  We derive a Hierarchical Equations of Motion (HEOM) description of
nonadiabatic Herzberg-Teller type coupling effects and of non-Condon effects in
a system of electronic transitions interacting with intra- and inter-molecular
vibrational modes. We point out analogies between the auxiliary density
operators (ADOs) of the hierarchy and the terms arising from explicit
description of the vibrational modes in the Hamiltonian. In comparison with the
standard formulation of HEOM, our equations contain additional connections
between ADOs in the hierarchy scheme, which account for the dependence of the
nonadiabatic coupling elements on the vibrational coordinates. We compare
absorption spectra calculated with our HEOM methodology and with explicit
treatment of vibrational DOF for a dimer system in the strong resonance
coupling regime. Furthermore, we show that for sufficiently strong excitonic
coupling, the corresponding effects in linear absorption spectra of vibronic
dimers can be captured very well by the concept of effective Huang-Rhys
factors.
