Vibrational Frequency given Fundamental Frequency Calculator

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Important formulae on Vibrational Spectroscopy

Vibrational energy levels

✖Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.ⓘ Fundamental Frequency [v_0->1]			+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%

✖The Vibrational Frequency is the frequency of photons on the excited state.ⓘ Vibrational Frequency given Fundamental Frequency [v_vib]

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Formula

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Vibrational Frequency given Fundamental Frequency

Formula

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

Example

`"1.346154Hz"="0.7Hz"/(1-2*"0.24")`

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Vibrational Frequency given Fundamental Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Vibrational Frequency - (Measured in Hertz) - The Vibrational Frequency is the frequency of photons on the excited state.
Fundamental Frequency - (Measured in Hertz) - Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.
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

Fundamental Frequency: 0.7 Hertz --> 0.7 Hertz No Conversion Required
Anharmonicity Constant: 0.24 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_vib = v_0->1/(1-2*x_e) --> 0.7/(1-2*0.24)

Evaluating ... ...

v_vib = 1.34615384615385

STEP 3: Convert Result to Output's Unit

1.34615384615385 Hertz --> No Conversion Required

FINAL ANSWER

1.34615384615385 ≈ 1.346154 Hertz <-- Vibrational Frequency

(Calculation completed in 00.020 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 Prashant Singh

K J Somaiya College of science (K J Somaiya), Mumbai

Prashant Singh has verified this Calculator and 500+ 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

< 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

Vibrational Frequency given Fundamental Frequency Formula

Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant)
v_vib = v_0->1/(1-2*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 Vibrational Frequency given Fundamental Frequency?

Vibrational Frequency given Fundamental Frequency calculator uses Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant) to calculate the Vibrational Frequency, The Vibrational frequency given fundamental frequency formula is defined as the frequency of photons on the excited state of a diatomic molecule. Vibrational Frequency is denoted by v_vib symbol.

How to calculate Vibrational Frequency given Fundamental Frequency using this online calculator? To use this online calculator for Vibrational Frequency given Fundamental Frequency, enter Fundamental Frequency (v_0->1) & Anharmonicity Constant (x_e) and hit the calculate button. Here is how the Vibrational Frequency given Fundamental Frequency calculation can be explained with given input values -> 1.346154 = 0.7/(1-2*0.24).

FAQ

What is Vibrational Frequency given Fundamental Frequency?

The Vibrational frequency given fundamental frequency formula is defined as the frequency of photons on the excited state of a diatomic molecule and is represented as v_vib = v_0->1/(1-2*x_e) or Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant). Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule & 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 Vibrational Frequency given Fundamental Frequency?

The Vibrational frequency given fundamental frequency formula is defined as the frequency of photons on the excited state of a diatomic molecule is calculated using Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant). To calculate Vibrational Frequency given Fundamental Frequency, you need Fundamental Frequency (v_0->1) & Anharmonicity Constant (x_e). With our tool, you need to enter the respective value for Fundamental Frequency & Anharmonicity Constant 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 Vibrational Frequency?

In this formula, Vibrational Frequency uses Fundamental Frequency & Anharmonicity Constant. We can use 4 other way(s) to calculate the same, which is/are as follows -

Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))
Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))

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