where ω is the frequency of the incident (ω 1 ) or emitted (ω 3 ) photon. The Boltzmann distribution of the initial state at temperature T is denoted by ρ(ν i , T ), and ϕ νi , ϕ ν f are the nuclear vibrational wave functions of the electronic state i and f, and the delta function is placed at the energy of absorption or emission, with + used for absorption and -for emission. The delta function is usually replaced by a Gaussian function, N ω ν f -ω νi ± ω, s , where the standard deviation, s, generally represents the solvent-induced broadening, which is usually chosen in an ad-hoc way but can also be estimated by Marcus theory. Solvent effects on the optimized geometry and frequencies are frequently included using implicit solvent models such as the polarizable continuum model (PCM). Savings in time for computation of the FTFC spectrum can be achieved using the vertical gradient approach that employs only the normal modes of the ground state optimized structure, instead of the full adiabatic Hessian that requires the normal mode computation for both the ground and the excited state optimized structures. FC spectral simulations can also account for Herzberg-Teller effects ; based on initial tests with both implicit and explicit solvents, we found these effects to be negligible for all three chromophores.