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Ideas of Quantum Chemistry P43

Ideas of Quantum Chemistry P43 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. | 386 8. Electronic Motion in the Mean Field Atoms and Molecules The formula can be easily interpreted. Let us first consider the electron density described by the orbital 2 2 1 S -1 a2 b2 2ab . Let us note that the density can be divided into the part close to nucleus a that close to nucleus b and that concentrated in the bonding region95 v Pa Pb Pab 8.66 where pa 2 1 S -1a2 pb 2 1 S -1b2 pab 1 S -1ab. It can be seen 96 that the charge associated with pa is -2 1 S -1 the charge connected with the nucleus b is the same and the overlap charge pab is -S 1 S . Their sum gives -2 2 1 S - 2S 2 1 S -1 the unit electronic charge . The formula for AE may also be written as we use symmetry the nuclei are identical and the a and b orbitals differ only in their centres A Vab a Vab b Vaa b Vbb a 1 2 1 S 2 1 S 2 1 S 2 1 S R 8.67 penetration energy Now it is clear that this formula exactly describes the Coulombic interaction Fig. 8.18.a b of the electron cloud from the a atom with density 2pab with the b nucleus and vice versa the first two terms of the expression of the electron cloud of density pa with the b nucleus third term of the electron cloud of density pb with the a nucleus fourth term of the a and b nuclei fifth term . If we consider classically a proton approaching a hydrogen atom the only terms for the total interaction energy are Fig. 8.18.c AEclass Vaa b 1 8.68 R The difference between AE and AEciass only originates from the difference in electron density calculated quantum mechanically and classically cf. Fig. 8.18.b c. The AEclass is a weak interaction especially for long distances and tends to for small R because97 of the 1 R term. This can be understood because AEclass is the difference between two Coulombic interactions of a point charge with a spherical charge cloud and of the respective two point charges called penetration energy . AE contains two more terms in comparison with AEclass Vab a 2 1 S and Vab b 2 1 S and both decrease exponentially to Vaa.a -1 a.u.