Quantum-Dynamical Theory of Electron Exchange Correlation

The relationship between the spin of an individual electron and Fermi-Dirac statistics (FDS), which is obeyed by electrons in the aggregate, is elucidated. The relationship depends on the use of spin-dependent quantum trajectories (SDQT) to evaluate Coulomb’s law between any two electrons as an instantaneous interaction in space and time rather than as a quantum-mean interaction in the form of screening and exchange potentials. Hence FDS depends in an ab initio sense on the inference of SDQT from Dirac’s equation, which provides for relativistic Lorentz invariance and a permanent magnetic moment (or spin) in the electron’s equation of motion. Schroedinger’s time-dependent equation can be used to evaluate the SDQT in the nonrelativistic regime of electron velocity. Remarkably FDS is a relativistic property of an ensemble of electron, even though it is of order in the nonrelativistic limit, in agreement with experimental observation. Finally it is shown that covalent versus separated-atoms limits can be characterized by the SDQT. As an example of the use of SDQT in a canonical structure problem, the energies of the 1Σg and 3Σu states of H2 are calculated and compared with the accurate variational energies of Kolos and Wolniewitz.