How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck‐Condon Analysis of Optical Spectrum

Abstract

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B 2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.

Estimation of Excited-State Geometries of Benzene and Fluorobenzene through Vibronic Analyses of Absorption Spectra

“…The theoretical approach to predict the excited-state geometries of molecules has been given in detail in our previous publication. 25 Therefore, only major steps are presented in this study. The following equation has been used to simulate the absorption line shapes within FC approximation In the above equation, f is the oscillator strength of relevant transition, γ is the linewidth of absorption lines which accounts for inhomogeneous broadening effects, S j is the dimensionless Huang–Rhys factor for the mode j with frequency ν j , N is the number of vibrational modes with significant Huang–Rhys factors, n j is the range of summation (0–5 for benzene, 0–3 for fluorobenzene), ν if is the electronic origin (0–0 peak location), and ν is the wavenumber (cm –1 ).…”

“… 28 , 30 , 31 Here, L g is the 3 N vector of the normal coordinates of the vibrational modes in the ground state, M is the 3 N × 3 N diagonal matrix of atomic masses, x e and x g are the 3 N dimensional vectors of Cartesian coordinates in the excited and ground states, respectively. After rearranging eq 3 , x e can be expressed as 25 where Z is …”

“…It is important to note that Z –1 must be evaluated using the singular value decomposition technique as outlined in ref ( 25 ). The Duschinsky matrix ( J ) for fluorobenzene is obtained by multiplying matrices L g T and L e composed of a 1 modes, which play major role in geometrical change in between the ground and the excited states.…”

“…In our recent study, we have successfully shown that the excited-state geometries of relatively large molecules can be predicted by using Franck–Condon (FC) analysis of optical spectrum (FC spectral fit method) and then performing reverse engineering on the simulation parameters to extract information regarding the structural changes occurring upon photoexcitation. 25 The only requirement for successful application of the FC spectral fit method is the need for availability of the vibrationally well-resolved optical spectrum of the molecule in question. In this regard, excited-state geometric parameters of naphthalene, perylene, and pyrene were successfully predicted due to vastly available experimental data reported on these polyaromatic hydrocarbons.…”

“…In this regard, excited-state geometric parameters of naphthalene, perylene, and pyrene were successfully predicted due to vastly available experimental data reported on these polyaromatic hydrocarbons. 25 …”