Exciton-vibration dynamics using real-time path integral methods

Kundu, Sohang

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https://hdl.handle.net/2142/121517 Copy

Description

Title

Exciton-vibration dynamics using real-time path integral methods

Author(s)

Kundu, Sohang

Issue Date

2023-07-14

Director of Research (if dissertation) or Advisor (if thesis)

Makri, Nancy

Doctoral Committee Chair(s)

Makri, Nancy

Committee Member(s)

• Hirata, So
• Luthey-Schulten , Zaida Anne
• Moore, Jeffrey

Department of Study

Chemistry

Discipline

Chemistry

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• quantum dynamics
• path integral
• energy transfer
• excitons
• vibrations
• vibronic
• photosynthesis
• light harvesting
• spectroscopy
• Herzberg-Teller

Abstract

Understanding how coupled electronic and nuclear motions modulate excitation energy transfer (EET) between molecules is essential for analyzing natural processes such as photosynthetic energy trapping, and for the design of viable synthetic frameworks for photovoltaic applications. Energy is typically transferred in molecular aggregates through excitonic couplings between electronic excited states, and the coupling to nuclear vibrations induces dynamic disorder through nonadiabatic interactions facilitating, hindering, or only spectating the energy transfer dynamics. Being condensed phase systems at finite temperatures, many spectroscopic measurements aimed at characterizing excitonic molecular aggregates must rely on accurate numerical simulations for predicting outcomes or rationalizing results. However, such simulations are often intractable or severely approximate owing to the exponential scaling of quantum mechanics with the number of degrees of freedom, and the need to sum over an astronomical number of wave function-based calculations to incorporate temperature effects within a statistical ensemble. This dissertation describes the recent development and use of novel dynamics methods based on Feynman’s path integral formulation of quantum mechanics that have shed light on EET in molecular aggregates of previously intractable sizes, and with unprecedented accuracy. The thesis is divided into two broad sections, I and II, of four and eight chapters respectively. In Part I, we discuss our development of two types of real-time path integral methods that are now integral to a set of complementary tools ideally suited for condensed phase quantum dynamics simulations. We first describe the crucial extensions of the modular path integral (MPI) that made it applicable to extended systems characterized by nondiagonal interactions, e.g., Frenkel excitonic molecular aggregates, and Heisenberg spin chains, incorporating nuclear normal modes at finite temperatures. Following this, we focus on the combination of two path integral methodologies – the established quantum classical path integral (QCPI) and the recent small matrix path integral (SMatPI), that makes the resulting tool (SMat-QCPI) significantly more powerful than its two precursors. Throughout Part I, we provide extensive numerical illustrations for both types of methods, in the context of studying condensed EET in model systems. Part II undertakes the task of deconstructing coupled electronic and vibrational effects in the dynamics of synthetic as well as photosynthetic systems. We use motions of probability densities on coupled potential surfaces, (analogous to wave-packet dynamics but at finite temperature) following a Franck-Condon (FC) excitation, and show that nonadiabatic interactions arising from exciton-vibration coupling manifest in nonlinearities and “effective” couplings between otherwise uncoupled nuclear normal modes. We then focus on J-aggregates of a bay-substituted perylene bisimide (PBI-1) and illustrate how high-frequency breathing vibrations of the perylene core result in vibronic features that dominate the early dynamics following the photoexcitation of these J-aggregates of varying sizes. Other relatively weakly coupled vibrations non-additively dampen and modulate the vibronic features becoming progressively more important at longer times, underlining the importance of collective vibrational motion. Next, we investigate the dynamics of light harvesting complexes (LH2) in photosynthetic bacteria Rhodospirillum molischianum, with three specific questions in mind. First, we include all intramolecular modes of each bacteriochlorophyll (BChl) molecule in extended linear and ring aggregates to show that excitations decay within 0.1 ps in aggregate sizes of >15 pigments solely based on dissipation enabled by intramolecular modes. This estimate is in excellent agreement with recent experiments, and aids us in resolving a debate in the photosynthetic literature about the role of discrete vibrations in modulating coherence lifetimes. Next, we turn towards the inter-ring energy transfer in the entire LH2 complex of 24 pigments. Our simulations recover the experimentally observed timescale of ~1 ps and find that 90% of the energy absorbed by the outer ring is transmitted inward at 300 K. Apart from providing the microscopic view of the exciton relaxation mechanism, this study raises the fundamental question of what enables the efficiency of the bacterial LH2 complex. Using a further set of probing calculations, we report how the arrangement of pigments in the two rings and the associated electronic couplings create the necessary thermodynamic bias for inward energy transfer but kinetically disfavor it, leading to < 20% energy transfer. Nuclear fluctuations including crucial nuclear quantum effects arising from exciton-vibration coupling enable the kinetics of the energy transfer process making it remarkably efficient. At the end, we focus on investigating the effects of Herzberg Teller (HT) coupling terms in transition dipole moments (beyond the FC approximation) on the shapes of condensed phase molecular spectra. We construct a model for incorporating FC-HT interferences and finite temperature effects to reveal important spectral features in single-mode peaks, as well as those that arise from combination bands. Using as few as three discrete vibrations and a dissipative solvent bath, our model is able to quantitatively rationalize the differences between temperature dependent linear spectra measured for Zn-tetraphenylporphyrin and Zn-phthalocyanine. A retrospective summary of our work and an outlook towards possible future directions are presented in the conclusions.

Graduation Semester

2023-08

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Sohang Kundu

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