Fermi contact interactions evaluated from hidden relations in the Schrödinger equation
Wednesday, November 12, 2008 - 4:00pm - 5:00pm
Fermi contact interactions between electrons and nuclei govern important properties such as the hyperfine coupling constants observed in Electron Spin Resonance Spectroscopy and the spin-spin coupling constants observed in Nuclear Magnetic Resonance Spectroscopy. But approximate wavefunctions of the kinds commonly used for molecules are generally optimized through some kind of overall energy criterion, and so may have significant errors for the electron density at position of a nucleus where the Fermi contact interaction occurs. It will be shown how hidden relations that are implicit in the Schrödinger equation allow the Fermi contact interactions to be reexpressed in terms of more global properties of the electron density. For exact wavefunctions the hidden relations would give the same results as would direct pointwise evaluation of the electron density, but for approximate wavefunctions the results may differ and in fact provide improved accuracy. The relevant equations will be derived, and numerical examples will be given that demonstrate the point. An extension to higher order will also be developed for the well-known Kato cusp condition that constrains the behavior of the wavefunction at the singularity that occurs when two particles coalesce.