The UV absorption and fluorescence of 3-methylindole in water at 300 K has been simulated over periods of 4 to 30 ps in length using a combination of classical molecular dynamics simulations and a spectroscopically calibrated semiempirical molecular orbital method (INDO/S-SCI). The absorption redshift is predicted to be 545 ±150 cm-1 for 1La, and 85 ±15 cm-1 for 1Lb. The distribution of transition energies due to solvent fluctuations suggests inhomogeneous broadening at lower temperatures of about 2000 cm-1 for 1La, and 400 cm-1 for 1Lb, (fwhm). The large time-dependent shift of the 1La fluorescence was determined both by direct nonequilibrium response to an instantaneous charge redistribution and from the autocorrelation function of the fluctuations of the 1La transition energies from the equilibrated ground state. The two methods gave similar response times, roughly fitting a double exponential with time constants of 17 and 290 fs. The magnitude of the calculated shifts with partial and complete solute polarizability are 3000 and 5000 - 6000 cm-1, bracketing an experimental estimate of 3800 cm-1. A connection with perturbation-free energy of solvation (ΔAs) results is made which identifies ΔAs as the average of absorption and fluorescence maximum shifts upon solvation, (▽TAνa + Δνf)/2.