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Electron Trajectories in Molecular Orbitals

revised on 16.06.2020, 13:52 and posted on 17.06.2020, 12:51 by Isaiah Sumner, Hannah Anthony
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, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic 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.


NSF CHE-1062629

NSF CHE-1229354

NSF CHE-1662030


Email Address of Submitting Author


James Madison University


United States

ORCID For Submitting Author


Declaration of Conflict of Interest

No conflicts of interest


Read the published paper

in International Journal of Quantum Chemistry