Visible-Ultraviolet Spectra of Molecules

The term spectroscopic states of molecules refers to states that may be involved in transitions seen by spectroscopic measurement. Through such measurements, we are able to extract information about the different bonding character, about the different electronic structure, of excited states of molecules. For molecules containing atoms of other than the very heavy elements, spectroscopic states have specific net electron spins. They are frequently singlet states, meaning the spin quantum number, S, is zero, or they can be doublet states (S = 1/2), triplet states (S = 1), or states with a still greater spin quantum number. They also have certain properties that reflect geometrical symmetry of the molecule, if any (see Appendix B). 

Using visible-ultraviolet spectroscopy of molecules, we examine the nature of excited electronic states since typically the absorption of a photon in this energy region electronically excites the molecule. For molecules composed of elements with low atomic number, the strongest selection rule at work in visible-ultraviolet spectroscopy is 

These transition frequencies correspond to a whole series of lines for a given n to n vibrational quantum number change. As in the case of infrared spectra, the transitions associated with Equation 10.62a are transitions of the P-branch, and those associated with Equation 10.62c are of fhe P-branch. Transitions associated with Equation 10.62b are those of a Q-branch. Erom fhe relative sizes of typical rotational constants, we should expect that AE ( separates the lines by a small amount in relation to the size of T. In other words, the spectrum should show a group of lines clustered about a transition energy that is roughly 

A vibrational band in an electronic spectrum is the clustering of lines about one such transition energy. 

Vibrational wavefunctions and overlaps for two identical harmonic oscillator wavefunctions with offset minima. 

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