This post concerns what may be the fast known internal conversion process in a chemical system, non-radiative decay times in the range of

**3-8 femtoseconds**. Internal conversion is the process whereby in a molecule there is a non-radiative transition between electronic excited states (without change in spin quantum number). This is by definition a break-down of the Born-Oppenheimer approximation.
Much is rightly made of the fascinating and important fact that excited states of DNA and RNA undergo "ultra-fast" non-radiative decay to their electronic ground state. This photo-stability is important to avoid mutations and protect genetic information. Conical intersections are key. The time scale for comparison is the order of a picosecond.

The figure below is taken from

Quantum Mechanical Study of Optical Emission Spectra of Rydberg-Excited H3 and Its Isotopomers Susanta Mahapatra and Horst Köppel

It shows the wavelength dependence of the intensity of emission from a 3d (Rydberg) excited state.

There are several things that are noteworthy about the experimental data, given that this is

**a gas phase spectra.**
1. The large width of the spectra. In energy units this is of the order of an eV. Gas phase spectra for electronic transitions in typical molecules are usually extremely sharp (See here for a typical example).

2. The two peaks, suggesting the presence of two electronic transitions.

3. The strong isotope effects. For strictly electronic transitions between adiabatic states, there should be no dependence on the nuclear masses. This suggests strong vibronic and quantum nuclear effects.

So what is going on?

The key physics is that of the

**Jahn-Teller effect**, conical intersections, and non-adiabatic effects.
For H3 there is geometry of an equilateral triangle which has C3 symmetry. There are then two degenerate electronic ground states with E symmetry, and experience E x epsilon Jahn-Teller effect leading to the two

**adiabatic**potential energy surfaces shown below. They touch at a conical intersection. The two peaks in the spectra above correspond to transitions to these two different surfaces.**Non-adiabatic coupling**leads to rapid transitions between the surfaces leading to the ultra-ultra-fast internal conversion and the very broad spectra. This is calculated in the paper, leading to the theoretical curves shown in the top figure.

More recently, Susanta and some of his students, have considered the relative importance of (off-diagonal) non-adiabatic effects, the geometric phase [associated with the conical intersection], and Born-Huang (diagonal) corrections to explaining the spectra.

They find that the first has by far the most dominant effect. The latter two have very small effects that look like they will be difficult to disentangle from experiment. I discussed the elusiveness of experimental signatures of the geometric phase in an earlier post.

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