Photodissociation dynamics in the first absorption band of pyrrole: I. Molecular Hamiltonian and the Herzberg-Teller absorption spectrum for the $1^1A_2(\pi\sigma^*) \leftarrow \tilde{X}^1A_1(\pi\pi)$ transition

Abstract

This paper opens a series in which the photochemistry of the two lowest $\pi\sigma^*$ states of pyrrole and their interaction with each other and with the ground electronic state $\tilde{X}$ are studied using ab initio quantum mechanics. New 24-dimensional potential energy surfaces for the photodissociation of the N-H bond and the formation of the pyrrolyl radical are calculated using the CASPT2 method for the electronic states $\tilde{X}(\pi\pi)$, $1^1A_2(\pi\sigma^*)$ and $1^1B_1(\pi\sigma^*)$ and locally diabatized. In the first paper, the ab initio calculations are described and the photodissociation in the state $1^1A_2(\pi\sigma^*)$ is analyzed. The excitation $1^1A_2 \leftarrow \tilde{X}$ is mediated by the coordinate dependent transition dipole moment functions constructed using the Herzberg-Teller expansion. Nuclear dynamics, including 6, 11, and 15 active degrees of freedom, is studied using the multi-configurational time-dependent Hartree method. The focus is on the frequency resolved absorption spectrum, as well as on the dissociation time scales and the resonance lifetimes. Calculations are compared with available experimental data. An approximate convolution method is developed and validated, with which absorption spectra can be calculated and assigned in terms of vibrational quantum numbers. The method represents the total absorption spectrum as a convolution of the diffuse spectrum of the detaching H-atom and the Franck-Condon spectrum of the heteroaromatic ring. Convolution calculation requires a minimal quantum chemical input and is a promising tool for studying the $\pi\sigma^*$ photodissociation in model biochromophores.