Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907-2084, USA.
Phys Chem Chem Phys. 2010 Mar 14;12(10):2331-43. doi: 10.1039/b919912h. Epub 2010 Jan 20.
(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 Q(45)-Q(48) in the S(1)<-- S(0), i.e. (L(a)) A (1)A'<-- X (1)A', 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 S(1) frequency of normal mode nu(48). 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 nu(45)-nu(48) 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 pi-pi* 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.
(E)-苯乙烯基乙炔先前已被证明（C.-P. Liu、J. J. Newby、C. W. Müller、H. D. Lee 和 T. S. Zwier，J. Phys. Chem. A，2008，112，9454）在 S(1)<-- S(0)，即 (L(a)) A (1)A'<-- X (1)A'，电子跃迁中，其四个最低频率面外非对称坐标 Q(45)-Q(48) 之间存在广泛的 Duschinsky 混合。由于较长的共轭侧链，这种混合的复杂性相对于其母体苯乙烯显著增加。在这里，我们定量分析了电子激发后这四个非完全对称振动的运动特征的变化。在七个 SVLF 光谱中，182 次泛频和组合跃迁的峰强度通过一个自动化的最小二乘法拟合程序，同时用七个参数进行拟合，该程序使用模式搜索算法最小化无权重最小二乘和。这七个参数包括六个 Duschinsky 旋转角和 S(1)频率的简正模式 nu(48)。所需的四个维度 Franck-Condon 重叠积分使用之前报道的谐振荡器波函数之间的递归关系进行计算。作为一致性检查，模拟了简正模式 nu(45)-nu(48)到个体振动量子数 v = 4 的所有可能的 434 个电偶极允许泛频和组合带的强度。与实验强度的比较表明，除了少数例外，一致性非常好。Duschinsky 分析的结果根据不同的从头算（HF、CIS、CASSCF）、密度泛函（B3LYP 和 BP86）和时间相关密度泛函（TD-B3LYP 和 TD-BP86）方法对 pi-pi*电子激发进行了讨论。我们的 Duschinsky 混合分析揭示了一种具有挑战性的复杂性，这在广泛使用的激发态量子化学方法中无法定量再现。因此，Duschinsky 混合系数对激发态平衡几何形状和力场的敏感性为激发态量子化学方法的改进提供了有价值的基准。
