Quantities related to electron density

To further characterize the electronic properties of the first and second excited states, let us examine the quantities related to electronic density. Panel (c), (d), and (e) of Fig. 7.26 exhibit the bond order at OH bond, the Mulliken charge of some selected parts, and the number of unpaired electrons of the first excited state of phenol and three membered ammonia cluster as a function of the bond length of OH. Likewise panel (f), (g), (h) show the similar quantities for the second lowest excited state, which strongly couples nonadiabatically with the first excited state. In panel (a) to (h) of Fig. 7.27 are displayed the similar graphs for phenol and five membered ammonia cluster. 

Bond order As clearly observed in panel (c) and (f) of Fig. 7.26, only smooth interchange between the bond orders of OH and NH takes place in positive values. This directly indicates that chemical bond is smoothly shifted from OH to NH site both in the first and second excited states. This kind of smooth interchange in positive value is often observed in the typical proton transfer in the ground states. Likewise, the similar interchange is observed in Fig. 7.27 for five membered ammonia cluster. 

Mulliken charge panel (d) and (g) of Fig. 7.26 show that the Mulliken 

Chemical Theory Beyond the Born-Oppenheimer Paradigm 

Unpaired electron population Panel (e) of Fig. 7.26 suggests that the initial tt - tt state contains about three radicals. It is obvious that there should exist at least two radicals, and it is likely that the additional one radical center appears due to the strong electron correlation arising from the nearly degenerate orbitals in the benzene ring (near degeneracy in each manifold of tt and tt orbital). Beyond the barrier, one radical remains localized in PhO site and another is found in AMC (mainly on AMI), which is really the biradical state. [71] 

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