## Probability of Symmetry Species occurring in Reducible Representation Solution

STEP 0: Pre-Calculation Summary
Formula Used
No. of Times Irrep occurs in Reducible = 1/Order of Group*add(Character of Reducible Representation+Character of Irreducible Representation+Number of Symmetry Operation)
This formula uses 1 Functions, 5 Variables
Functions Used
Variables Used
No. of Times Irrep occurs in Reducible - No. of times irrep occurs in reducible is the No of times an irreducible representation appears in reducible representation.
Order of Group - Order of Group is defined as number of elements present in that group.
Character of Reducible Representation - Character of Reducible Representation is defined as the characters of all matrices belonging to symmetry operations in the same class are identical.
Character of Irreducible Representation - Character of Irreducible Representation is defined as the characters of all matrices belonging to symmetry operations in the same class are identical.
Number of Symmetry Operation - Number of Symmetry Operation is the number of symmetry operations in each class.
STEP 1: Convert Input(s) to Base Unit
Order of Group: 12 --> No Conversion Required
Character of Reducible Representation: 4 --> No Conversion Required
Character of Irreducible Representation: 8 --> No Conversion Required
Number of Symmetry Operation: 10 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Evaluating ... ...
ni = 1.83333333333333
STEP 3: Convert Result to Output's Unit
1.83333333333333 --> No Conversion Required
1.83333333333333 1.833333 <-- No. of Times Irrep occurs in Reducible
(Calculation completed in 00.001 seconds)
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## < 10+ Group Theory Calculators

Probability of Symmetry Species occurring in Reducible Representation
No. of Times Irrep occurs in Reducible = 1/Order of Group*add(Character of Reducible Representation+Character of Irreducible Representation+Number of Symmetry Operation)
Angle of Rotation in Cn Axis
Angle of Rotation in Cn Axis = 2*pi/Order of Rotation Axis
Order of Rotation Axis in Cn Operation
Order of Rotation Axis = (2*pi)/Theta
Character of Cn Matrix
Character of Cn Matrix = 2*cos(Theta)+1
Character of Sn Matrix
Character of Sn Matrix = 2*cos(Theta)-1
Order of Dnh Point Group
Order of Dnh Point Group = 4*Principal Axis
Order of Cnh Point Group
Order of Cnh Point Group = 2*Principal Axis
Order of Cnv Point Group
Order of Cnv Point Group = 2*Principal Axis
Order of Dnd Point Group
Order of Dnd Point Group = 4*Principal Axis
Order of Dn Point Group
Order of Dn Point Group = 2*Principal Axis

## Probability of Symmetry Species occurring in Reducible Representation Formula

No. of Times Irrep occurs in Reducible = 1/Order of Group*add(Character of Reducible Representation+Character of Irreducible Representation+Number of Symmetry Operation)

## What is Reduction Formula ?

The reduction can be achieved using the reduction formula. It is a mathematical way of reducing that will always work when the answer cannot be spotted by eye. It is particularly useful when there are large numbers of bonds involved. The vibrational modes of the molecule are reduced to produce a reducible representation into the irreducible representations.

## How to Calculate Probability of Symmetry Species occurring in Reducible Representation?

Probability of Symmetry Species occurring in Reducible Representation calculator uses No. of Times Irrep occurs in Reducible = 1/Order of Group*add(Character of Reducible Representation+Character of Irreducible Representation+Number of Symmetry Operation) to calculate the No. of Times Irrep occurs in Reducible, Probability of Symmetry Species occurring in Reducible Representation means that the vibrational modes of the molecule are reduced to produce a reducible representation into the irreducible representations. No. of Times Irrep occurs in Reducible is denoted by ni symbol.

How to calculate Probability of Symmetry Species occurring in Reducible Representation using this online calculator? To use this online calculator for Probability of Symmetry Species occurring in Reducible Representation, enter Order of Group (h), Character of Reducible Representation r), Character of Irreducible Representation i) & Number of Symmetry Operation (gc) and hit the calculate button. Here is how the Probability of Symmetry Species occurring in Reducible Representation calculation can be explained with given input values -> 1.833333 = 1/12*add(4+8+10).

### FAQ

What is Probability of Symmetry Species occurring in Reducible Representation?
Probability of Symmetry Species occurring in Reducible Representation means that the vibrational modes of the molecule are reduced to produce a reducible representation into the irreducible representations and is represented as ni = 1/h*add(χr+χi+gc) or No. of Times Irrep occurs in Reducible = 1/Order of Group*add(Character of Reducible Representation+Character of Irreducible Representation+Number of Symmetry Operation). Order of Group is defined as number of elements present in that group, Character of Reducible Representation is defined as the characters of all matrices belonging to symmetry operations in the same class are identical, Character of Irreducible Representation is defined as the characters of all matrices belonging to symmetry operations in the same class are identical & Number of Symmetry Operation is the number of symmetry operations in each class.
How to calculate Probability of Symmetry Species occurring in Reducible Representation?
Probability of Symmetry Species occurring in Reducible Representation means that the vibrational modes of the molecule are reduced to produce a reducible representation into the irreducible representations is calculated using No. of Times Irrep occurs in Reducible = 1/Order of Group*add(Character of Reducible Representation+Character of Irreducible Representation+Number of Symmetry Operation). To calculate Probability of Symmetry Species occurring in Reducible Representation, you need Order of Group (h), Character of Reducible Representation r), Character of Irreducible Representation i) & Number of Symmetry Operation (gc). With our tool, you need to enter the respective value for Order of Group, Character of Reducible Representation, Character of Irreducible Representation & Number of Symmetry Operation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know