A novel formulation of an approximate valence bond model (AVB2) and its application to the tautomeric forms of porphyrin and porphycene

This study presents a novel formulation of the approximate valence bond method, which can be applied as a very fast generator of the molecular potential energy function. The AVB2 model was formulated and parameterized for porphyrin and porphycene using results of quantum mechanical computations at the B3LYP/6-31G (d, p) level. The DFT potential energy, its gradients, and the Hessian-matrix elements, as well as effective atomic charges at local energy minima and transition states, were used for the parameterization of the AVB2 Hamiltonian matrix. The AVB2 method, and in particular its anharmonic version, very well reproduce the potential energy maps for all representative geometries of the studied systems, including harmonic frequencies, and possible proton translocations. For validation of the method, we performed molecular dynamics simulations for isolated molecules accounting for internal double proton transfer processes, which are strongly correlated with changes of the electronic charge density. The simulated power spectra were compared with the experimental infrared spectra. More precise simulations of IR spectra at the classical and quantum dynamics levels, as well as extensions of the AVB2 parameterization to electronic excited states, are the subject of further research.