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Anharmonic Potential Constant Calculator

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Important formulae on Vibrational Spectroscopy Vibrational energy levels

✖Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule.ⓘ Rotational Constant vib [B_v]			+10% -10%
✖Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule.ⓘ Rotational Constant Equilibrium [B_e]			+10% -10%
✖Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.ⓘ Vibrational Quantum Number [v]			+10% -10%

✖Anharmonic Potential Constant is a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state.ⓘ Anharmonic Potential Constant [α_e]

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Anharmonic Potential Constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
α_e = (B_v-B_e)/(v+1/2)
This formula uses 4 Variables

Variables Used

Anharmonic Potential Constant - Anharmonic Potential Constant is a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state.
Rotational Constant vib - (Measured in Diopter) - Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule.
Rotational Constant Equilibrium - (Measured in Per Meter) - Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule.
Vibrational Quantum Number - Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.

STEP 1: Convert Input(s) to Base Unit

Rotational Constant vib: 35 1 per Meter --> 35 Diopter (Check conversion here)
Rotational Constant Equilibrium: 20 Per Meter --> 20 Per Meter No Conversion Required
Vibrational Quantum Number: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α_e = (B_v-B_e)/(v+1/2) --> (35-20)/(2+1/2)

Evaluating ... ...

α_e = 6

STEP 3: Convert Result to Output's Unit

6 --> No Conversion Required

FINAL ANSWER

6 <-- Anharmonic Potential Constant

(Calculation completed in 00.020 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< Vibrational Spectroscopy Calculators

Anharmonic Potential Constant

LaTeX Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)

Anharmonicity Constant given Fundamental Frequency

LaTeX Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)

Anharmonicity Constant given Second Overtone Frequency

LaTeX Go Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))

Anharmonicity Constant given First Overtone Frequency

LaTeX Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))

< Important Calculators of Vibrational Spectroscopy Calculators

Rotational Constant Related to Equilibrium

LaTeX Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))

Rotational Constant for Vibrational State

LaTeX Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))

Vibrational Quantum Number using Vibrational Frequency

LaTeX Go Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2

Vibrational Quantum Number using Vibrational Wavenumber

LaTeX Go Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2

Anharmonic Potential Constant Formula

LaTeX Go

Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
α_e = (B_v-B_e)/(v+1/2)

How do you obtain Anharmonic potential constant?

When changing the energy of the vibrational levels, anharmonicity has another, less obvious effect: for a molecule with an Anharmonic potential, the rotational constant changes slightly with vibrational state. The rotational constant for a given vibrational state can be described by the obtained expression, where Be is the rotational constant corresponding to the equilibrium geometry of the molecule, αe is a constant determined by the shape of the Anharmonic potential, and v is the vibrational quantum number.
Anharmonic potential constant is obtained when we reframe the expression to obtain the desired output.

How to Calculate Anharmonic Potential Constant?

Anharmonic Potential Constant calculator uses Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2) to calculate the Anharmonic Potential Constant, The Anharmonic potential constant formula is defined as a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state. Anharmonic Potential Constant is denoted by α_e symbol.

How to calculate Anharmonic Potential Constant using this online calculator? To use this online calculator for Anharmonic Potential Constant, enter Rotational Constant vib (B_v), Rotational Constant Equilibrium (B_e) & Vibrational Quantum Number (v) and hit the calculate button. Here is how the Anharmonic Potential Constant calculation can be explained with given input values -> 6 = (35-20)/(2+1/2).

FAQ

What is Anharmonic Potential Constant?

The Anharmonic potential constant formula is defined as a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state and is represented as α_e = (B_v-B_e)/(v+1/2) or Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2). Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule, Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule & Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.

How to calculate Anharmonic Potential Constant?

The Anharmonic potential constant formula is defined as a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state is calculated using Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2). To calculate Anharmonic Potential Constant, you need Rotational Constant vib (B_v), Rotational Constant Equilibrium (B_e) & Vibrational Quantum Number (v). With our tool, you need to enter the respective value for Rotational Constant vib, Rotational Constant Equilibrium & Vibrational Quantum Number 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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