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Ideas of Quantum Chemistry P55

Ideas of Quantum Chemistry P55 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. | 506 10. Correlation of the Electronic Motions The nucleus-electron case When one of the particles is a nucleus of charge Z then 1 and we get d dr r 0 -Zÿ r 0 . Thus the correct wave function for the electron in the vicinity of a nucleus should have an expansion const 1 - Zra1 - where ra1 is the dis- tance from the nucleus Let us see how it is with the 1s function for the hydrogen-like atom the nucleus has charge Z expanded in a Taylor series in the neighbourhood of r 0. We have 1s N exp -Zr N 1 - Zr . It works. The correlation cusp condition shows that the wave function is not differentiable at r 0. 10.2 THE HYLLERAAS FUNCTION In 1929 two years after the birth of quantum chemistry a paper by Hylleraas9 appeared where for the ground state of the helium atom a trial variational function containing the interelectronic distance explicitly was applied. This was a brilliant idea since it showed that already a small number of terms provide very good results. Even though no fundamental difficulties were encountered for larger atoms the enormous numerical problems were prohibitive for atoms with larger numbers of electrons. In this case the progress made from the nineteen twenties to the end of the twentieth century is exemplified by transition from two- to ten-electron systems. 10.3 THE HYLLERAAS CI METHOD In this method 10 we exploit the Hylleraas idea in such a way that the electronic wave function is expressed as a linear combinations of Slater determinants and in front of each determinant j 1 2 3 . N we insert next to the variational coefficient cj correlational factors with some powers v u . of the interelectronic 9E.A. Hylleraas Zeit. Phys. 54 1929 347. Egil Andersen Hylleraas arrived in 1926 in Gottingen to collaborate with Max Born. His professional experience was related to crystallography and to the optical properties of quartz. When one of the employees fell ill Born told Hylleraas to continue his work on the helium atom in the context of the newly developed .