Effective Harmonic and Anharmonic Models for Vibronic Spectra

Abstract

Vibrationally resolved spectra of medium-sized molecules contain dense progressions, weak borrowed-intensity bands and large-amplitude structural motions. Their interpretation requires state-to-state assignments together with a complete spectral envelope, while a fully anharmonic treatment of every normal coordinate is usually impractical. We introduce a general workflow that builds both outputs from automatically generated nonredundant internal coordinates and a common transition-operator representation. The harmonic level combines time-independent (TI) assignments with time-dependent (TD) thermal correlations and an explicit omitted-strength bound for the positive harmonic dipole sum. A discrete-variable representation (DVR) promotes selected flexible coordinates while the remaining modes are contracted analytically. Perturbative and variational nuclear states extend the same operator treatment to separate-state modes with Duschinsky mixing or to shared modes with residual quadratic couplings. The workflow recovers approximately 99% of the harmonic intensity for strongly reorganized medium-sized examples, reproduces measured absorption and fluorescence trends for anthracene and p-terphenyl, and gives signed electronic circular dichroism (ECD) profiles for camphor. Water photoionization, a diffuse-basis two-photon response tensor for the pyrazine $n\to3s$ Rydberg band, and nonplanar 4-pyrone calculations test continuum and anharmonic extensions. The result is a unified route from molecular structure to resolved assignments and numerically converged finite-model spectra.