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Cis-trans isomerization in retinal, the first step in vision, is oftencomputationally studied from a time dependent viewpoint. Motivation for suchstudies lies in coherent pulsed laser experiments that explore theisomerization dynamics. However, such biological processes take place naturallyin the presence of incoherent light, which excites a non-evolving mixture ofstationary states. Here the isomerization problem is considered from the latterviewpoint and applied to a standard two-state, two-mode linear vibroniccoupling model of retinal that explicitly includes a conical intersectionbetween the ground and first excited electronic states. The calculated quantumyield at 500 nm agrees well with both the previous time-dependent calculationsof Hahn and Stock (0.63) and with experiment ($0.65\pm0.01$), as does itswavelength dependence. Significantly, the effects of environmental relaxationon the quantum yield in this well-established model are found to be negligible.The results make clear the connection of the photoisomerization quantum yieldto properties of stationary eigenstates, providing alternate insights intoconditions for yield optimization.

Quantum Yields from Stationary States: Cis-Trans Isomerization of Model Retinal