arXiv subjects

Nadine Bradbury

Publications and source records attributed to Nadine Bradbury.

8 recordsLinked to original sources

arXiv2026

A Perspective on Phase Space Electronic Structure Theory : From Its Surface Hopping Origins Through To Its Future Promise

We trace the history of phase space electronic structure theory (PSEST), high- lighting how this powerful approach emerged from fundamental questions in semi- classical surface hopping dynamics and evolved into an alternative to standard Born- Oppenheimer based electronic structure theory (with moving instead of frozen nuclei). Our goal herein is not to recapitulate the mathematical details of phase space electronic structure calculations, and few equations are presented so as to maximize readability. Instead, our goal is to provide intuition for those new to the field both (i) regarding the physics present when solving the Schrodinger equation in a non-inertial frame as well as (ii) regarding why PSEST is a necessary step forward towards understanding chemical problems involving spin (with limited practical alternatives). We further high- light some of the many open questions in this fast developing area, which will hopefully inspire new practitioners in this field. This intuitive perspective lacks many equations and is meant to complement (rather than replace) the more technical review given in Bian et al, Chem. Phys. Rev. 7, 011303 (2026)

physics.chem-ph↗

arXiv2026

A Phase Space Electronic Structure View of The Solid State

We develop a phase space electronic structure view of the solid state, where electronic bands are parameterized by both nuclear position $\mathbf{Q}$ and nuclear momentum $\mathbfΠ$ (rather than the standard practice of only $\mathbf{Q}$). Within this phase space, non-Born-Oppenheimer electronic structure context, we prove a nuclear wavevector ($\mathbf{q}$)-dependent version of Nafie's equality relating the change in electronic momentum as a function of nuclear momentum, $\partial \langle\mathbf{p}\rangle/\partial \mathbfΠ_q$, to the change in electronic position as a function of nuclear position, $\partial \langle\mathbf{r}\rangle/\partial \mathbf{Q}_q$. Furthermore, we show how information about electron-phonon interactions, specifically nuclear-induced electronic momentum, can be extracted from simple band structure calculations -- without Berry curvature calculations.

physics.chem-ph↗

arXiv2026

A Conceptual Shift In Our Understanding of Degenerate Radical Spin Systems: Spin-Rotation Coupling Turned On Its Head

For most chemists, Kramers' degeneracy refers to the fact that for any radical system, every potential energy surface is at least doubly degenerate (with spin up and spin down, time-reversed solutions) for all nuclear positions $\mathbf{X}$. That being said, as is well-known to the community of spin chemists, one can experimentally detect a splitting of almost every rotational energy level for a doublet system -- highlighting the fact that nuclear motion breaks the spin degeneracy of such BO electronic states. Thus, as far as predicting experimental spectra, the implications of BO degeneracy are very limited unless one further includes a complete treatment of nuclear-electronic entanglement in a robust fashion; indeed, understanding radical molecules (and the degeneracy of their stationary states) can be extremely non-intuitive within the paradigm of Born-Oppenheimer potential energy surfaces. Now, as an alternative to BO theory, recent theory has suggested characterizing radical potential energy surfaces as functions of both nuclear position $\mathbf{X}$ and nuclear momentum $\mathbf{P}$, an approach which has been shown to recover a host of observables outside of BO theory, e.g., vibrational circular dichroism, Raman optical activity, and lambda doubling. Here, we show that such a technique predicts that different spin states will follow different (nondegenerate) potential energy surfaces and that the differences in these spin-dependent surfaces is quantitatively consistent with experimental spin-rotation couplings -- all without any contradiction with regard to Kramers' degeneracy. Thus, the present finding suggests there is still a great deal to learn about spin-resolved molecular reactivity, demanding a conceptual shift in our understanding of coupled spin-nuclear motion, especially in the context of chiral molecules and materials where spin-separation is known to arise.

physics.chem-ph↗

arXiv2026

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

$Λ$-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.

physics.chem-ph↗

arXiv2025

The Phase-Space Way To Electronic Structure Theory and Subsequently Chemical Dynamics

