Polyacetylene energy calculations

A reasonable choice of parameters for the polyacetylene is given by U = 3t and V = 1.2/ [13, 15]. In table 3, we show the energy per site obtained from DMRG and RVA calculations for different values of the dimerization parameter A. For A = 2, the chain is fully dimerized the results... 

Fig. 4.5 The experimental UPS spectra, obtained with two different photon energies, are compared with the VEH-derived band structure of ttans-polyacetylene. An intermediate step, the DOVS calculated from the band diagram, are shown fir comparison.

Table 4 lists the MBPT(2) band gaps of polyacetylene calculated with basis set 6-31G and DZP at three different geometries by us [36]. The cutoffs N and K are both 21. The geometries used in the calculations are listed in Table 5. The first two were given by Suhai [53,55] and the last one was an experimentally estimated geometry [97], The band gaps obtained are 4.033, 3.744, and 3.222 eV, respectively. There is no direct measurement of the band gap, defined as a quasi-particle energy difference of the lowest unoccupied and highest occupied orbitals. Instead, the absorption spectrum of polyacetylene crystalline films rises sharply at 1.4 eV and has a peak around 2.0 eV [97]. To explain this measured spectrum, one needs to calculate the density of the system s excited states and the absorption coefficients of the states.

The interaction of long-chain molecules such as polymers is a problem area where the nature of polarization response can be a significant concern on its own. An example is from a study of parallel hexatriene molecules carried out to represent a truncated form of solid-state polyacetylene [192]. This smdy included both ab initio calculations and an electrostatic model using polarizability, a, and second hyperpolarizability, y, tensors distributed to the carbon centers. The ab initio calculations on a single hexatriene molecule were used to find the distributed tensors for the electrical analysis. The objective in this smdy was not the interaction energy, but the effect on each molecule s polarizability and hyperpolarizability due to intermolecular interaction. The ab initio evaluations benchmarked the electrostatic model calculations both for... 

For long (infinite) trani -polyacetylene chains, the treatment of quantum lattice fluctuations is very complicated, because many lattice degrees of freedom couple in a non-linear way to the lowest electronic transitions. We have recently shown that for chains of up to 70 CH units, the amount of relevant lattice degrees of freedom reduces to only one or two, which makes it possible to calculate the low-energy part of the absorption spectmm in an essentially exact way [68]. It remains a challenge to study models in which both disorder and the lattice quantum dynamics are considered. 

Figure 5-5. Valence band spectra of trara -polyacetylene, recorded using synchrotron radiation at 27 eV and 50 eV photon energy, and the corresponding DOVS derived from VEH calculations. The VEH band structure is shown in the lower part of the figure (from Ref [28]).

Two recent ab-initio studies are devoted to the determination of the ground-state structure of Cg. Parasuk and AlmlOf concluded that the cyclic polyacetylenic structure ( Ag) and the linear cumulenic g state are essentially isoenergetic [260]. However, the choice of basis sets and methods (MRCI modified coupled-pair functional, MCPF) heavily affects the difference in energy between the linear and cyclic forms of Cg, and so the results are quite uncertain. On the other hand, Slanina et al. proposed a nonplanar Z)2d symmetrical cyclic structure as the minimum-energy structure of Cg [261]. According to their MP2/6-31G calculations, this form is 13 kcal/mol lower in energy than the planar Qa structure. Unexpectedly, all the C-C bond lengths in the species are equivalent (1.339 A). DFT calculations favor the linear structure as compared with a planar cyclic one, but nonplanar species seem to have not been considered in this study [236]. 

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