TAILIEUCHUNG - Ideas of Quantum Chemistry P108

Ideas of Quantum Chemistry P108 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. | 1036 W. NMR SHIELDING AND COUPLING CONSTANTS - DERIVATION involving4 the electronic momenta pj and angular momenta LAj with respect to the nucleus A where j means electron number j T 1 i 1 i f 0 IA Th rAj X Pj R0lB h rBl X p Z 2 E YAYB I A rAj X p j RqIb Tin X p I Weaver A B j l X2 EE YAYB O 0 1 A L AjR 0IB LBl Q aver j aq avct V 7 A B j l EE YAYB1 A IB1 l o Aj xl O Bl x l o mc t 3 o v 7 a b j l I 0 If A . l 0 I i 0 t nt I 0 l 0 LAj yROLBl y o 0 LAj zROLBl z o Thus finally EpSO 1 j L L YAYB IA IB L A Bl l - mc a b jyl i SD oiBe i aver 4 Let us have a closer look at the operator Vj x -A- acting on a function it is necessary to remember that Vj in Vj x -al is not just acting on the components of -al alone but in fact on -Al times a wave rAj rAj rAj function f Let us see Vj X r-AL f v X f j Vj X f k Vj X f k rAj V r x x V y V rA z i --AL - -L AL A f similarly with y and z dyj rAj Zj rAi x y yAjzAj zAj d yAjzAj yAj d H -3 4 ----- 3 -4 ------------ I f similarly with y and z rAj rAj dyj rAj rAj x y zAj 3 yAj 3 . i ------------yt----f similarly with y and z r 3 3yi r3 . 3zA x Aj j Aj j x y zAj 3 yAj 3 . i I ----------y-----I f similarly with y and z rA dyj rAj dzAx - Th -rAj X pj f Th rAj X pjf 2 Coupling constants 1037 S j IA r3 rAj S l IB 3 Sj rAj Ia rAj 3 5 rAj r3 rBl 3 Si rBi Ib rBi 3 5 rB I aver 2 T r 1 17 0 r Sj x n Sj rAj xAj Y2i x x yayb 1 a ib 3 j o - 3 r sl x sI rBl XBl 3 3 5 rBl rBl Sii_ 3 Sj rAj yAj Aj - s j z r 3 rAj 3 Sj rAj ZAj 3 5 rAj R o Sl y Q SI rBl yBl 3 3 5 rBl rBl Sl z Ast rBl ZBl 3 3 5 rBl rBl x R 0 x R o - R o Therefore i 2 X SD 3Y2l X X YAYBIA IB j l 1 A B X j - 3 LrA Sj rAj rj --------- Ro r r 5 rAj Sl 3 3 Bl Si rBl rBl l . o ------------- o r 5 rBl E fc oo JB7RR oB7 oo Y2i X X YAYB 8 rAj Sj IARRo8 rBl Sl IB oo aver j l 1 A B Y2 X X YaYbIa Ib 1 oo 5 rAj S j Ro rBdSl oA j l 1 A B o 8 rAj S j yRR o8 rBl S l y o oAS rAj S j zlR o8 rBl S i z qA - Hence E FC j -y Y2i X XYaYbIa Ib o 8 rAj SjRo8 rBl Sl . The results mean that the coupling constants

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