Nonlinear Spectroscopic Theory of Displaced Harmonic
Oscillators with Differing Curvatures: A Correlation Function Approach
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Abstract
We present a theory for a bath model
in which we approximate the
adiabatic nuclear potential surfaces on the ground and excited electronic
states by displaced harmonic oscillators that differ in curvature.
Calculations of the linear and third-order optical response functions
employ an effective short-time approximation coupled with the cumulant
expansion. In general, all orders of correlation contribute to the
optical response, indicating that the solvation process cannot be
described as Gaussian within the model. Calculations of the linear
absorption and fluorescence spectra resulting from the theory reveal
a stronger temperature dependence of the Stokes shift along with a
general asymmetry between absorption and fluorescence line shapes,
resulting purely from the difference in the phonon side band. We discuss
strategies for controlling spectral tuning and energy-transfer dynamics
through the manipulation of the excited-state and ground-state curvature.
Calculations of the nonlinear response also provide insights into
the dynamics of the system–bath interactions and reveal that
multidimensional spectroscopies are sensitive to a difference in curvature
between the ground- and excited-state adiabatic surfaces. This extension
allows for the elucidation of short-time dynamics of dephasing that
are accessible in nonlinear spectroscopic methods