The structure of character tables
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
416
2025-12-02
60
The structure of character tables
In general, the columns in a character table are labelled with the symmetry operations of the group. For instance, for the group C3v the columns are headed E, C3, and σv (Table 12.3). The numbers multiplying each operation are the numbers of members of each class. In the C3v character table we see that the two threefold rotations (clock wise and counter-clockwise rotations by 120°) belong to the same class: they are related by a reflection (Fig. 12.18). The three reflections (one through each of the three vertical mirror planes) also lie in the same class: they are related by the three-fold rotations. The two reflections of the group C2v fall into different classes: although they are both reflections, one cannot be transformed into the other by any symmetry operation of the group. The total number of operations in a group is called the order, h, of the group. The order of the group C3v, for instance, is 6. The rows under the labels for the operations summarize the symmetry properties of the orbitals. They are labelled with the symmetry species (the analogues of the labels σ andπ). More formally, the symmetry species label the irreducible representations of the group, which are the basic types of behaviour that orbitals may show when subjected to the symmetry operations of the group, as we have illustrated for the group C. By convention, irreducible representations are labelled with upper case Roman letters (such as A1 and E) but the orbitals to which they apply are labelled with the lower-case italic equivalents (so an orbital of symmetry species A1 is called an a1 orbital). Examples of each type of orbital are shown in Fig. 12.19.
Fig. 12.18 Symmetry operations in the same class are related to one another by the symmetry operations of the group. Thus, the three mirror frames shown here are related by threefold rotations, and the two rotations shown here are related by reflection in σv.
Fig. 12.19 Typical symmetry-adapted linear combinations of orbitals in a C3v molecule.
الاكثر قراءة في مواضيع عامة في الكيمياء الفيزيائية
اخر الاخبار
اخبار العتبة العباسية المقدسة
