Vibrationally resolved electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy

Abstract

Vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation are computed in order to interpret and predict vibronic transitions that are probed in the Vibrationally Promoted Electronic Resonance (VIPER) experiment [L. J. G. W. van Wilderen et al., Angew. Chem., Int. Ed. 53, 2667 (2014)]. To this end, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformation of time-domain wavepacket autocorrelation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method [F. Santoro et al., J. Chem. Phys. 126, 084509 (2007)]. In the time-dependent approach, autocorrelation functions are obtained by wavepacket propagation and by the evaluation of analytic expressions, within the harmonic approximation including Duschinsky rotation effects. For several medium-sized polyatomic systems, it is shown that selective pre-excitation of particular vibrational modes leads to a redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. This effect is typically most pronounced upon excitation of modes that are significantly displaced during the electronic transition, such as ring distortion modes within an aromatic π-system. Theoretical predictions as to which modes show the strongest VIPER effect are found to be in excellent agreement with experiment.

Generating Function Approach to Single Vibronic Level Fluorescence Spectra

“…Here, an extension to the recently developed generating function approach 12 is presented, allowing one to compute radiative transitions from singly excited vibronic initial states individually. The derived expression is similar to the VIPER (vibrationally promoted electronic resonance) generating function derived by von Cosel et al 39 In fact, the VIPER generating function becomes identical to the one presented here if initial and final states are interchanged. Because von Cosel et al used a different derivation (Feyman's path integral formula), their route to compute the generating function differs from the one presented here.…”

Large-Scale Quantum Dynamics with Matrix Product States

“…[1][2][3][4][5] Such spectra are readily obtained from a direct solution of the time-dependent Schrödinger equation with quantum dynamics approaches. [6][7][8][9] Similarly, high-order response properties or high-lying excited states can, in principle, be obtained with time-independent approaches, but their calculation is easier within a time-dependent framework. [10][11][12] Multiconfigurational time-dependent Hartree (MCTDH) 13 is currently the reference method for quantum-dynamics simulations with vibrational 14,15 and electronic Hamiltonians.…”

Fluorescence-Encoded Infrared Vibrational Spectroscopy with Single-Molecule Sensitivity

“…Differences in relative peak amplitudes between the FEIR and conventional IR spectra are due to the contribution of vibrational-electronic coupling in the former, which controls the strength of the electronic encoding transition. Specifically, the factor of 5 difference in FEIR intensity between the similarly IR-intense ν R2 and ν R1 modes at 1586 and 1616 cm –1 as well as the nearly absent ν CO band at 1712 cm –1 is well described by these vibrations’ respective Huang–Rhys factors …”

“…Specifically, the factor of 5 difference in FEIR intensity between the similarly IR-intense ν R2 and ν R1 modes at 1586 and 1616 cm −1 as well as the nearly absent ν CO band at 1712 cm −1 is well described by these vibrations' respective Huang−Rhys factors. 24 The ultimate detection sensitivity of an FEIR measurement hinges upon the ability to resolve the FEIR signal F 1 against the background F 0 + B, quantified by the modulation ratio M = F 1 /(F 0 + B). Maximizing M therefore requires simultaneously optimizing the brightness of molecular fluorescence F 1 + F 0 against B, as well as F 1 against F 0 −−a nontrivial problem strongly influenced by the double resonance condition discussed above.…”