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Probability of Symmetry Species occurring in Reducible Representation Calculator

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✖Order of Group is defined as number of elements present in that group.ⓘ Order of Group [h]			+10% -10%
✖Character of Reducible Representation is defined as the characters of all matrices belonging to symmetry operations in the same class are identical.ⓘ Character of Reducible Representation [χ_r]			+10% -10%
✖Character of Irreducible Representation is defined as the characters of all matrices belonging to symmetry operations in the same class are identical.ⓘ Character of Irreducible Representation [χ_i]			+10% -10%
✖Number of Symmetry Operation is the number of symmetry operations in each class.ⓘ Number of Symmetry Operation [g_c]			+10% -10%

✖No. of times irrep occurs in reducible is the No of times an irreducible representation appears in reducible representation.ⓘ Probability of Symmetry Species occurring in Reducible Representation [n_i]

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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)
n_i = 1/h*add(χ_r+χ_i+g_c)
This formula uses 1 Functions, 5 Variables

Functions Used

add - Add function that involves adding two or more numbers together to get their sum., add(a1, …, an)

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

n_i = 1/h*add(χ_r+χ_i+g_c) --> 1/12*add(4+8+10)

Evaluating ... ...

n_i = 1.83333333333333

STEP 3: Convert Result to Output's Unit

1.83333333333333 --> No Conversion Required

FINAL ANSWER

1.83333333333333 ≈ 1.833333 <-- No. of Times Irrep occurs in Reducible

(Calculation completed in 00.004 seconds)

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Probability of Symmetry Species occurring in Reducible Representation Formula

LaTeX Go

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

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 n_i 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 (χ_r), Character of Irreducible Representation (χ_i) & Number of Symmetry Operation (g_c) 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 n_i = 1/h*add(χ_r+χ_i+g_c) 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 (χ_r), Character of Irreducible Representation (χ_i) & Number of Symmetry Operation (g_c). 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.

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