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This lists the character tables for the more common molecular point groups used in the study of molecular symmetry. These tables are based on the group-theoretical treatment of the symmetry operations present in common molecules, and are useful in molecular spectroscopy and quantum chemistry. Information regarding the use of the tables, as well ...
The first character tables were compiled by László Tisza (1933), in connection to vibrational spectra. Robert Mulliken was the first to publish character tables in English (1933), and E. Bright Wilson used them in 1934 to predict the symmetry of vibrational normal modes. [14]
The irreducible complex characters of a finite group form a character table which encodes much useful information about the group G in a concise form. Each row is labelled by an irreducible character and the entries in the row are the values of that character on any representative of the respective conjugacy class of G (because characters are class functions).
The following table lists several notations for point groups: Hermann–Mauguin notation (used in crystallography), Schönflies notation (used to describe molecular symmetry), orbifold notation, and Coxeter notation. The latter three are not only conveniently related to its properties, but also to the order of the group.
Point-group symbols in International Tables for Crystallography (2006). Vol. A, ch. 12.1, pp. 818-820; Names and symbols of the 32 crystal classes in International Tables for Crystallography (2006). Vol. A, ch. 10.1, p. 794; Pictorial overview of the 32 groups
From the right side of the character table, the non-vibrational degrees of freedom, rotational (R x and R y) and translational (x, y, and z), are subtracted: Γ vib = Γ 3N - Γ rot - Γ trans. This yields the Γ vib, which is used to find the correct normal modes from the original symmetry, which is either C ∞v or D ∞h, using the ...
The number of stages in Krypton Egg depends on versions being released. For block-breaking stages, Hitsoft versions includes 60 stages; C2V shareware versions can include 5, 8, or 10 stages; in C2V registered versions, a game can include 50, 60, 100 stages; DotEmu iOS demo version includes 2 stages, [2] and 60 stages in full version ('72' refers to addition of bonus stages).
In other cases there is no point around which the point group applies. The notation is somewhat ambiguous, without a table giving more information. For example, space groups I23 and I2 1 3 (nos. 197 and 199) both contain two-fold rotational axes as well as two-fold screw axes. In the first, the two-fold axes intersect the three-fold axes ...