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Ideas of Quantum Chemistry P109

Ideas of Quantum Chemistry P109 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. | 1046 X. MULTIPOLE EXPANSION This means that to maintain the invariance of the energy with respect to equal translations of both coordinate systems we have to calculate all terms satisfying nk n nmax in the multipole expansion. If e.g. nmax 2 we have to calculate the term proportional to R-1 or the charge-charge interaction it will be invariant proportional to R-2 or charge-dipole and dipole-charge terms their sum is also invariant proportional to R-3 or charge-quadrupole quadrupole-charge and dipole-dipole their sum is invariant as well . Let us imagine scientists calculating the interaction energy of two molecules. As will be shown later in their multipole expansion they will have the charges of both interacting molecules their dipole moments their quadrupole moments etc. Our scientists are systematic fellows and therefore I bet they will begin by calculating the multipole moments for each molecule up to a certain maximum multipole moment say the quadrupole the calculations become more and more involved which makes their decision easier . Then they will be ready to calculate all the individual multipole-multipole interaction contributions. They will make a table of such interactions rows the multipole moments of A columns the multipole moments of B and calculate all the entries in their table. Then many of their colleagues would sum all the entries of the table in order not to waste their time. This will be a mistake. The scientists might not suspect that due to this procedure their result depends on the choice of coordinate system which is always embarrassing. However our scientists will do something else. They will sum the entries corresponding to charge-charge charge-dipole dipole-charge charge-quadrupole quadrupole-charge dipole-dipole and they will throw the other entries into the waste paper basket. Having made this decision the scientists will gain a lot their interaction energy will not depend on how they translated the a and b coordinate systems. Now we .