Evaluation of symmetry-forbidden or weakly-allowed vibronic spectra requires treating the transition dipole moment beyond the Condon approximation. To include vibronic spectral features not captured in the global harmonic models, we have recently implemented an on-the-fly ab initio extended thawed Gaussian approximation, where the propagated wavepacket is a Gaussian multiplied by a linear polynomial. To include more anharmonic effects, here we represent the initial wavepacket by a superposition of three independent Gaussian wavepackets—one for the Condon term and two displaced Gaussians for the Herzberg–Teller part. Application of this ab initio “three thawed Gaussians approximation” to vibrationally resolved electronic spectra of the phenyl radical and benzene shows a clear improvement over the global harmonic and Condon approximations. The orientational averaging of spectra, the relation between the gradient of the transition dipole moment and nonadiabatic coupling vectors, and the details of the extended and three thawed Gaussians approximation are discussed.

评估对称性禁止或弱允许的振动光谱需要处理超出康登近似的跃迁偶极矩。为了包括全局谐波模型中未捕获的振动频谱特征，我们最近实现了动态从头算扩展的解冻高斯近似，其中传播的波包是高斯乘以线性多项式。为了包括更多的非谐波效应，在这里，我们通过叠加三个独立的高斯波包来表示初始波包，其中一个用于康登术语，两个用于置换位移的高斯用于Herzberg-Teller部分。此从头算起的应用“三解高斯近似” 振动解析得到的苯基和苯的电子光谱显示，与全局谐波和Condon近似相比有明显改善。讨论了光谱的定向平均，跃迁偶极矩的梯度与非绝热耦合矢量之间的关系，以及扩展和三解高斯近似的细节。