In the hypothetical case of a system that may require crossing between manifolds of different multiplicities:
Two PESs are created for a heavy atom abstracting a hydrogen atom. One is the triplet PES and the other is the singlet PES. Ground state singlet-triplet gaps are non-trivial.
The triplet TS is lower in energy, but at some point in the reaction coordinate, the singlet reaction path becomes energetically favorable. The experimentally observed product is in the singlet state. Where does the system undergo inter-system crossing (ICS) to arrive at the product? At the crossing point or at the product? How does ICS figure into kinetics? How does one describe kinetics if this point of intersection is before the TS? Is there a name for these kinds of scenarios?
This is known now as two-state reactivity (TSR) or many-state reactivity (MSR). See for example in: Acc. Chem. Res., 40, 532-542 (2007); Int. J. Mass Spectrom., 354-355, 5-14 (2013) ; Helv. Chem. Acta, 78, 1393-1407 (1995); J. Am. Chem. Soc., 119, 1773-1786 (1997).
Cheers,
Sason
When the levels of the two states converge close enough, the system is not in one of them, and is in a superposition of these states. You have to solve the corresponding equations for the wave function represented by a superposition of the states
This is known now as two-state reactivity (TSR) or many-state reactivity (MSR). See for example in: Acc. Chem. Res., 40, 532-542 (2007); Int. J. Mass Spectrom., 354-355, 5-14 (2013) ; Helv. Chem. Acta, 78, 1393-1407 (1995); J. Am. Chem. Soc., 119, 1773-1786 (1997).
Cheers,
Sason
You have a case of spin-forbidden process where in some point of your PES the your system jump from singlet PES to triplet PES or viceversa. you need to locate the minimum-energy crossing point (MECP) of your structure, for this first you need to have the complete PES of your process in the two states (the major part at least), once you have them, then you know more or less where your system jump (qualitative of course), the through a method develop by Harvey you can obtain the structure where your system jump, this method is discribe in (coordination Chemistry Reviews, 238-239, (2003), 347-361 or Phys. Chem. Chem. Phys., 2007, 9, 331–343).
Orca software has implemented this method
I hope I've been helpful
The overall rate of your reaction will be proportional to the barriers involved one either or both surfaces (as usual) multiplied by the probability of the non-adiabatic transition. You can calculate this from the Landau-Zener equation, where the coupling value between the two surfaces is provided by the spin-orbit coupling due to your heavy atoms. In order to get the rate, you'll need to know the slope of one potential surface relative to the other where they cross. A way to calculate this is using the Nudged Elastic Band method, as that will give you the geometries of the minimum energy paths on each surface. Once you have these geometries for both the singlet->singlet and triplet->triplet reactions (making sure to use the fully relaxed configurations for both the starting and final points ON THEIR ground state spin surfaces), you can do single point calculations on each of minimum energy pathway geometries but constrained to the OTHER spin state. That is, take the geometries for the singlet minimum energy path and so single point energy calculations with them to get their energy as triplets. Do the same with the triplets. Then, compare, say, the singlet state run as a singlet to that run as a triplet and see where they meet; this geometry is what you'll use at the crossing point. You can then take that geometry and do another NEB calculation from that point to the final GS spin state configuration, and get calculate the slope at that crossing for your Landau-Zener transition value.
Just so you know, for this to be at all accurate you'll have to do a pretty involved NEB calculations with lots of beads so that the resolution (beads near the crossing point or points) is large enough to get the slopes. Also, you'll have to calculate your spin-orbit coupling.
Good luck. Fun stuff.
YOU MAY READ ABOUT IT IN THE FOLLOWING PAPER:
D. Danovich, S. Shaik
“Spin-Orbit Coupling in the Oxidative Activation of H-H by FeO+. Selection Rules and Reactivity Effects”
J. Am. Chem. Soc., 119, 1773-1786 (1997).
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