Phase Space Electronic Structure Theory: From Diatomic Lambda-Doubling to Macroscopic Einstein-de Haas

• URL: http://arxiv.org/abs/2512.13448v1
• Date: Mon, 15 Dec 2025 15:46:15 GMT
• Title: Phase Space Electronic Structure Theory: From Diatomic Lambda-Doubling to Macroscopic Einstein-de Haas
• Authors: Linqing Peng, Tian Qiu, Nadine Bradbury, Xuezhi Bian, Mansi Bhati, Robert Littlejohn, Nathanael M. Kidwell, Joseph E. Subotnik,
• Abstract summary: We show that a phase space theory can capture electronic momentum and model vibrational circular dichroism.<n>By parameterizing the electronic Hamiltonian in terms of both nuclear position and nuclear momentum, a phase space method yields potential energy surfaces.
• Score: 1.1730993190704666
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: $Λ$-doubling of diatomic molecules is a subtle microscopic phenomenon that has long attracted the attention of experimental groups, insofar as rotation of molecular $\textit{nuclei}$ induces small energetic changes in the (degenerate) $\textit{electronic}$ state. A direct description of such a phenomenon clearly requires going beyond the Born-Oppenheimer approximation. Here we show that a phase space theory previously developed to capture electronic momentum and model vibrational circular dichroism -- and which we have postulated should also describe the Einstein-de Haas effect, a macroscopic manifestation of angular momentum conservation -- is also able to recover the $Λ$-doubling energy splitting (or $Λ$-splitting) of the NO molecule nearly quantitatively. The key observation is that, by parameterizing the electronic Hamiltonian in terms of both nuclear position ($\mathbf{X}$) and nuclear momentum ($\mathbf{P}$), a phase space method yields potential energy surfaces that explicitly include the electron-rotation coupling and correctly conserve angular momentum (which we show is essential to capture $Λ-$doubling). The data presented in this manuscript offers another small glimpse into the rich physics that one can learn from investigating phase space potential energy surfaces $E_{PS}(\mathbf{X},\mathbf{P})$ as a function of both nuclear position and momentum, all at a computational cost comparable to standard Born-Oppenheimer electronic structure calculations.

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