Polyacetylenes geometry

It is instructive to compare the approximate weak-coupling theory to essential exact, numerical (density matrix renormalization group) calculations on the same model (namely the Pariser-Parr-Pople model). The numerical calculations are performed on polymer chains with the polyacetylene geometry. Since these chains posses inversion symmetry the many-body eigenstates are either even (Ag) or odd By). As discussed previously, the singlet exciton wave function has either even or odd parity when the particle-hole eigenvalue is odd or even. Conversely, the triplet exciton wavefunction has either even or odd parity when the particle-hole eigenvalue is even or odd. As a consequence, we can express a B state as... 

The Durham precursor route to polyacetylene is an excellent example of the application of organic synthesis to produce a precursor polymer whose structure is designed for facile conversion to polyacetylene. Durham polyacetylene was first disclosed by Edwards and Feast, working at the University of Durham, in 1980 227). The polymer (Fig. 6 (I)) is effectively the Diels-Alder adduct of an aromatic residue across alternate double bonds of polyacetylene. The Diels-Alder reaction is not feasible, partly for thermodynamic reasons and partly because it would require the polymer to be in the all m-conformation to give the required geometry for the addition to take placed 228). However, the polymer can be synthesised by metathesis polymerization of the appropriate monomer. 

Fig. 12 Example polyacetylenes with pendant radical groups, with a computed geometry example of pendant twisting that severely limits exchange along the main chain.

Polyacetylene is a physical realization of such a system and it is known-that it does present bond alternation [46,47]. Since a parameterization to a model spin Hamiltonian is available [18] for conjugated hydrocarbons, this system is a good test for the NSBA and RVB ansatze. Therefore, in Ref. 34 the geometry of polyacetylene has been computed using this sort of ansatze. 

As we can see from the Table all the three chains (and this is the case also for further two other polyacetylene and three polydiacetylene chains (7) which also have been calculated) have broad valence and conduction bands with widths between 4.4 and 6.5 eV-s. Comparing the band structure of the two polyacetylene chains we can find that the position of the bands and their widths is not very strongly influenced by the different geometries. This is again the case if we compare the here not described band structures of the further polyacetylene and polydiacetylene chains. On the other hand the position of the valence and conduction bands and the widths of the valence bands of the polydiacetylene chains is more different from those of the polyacetylene chains. To conclude we can say that due to the broad valence and conduction bands of these systems (which mean rather large hole and electron mobilities,respectively) one can expect that if doped with electron acceptors or donors these systems will become good conductors, which is, as it is experimentally estab-... 

MBPT(2) has also been applied to calculate vibrational frequencies of polymers. With the translational symmetry, one can only calculate the vibrational modes with the reciprocal vector k = 0. These modes are of particular importance since they give rise to infrared and Raman spectra [67]. We applied MBPT(2) to polymethineimine and calculated its equilibrium structure, band gap, and vibrational frequencies with basis sets STO-3G, 6-31G and 6-31G [68]. Both basis set and electron correlation have a strong influence on its vibrational frequencies as well as its optimized geometry and band gap. With respect to in-phase (k=0) nuclear displacements, Hirata and Iwata very recently calculated the MBPT(2) vibrational frequencies of polyacetylene for basis sets STO-3G and 6-31G with analytical gradients [69], They showed that MBPT(2) greatly improves the HF vibrational frequencies for polyacetylene. 

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.

Table 5. The geometries of polyacetylene used in Table 4 (units A and degree) [26] ...

The Pariser-Parr-Pople Hamiltonian for the description of the 7i-electrons in trans-polyacetylene is reparametrized using ab initio Coupled Cluster Doubles calculations based on a Restricted Hartree Fock reference on trans-butadiene. To avoid the spin contaminations inherent in Unrestricted Hartree Fock (UHF) type calculations on polymethine chains in the doublet state the Annihilated Unrestricted Hartree Fock (AUHF) model is applied in our PPP calculations (tPA (CH) , polyenes H-(CH)2N-H, polymethines H-(CH)2N+1-H). In geometry optimizations on polymethine chains it is shown that in contrast to results from Hiickel type models the width of neutral solitons is strongly... 

The electronic structures of poiy(fluoroacetylene) and poly(difluoroacetylene) have been investigated previously using the ab initio Hartree-Fock crystal orbital method with a minimum basis set (42). Only the cis and trans isomers with assumed, planar geometries were studied. The trans isomer was calculated to be more stable in both cases, and the trans compounds were predicted to be better intrinsic semiconductors and more conductive upon reductive doping than trans polyacetylene. However, our results show that head-to-tail poly(fluoroacetylene) prefers the cis structure and that the trans structure for poly(difluoroacetylene) will not be stable. Thus the conclusions reached previously need to be re-evaluated based on our new structural information. Furthermore, as noted above, addition of electrons to these polymers may lead to structural deformations that could significantly change the conductive nature of the materials. 

The fact that doping does indeed largely perturb the geometry of ID chains has been confirmed by several computer experiments on isolated chains of equidistant hydrogen atoms [49] and on a more realistic model of polyacetylene [50]. In both cases, the doping is shown to have the same effect, i.e. the amount of bond alternation is calculated to be drastically reduced bond lengths of 1.41 and 1.43 A versus 1.33 and 1.48 A for the double and single bonds, respectively (already in minimal basis sets calculations). 

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