Quasi-Diabatic Band Theory with Localized Crystal Orbital Transformation

Abstract

Quasi-diabatic band theory has been developed by using the localized crystal orbital (LCO) transformation to study the electronic structure representing the diabatic behavior of electrons. The theory has been applied to nondoped alternating trans-polyacetylene (t-PA) to understand better the electronic structure from this new standpoint. The results show that the π-(π*-) band of the newly constructed crystal orbital becomes higher (lower) than that of the canonical crystal orbital. The occupation number analysis also indicates that the π-bands near the Fermi energy level play a significant role in the electron transport. These results have been discussed in terms of the LCOs representing the biradical and zwitterionic states.

Theoretical Studies on Quasi-Diabatic Electronic Effects in Lithium Heavily-Doped Polyacetylene

“… a See figure 3. b Previous work taken from ref . c φ‘ 1 and φ‘ 2 represent the CCOs with π and π* natures, respectively. …”

“…The details of the theoretical treatment have already been described previously . Here, the outline of the method is briefly mentioned.…”

“…They are something in between, depending on the type of coupling. Accordingly, the change of the occupation number ν j ( k ) of the CCO φ‘ j ( k ) can be a criterion of the degree of electron transport along k -space in the quasi-diabatic states. , Then, the energy dependence of the occupation and the unoccupation (hole) numbers, which we have called “the effective number of free carriers”, is given by and respectively, where E F stands for the Fermi energy level. The integration is taken over a first Brillouin zone (BZ).…”

“…To investigate theoretically the lattice deformation as mentioned above, crystal orbital (CO) calculations on heavily-doped PAs have been successfully carried out. ,− However, the conventional crystal orbital (CO) calculations only give adiabatic electronic structures. The adiabatic electronic structures here mean that electrons move infinitely slowly on one partially-filled band along the k -space and remain on the same band up to the zone boundary. , On the other hand, one should take care, in metallic states, that there will be a finite probability of breakdown of the adiabatic electronic structures when electrons move with a finite velocity . In other words, there will be a finite probability that electrons will change from one band to the other vacant band (band crossing), that is, diabatic electronic structures. , Such a diabatic electronic structure might influence chemical and physical properties in heavily-doped PAs since the metallic properties measured would be associated with the electrons moving with a finite velocity.…”

“…We previously proposed a quasi-diabatic CO theory with the localized crystal orbital transformation to study the electronic structure representing the diabatic behavior of electrons . This method is characterized by a quasi-diabatic treatment of the coupling between canonical COs due to the derivative operator of crystal momentum.…”