  While dark transitions made bright by molecular motions determine the
optoelectronic properties of many materials, simulating such non-Condon effects
in condensed-phase spectroscopy remains a fundamental challenge. We derive a
Gaussian theory to predict and analyze condensed phase optical spectra beyond
the Condon limit. Our theory introduces novel quantities that encode how
nuclear motions modulate the energy gap and transition dipole of electronic
transitions in the form of spectral densities. By formulating the theory
through a statistical framework of thermal averages and fluctuations, we
circumvent the limitations of widely used microscopically harmonic theories,
allowing us to tackle systems with generally anharmonic atomistic interactions
and non-Condon fluctuations of arbitrary strength. We show how to calculate
these spectral densities using first-principles simulations, capturing
realistic molecular interactions and incorporating finite-temperature,
disorder, and dynamical effects. Our theory accurately predicts the spectra of
systems known to exhibit strong non-Condon effects (phenolate in various
solvents) and reveals distinct mechanisms for electronic peak splitting:
timescale separation of modes that tune non-Condon effects and spectral
interference from correlated energy gap and transition dipole fluctuations. We
further introduce analysis tools to identify how intramolecular vibrations,
solute-solvent interactions, and environmental polarization effects impact dark
transitions. Moreover, we prove an upper bound on the strength of cross
correlated energy gap and transition dipole fluctuations thereby elucidating a
simple condition that a system must follow for our theory to accurately predict
its spectrum.
