arXiv subjects

Mansi Bhati

Publications and source records attributed to Mansi Bhati.

11 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

Electronic Structure in a Phase Space, non-Born-Oppenheimer Framework: Geometric Forces and Moody-Shapere-Wilzcek Revisited

We revisit the three-body problem in quantum mechanics in two and three dimensions, generating both exact eigenvalues and eigenvectors of the Hamiltonian and a series of approximate solutions as calculated with a variety of different schemes to separate heavy ("nuclear") and light ("electronic") particles. We show that, with minimal extra cost, one can go beyond the Born-Oppenheimer approximation by performing electronic structure calculations parameterized by both the nuclear position (${\mathbf X})$ and the nuclear momentum ($\mathbf{P}$), a so-called phase space theory of electronic structure. In particular, we demonstrate that such phase space electronic structure calculations correctly incorporate the non-inertial Coriolis and centrifugal forces felt by electrons in a moving nuclear frame, thus leading to far more accurate eigenenergies and electronic angular momenta than has been possible before. We also demonstrate that our approach naturally incorporates and generalizes the Moody-Shapere-Wilczek magnetic monopole for the non-abelian Berry curvature (now allowing for vibrational motion rather than a diatomic of fixed length). We argue that the resulting approach should be extremely useful for propagating dynamics where angular momentum flows between nuclei and electrons; in particular, if extended to include spin degrees of freedom, the present approach will offer a practical means to study chiral induced spin selectivity through the lens of chiral phonons and coupled nuclear-electronic motion.

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↗

arXiv2025

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

$\Lambda$-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 $\Lambda$-doubling energy splitting (or $\Lambda$-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 $\Lambda-$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

Non-Resonant Raman Optical Activity From Phase-Space Electronic Structure Theory

In order to model experimental non-resonant Raman optical activity, chemists must compute a host of second-order response tensors, (e.g. the electric-dipole magnetic-dipole polarizability) and their nuclear derivatives along a set of vibrational modes. While these response functions are almost always computed within a Born-Oppenheimer (BO) framework, here we provide a natural interpretation of the electric-dipole magnetic-dipole polarizability within phase space electronic structure theory, a beyond-BO model whereby the electronic structure depends on nuclear momentum (P) in addition to nuclear position (R). By coupling to nuclear momentum, phase space electronic structure theory is able to capture the asymmetric response of the electronic properties to an external field, in sofar as for a vibrating (non-stationary) molecule, dmu/dB \ne dm/dF, where mu and m are the electrical linear and magnetic dipoles, and F and B are electric and magnetic fields. As an example, for a prototypical methyloxirane molecule, we show that phase space electronic structure theory is able to deliver a reasonably good match with experimental results in a manner that is invariant to gauge origin G0.

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↗

arXiv2024

A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field I: Conservation of Total Pseudomomentum and Angular Momentum

We develop a phase-space electronic structure theory of molecules in magnetic fields. For a system of electrons in a magnetic field with vector potential $\bf{A}(\hat{\bf{r}})$, the usual Born-Oppenheimer Hamiltonian is the sum of the nuclear kinetic energy and the electronic Hamiltonian, $\frac{(\bf{P} - q\bf{A}(\bf{X}) )^2}{2M} + \hat{H}_{e}(\bf{X})$ (where $q$ is a nuclear charge). To include the effects of coupled nuclear-electron motion in the presence of magnetic field, we propose that the proper phase-space electronic structure Hamiltonian will be of the form $\frac{(\bf{P} - q^{\textit{eff}}\bf{A}(\bf{X}) - e\hat{\bf{\Gamma}})^2}{2M} + \hat{H}_{e}(\bf{X})$. Here, $q^{\textit{eff}}$ represents the {\em screened} nuclear charges and the $\hat{\bf{\Gamma}}$ term captures the local pseudomomentum of the electrons. This form reproduces exactly the energy levels for a hydrogen atom in a magnetic field; moreover, single-surface dynamics along the eigenstates is guaranteed to conserve both the total pseudomomentum as well as the total angular momentum in the direction of the magnetic field. This Hamiltonian form can be immediately implemented within modern electronic structure packages (where the electronic orbitals will now depend on nuclear position ($\bf{X}$) and nuclear momentum ($\bf{P}$)). One can expect to find novel beyond Born-Oppenheimer magnetic field effects for strong enough fields and/or nonadiabatic systems.

physics.chem-ph↗

arXiv2024

A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field II: Quantum Chemistry Calculations with Gauge Invariant Atomic Orbitals

In a companion paper, we have developed a phase-space electronic structure theory of molecules in magnetic fields, whereby the electronic energy levels arise from diagonalizing a phase-space Hamiltonian $\hat H_{PS}(\bf{X},\bf{\Pi})$ that depends parametrically on nuclear position and momentum. The resulting eigenvalues are translationally invariant; moreover, if the magnetic field is in the $z-$direction, then the eigenvalues are also invariant to rotations around the $z-$direction. However, like all Hamiltonians in a magnetic field, the theory has a gauge degree of freedom (corresponding to the position of the magnetic origin in the vector potential), and requires either $(i)$ formally, a complete set of electronic states or $(ii)$ in practice, gauge invariant atomic orbitals (GIAOs) in order to realize such translational and rotational invariance. Here we describe how to implement a phase-space electronic Hamiltonian using GIAOs within a practical electronic structure package (in our case, Q-Chem). We further show that novel phenomena can be observed with finite $\bf{B}-$fields, including minimum energy structures with $\bf{\Pi}_{min} \ne 0$, indicating non-zero electronic motion in the ground-state.

physics.chem-ph↗

arXiv2024

A Phase Space Approach to Vibrational Circular Dichroism

We show empirically that a phase-space non-Born-Oppenheimer electronic Hamiltonian approach to quantum chemistry (where the electronic Hamiltonian is parameterized by both nuclear position and momentum, (H(R,P)) is both a practical and accurate means to recover vibrational circular dichroism spectra. We further hypothesize that such a phase space approach may lead to very new dynamical physics beyond spectroscopy circular dichroism, with potential implications for understanding chiral induced spin selectivity (CISS), noting that classical phase space approaches conserve the total nuclear plus electronic momentum, whereas classical Born-Oppenheimer approaches do not (they conserve only the nuclear momentum)

physics.chem-ph↗

arXiv2024

Practical Phase-Space Electronic Hamiltonians for Ab Initio Dynamics

Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian H_{el}(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Gamma') and rotational (Gamma'') factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, H_{PS}(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator H_{el}(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of H_{PS}(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.

physics.chem-ph↗

arXiv2024

A Simple One-Electron Expression for Electron Rotational Factors

Within the context of FSSH dynamics, one often wishes to remove the angular component of the derivative coupling between states $\left|J\right>$ and $\left|K\right>$. In a set of previous papers, Truhlar {\em et al.} posited one approach for such a removal based on direct projection, while we isolated a second approach by constructing and differentiating rotationally invariant basis. Unfortunately, neither approach was able to demonstrate a {\em one-electron operator} $\hat{O}$ whose matrix element $\left $ was the angular component of the derivative coupling. Here, we show that a one-electron operator can in fact be constructed efficiently in a semi-local fashion. The present results yield physical insight into designing new surface hopping algorithms and be of immediate use for FSSH calculations.

physics.comp-ph↗