tailieunhanh - Ideas of Quantum Chemistry P52

Ideas of Quantum Chemistry P52 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. | 476 9. Electronic Motion in the Mean Field Periodic Systems number of them and this makes us a little nervous. In eq. for Fpq we have a summation over the whole infinite crystal of the interactions of an electron with all the nuclei and in the next term a summation over the whole crystal of the electron-electron interactions. This is of course perfectly natural because our system is infinite. The problem is however that both summations diverge the first tends to -rc the second to rc . On top of this to compute the bond order matrix P we have to perform another summation in eq. over the FBZ of the crystal. We have a similar very unpleasant situation in the total energy expression where the first term tends to -rc while the nuclear repulsion term goes rc . The routine approach was to replace the infinity by taking the first-neighbour interactions. This approach is quite understandable because any attempt to take further neighbours ends up with an exorbitant bill to FOCK MATRIX CORRECTIONS A first idea we may think of is to carefully separate the long-range part of the Fock matrix elements and of the total energy from these quantities as calculated in a traditional way . by limiting the infinite-range interactions to those for the N neighbours on the left from cell 0 and N neighbours on the right of it. For the Fock matrix element we would have Z70j Z70j A 0 Fpq Fpq N Cpq N 9. 5 where cPjq N stands for the long-range correction while Fpjq N is calculated assuming interactions with the N right and N left neighbours of cell 0 FOpjq N T0j 7 V0j Ah plhi 0h jl 1 h ll 9 76 Tpq I ZuVpq Au Z_ Psr pr qs 2 pr sq lh 9. 6 h -N u l h-N rs C0j N f 7 V0j Ah plhrOhjl A 9 77 Cpq N I J 7uVpq Au 2- Psr pr qs 1 9. where the symbol will mean a summation over all the unit cells except the section of unit cells with numbers -N -N 1 . 0 1 . N . the neighbourhood of cell 0 short-range . The nuclear attraction integral 51 TZ0j A h __ 0 __1 j I to Vpq .