Date of Award

Spring 2026

Document Type

Open Access Dissertation

Department

Chemistry and Biochemistry

First Advisor

Vitaly Rassolov

Second Advisor

Sophya Garashchuk

Abstract

In the Born-Oppenheimer (BO) approximation, nuclei are treated as classical particles. The theoretical and computational approaches that go beyond it are impractical for all but the smallest chemical systems. However, such methods are necessary to simulate many photochemical and biological processes. This thesis discusses two important topics of research in this feld: frst, improving electronic structure theory to efciently describe quantum nuclei; second, developing a scalable quantum dynamics method, the factorized electron-nuclear dynamics (FENDy).

Following the BO approximation, the electronic structure of molecules is routinely examined for static arrangements of point nuclei, which is a highly useful premise but not without limitations. A model system of electron-nuclear correlation is necessary for the development of electronic structure methods that include nuclear quantum efects. In Chapter 3, the electron-nuclear correlation energy is analyzed in the context of the quantized nuclear energy associated with chemical bond vibrations using the simple model of a hydrogen atom confned in a harmonic potential. The electron-nuclear correlation energy is found to be smaller in magnitude than the electron correlation in two-electron atomic systems. This suggests that a density functional theory (DFT)-like treatment of electron-nuclear correlation is possible.

To address the problem of scalability for fully quantum dynamics methods, I worked on the development of an exact factorization (XF)-based method that goes beyond the framework of the standard Born-Huang expansion. In Chapter 4, I describe the formalism and implementation of FENDy with an efective complex potential [J. Chem. Theory Comput. 19 (2023), pp 1393–1408] to study the dynamics of the H2+ molecular ion under a femtosecond laser pulse. In FENDy, the electronic wavefunction is represented using the atomic orbitals, without any need for the actual electronic eigenstates. The nuclear wavefunction is described by a quantum-trajectory ensemble, acting as a time-dependent optimal grid, thus circumventing the exponential scaling of a static grid with the system size. The challenging evaluation of the gradients on unstructured grids is performed by projection onto auxiliary bases.

Finally, in Chapter 5, I explore the limitations of FENDy in the case of diverging nuclear wavepackets that I encountered in the study of H2+. Using a minimal model of photodissociation, I analytically investigate the origins of this XF-challenge. I conclude that the singularity in the electronic wavefunction derivatives depends on the bifurcation of the nuclear wavepacket, and that it persists in a localized basis. The insights from this work could lead to further development of XF methods.

Rights

©2026, Julian Stetzler

Download

Included in

Chemistry Commons

Share

COinS