A pseudo-Jahn-Teller system modeled through generalized spin Hamiltonian the C4H4 molecule

A PSEUDO-JAHN-TELLER SYSTEM MODELED THROUGH GENERALIZED SPIN HAMILTONIAN THE C4H4 MOLECULE 

The shallow double well shape of the ground-state energy curve has the well-known pattern of PJT effect corresponding to different directions of square elongation. Among the many excited states, two spin singlets, three spin triplets, and 

The spin singlet states of HDVV Hamiltonian are those forming the problem of PJT effect related to the bond alternation. Using the symmetry labels of D4h one may write the following model Hamiltonian whose non-diagonal matrix element 

It is interesting to note that the spin triplet states of the HDVV-type have an orbital degenerate state at DAh which can be presented as an excited state JT effect, the corresponding matrix formulation being  

We encountered in this case the interesting situation of expressing the PJT and a JT vibronic constants by an unique set of parameters offered by the spin Hamiltonian expansion  

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