First Overtone Frequency Calculator

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Physical spectroscopy

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Important formulae on Vibrational Spectroscopy

Vibrational energy levels

✖The Vibrational Frequency is the frequency of photons on the excited state.ⓘ Vibrational Frequency [v_vib]			+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 [x_e]			+10% -10%

✖First Overtone Frequency is the frequency of photons on the first excited state/ overtone band of a diatomic molecule.ⓘ First Overtone Frequency [v_0->2]

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Formula

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First Overtone Frequency

Formula

`"v"_{"0->2"} = (2*"v"_{"vib"})*(1-3*"x"_{"e"})`

Example

`"0.728Hz"=(2*"1.3Hz")*(1-3*"0.24")`

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First Overtone Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
v_0->2 = (2*v_vib)*(1-3*x_e)
This formula uses 3 Variables

Variables Used

First Overtone Frequency - (Measured in Hertz) - First Overtone Frequency is the frequency of photons on the first 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.
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.

STEP 1: Convert Input(s) to Base Unit

Vibrational Frequency: 1.3 Hertz --> 1.3 Hertz No Conversion Required
Anharmonicity Constant: 0.24 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_0->2 = (2*v_vib)*(1-3*x_e) --> (2*1.3)*(1-3*0.24)

Evaluating ... ...

v_0->2 = 0.728

STEP 3: Convert Result to Output's Unit

0.728 Hertz --> No Conversion Required

FINAL ANSWER

0.728 Hertz <-- First Overtone Frequency

(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

Shivam Sinha has verified this Calculator and 25+ more calculators!

< 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

< 10+ Important formulae on Vibrational Spectroscopy Calculators

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))

Anharmonicity Constant given First Overtone Frequency

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

First Overtone Frequency

Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*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

First Overtone Frequency Formula

First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
v_0->2 = (2*v_vib)*(1-3*x_e)

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 First Overtone Frequency?

First Overtone Frequency calculator uses First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant) to calculate the First Overtone Frequency, The First overtone frequency formula is defined as the frequency of photons on the first excited state/ overtone band of a diatomic molecule. First Overtone Frequency is denoted by v_0->2 symbol.

How to calculate First Overtone Frequency using this online calculator? To use this online calculator for First Overtone Frequency, enter Vibrational Frequency (v_vib) & Anharmonicity Constant (x_e) and hit the calculate button. Here is how the First Overtone Frequency calculation can be explained with given input values -> 0.728 = (2*1.3)*(1-3*0.24).

FAQ

What is First Overtone Frequency?

The First overtone frequency formula is defined as the frequency of photons on the first excited state/ overtone band of a diatomic molecule and is represented as v_0->2 = (2*v_vib)*(1-3*x_e) or First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant). The Vibrational Frequency is the frequency of photons on the excited state & Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule.

How to calculate First Overtone Frequency?

The First overtone frequency formula is defined as the frequency of photons on the first excited state/ overtone band of a diatomic molecule is calculated using First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant). To calculate First Overtone Frequency, you need Vibrational Frequency (v_vib) & Anharmonicity Constant (x_e). With our tool, you need to enter the respective value for Vibrational Frequency & Anharmonicity Constant 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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