Duschinsky mixing between four non-totally symmetric normal coordinates in the S1–S0 vibronic structure of (E)-phenylvinylacetylene: a quantitative analysis

(E)-Phenylvinylacetylene was shown previously (C.-P. Liu, J. J. Newby, C. W. Müller, H. D. Lee, T. S. Zwier, J. Phys. Chem. A, 2008, 112, 9454.) to support extensive Duschinsky mixing among its four lowest-frequency out-of-plane normal coordinates Q45–Q48 in the S1 ← S0, i.e. (La) Ã 1A′ ←  1A′, electronic transition. The complexity of this mixing is considerably increased relative to that of its parent styrene due to the longer conjugated side chain. Here we quantitatively analyze this change of the motional character of the four non-totally symmetric vibrations upon electronic excitation. The peak intensities of 182 overtone and combination transitions spread over seven SVLF spectra were fit simultaneously with seven parameters in an automated least-squares fitting procedure in which an unweighted least-squares sum was minimized using a pattern search algorithm. The seven parameters consisted of the six Duschinsky rotation angles and the S1 frequency of normal mode ν48. The required four-dimensional Franck–Condon overlap integrals were calculated using previously reported recursion relations between harmonic oscillator wavefunctions. As a consistency check, the intensities of all possible 434 electric dipole allowed overtone and combination bands of normal modes ν45–ν48 up to individual vibrational quantum numbers of v = 4 were simulated. The comparison with the experimental intensities revealed with few exceptions very good agreement. The results of the Duschinsky analysis are discussed in light of the π–π* electronic excitation as represented by different ab initio (HF, CIS, CASSCF), density functional (B3LYP and BP86) and time-dependent density functional (TD-B3LYP and TD-BP86) methods. Our Duschinsky mixing analysis reveals a challenging complexity that is not quantitatively reproduced by widely used excited state quantum chemical methods. The sensitivity of Duschinsky mixing coefficients to both excited state equilibrium geometries and force fields thus provides a valuable benchmark for the improvement of excited state quantum chemical methods.