Valence-bond description of chemical reactions on Born-Oppenheimer molecular dynamics trajectories

The nature of chemical bonds on dynamic paths was investigated using the complete active space valence-bond (CASVB) method and the Born-Oppenheimer dynamics. To extract the chemical bond picture during reactions, a scheme to collect contributions from several VB (resonance) structures into a small numbers of indices was introduced. In this scheme, a tree diagram for the VB structures is constructed with the numbers of the ionic bonds treated as generation. A pair of VB structures is related to each other if one VB structure is transferred into the other by changing a covalent bond to an ionic bond. The former and latter VB structures are named parent and child structures, respectively. The weights of the bond pictures are computed as the sum of the CASVB occupation numbers running from the top generation to the bottom along the descent of the VB structures. Thus, a number of CASVB occupation numbers are collected into a small number of indices, and a clear bond picture may be obtained from the CASVB wave function. The scheme was applied to the hydrogen exchange reaction H(2)+F-->H+HF and the Diels-Alder reaction C(5)H(6)(cyclopentadiene)+CH(2)=CH(2)(ethylene)-->C(7)H(10)(norbornene). In both the reactions, the scheme gave a clear picture for the Born-Oppenheimer dynamics trajectories. The reconstruction of the bonds during reactions was well described by following the temporal changes in weight.