Interpretation of energy bands of polyethylene in terms of effective interactions between first- and second-neighboring CH2 groups
✍ Scribed by V. Gineityte
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 253 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0020-7608
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✦ Synopsis
The alternative way of solving secular problems for the Hamiltonian w matrices of regular quasi-one-dimensional systems developed previously V. Gineityte, Ž . Ž .x Int. J. Quant. Chem. 60 3 , 717 1996 has been applied to polyethylene. An implicit form of the dispersion relation has been obtained in terms of three local-structure-determined Ž . Ž . Ž . energy-dependent functions ␦ , , and , describing the effective interactions inside a separate CH group and those between first-and second-neighboring CH 2 2 groups, respectively. The actual shapes of dispersion curves proved to be determined by Ž . Ž . relative mean values of the functions and within the region under interest. The unusual minimum within the low-energy branch of dispersion curves situated at a Ž . low-symmetry point of the first Brillouin zone k f 0.6ra has been established to appear owing to considerable values of effective interactions between the secondneighboring CH groups within the respective energy interval. Just the latter type of 2 interactions has been concluded to be responsible also for non-one-dimensionality of the polyethylene chain. The Hamiltonian matrix eigenfunctions of this chain have been expressed as the Bloch sums of eigenvalue-dependent local-structure-determined basis orbitals.