The vibronic absorption spectrum of the electric dipole forbidden and vibronically allowed S₁(¹A₂) ← S₀(¹A₁) transition of formaldehyde is calculated by Gaussian wavepacket and semiclassical methods, along with numerically exact reference calculations, using the potential energy surface of Fu, Shepler, and Bowman (J. Am. Chem. Soc.2011, 133, 7957). Specifically, the variational multiconfigurational Gaussian (vMCG) approach and the Herman–Kluk semiclassical initial value representation (HK-SCIVR) are compared to assess the accuracy and convergence of these methods, benchmarked against numerically exact time-dependent wavepacket propagation (TDWP) on the reference potential energy surface. The vMCG calculation is shown to converge quite well with about 100 variationally evolving Gaussian functions and using a local cubic expansion instead of the conventional local harmonic approximation. By contrast, the HK-SCIVR approach with ∼10⁵ trajectories reproduces the vibrationally structured spectral envelope correctly but yields a strongly broadened spectrum. The comparison of the computed absorption spectrum with experiment shows that the relevant vibronic progressions are reasonably reproduced by all computations, but deviations of the order of 10–100 cm^–1 occur, underscoring that both electronic structure calculations and dynamical approaches remain challenging in the calculation of typical small-molecule excited-state spectra by trajectory-based methods.

中文翻译：

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变分高斯波包和半经典IVR方法计算甲醛的S ₁ ← S ₀振动吸收光谱

高斯波包和半经典方法计算并利用势能计算出了偶极子的S ₁（¹ A ₂）← S ₀（¹ A ₁）转变对甲醛的振动吸收光谱，并进行了精确的数值计算。赋，Shepler，和鲍曼（的表面J.化学会会志。2011，133，7957）。具体来说，将变分多配置高斯（vMCG）方法和Herman-Kluk半经典初始值表示（HK-SCIVR）进行比较，以评估这些方法的准确性和收敛性，并以数值精确的随时间变化的波包传播（TDWP）为基准参考势能面。显示出vMCG计算可以很好地收敛于约100个变化演化的高斯函数，并且使用局部三次展开代替常规的局部谐波近似。相比之下，使用HK-SCIVR方法约^{10 5}轨迹正确地再现了振动结构的频谱包络线，但产生了很宽的频谱。计算的吸收光谱与实验的比较表明，所有的计算都合理地再现了相关的电子振动过程，但是出现了10–100 cm ^–1数量级的偏差，这突显了电子结构计算和动力学方法在计算中仍然具有挑战性基于轨迹的方法分析典型的小分子激发态光谱。