Electron trajectories in molecular orbitals. Issue 20 (16th July 2020) - Sumner, Isaiah
Abstract: The time‐dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well‐known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations as they predict that the electrons in a ground‐state, real, molecular wavefunction are motionless. However, a spin‐dependent momentum can be recovered from the nonrelativistic limit of the Dirac equation. Therefore, we developed new, spin‐dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin‐dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules. Abstract : Typically, electrons in molecules are shown as "molecular orbitals"—regions of space where the electron is likely to be found. However, it is possible to reimagine molecular orbitals as a flowing fluid. For example, the π ‐orbitals in benzene can be depicted as a fluid swirling around the carbon atoms and the benzene ring. The equations for this current are derived this article and are used to gain a new perspective on electrons in molecules.