On-the-fly ab initio three thawed Gaussians approximation: A semiclassical approach to Herzberg-Teller spectra

Abstract

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. * jiri.vanicek@epfl.ch.

Single-Hessian thawed Gaussian approximation

“…Two well-known special choices are the adiabatic Hessian-Hessian of the final electronic potential energy surface evaluated at its minimum 13,50 We refer to the combinations of these two Hessian choices with the global harmonic approach as the adiabatic harmonic and vertical harmonic methods. 31,33,51 In the literature, these global harmonic models are sometimes referred to as the adiabatic and vertical Hessian; 13,18,50 here, we use these names exclusively for the Hessians themselves to avoid the confusion between the single-Hessian thawed Gaussian propagation and global harmonic methods. The combinations of the single-Hessian approach with the different reference Hessians will be referred to as the adiabatic single-Hessian and vertical single-Hessian methods.…”

Ab Initio Semiclassical Evaluation of Vibrationally Resolved Electronic Spectra With Thawed Gaussians

“…Appendix D of Begušić et al (2018a) provides a detailed proof that the local harmonic approximation implies that the ETGA wavepacket at time t has the simple form (Lee and Heller, 1982) φ(q, t) = P i…”

“…As for the parameters of the polynomial, the simplest possibility beyond the original TGA is to consider only the constant and linear terms, which will be the only ones required in the Herzberg-Teller approximation (66) for the transition dipole moment, used in Subsection V D for calculations of electronic spectra beyond the Condon approximation. Appendix D of Begušić et al (2018a) provides a detailed demonstration that in this case (Lee and Heller, 1982) φ…”

Semiclassical Approach to Photophysics Beyond Kasha’s Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene

“…Finally, the spectrum averaged over all molecular orientations is evaluated simply as 42,51 σ av. (ω) = (1/3) i σ( e i , ω), where e i (i = x, y, z) denotes the unit vector along the i-axis.…”

“…27,28 Because it can detect more subtle nonadiabatic effects, the adiabaticity goes beyond the standard analysis based on population dynamics. [29][30][31][32][33][34][35][36][37][38] (ii) Building on the joint analysis of adiabaticity and population dynamics, we introduce a new method for computing vibrationally resolved electronic spectra by combining the single-Hessian 39 and extended [40][41][42] thawed Gaussian approximations. The new methodology, augmented with on-the-fly ab initio electronic structure calculations, is applied to study nonadiabatic, non-Condon, anharmonicity, and mode-mixing effects in the first two excited states of azulene.…”