principal quantum number, and are the orbital angular momentum of the electron and its projection on the quantization axis, and is the spin (up or down), Dirac states of a hydrogenic atom must be labelled by where now