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Ideas of Quantum Chemistry P59

Ideas of Quantum Chemistry P59 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. | 546 10. Correlation of the Electronic Motions Taking advantage of the commutator expansion we have mn L -12 A A-dt mn a T _l 1 T 2 1 A 1 i T _1_ 1 T2 i t m ab e 2He 2 ab I 1 - 12 2 T2 H 1 12 2 12 J lmn 77.1 . imn r 7 1. . 1 mn I fr7-ih lmn I T l ld ab H I ab H12 2 ab H12 - ab 12H - T2HTA A . However A 1 y iyj- fIT2. 1 mnpi 2 n i 1 mn 2 UTih i 1 mnlT2 fITp. A - 2 ab 12H12 2 ab 12 H l 2 ab 12 H 12 4 ab 12 H12 . The last equality follows from the fact that each term is equal to zero. The first vanishes since both determinants differ by four excitations. Indeed 12 deexcitations and notes a double deexcitation19 of the doubly excited function i.e. something propor- deexcitations tional to oI- For similar reasons too strong deexcitations give zero the remain- ing terms in A also vanish. As a result we need to solve the equation mn I 77.1. . mn I r Y i. . 1 mn I AT- 1 lmn IT Am mn I T AT ih 0 ab H I ab H12 2 ab H12 - ab 12H - ab 12H 12 After several days79 80 of algebraic manipulations we get the equations for the t amplitudes for each t amplitude one equation Sm n - a - SbA __ m n I ft si tpq A z- z7 I z A mn mniau y J mn pq tab J cd au tcd f cn Ih tmp cm I b t p cn I a r tmp cm I a r tnpl I cn p tac cmIyP tac cn aP vbc cm apivbcl E I V Pq mn .mp.nq . .nq.mp caIpq l tJbtcd - 2htb t d ttbt d -1 l ab cd ab cd ab cu c d p q ry mn.pq . PQ mn tijmptiq nq mp i n 7 i fmn fpq I fpqfmn _i_Aifpfqifqfp ilil d.Q 2 tac tbd tac lbd 41 lac d lac tb l 1 .49 It can be seen that the last expression includes the term independent of t the linear terms and the quadratic terms. How can we find the t s We do it with the help of the iterative method.81 First we substitute zeros for all t s on the right-hand side of the equation. Thus from 79 Opposite to excitation. 8 Students - more courage 81 We organize things in such a way that a given unknown parameter will occur in the simple form on one side of the equation whereas the more complicated terms also containing the parameter sought 10.14