Ab initio spectroscopy and photoinduced cooling of the trans-stilbene molecule

Abstract

We present a theoretical study of the S(0)-->S(1) and S(0)<--S(1) vibronic spectra for trans-stilbene. Franck-Condon spectra in the harmonic approximation are generated for the complete system with 72 degrees of freedom by means of an analytic time-dependent approach accounting for Dushinsky rotations and thermal effects. The force fields are computed by means of density functional theory (DFT) and time-dependent DFT, on the one hand, and ab initio complete active space self-consistent field theory, on the other hand. The B3LYP functional shows that almost planar potential energy surface minima are found for the S(0) and S(1) state. Imposing C(2h) symmetry constraints, we obtain low-temperature high-resolution Franck-Condon spectra for both absorption and emission which are in reasonably good agreement with the experimental spectra measured by Syage et al. [J. Chem. Phys. 81, 4685 (1984)] in supersonic jets. Due to thermal population of low-energy modes, the room temperature absorption spectrum is very broad. An almost structureless band which extends over several thousand cm(-1) is obtained from the present theory and agrees with the experimental absorption band shape. Finally, within the harmonic model, we study the effect of photoexcitation on the energy distribution in the excited S(1) state. We find noticeable cooling of approximately 20 K within a frequency interval spanning from -400 to 200 cm(-1) around the 0-0 transition. This indicates that photoinduced cooling must be taken into account when considering the dynamics of the photoinduced isomerization of trans-stilbene. Moreover, this is not the final word, as anharmonicity of the low frequency modes must be taken into account to obtain a full picture which would explain both the energy dependence of the isomerization rates as well as the dependence on the pressure of an external buffer gas.

Photoisomerization of Stilbene: A Spin-Flip Density Functional Theory Approach

“…In addition, the present SFDFT approach can access the twisted stilbene species, whereas the previous LR-TDDFT study was unable to access this structure. 53,55 By using a penaltyconstrained optimization method, 86,96 SFDFT can successfully locate the two CI points of stilbene: the twisted-pyramidalized CI observed also in the previous SFDFT study of ethylene 94 and another CI point which possibly lies on the cyclization reaction path. The relationship between the CI and minimum energy points is discussed.…”

“…As mentioned in the Introduction, the conventional LR-TDDFT method cannot access the twisted stilbene structure. 53,55 Therefore, the present SFDFT approach can fill in a missing part of the excitedstate PES for S 1 stilbene. The twisted minimum geometry (Figure 3a) has a nearly perpendicular (τ = 86°) arrangement and is considerably pyramidalized (ω = 52°), and thus the label (S 1 ) pyr is assigned.…”

Communication: Optical cooling of trans-stilbene

“…Fast collisions with a buffer gas or liquid reheat the molecule and the reaction rate increases. [25][26][27][28] (iv) Intramolecular vibrational redistribution (IVR) may be slow (restricted) in isolated stilbene, but becomes faster (unrestricted) in solution due to solute-solvent interactions. 15,[29][30][31][32] (v) Solute-solvent collisions may directly increase the isomerization rate; and (vi) dynamic polarization in the excited state.…”

A general time-dependent route to Resonance-Raman spectroscopy including Franck-Condon, Herzberg-Teller and Duschinsky effects

“…By considering that is an eigenbra of the operator with eigenvalue , it is easy to derive the following expression: (36) The last term, , is more complex but can be taken out by applying the same strategy as for the previous terms. The Duschinsky transformation is used to rewrite as, (37) By rewriting the final-state normal coordinates in terms of the auxiliary variables Z and U as done before, we obtain the following expression: (38) The explicit expressions for the second-and third-order derivatives of the autocorrelation function χ 0 (t) are the following, …”

“…We will define this function as the crosscorrelation function χ k (t), where the index k refers to the dependence of this crosscorrelation function on the excited oscillator of the final state. Analytic formulae for the cross-correlation function χ k (t) can be derived in the framework of the Feynman pathintegral formulation of quantum mechanics 38 . The starting point is the following expression for the matrix element 38,39 : (18) where we have introduced the auxiliary time variable, , and the diagonal matrices and , defined as: (19) After the introduction of equations 16, 17 and 18 in equation 15 the orthogonality property and is used to carry out the Baiardi et al Page 8 integrals over the sets of coordinates and .…”