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Ideas of Quantum Chemistry P78

Ideas of Quantum Chemistry P78 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. | 736 13. Intermolecular Interactions non-zero indices will make a contribution to Eind ABC while all the terms with only-one-zero or two non-zero indices will sum to Edisp ABC E 2 ABC Eind ABC Edisp ABC 13.55 where the first term represents the induction energy Eind ABC Eind AB C EM AC B EM BC A where Eind BC A v K a0b0c V 0a0b0c l2 tEA 0A - EA nA nA 0 means that the frozen molecules B and C acting together polarize molecule A etc. The second term in 13.55 represents the dispersion energy this will be considered later on see p. 740 . For the time being let us consider the induction energy Eind ABC . Writing V as the sum of the Coulomb interactions of the pairs of molecules we have Eind BC A a0b0c Vab VBc VAc 0a0b0c 0a0b0cIVab VBc VacI a0b0c nA 0 X ea 0a - ea a -1 nA0B VAB 0A0B nA0C VAC 0A0C nA 0 X 0A0B VAB nA0B 0A0C VAC nA0C x Ea 0a - Ea a -1- Look at the product in the nominator. The induction non-additivity arises just because of this product. If the product being the square of the absolute value of nA0BIVab 0a0b nA0C Vac 0a0c were equal to the square of the absolute values of the first and second component the total expression shown explicitly would be equal to the induction energy corresponding to the polarization of A by the frozen charge distribution of B plus a similar term corresponding to the polarization of A by C i.e. the polarization occurring separately. Together with the other terms in Ejnd AB C Ejnd AC B we would obtain the additivity ofthe induction energy Eind ABC . However besides the sum of squares we also have the mixed terms. They will produce the non-additivity of the induction energy Eind ABC Eind AB Eind BC Eind AC Aind ABC . 13.56 Thus we obtain the following expression for the induction non-additivity Aind ABC n.l Vl . l n.l VAC 0A0c Aind ABC 2Re ---------- - ------------------- 13.57 Ea 0a - Ea a A 0 where ----- stands for the non-additivities of Eind AB C Eind AC B . 13.9 Non-additivity of intermolecular interactions 737 Example 4. .