Hazra Anirban, Chang Hannah H, Nooijen Marcel
Department of Chemistry, Princeton University, New Jersey 08544, USA.
J Chem Phys. 2004 Aug 1;121(5):2125-36. doi: 10.1063/1.1768173.
A new method which we refer to as vertical Franck-Condon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the short-time picture of spectroscopy, the excited-state potential energy surface is expanded at the ground-state equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 0-0 lines. The Born-Oppenheimer approximation and the separability of the excited-state potential energy surface along the excited-state normal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full one-dimensional potential is considered along this mode. The vertical Franck-Condon approach is applicable therefore even in cases where the excited state potential energy surface is highly anharmonic and the conventional harmonic Franck-Condon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50,000 cm(-1)) and 8.7 eV (70,000 cm(-1)) is simulated, using the Similarity Transformed Equation of Motion Coupled-Cluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the pi --> 3s (Rydberg) state superimposed on top of a broad band resulting from the pi --> pi* (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, CH2 scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical Franck-Condon method is required.
我们提出了一种称为垂直弗兰克 - 康登的新方法来计算多原子分子的电子吸收光谱。根据光谱学的短时间图像，激发态势能面在基态平衡几何结构处展开，该方法的重点更多地放在光谱的整体形状和谱带最大值的位置上，而不是0 - 0线的精确位置。假定了玻恩 - 奥本海默近似以及激发态势能面沿激发态简正坐标的可分离性。然而，势能面并不一定沿各个简正模式近似为简谐振子势。相反，根据沿特定简正模式的势能面的性质，要么在简谐近似下处理，要么沿此模式考虑完整的一维势能。因此，垂直弗兰克 - 康登方法即使在激发态势能面高度非简谐且传统的简谐弗兰克 - 康登方法不适用的情况下也适用。作为该方法的一个应用，使用相似变换运动方程耦合簇方法来描述势能面的所需特征，模拟了乙烯在6.2电子伏特（50,000厘米⁻¹）至8.7电子伏特（70,000厘米⁻¹）之间的紫外光谱。该光谱显示为源于π→3s（里德堡）态的尖锐双峰结构叠加在源于π→π*（价）态的宽带之上的结果。对于里德堡态，对称的C = C伸缩和扭转模式对光谱有贡献，而宽的价带是由激发到C = C伸缩、CH₂剪式振动和扭转模式产生的。对于这两个态，沿扭转模式的势能都是高度非简谐的，并且在垂直弗兰克 - 康登方法中需要对沿此模式的势能进行完整处理。
