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Electron trajectories in molecular orbitals
Author(s) -
Sumner Isaiah,
Anthony Hannah
Publication year - 2020
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26371
Subject(s) - physics , wave function , electron , quantum mechanics , atomic orbital , zitterbewegung , classical mechanics , spin (aerodynamics) , thermodynamics
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.