TAILIEUCHUNG - Ideas of Quantum Chemistry P96

Ideas of Quantum Chemistry P96 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. | 916 C. GROUP THEORY IN SPECTROSCOPY R2 r3 Ri Rg r complete decomposition into the smallest blocks possible Fig. . Reducible representation block form and irreducible representation. In the first row the matrices F 7 i are displayed which form a reducible representation each matrix corresponds to the symmetry operation Ri the matrix elements are in general non-zero. The central row shows a representation r equivalent to the first . related by a similarity transformation through matrix P the new representation exhibits block form . in this particular case each matrix has two blocks of zeros identical in all matrices. The last row shows an equivalent representation T that corresponds to the smallest square blocks of non-zeros . the maximum number of blocks of identical form in all matrices. Not only r r and T are representations of the group but also any sequence of individual blocks as this shaded is a representation. Thus T is decomposed into the four irreducible representations. similarity transformation This is easy to show. Indeed group operations Ri and Rj correspond to matrices T TRi and T Rj in the original representation and to T Ri P-1T Ri P and r Rfj P-1r 7Rj P in the equivalent representation we will check in a moment whether this is indeed a representation . The product V Ri T j equals to P-1T RRi PP-1T R j P P-1r Ri I Rf P . to the matrix r jRi T Rij transformed by similarity transformation therefore everything goes with the same multiplication table. Thus matrices V R also form a representation F . This means that we can create as many representations as we wish it is sufficient to change 2 Representations 917 matrix P and this is easy since what we want is its singularity . the P-1 matrix has to exist . The blocks are square matrices. It turns out that the set of the first blocks T1 T 1 r1 7R2 r1 T g each block for one operation is a representation the set of the second blocks T2 T 1 T2 T 2 . r2 Rg forms a representation as well etc.

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