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Point groups axial

If the atom or moleeule has additional symmetries (e.g., full rotation symmetry for atoms, axial rotation symmetry for linear moleeules and point group symmetry for nonlinear polyatomies), the trial wavefunetions should also eonform to these spatial symmetries. This Chapter addresses those operators that eommute with H, Pij, S2, and Sz and among one another for atoms, linear, and non-linear moleeules. [Pg.245]

Close study of the angles, indices, and axial ratios long since made it clear that every crystalline substance has a structure built upon a space -lattice" characteristic rtf the substance. It lias been established that this is due to the regular arrangement of the alums, molecules, or ions composing the substance. As shown by Table I. the lattice structures of crystals may be classified into 32 symmetry classes (point groups), which are further divided into seven systems. This topic also is discussed under Mineralogy. [Pg.454]

This completes the list of proper point groups, P. A summary is given in the first column of Table 2.6. All the remaining axial point groups may be generated from the proper point groups P by one or other of two methods. [Pg.39]

In addition to the proper point groups P and the improper point groups that are either isomorpous with P or equal to P C there is the non-axial group 1 or Cj = E). [Pg.46]

The values of 2% If n (where n is the order of the axis of rotation) that satisfy eq. (16) and therefore are compatible with translational symmetry, are shown in Table 16.1. It follows that the point groups compatible with translational symmetry are limited to the twenty-seven axial groups with n= 1, 2, 3, 4, or 6 and the five cubic groups, giving thirty-two... [Pg.310]


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