Triplet states and optical absorptions in finite polyenes and conjugated polymers

Extracting infinite system properties from finite size clusters: “phase randomization/boundary condition averaging”

“…3c. We feel that these results, and those in Ref.s (2,3], demonstrate that RVA is an effective means for reducing (and in some cases practically eliminating) finite size dependence, yielding results that can be confidently extrapolated to the infinite size limit, and which are in good agreement with known analytic results.…”

“…for small clusters are strongly dependent on the boundary condition (BC); i.e., for the case of polyacetylene, whether the carbon atoms are viewed as being on a real ring, such as benzene, a real chain, such as (1,3,5)-hexatriene, or a more exotic geometry, such as anti-periodic BCs. We have found that [2,31 to reduce finite size corrections to the calculated optical gaps and spectra, thus improving the extrapolation to the infinite case, it is effective to employ novel "averaging" techniques to "randomize" the many-body levels which influence those correlation functions of interest.…”

Extracting Infinite System Properties from Finite Size Clusters: Phase Randomization/Boundary Condition Averaging

“…We have found that [2,3] to reduce finite size corrections to the calculated optical gaps and spectra, thus improving the extrapolation to the infinite case, it is effective to employ novel "averaging" techniques to "randomize" the many-body levels which influence those correlation functions of interest. Briefly, by randomization, we mean simply that the total energy of the system is to be viewed as a weighted average of the energies derived separately for each of several different "random" values (RV) of a particular parameter, which may be the BC, a hopping integral, an on-site energy, or the Hubbard U : E = {RV } x RV E [RV ], where x RV is a normalized weighting factor with {RV } x RV = 1.…”

“…However, RVA is equally applicable to the calculation of, e.g., the phonon modes of the ground state, as well as the geometry and self-consistent absorptions of doped or higher lying (e.g., triplet) states [3], luminescence spectra, structure factors, etc., in single-or multi-band models in 1-, 2-, and 3-D, via Lanczös diagonalization, as well as other numerical procedures on small lattices, such as Monte Carlo.…”

“…Solutions of the Peierls-Hubbard Hamiltonian (PHH) [1] for small clusters are strongly dependent on the boundary condition (BC); i.e., for the case of polyacetylene, whether the carbon atoms are viewed as being on a real ring, such as benzene, a real chain, such as (1,3,5)-hexatriene, or a more exotic geometry, such as anti-periodic BCs. We have found that [2,3] to reduce finite size corrections to the calculated optical gaps and spectra, thus improving the extrapolation to the infinite case, it is effective to employ novel "averaging" techniques to "randomize" the many-body levels which influence those correlation functions of interest.…”