Park G Barratt
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
J Chem Phys. 2014 Oct 7;141(13):134304. doi: 10.1063/1.4896532.
Franck-Condon vibrational overlap integrals for the à Au1-X̃ 1Σg+ transition in acetylene have been calculated in full dimension in the harmonic normal mode basis. The calculation uses the method of generating functions first developed for polyatomic Franck-Condon factors by Sharp and Rosenstock [J. Chem. Phys. 41(11), 3453-3463 (1964)], and previously applied to acetylene by Watson [J. Mol. Spectrosc. 207(2), 276-284 (2001)] in a reduced-dimension calculation. Because the transition involves a large change in the equilibrium geometry of the electronic states, two different types of corrections to the coordinate transformation are considered to first order: corrections for axis-switching between the Cartesian molecular frames and corrections for the curvilinear nature of the normal modes at large amplitude. The angular factor in the wavefunction for the out-of-plane component of the trans bending mode, ν4(″), is treated as a rotation, which results in an Eckart constraint on the polar coordinates of the bending modes. To simplify the calculation, the other degenerate bending mode, ν5(″), is integrated in the Cartesian basis and later transformed to the constrained polar coordinate basis, restoring the conventional v and l quantum numbers. An updated Ã-state harmonic force field obtained recently in the R. W. Field research group is evaluated. The results for transitions involving the gerade vibrational modes are in qualitative agreement with experiment. Calculated results for transitions involving ungerade modes are presented in Paper II of this series [G. B. Park, J. H. Baraban, and R. W. Field, "Full dimensional Franck-Condon factors for the acetylene à Au1-X̃ 1Σg+ transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes," J. Chem. Phys. 141, 134305 (2014)].
在简正振动模式基组下，已在全维空间中计算了乙炔中Ã(A_u^1)-X̃(^1\sum_g^+)跃迁的弗兰克-康登振动重叠积分。该计算采用了夏普和罗森斯托克最初为多原子弗兰克-康登因子开发的生成函数方法[《化学物理杂志》41(11)，3453 - 3463(1964)]，此前沃森[《分子光谱学杂志》207(2)，276 - 284(2001)]已将其应用于乙炔的降维计算。由于该跃迁涉及电子态平衡几何结构的巨大变化，因此对坐标变换的两种不同类型的一阶修正被考虑在内：笛卡尔分子框架之间轴切换的修正以及大振幅下简正模式曲线性质的修正。反式弯曲模式(ν_4(″))的面外分量波函数中的角因子被视为旋转，这导致了对弯曲模式极坐标的埃卡特约束。为简化计算，另一个简并弯曲模式(ν_5(″))在笛卡尔基组中积分，随后转换到受约束的极坐标基组，恢复传统的(v)和(l)量子数。对最近在R. W. 菲尔德研究小组中获得的更新的Ã态简正力场进行了评估。涉及 gerade 振动模式的跃迁结果与实验定性一致。本系列论文II [G. B. 帕克、J. H. 巴拉班和R. W. 菲尔德，“乙炔Ã(A_u^1)-X̃(^1\sum_g^+)跃迁的全维弗兰克-康登因子。II. 涉及非 gerade 模式激发的能级的振动重叠因子”，《化学物理杂志》141，134305(2014)]给出了涉及 ungerade 模式跃迁的计算结果。
