Calculator inputs
Use a common preset or enter custom masses and force constant values. The page keeps a single-column layout, while the form fields adapt responsively.
Formula used
μ = (m1 × m2) / (m1 + m2)
ν = (1 / 2π) × √(k / μ)
ṽ = ν / c = (1 / 2πc) × √(k / μ)
ṽadjusted = ṽharmonic × scale factor × (1 − anharmonic correction / 100)
The calculator converts atomic masses from amu to kilograms for the SI calculation, then reports the final stretching estimate in cm⁻¹. This is a harmonic-oscillator style approximation, so real spectra can shift because of coupling, hydrogen bonding, resonance, solvent effects, and molecular environment.
How to use this calculator
- Select a preset bond or keep the custom option.
- Enter the two atomic masses in amu. Use isotopic masses when needed.
- Enter the force constant in N/m for the stretching bond.
- Adjust the scale factor if you want a calibrated theoretical estimate.
- Apply a small anharmonic correction when you want a lower realistic value.
- Set peak width and intensity for the simulated IR band display.
- Choose the sensitivity range to see how changing bond strength affects the estimate.
- Press the calculate button to show the result above the form.
- Use the CSV or PDF buttons to export the current summary.
Example data table
| Bond | Atom 1 Mass (amu) | Atom 2 Mass (amu) | Force Constant (N/m) | Approx. Stretch (cm⁻¹) | Typical Assignment |
|---|---|---|---|---|---|
| C-H | 12.011 | 1.008 | 500 | ~3,030 | Aliphatic or aromatic C-H stretching |
| O-H | 15.999 | 1.008 | 640 | ~3,580 | Hydroxyl stretching |
| N-H | 14.007 | 1.008 | 560 | ~3,380 | Amine or amide N-H stretching |
| C=O | 12.011 | 15.999 | 1,165 | ~1,715 | Carbonyl stretching |
| C≡N | 12.011 | 14.007 | 890 | ~2,230 | Nitrile stretching |
Why these inputs matter
Reduced mass
Heavier atom pairs usually lower the stretching wavenumber because the bond vibrates more slowly for the same force constant.
Force constant
A larger force constant represents a stiffer bond, which raises the stretching frequency and pushes the IR band to higher wavenumber.
Scaling and correction
These settings help bridge the gap between ideal harmonic estimates and practical values observed in real molecules and instruments.
Frequently asked questions
1. What does this calculator estimate?
It estimates an IR stretching wavenumber from bond masses and force constant. It also applies optional scaling and anharmonic correction, then plots a simulated absorption peak for quick interpretation.
2. Why is reduced mass important?
Reduced mass captures how the two bonded atoms move together. For the same bond stiffness, a larger reduced mass lowers the vibrational frequency and shifts the absorption band downward.
3. How does the force constant affect IR stretching?
A stronger bond has a larger force constant, so it resists stretching more. That increases the vibrational frequency and usually gives a higher wavenumber in the IR spectrum.
4. Can I estimate isotope shifts with this tool?
Yes. Enter isotopic masses directly, such as replacing hydrogen with deuterium. The calculator updates the reduced mass, which lets you compare the expected wavenumber shift immediately.
5. Why would I use a scaling factor?
The harmonic model is simplified. A scaling factor lets you tune calculated values toward empirical or computational references, especially when you compare predicted bands with measured spectra.
6. Does this replace an experimental IR spectrum?
No. It gives an informed estimate, not a full experimental assignment. Real spectra can show coupling, broadening, solvent effects, hydrogen bonding, and intensity changes that simple models do not fully capture.
7. What units does the calculator use?
Atomic masses are entered in amu, force constant in N/m, and the final result is reported in cm⁻¹. The page also provides wavelength in micrometers and energy in kJ/mol.
8. Can this help with polyatomic molecules?
Yes, as a first approximation for a selected bond. However, real polyatomic molecules may have coupled vibrations, symmetry effects, and environment-dependent shifts beyond the simple diatomic model.