Nonlinear effects in dipole solvation. II. Optical spectra and electron transfer activation

We present a theoretical analysis of the effect of nonlinear dipole solvation on steady-state optical spectra and intramolecular electron transfer (ET) reactions. The solvation nonlinearity is attributed to saturation of a dipolar liquid produced by the solute dipole. The treatment explores the perturbation expansion over the solute-solvent dipolar interaction truncated in the form of a Padé approximant. The optical line shape and the free energies along the ET reaction coordinate are related to the chemical potential of solvation of a fictitious solute with a complex-valued dipole moment. Due to solvent dipolar saturation the spectrum of dipolar fluctuations is confined by a band of the width 2E_lim. Solvation nonlinearity was found to manifest itself for optical transitions with high dipole moments in the initial state, most often encountered for emission lines. In this case, the spectral line approaches the saturation boundary E_lim bringing about "line squeezing" and decrease of the line shift compared to the linear response prediction. In the nonlinear region, the line shift dependence on the solute dipole variation Δm switches from the quadratic linear response form ∝ Δm² to a linear trend ∝| Δm|. The bandwidth may pass through a maximum as a function of |Δm| in the saturation region. Nonlinear solvation results thus in a narrowing of spectral lines. For a transition with solute dipole enhancement, the bandwidth in emission Δ_e is therefore lower that in absorption Δ_a: Δ_e < Δ_a. As a result, the plot of βΔ²_a,e, β= 1/k_BT against the Stokes shift ℏΔ_st demonstrates the upward deviation of βΔ²_a and downward deviation of βΔ²_e from the linear response equality βΔ²_a,e=ℏΔω_st. We also explored the nonlinearity effect on charge separation/ charge recombination activation thermodynamics. The solvent reorganization energy was found to be higher for charge separation (λ₁) than for charge recombination (λ₂). Both are smaller than the linear response result. For the reorganization energies, the discrepancy between λ₁ and λ₂ is relatively small, whereas their temperature derivatives deviate significantly from each other. The theory predictions are tested on spectroscopic computer simulations and experiment. Generally good quantitative agreement is achieved.