Approximations to Matsubara Dynamics for Vibrational Spectra

In this thesis, we investigate path-integral methods for the purpose of accurately and efficiently including nuclear quantum effects in vibrational spectra, with a particular focus on anharmonic dynamics and non-fundamental transitions. All the methods investigated are approximations to Matsubara dynamics, which is a rigorous theoretical framework that recovers quantum Boltzmann-conserving classical dynamics in an extended space of smooth imaginary-time Feynman paths by removing real-time quantum coherence. Standard path-integral methods like ring-polymer molecular dynamics and centroid molecular dynamics introduce well-understood artefacts in the high-frequency stretching modes. Quasicentroid molecular dynamics (QCMD), a curvilinear mean-field approximation to Matsubara dynamics, alleviates the curvature problem encountered by centroid molecular dynamics. We develop two methods, using a local and global coordinate system, that generalize the original implementation of QCMD beyond water to more complex geometries. We report the first QCMD results for gas-phase ammonia, demonstrating excellent line shapes and frequencies for fundamental transitions. This method also introduces artefacts into the calculation, near reaction barriers, but the resulting errors are found to be minor. With classical and path-integral simulations of isotopically substituted systems we investigate the role of dynamical vibrational couplings in condensed-phase water. We show that the assumption that the vibrational couplings can be treated as independent is valid for infrared and anisotropic Raman spectroscopy, but not for isotropic Raman spectroscopy, and that the magnitude of nuclear quantum effects is minor. Finally, we investigate including centroid-Matsubara fluctuation mode coupling in dynamics by using a harmonic approximation to Matsubara dynamics, with the aim of capturing the full quantum intensity of combination, overtone and difference bands in vibrational spectra. Through simulations of the OH bond we show this works well in one dimension but is too drastic an approximation to work in multi-dimensions.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Haggard, Christopher

Advisor dc:contributor.advisor

• Althorpe, Stuart

• Matsubara Dynamics
• Nuclear Quantum Effects
• Path Integrals
• Quantum Dynamics
• Vibrational Spectroscopy

Licence

• https://www.repository.cam.ac.uk/bitstreams/466cb8cb-a749-46a8-a5eb-33eeba5af29d/download
• http://purl.org/NET/rdflicense/allrightsreserved

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.116562

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/381346