## Saturday, May 24, 2008

### Calculating predicting Ultraviolet-Visible Spectra

Calculating Ultraviolet-Visible Spectra
The ability to calculate the UV-Vis spectrum of a molecule can help in the interpretation of an
experimental spectrum, will show the orbitals involved in a given electronic transition, and can
also shed light on the electronic structure of the molecule.  The first step in the calculation is to
perform a geometry optimization.  Any of the four methods (molecular mechanics, ab initio,
semiempirical, or density functional theory) could be used for this.

Next, the ground state wavefunction is calculated.

This generates occupied (filled with two electrons each) and
unoccupied (virtual) molecular orbitals.  Molecular mechanics cannot be used for this step, since
no electrons or orbitals are used in this method.  Any of the other techniques could be used.
Next, a calculation is performed that mixes some of the virtual orbitals into the ground state
wavefunction while the geometry is held constant.  This process provides an approximation to
the energy of the excited electronic states at the fixed geometry of the ground state.  The
transition frequency is calculated by finding the difference between the excited state and ground
state energies.

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Since certain functional groups present in organic molecules absorb light at characteristic
wavelengths in the UV-Vis region, the technique can be used to qualitatively identify the
presence of these groups.  Tables of absorption data for various functional groups are available.
If the molecule of interest contains a conjugated system of double bonds, a set of simple rules,
called the Woodward-Fieser Rules, can be used to predict the wavelength of maximum
absorption (_max).  Many transition metal ion containing complexes absorb light in the visible
region of the spectrum.  The light absorbed causes electronic transitions of the d-electrons.
Different groups attached to the metal will change the electronic energy levels, thus changing the
color (value of _max).  Quantitative analysis of the electronic structure of inorganic molecules can
be performed in this manner.