The following QuickTime movies accompany M. H. Hennessy and A. M. Kelley's
Using real-valued multi-objective genetic algorithms to model
molecular absorption spectra and Raman excitation profiles in solution.
Modeling the absorption spectra and resonance Raman excitation
profiles of a large molecule in solution requires the determination of
a minimum of dozens of highly coupled parameters to fit several hundred data points.
We consider the condensed--phase optical absorption spectrum and resonance
Raman excitation profiles of a molecule having a single, isolated electronic transition.
We make the Condon approximation (no vibrational coordinate dependence of the electronic transition moment),
assume that the ground and excited state normal modes are the same (no Duschinsky rotation)
and treat the potential energy surfaces as harmonic. We take the solvent--induced
vibronic line broadening function to be that produced by a
single Brownian oscillator in the overdamped, high temperature limit.
Within this model, the absorption spectrum and Raman excitation profiles can be exactly calculated
given the following parameters:
- Δ,
the displacement for each normal mode between ground and excited state potential minima
in ground state dimensionless normal coordinates.
- ωe/ωg,
the ratio of the excited and ground state vibrational frequencies for each normal mode.
- Γ,
the vibronic linewidth which is incorporated in the solvent--induced broadening
governed by the Brownian oscillator damping function.
- ω0-0,
the purely electronic transition frequency which governs the position along the frequency axis.
- M,
the electronic transition length which determines the integrated intensity (oscillator strength).
Each parameter is linked to a quicktime movie which shows its effect on the absorption
(------ red line), fundamental
Raman excitation profile (-- -- blue line)
and overtone Raman excitation profile (- - - green line) for the case of a molecule
with a single coupled vibrational mode with ωg = 4000 cm-1. All other parameters
are held at their initial values as shown in Table 1 while the parameter of interest varies over its range.
On the left, the change in the molecular parameter is shown on a potential
energy level diagram. The energy axis has units of 1000 cm-1 and the displacement axis is in ground state
dimensionless normal coordinates. The ground state wavefunction that evolves on the excited state surface is shown
as a blue dotted line (-- --).
On the right, the energy scale remains fixed but the scattering cross section is shown;
the length of the axis corresponds to an absorption cross section of 5 A2,
and a Raman cross section of 10000 A2.
| Parameter | Initial | Range
|
| Δ | 1.5 | 0-3
|
| ωe | 4000 cm-1 | 2000-6000 cm-1
|
| Γ | 1500 cm-1 | 500-3000 cm-1
|
| ω0-0 | 20000 cm-1 | 17000-23000 cm-1
|
| M | 2.5 | 0-3
|
Table 1: Initial value and range of each parameter.
Our real-valued genetic algorithm forces a broad search through parameter space and successfully inverts the
absorption spectrum and Raman excitation profiles to determine the molecular parameters.