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Anharmonicity Constant given Second Overtone Frequency Calculator

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✖Second Overtone Frequency is the frequency of photons on the second excited state/ overtone band of a diatomic molecule.ⓘ Second Overtone Frequency [v0->3]
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-10%
✖The Vibrational Frequency is the frequency of photons on the excited state.ⓘ Vibrational Frequency [vvib]
+10%
-10%
✖Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule.ⓘ Anharmonicity Constant given Second Overtone Frequency [xe]
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Anharmonicity Constant given Second Overtone Frequency

Formula
`"x"_{"e"} = 1/4*(1-("v"_{"0->3"}/(3*"v"_{"vib"})))`

Example
`"0.217949"=1/4*(1-("0.50Hz"/(3*"1.3Hz")))`

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Anharmonicity Constant given Second Overtone Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))
xe = 1/4*(1-(v0->3/(3*vvib)))
This formula uses 3 Variables
Variables Used
Anharmonicity Constant - Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule.
Second Overtone Frequency - (Measured in Hertz) - Second Overtone Frequency is the frequency of photons on the second excited state/ overtone band of a diatomic molecule.
Vibrational Frequency - (Measured in Hertz) - The Vibrational Frequency is the frequency of photons on the excited state.
STEP 1: Convert Input(s) to Base Unit
Second Overtone Frequency: 0.5 Hertz --> 0.5 Hertz No Conversion Required
Vibrational Frequency: 1.3 Hertz --> 1.3 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
xe = 1/4*(1-(v0->3/(3*vvib))) --> 1/4*(1-(0.5/(3*1.3)))
Evaluating ... ...
xe = 0.217948717948718
STEP 3: Convert Result to Output's Unit
0.217948717948718 --> No Conversion Required
FINAL ANSWER
0.217948717948718 ≈ 0.217949 <-- Anharmonicity Constant
(Calculation completed in 00.004 seconds)
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Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Shivam Sinha
National Institute Of Technology (NIT), Surathkal
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22 Vibrational Spectroscopy Calculators

Maximum Vibrational Number using Anharmonicity Constant
Go Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)
Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
Rotational Constant Related to Equilibrium
Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Rotational Constant for Vibrational State
Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Anharmonic Potential Constant
Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
Maximum Vibrational Quantum Number
Go Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
Anharmonicity Constant given Fundamental Frequency
Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
Vibrational Quantum Number using Vibrational Frequency
Go Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2
Vibrational Quantum Number using Vibrational Wavenumber
Go Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2
Anharmonicity Constant given Second Overtone Frequency
Go Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))
Anharmonicity Constant given First Overtone Frequency
Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
Energy Difference between Two Vibrational States
Go Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant))
Vibrational Frequency given Second Overtone Frequency
Go Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))
Second Overtone Frequency
Go Second Overtone Frequency = (3*Vibrational Frequency)*(1-4*Anharmonicity Constant)
First Overtone Frequency
Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
Vibrational Frequency given First Overtone Frequency
Go Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency given Fundamental Frequency
Go Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant)
Fundamental Frequency of Vibrational Transitions
Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

21 Important Calculators of Vibrational Spectroscopy Calculators

Maximum Vibrational Number using Anharmonicity Constant
Go Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)
Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
Rotational Constant Related to Equilibrium
Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Rotational Constant for Vibrational State
Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Anharmonic Potential Constant
Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
Maximum Vibrational Quantum Number
Go Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
Anharmonicity Constant given Fundamental Frequency
Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
Vibrational Quantum Number using Vibrational Frequency
Go Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2
Vibrational Quantum Number using Vibrational Wavenumber
Go Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2
Anharmonicity Constant given Second Overtone Frequency
Go Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))
Anharmonicity Constant given First Overtone Frequency
Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
Vibrational Frequency given Second Overtone Frequency
Go Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))
Second Overtone Frequency
Go Second Overtone Frequency = (3*Vibrational Frequency)*(1-4*Anharmonicity Constant)
First Overtone Frequency
Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
Vibrational Frequency given First Overtone Frequency
Go Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency given Fundamental Frequency
Go Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant)
Fundamental Frequency of Vibrational Transitions
Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

Anharmonicity Constant given Second Overtone Frequency Formula

Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))
xe = 1/4*(1-(v0->3/(3*vvib)))

What is vibrational energy?

Vibrational spectroscopy looks at the differences in energy between the vibrational modes of a molecule. These are larger than the rotational energy states. This spectroscopy can provide a direct measure of bond strength. The vibration energy levels can be explained using diatomic molecules.
To a first approximation, molecular vibrations can be approximated as simple harmonic oscillators, with an associated energy known as vibrational energy.

How to Calculate Anharmonicity Constant given Second Overtone Frequency?

Anharmonicity Constant given Second Overtone Frequency calculator uses Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency))) to calculate the Anharmonicity Constant, The Anharmonicity constant given second overtone frequency formula is defined as the deviation of a system from being a harmonic oscillator in relation to the vibrational energy levels of a diatomic molecule. Anharmonicity Constant is denoted by xe symbol.

How to calculate Anharmonicity Constant given Second Overtone Frequency using this online calculator? To use this online calculator for Anharmonicity Constant given Second Overtone Frequency, enter Second Overtone Frequency (v0->3) & Vibrational Frequency (vvib) and hit the calculate button. Here is how the Anharmonicity Constant given Second Overtone Frequency calculation can be explained with given input values -> 0.217949 = 1/4*(1-(0.5/(3*1.3))).

FAQ

What is Anharmonicity Constant given Second Overtone Frequency?
The Anharmonicity constant given second overtone frequency formula is defined as the deviation of a system from being a harmonic oscillator in relation to the vibrational energy levels of a diatomic molecule and is represented as xe = 1/4*(1-(v0->3/(3*vvib))) or Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency))). Second Overtone Frequency is the frequency of photons on the second excited state/ overtone band of a diatomic molecule & The Vibrational Frequency is the frequency of photons on the excited state.
How to calculate Anharmonicity Constant given Second Overtone Frequency?
The Anharmonicity constant given second overtone frequency formula is defined as the deviation of a system from being a harmonic oscillator in relation to the vibrational energy levels of a diatomic molecule is calculated using Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency))). To calculate Anharmonicity Constant given Second Overtone Frequency, you need Second Overtone Frequency (v0->3) & Vibrational Frequency (vvib). With our tool, you need to enter the respective value for Second Overtone Frequency & Vibrational Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Anharmonicity Constant?
In this formula, Anharmonicity Constant uses Second Overtone Frequency & Vibrational Frequency. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
  • Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
  • Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
  • Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
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