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Electron Trajectories in Molecular Orbitals

preprint
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.

Funding

NSF CHE-1062629

NSF CHE-1229354

NSF CHE-1662030

History

Email Address of Submitting Author

sumneric@jmu.edu

Institution

James Madison University

Country

United States

ORCID For Submitting Author

0000-0002-1422-5476

Declaration of Conflict of Interest

No conflicts of interest

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in International Journal of Quantum Chemistry

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