The character table for a particular point group is given below. The characters in the irreducible representations
and
respectively, are
The elements of the matrices which constitute the irreducible representations of a group follow ‘the great orthogonality theorem’ which is stated as follows:
Where
i. The summation R represents the summation of various operations in a group.
ii.
represents the matrix element Rmn of the matrix R representing Rth symmetry operation of the ith representation of a group.
iii.
In option B, (1×1×2) + (2×(-1)×0)+(1×1×(-2))+(2×1×0)+(2×(-1)×0)=0
The equivalent symmetry operations for and are, respectively,
The observed IR spectrum for BCl3 exhibits three bands at 995, 480 and 244 cm-1, while the Raman bands are observed at 995, 471 and 244cm-1. Given that for BCl3,
the frequency of A1'mode in cm-1is:
Given the matrices for C3 and σh below,
the trace of the matrix representing for S32 is
The following is the character table for the C2v point group
There are two functions f1 and f2 belonging to A2 and B1 representations, respectively. The correct option for the product of two functions f1 and f2 and the integral ∫f1f2dτ is
The combination of two reflections, σv'σv", about an intersecting mirror plane is equivalent to
The equivalent symmetry operations for S63 and S36 are, respectively,
For every atom that is not shifted under C4 and σ symmetry operations, the characters are, respectively,
For the formaldehyde molecule H2CO having C2v symmetry with the character table as given below:
the reducible representation . The reducible representation for the vibrational modes alone, namely will be
the structure of which is given below, is a bi-substituted isotopomer of cubane, where two hydrogens are substituted by deuterium.