Phase-space electronic structure theory offers up a new and powerful approach for tackling problems with coupled nuclear-electronic dynamics in a fashion that goes beyond Born-Oppenheimer (BO) theory. Whereas BO theory stipulates that we consider electronic states parameterized by nuclear position $X$ only, i.e. molecular orbitals are functions of nuclear positions but not nuclear velocities, phase-space (PS) theory allows for electronic states to be parameterized by both nuclear position X and nuclear momentum $P$. As a result, within a phase-space approach, one can directly recover many new features, including electronic momentum and vibrational circular dichroism spectra. Moreover, phase-space electronic structure theory is exact for the hydrogen atom and, for a set of model problems, the method can even improve upon vibrational energies relative to BO theory. Perhaps most importantly, the phase-space approach offers up a very new perspective on spin physics, stipulating that molecules and materials with degenerate or nearly degenerate ground states (due to spin degeneracy) display broken-symmetry ground states in their phase-space potential energy surfaces. This last feature opens up very new possibilities for exploring spin chemistry (including the Einstein-de Haas effect and chiral induced spin selectivity) within the context of more established electronic structure theory. At the end of the day, in order to tackle electronic dynamical phenomena, especially subtle problems in magnetic chemistry, it will be essential for the electronic structure community to pivot towards diagonalizing $\hat H_{PS}(X, P)$ rather than $\hat H_{BO}(X)$.

physics.chem-ph↗

arXiv2025

Conical Intersections and Electronic Momentum As Viewed From Phase Space Electronic Structure Theory

We investigate the structure of a prototypical two-state conical intersection (BeH$_2$) using a phase space electronic Hamiltonian $\hat{H}_{PS}(\bR,\bP)$ that goes beyond the Born-Oppenheimer framework. By parameterizing the electronic Schr{ö}dinger equation by both nuclear position ($\bR$) and momentum ($\bP$), we solve for quantum electronic states in a moving frame that can break time reversal symmetry and, as a result, the branching plane of the conical intersection within a phase space framework now has dimension three (rather than dimension two as found within the standard Born-Oppenheimer framework). Moreover, we note that, if one fixes a geometry in real space that lies in the conical intersection seam and scans over the corresponding momentum space, one finds a double well (with minima at $\pm \bP_{min} \ne 0$), indicating that the stationary electronic states of the phase space electronic Hamiltonian carry electronic momentum -- a feature that cannot be captured by a Born-Oppenheimer electronic state. Interestingly, for $BeH_2$, this electronic momenta (as calculated with full configuration interaction) agrees with what is predicted by approximate complex restricted Hartree-Fock calculations, indicating a physical interpretation of complex instabilities in modern electronic structure calculations. Altogether, this study suggests that we have still have a lot to learn about conical intersections when it comes to electronic momentum, and highlights the urgent need for more experiments to probe what photochemical observables can and/or cannot be captured by standard electronic structure that isolates conical intersections within the Born-Oppenheimer framework.

physics.chem-ph↗

arXiv2024

Stochastic Metholodgy Shows Molecular Interactions Protect 2D Polaritons

We introduce stochastic techniques that enable the simulations of polaritons resulting from placing giant 2D molecular aggregate crystals with $10^8$ interacting excitonic dyes in realistic multi-mode cavities. We show that the intermolecular coupling protects the formation of polariton states in the face of strong molecular disorder due to persistent delocalization of the dark molecular states. This demonstrates the nontrivial role of internal aggregate Hamiltonian in polariton properties, and the new computational method opens horizons for stochastic simulations of related systems.

physics.chem-ph↗

arXiv2022

Bethe Salpeter Equation Spectra for Very Large Systems

We present a highly efficient method for the extraction of optical properties of very large molecules via the Bethe-Salpeter equation. The crutch of this approach is the calculation of the action of the effective Coulombic interaction, $W$, through a stochastic TD Hartree propagation, which uses only 10 stochastic orbitals rather than propagating the full sea of occupied states. This leads to a scaling that is at most cubic in system size, with trivial MPI parallelization. We apply this new method to calculate the spectra and electronic density of the dominant excitons of a carbon-nanohoop bound fullerene system with 520 electrons, using less than 4000 core hours.

physics.chem-ph↗