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Summary
A phase-space electronic Hamiltonian is presented, which recovers beyond Born-Oppenheimer electronic momentum and current density without presuming an atomic orbital basis. The approach is shown to conserve momentum and recover electronic current density reasonably well.
Highlights
- A phase-space electronic Hamiltonian is developed, which boosts each electron into the moving frame of the nuclei closest in real space.
- The approach is shown to conserve momentum and recover electronic current density reasonably well.
- The method is tested on small organic molecules, and the results are benchmarked against finite-difference calculations.
- The approach is found to capture a significant portion of the electronic momentum in the adiabatic limit.
- The method is also shown to recover the electronic current density, which is essential for recovering the missing velocity-form of the electronic dipole moment and the magnetic dipole moment within BO theory.
- The approach is inexpensive and can be immediately applied to simulations of chiral-induced spin-selectivity experiments.
- The method has the potential to offer a new and powerful approach to post-Born-Oppenheimer electronic structure theory.
Key Insights
- The phase-space electronic Hamiltonian approach offers a new and powerful way to include non-Born-Oppenheimer effects in electronic structure theory, which is essential for understanding various phenomena, including chiral-induced spin-selectivity.
- The approach is based on a simple and intuitive idea of boosting each electron into the moving frame of the nuclei closest in real space, which allows for the recovery of electronic momentum and current density.
- The method is shown to conserve momentum, which is a critical aspect of any electronic structure theory, and it is also found to recover the electronic current density reasonably well.
- The approach has the potential to be widely applicable, as it is inexpensive and can be immediately applied to simulations of chiral-induced spin-selectivity experiments.
- One of the key advantages of the approach is that it does not presume an atomic orbital basis, which makes it more flexible and widely applicable.
- The method is tested on small organic molecules, and the results are benchmarked against finite-difference calculations, which provides a strong validation of the approach.
- The approach has the potential to offer new insights into the behavior of electrons in molecules, particularly in situations where non-Born-Oppenheimer effects are significant.
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Citation
Tao, Z., Qiu, T., Bian, X., & Subotnik, J. E. (2024). A Basis-Free Phase Space Electronic Hamiltonian That Recovers Beyond Born-Oppenheimer Electronic Momentum and Current Density (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2407.16918