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Ideas of Quantum Chemistry P50

Ideas of Quantum Chemistry P50 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 456 9. Electronic Motion in the Mean Field Periodic Systems a conduction band energy gaP valence band insulator Fig. 9.9. Valence bands highest occupied by electrons and conduction bands empty . The electric properties of a crystal depend on the energy gap between them i.e. HOMO-LUMO separation . A large gap a is typical for an insulator a medium gap b means a semiconductor and a zero gap c is typical of metals. Finally insulator an insulator has a large band gap separating the valence band from the conduction band. band gap We know metallic systems typically represent microscopically 3D objects. Recently 2D and 1D metals have become more and more fashionable the latter molecular wires called molecular wires. They may have unusual properties but are difficult to pre-Peieris pare for they often undergo spontaneous dimerization of the lattice known as the transition Peierls transition . Rudolph Peierls 1907-1995 British physicist professor at the universities of Birmingham and Oxford. Peierls participated in the Manhattan Project atomic bomb as leader of the British group. As Fig. 9.10.a shows dimerization makes the bonding and antibonding effects stronger a little below and above the middle of the band whereas at k 0 the effect is almost zero since dimerization makes the bonding or antibonding effects cancel within a pair of consecutive bonds . As a result the degeneracy is removed in the middle of the band Fig. 9.10.b i.e. the band gap ap- pears and the system undergoes metal-insulator or metal-semiconductor transition Fig. 9.10.c . This is why polyacetylene instead of having all the CC bonds equivalent Fig. 9.10.d which would make it a metal exhibits alternation of bond lengths Fig. 9.10.e and it becomes an insulator or semiconductor. To a chemist the Peierls transition is natural. The hydrogen atoms will not stay equidistant in a chain but will simply react and form hydrogen molecules i.e. will 9.9 Band structure 457 Fig. 9.10. The Peierls effect has the same .