New proof explores electric and magnetic fields in molecules

Researchers calculate molecular magnetic response properties to and visualize electronic current densities for atoms and molecules. Traditionally, this work applies the quantum mechanical definitions for charge and current density using the continuity equation.

Paolo Lazzeretti reversed the conventional approach and applied perturbation theory to calculate current and charge densities for diamagnetic atoms and molecules with an even number of electrons. Through a series of proofs, Lazzeretti found that the continuity equation could be satisfied by the exact eigenfunctions of model Hamiltonian and with variationally optimal wave functions.

“Tests have been suggested to improve accuracy in computations of current density and charge density in molecules,” Lazzeretti said.

The density of charge and current produced by the optical electric and magnetic fields of a monochromatic plane wave satisfies continuity equations for real and complex electronic eigenfunctions for a model Hamiltonian with optimal variational wave functions.

Lazzeretti cautions that this approach is limited by the size of the molecule being studied. Larger molecules have greater data requirements to illustrate the three-dimensional current density grid. He believes future work mapping the continuity equation could provide clues about where the electron density fields deviate. This information could be used to improve charge and current density maps for a specific region of a molecule.

“The proof of continuity equations fills a gap in the theory,” Lazzeretti said. “It gives a way to estimate lack of continuity in computed current-density maps.”

Source: “Continuity equations for electron charge densities and current densities induced in molecules by electric and magnetic fields,” by Paolo Lazzeretti, The Journal of Chemical Physics (2019). The article can be accessed at https://doi.org/10.1063/1.5124250 .