Formula Used:
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Definition: This calculator determines how many times an irreducible representation appears in a reducible representation using group theory in chemistry.
Purpose: It helps chemists and physicists analyze molecular symmetry and vibrational modes by decomposing reducible representations into irreducible ones.
The calculator uses the formula:
Where:
Explanation: The formula calculates the projection of the reducible representation onto each irreducible representation of the group.
Details: This calculation is fundamental in molecular spectroscopy, helping predict vibrational modes, orbital symmetries, and selection rules in quantum chemistry.
Tips: Enter the order of the group, characters of reducible and irreducible representations, and number of symmetry operations. Order and symmetry operations must be > 0.
Q1: What is the order of a group?
A: The order is the total number of symmetry operations in the point group (e.g., 6 for C3v).
Q2: Where do I find character values?
A: Character tables for common point groups are available in chemistry textbooks or online resources.
Q3: What if my result isn't an integer?
A: Check your inputs. The result should be a whole number as it counts occurrences. Non-integer results suggest incorrect inputs.
Q4: How is this used in spectroscopy?
A: It helps determine which vibrational modes are IR or Raman active by analyzing how they transform under symmetry operations.
Q5: Can this be used for any point group?
A: Yes, the formula works for all finite point groups in molecular symmetry analysis.