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轨道对称性标记的理解
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各种电子轨道、分子轨道或振动频率对称性标记的含义和理解： 1. Mulliken Symmetry Labels：可参考这里: http://chemistry.umeche.maine.edu/Modeling/mulliken.html http://www.cup.uni-muenchen.de/ch/compchem/geom/point3.html 更详细的，可参考原始的文献： R. S. Mulliken, J. Chem. Phys. 23, 1997 (1955); http://dx.doi.org/10.1063/1.1740655 Report on Notation for the Spectra of Polyatomic Molecules (这篇文章出版的时候，作者名没有写上去。作者注明在：J. Chem. Phys. 24, 1118 (1956)一文的右下角勘误里。) Reflection through an inversion center: u and g symmetry Taking the molecule center of mass as origin of coordinates, consider the change of all electrons' position from (xi, yi, zi) to (−xi, −yi, −zi). If the resulting wave function is unchanged, it is said to be gerade (German for even); if the wave function changes sign then it is said to be ungerade (odd). For a molecule with a center of inversion, all orbitals will be symmetric or antisymmetric. The resulting wavefunction for the whole multielectron system will be gerade if an even number of electrons is in ungerade orbitals, and ungerade if there is an odd number of electrons in ungerade orbitals, independently of the number of electrons in gerade orbitals. |
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Symbol Property A symmetric with respect to rotation around the principal rotational axis (one dimensional representations) B anti-symmetric with respect to rotation around the principal rotational axis (one dimensional representations) E degenerate (German: entartet; two dimensional representations, e.g. in systems with higher order principal axes) subscript 1 symmetric with respect to a vertical mirror plane perpendicular to the principal axis subscript 2 anti-symmetric with respect to a vertical mirror plane perpendicular to the principal axis subscript g symmetric with respect to a center of symmetry (German: "gerade"  subscript u anti-symmetric with respect to a center of symmetry (German: "ungerade) prime (') symmetric with respect to a mirror plane horizontal to the principal rotational axis double prime ('') anti-symmetric with respect to a mirror plane horizontal to the principal rotational axis |
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