# What does oscillator strength have to do with state character?

I was reading S.H.A.R.C. Manual (Surface Hopping in the Adiabatic Representation Including Arbitrary Couplings) and came across the following paragraph:

"Each state is colored, with one color as contour and another at the core of the line. The contour color represents the total spin expectation value of the state. The core color represents the oscillator strength of the state with the lowest state. See figure 7.3 for the relevant color code. Note that by definition the “oscillator strength” of the lowest state with itself is exactly zero, hence the lowest state is also light grey. This dual coloring allows for a quick recognition of different types of states in the dynamics, e.g. singlets vs. triplets or nπ ∗ vs. ππ ∗ states."

How can one recognize nπ ∗ vs. ππ ∗ from this kind of colour scheme? What does oscillator strength have to do with state character?

• I've never seen such a plot, but since the oscillator strength of a transition relates to the transition dipole moment, only such states contribute that have the right symmetry for the dipole operator. By projecting out "self-interaction", the picture is decluttered for states that don't have point inversion symmetry. The plot should show clusters. It'd be nice if you had an example of such a plot. I assume it is 2-D. – Deathbreath Sep 27 '16 at 14:24

$n\pi ^*$ transitions are often symmetry forbidden (e.g. in carbonyls) and so weak compared to $\pi \pi ^*$. Other than these general rules you just have to look at the individual molecules to work out what is going on, it might be quicker than trying to understand the diagram.