Quantum dissipative systems beyond the standard harmonic model: Features of linear absorption and dynamics

Abstract

Current simulations of ultraviolet-visible absorption lineshapes, and dynamics of condensed phase systems, largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have the same curvature. Although convenient, for many realistic molecular systems this approximation no longer suffices. We elucidate non-standard harmonic, and anharmonic effects, on linear absorption and dynamics using a stochastic Schrödinger equation approach to account for the environment. Firstly, a harmonic oscillator model with ground and excited potentials that differ in curvature is utilised. Using this model, it is shown that curvature difference gives rise to an additional sub-structure in the vibronic progression of absorption spectra. This effect is explained, and subsequently quantified, via a derived expression for the Franck-Condon coefficients. Subsequently, anharmonic features in dissipative systems are studied, using a Morse potential, and parameters that correspond to the diatomic molecule H 2 for differing displacements and environment interaction. Lastly using a model potential, the population dynamics and absorption spectra for the stiff-stilbene photoswitch is presented and features are explained by a combination of curvature difference and anharmonicity in the form of potential energy barriers on the excited potential.

(De)localization dynamics of molecular excitons: comparison of mixed quantum-classical and fully quantum treatments

“…Further, in the approximation of displaced harmonic oscillators with the same frequency ω the ratio of intensities of 0–1 to 0–0 transitions is equal to the Huang–Rhys factor, defined as . 56 Here, d is the displacement of the excited-state PES with respect to the ground-state PES, and m is the mass, taken to be the reduced mass of the 62nd normal mode of the tetracene monomer (reported in the output of Gaussian 16 frequency calculation for the excited state). The displacement d , needed to construct the Hamiltonian, is thus obtained as .…”

Correlating Stokes Shift with Huang‐Rhys Parameter for Diatomic Molecules: Effects of Finite Temperature, Anharmonicity and Breakdown of Franck‐Condon Approximation

“…[29] The HR parameter correlates the coupling of the electronic states to the nuclear coordinates, defined in the context of a displaced harmonic oscillator model with similar curvature for both the ground and excited PESs. [30,31] It is defined as a function of the equilibrium position offset (Δr) [32,33] and has a linear variation with the Stokes shift for the harmonic oscillator model. [34] In this article, we investigate the effects of systematic introduction of anharmonicity, the difference in curvature, the displacement of the excited-state PES, and temperature on the optical absorption and emission spectra.…”

“…The HR parameter correlates the coupling of the electronic states to the nuclear coordinates, defined in the context of a displaced harmonic oscillator model with similar curvature for both the ground and excited PESs [30,31] . It is defined as a function of the equilibrium position offset (Δ$${r}$$ ) [32,33] and has a linear variation with the Stokes shift for the harmonic oscillator model [34] …”

Empirical quality criteria for the approximation of the electronic term of a diatomic molecule by the Morse formula

“…The Morse model potential [1], despite a very rough approximation, is widely used in molecular spectroscopy and in other areas of optics and chemical physics. According to the Chemical Abstracts Service, over 6,000 references are given on the request " Morse Formula" Ȧs an example, we present random selections of recent studies in the field of spectroscopy [2][3][4][5][6][7][8][9][10][11][12][13], the influence of an external field, laser dissociation of moleculescool [14][15][16][17][18][19][20][21][22][23][24], thermodynamics, kinetics [25][26][27][28][29][30][31][32][33][34], solid and liquid physicssti [35][36][37][38][39][40][41][42][43][44], intermolecular interactions [45][46][47]…”