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¸÷ÖÖµç×Ó¹ìµÀ¡¢·Ö×Ó¹ìµÀ»òÕñ¶¯ÆµÂʶԳÆÐÔ±ê¼ÇµÄº¬ÒåºÍÀí½â£º 1. Mulliken Symmetry Labels£º¿É²Î¿¼ÕâÀï: http://chemistry.umeche.maine.edu/Modeling/mulliken.html http://www.cup.uni-muenchen.de/ch/compchem/geom/point3.html ¸üÏêϸµÄ£¬¿É²Î¿¼ÔʼµÄÎÄÏ×£º 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 (ÕâÆªÎÄÕ³ö°æµÄʱºò£¬×÷ÕßÃûûÓÐдÉÏÈ¥¡£×÷Õß×¢Ã÷ÔÚ£ºJ. Chem. Phys. 24, 1118 (1956)Ò»ÎĵÄÓÒϽǿ±ÎóÀï¡£) 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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