Unspecified verticality of Franck-Condon transitions, absorption and emission spectra of cyanine dyes, and a classically inspired approximation.

Joseph D Alia,Joseph A Flack

doi:10.1039/d0ra06774a

Abstract

The computed vertical energy, Ev,a/f, from the equilibrium geometry of the initial electronic state is frequently considered as representative of the experimental excitation/emission energy, Eabs/fl = hc/λmax. Application of the quantum mechanical version of the Franck–Condon principle does not involve precise specification of nuclear positions before, after, or during an electronic transition. Moreover, the duration of an electronic transition is not experimentally accessible in spectra with resolved vibrational structure. It is shown that computed vibronic spectra based on TDDFT methods and application of quantum mechanical FC analysis predict Eabs = hc/λmax with a 10-fold improvement in accuracy compared to Ev,a for nine cyanine dyes. It is argued that part of the reason for accuracy when this FC analysis is compared to experiment as opposed to Ev,a/f is the unspecified verticality of transitions in the context of the quantum version of the FC principle. Classical FC transitions that preserve nuclear kinetic energy before and after an electronic transition were previously found to occur at a weighted average of final and initial electronic state molecular geometries known as the r-centroid. Inspired by this approach a qualitative method using computed vertical and adiabatic energies and the harmonic approximation is developed and applied yielding a 5-fold improvement in accuracy compared to Ev,a. This improvement results from the dominance of low frequency vibronic transitions in the cyanine dye major band. The model gives insight into the nature of the redshift when qPCR dye EvaGreen is complexed to λDNA and is applicable to the low frequency band of similar non cyanine dyes such as curcumin. It is found that the computed vibronic cyanine dye spectra from time-dependent FC analysis at 0 K and 298 K show decreased intensity at higher temperature suggestive of increased intensity with restricted motion shown when cyanine dyes are used in biomedical imaging. A 2-layer ONIOM model of the DNA minor groove indicates restricted motion of the TC-1 dye excited state in this setting indicative of enhanced fluorescence.

Highlights

How should one think of the motion of nuclei during an electronic transition of a molecule? Usual statements of the Franck– Condon principle tell us change in position of nuclei is negligible during an electronic transition
It is shown that computed vibronic spectra based on TDDFT methods and application of quantum mechanical FC analysis predict Eabs 1⁄4 hc/lmax with a 10-fold improvement in accuracy compared to Ev,a for nine cyanine dyes
Ev,a/f from the equilibrium geometry of the initial electronic state in a transition are frequently considered to be representative of the Eabs/ 1⁄4 hc/lmax from experiment

Summary

Introduction

How should one think of the motion of nuclei during an electronic transition of a molecule? Usual statements of the Franck– Condon principle tell us change in position of nuclei is negligible during an electronic transition. Quantum and classical versions of the FC principle differ on this and whether there is even a meaningful answer. We develop a qualitative classically inspired approach to a vertical energy that gives closer agreement to experiment for nine cyanine dye examples than do vertical TDDFT energies calculated from the optimized geometry of the initial electronic state. We nd our applications both of the quantum mechanical FC principle and of our newly developed classically inspired approach yield high accuracy compared to experiment for the dyes studied. Unspeci ed verticality in the quantum FC principle

Methods

Results

Conclusion