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Fundamental Frequency of Vibrational Transitions Calculator

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✖The Vibrational Frequency is the frequency of photons on the excited state.ⓘ Vibrational Frequency [vvib]
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✖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 [xe]
+10%
-10%
✖Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.ⓘ Fundamental Frequency of Vibrational Transitions [v0->1]
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Fundamental Frequency of Vibrational Transitions

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

Example
`"0.676Hz"="1.3Hz"*(1-2*"0.24")`

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Fundamental Frequency of Vibrational Transitions Solution

STEP 0: Pre-Calculation Summary
Formula Used
Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
v0->1 = vvib*(1-2*xe)
This formula uses 3 Variables
Variables Used
Fundamental Frequency - (Measured in Hertz) - Fundamental Frequency is the frequency of photons on the fundamental 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
v0->1 = vvib*(1-2*xe) --> 1.3*(1-2*0.24)
Evaluating ... ...
v0->1 = 0.676
STEP 3: Convert Result to Output's Unit
0.676 Hertz --> No Conversion Required
FINAL ANSWER
0.676 Hertz <-- Fundamental 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 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

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

Fundamental Frequency of Vibrational Transitions Formula

Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
v0->1 = vvib*(1-2*xe)

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 Fundamental Frequency of Vibrational Transitions?

Fundamental Frequency of Vibrational Transitions calculator uses Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant) to calculate the Fundamental Frequency, The Fundamental frequency of vibrational transitions formula is defined as the frequency of photons on the fundamental excited state of a diatomic molecule. Fundamental Frequency is denoted by v0->1 symbol.

How to calculate Fundamental Frequency of Vibrational Transitions using this online calculator? To use this online calculator for Fundamental Frequency of Vibrational Transitions, enter Vibrational Frequency (vvib) & Anharmonicity Constant (xe) and hit the calculate button. Here is how the Fundamental Frequency of Vibrational Transitions calculation can be explained with given input values -> 0.676 = 1.3*(1-2*0.24).

FAQ

What is Fundamental Frequency of Vibrational Transitions?
The Fundamental frequency of vibrational transitions formula is defined as the frequency of photons on the fundamental excited state of a diatomic molecule and is represented as v0->1 = vvib*(1-2*xe) or Fundamental Frequency = Vibrational Frequency*(1-2*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 Fundamental Frequency of Vibrational Transitions?
The Fundamental frequency of vibrational transitions formula is defined as the frequency of photons on the fundamental excited state of a diatomic molecule is calculated using Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant). To calculate Fundamental Frequency of Vibrational Transitions, you need Vibrational Frequency (vvib) & Anharmonicity Constant (xe). 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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