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August 18, 2010 11:37      9in x 6in     b985-ch10     Elementary Physical Chemistry





                               114                   Elementary Physical Chemistry

                               where S is

                                                        S =   ψ A ψ Bdv                 (10.16b)

                               called the overlap integral. Obviously, the molecular normalization coeffi-
                               cient is

                                                      N =1/ 2(1 + S)                    (10.16c)
                                  A heteronuclear diatomic molecule has the wave-function
                                                       Ψ= ψ sA + λΨ sB                   (10.17)
                               Normalization gives



                                                 2
                                         N 2    ψ dv +2λ    ψ sAψ sBdv + λ 2  ψ 2  =1
                                                 sA                          sB
                                                                   2          2
                                                                 N [1 + 2λS + λ ]= 1
                                                                              2  1/2
                                                            N = {1/(1 + 2λS + λ )}       (10.18)
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