Much effort has been expended in the computational chemistry community in developing methods to simulate the dynamics of vibrational wave packets moving through such conical intersections. These methods have been used to simulate a number of important photophysical processes in condensed phases (e.g., the isomerisation of retinal in the protein rhodopsin).
I have often wondered what are the key energy, length, and time scales in this problem?
While in Toronto, Valentyn Prokhorenko, brought to my attention a really nice PRL that answers my questions. Unfortunately, this paper does not seem to have drawn the attention that it deserves.
The authors define a semi-classical expansion parameter g which is essentially the ratio of the particle deBroglie wavelength to the scattering length associated with the conical intersection. They estimate that for typical photochemical processes this parameter will be small, justifying the semi-classical approximation.
The probability of a wave packet to remain on the diabatic surface it starts on is shown to be
Pd = exp (-pi alpha^2/2)
where alpha is a dimensionless parameter proportional to the ratio of the impact parameter a of the wave packet and the scattering length rs.
A few questions I have are:
How do these results change with the shape of the conical intersection? e.g., if it is tilted?
How do these results relate to earlier work of Teller and Nikitin and more recently Malhado & Hynes?
How does decoherence change these results?
In our recent submission on methine dyes, I chose to say that the photoisomerization reaction "erases and resets" the conformation of the molecule, rather than saying that it is "changed". This is true - the system can decay by the intersection mediating the photoreaction without actually populating another isomer. However, I knew at the time that this language was suggestive, because there is a minimum entropic cost associated with information erasure. I am interested in knowing such things as: does the topography of the intersection affect the information loss?
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