Interpretation:
The cubane,
Concept introduction:
The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by
Answer to Problem 14.82E
The cubane,
Explanation of Solution
The structure of cubane is shown below.
Figure 1
The point group of cubane is
The character table for point group
The expression
Similarly, the value of
The expression
The positive sign is taken for the proper rotation and negative sign is taken for improper axis.
Substitute the value of
Similarly, the value of
The expression
Substitute the value of
Similarly, the value of
The expression
The positive sign is taken for the proper rotation and negative sign is taken for improper axis.
Substitute the value of
Similarly, the value of
The expression
The positive sign is taken for the proper rotation and negative sign is taken for improper axis.
Substitute the value of
Similarly, the value of
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The term
The irreducible representation for point group
Substitute the
Therefore, the cubane,
The cubane,
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Chapter 14 Solutions
EBK PHYSICAL CHEMISTRY
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