Minimum total energy calculations for conjugated polymer chains

Abstract

Results from a set of minimum energy calculations performed for the Su Schrieffer Heeger Hamiltonian for trans-polyacetylene are presented. We fix the occupation numbers of the electronic states and look for the bond geometry which minimizes the total energy. The usual nonlinear solutions (polarons, solitons) are recovered for appropriate sets of occupation numbers of the electronic states. We study the spectrum of excited states and the properties of the model in the case of arbitrary doping. The situation where the original SSH Hamiltonian is modified in such a way as to account for the intrinsic periodicity of the monomeric units of conjugated polymers without a degenerate ground state is also examined.

Electron-lattice and electron-electron coupling in conjugated polymers: Minimum total-energy calculations on the Hubbard-Peierls Hamiltonian

“…This is because, upon excitation of one electron from the highest occupied to the lowest unoccupied molecular orbital, lack of ground state degeneracy leads to two separate bipolaron levels as opposed to a pair of degenerate soliton levels. E-e repulsion favors the 2 1 A g over the 1 1 B u level [10], and the results of ref. [6][7] suggest that this latter effect is not strong enough to overcome the energy difference between bipolaron levels in these systems.…”

“…Within the framework outlined above, the first 1 B u excited state is obtained by moving one of the two electrons occupying the N th level to the (N + 1) th level. In a long chain (even N → ∞) the set of bond lengths (i.e., the set of values of β n ) which minimizes E T ({β n }) for this electronic configuration displays two kinks: these delimit a central portion of chain where the dimerization is inverted [10]. Corresponding to this bond geometry the N th and (N + 1) th levels are degenerate and are found at the center of the Peierls gap.…”

“…Indeed, for realistic values of γ, if one allows bond geometry relaxation, the lowest 1 A g excited state corresponds to moving both the N th level electrons to the (N + 1) th level: in the N → ∞ limit both the total energy and the bond geometry corresponding to this situation are the same as those of the first 1 B u excited state [12]. However, if the bond geometry of the ground state is kept fixed, the electronic configuration which gives the lowest excited 1 A g state, is different: it corresponds to moving one of the N th level electrons to the (N + 2) th level [10].…”

“…It should be noted that three dimensionless parameters (γ, v 0 and v 1 ) completely determine the ratios between the energies of the electronic states as well as the relative size of the hopping integrals. On the other hand in order to estimate bond lengths and absolute energies additional phenomenological constants [10] are needed. To avoid introducing other parameters, table 1 shows examples of how the hopping constants (rather than the bond lengths) change as e-e interactions are turned on: note that large hopping constants correspond to short bonds and vice versa.…”

Breakdown of Polarons in Conducting Polymers at Device Field Strengths

“…The PA structure using the same tight-binding Model has the energy level and band gap according to Ref. [ 23,25,40], while using the same set of parameters for PPP, as first order of approximation, would give a different electronic structure and band gap in our calculations.…”