Calculator Inputs
This single-column page uses a responsive input grid. Large screens show three columns, medium screens show two, and mobile shows one.
Plotly Graph
The graph shows the estimated spectrum across all computed mode indices.
Example Data Table
These examples show how atom count and geometry affect the mode count.
| System | Atoms | Geometry | Total DOF | Vibrational Modes | Estimated Band (cm-1) |
|---|---|---|---|---|---|
| Water | 3 | Nonlinear Molecule | 9 | 3 | 2,852.0 |
| Carbon Dioxide | 3 | Linear Molecule | 9 | 4 | 1,510.3 |
| Methane | 5 | Nonlinear Molecule | 15 | 9 | 2,450.2 |
| Nitrogen | 2 | Linear Molecule | 6 | 1 | 2,337.9 |
| Benzene | 12 | Nonlinear Molecule | 36 | 30 | 1,350.9 |
Formula Used
1. Total degrees of freedom: Total DOF = 3N, where N is the atom count.
2. Vibrational modes: Linear molecules use 3N - 5. Nonlinear molecules use 3N - 6. Monatomic systems use 0.
3. Harmonic frequency: ν = (1 / 2π) × √(k / μ), where k is force constant and μ is reduced mass.
4. Wavenumber: ν̃ = ν / c, using c in cm/s.
5. Zero-point energy: E₀ = ½hν. This page reports per-mode and total zero-point energy in kJ/mol.
The vibrational mode count is exact for the selected geometry. The plotted spectrum is an estimated spread around the fundamental frequency for clearer visualization.
How to Use This Calculator
- Enter a system name for your own reference.
- Provide the total number of atoms in the system.
- Select whether the system is monatomic, linear, or nonlinear.
- Enter the force constant in newtons per meter.
- Enter the reduced mass in atomic mass units.
- Choose a scaling factor if you want adjusted estimates.
- Set the spectrum spread percentage for chart spacing.
- Click the calculate button to view results above the form.
- Use the CSV or PDF buttons to export the results.
Frequently Asked Questions
1. What does this calculator measure?
It calculates total degrees of freedom, translational modes, rotational modes, and vibrational modes. It also estimates vibrational frequency, wavenumber, and zero-point energy from the harmonic oscillator model.
2. Why do linear and nonlinear molecules differ?
Linear molecules have two rotational degrees of freedom. Nonlinear molecules have three. That difference changes the vibrational count from 3N - 5 to 3N - 6.
3. Why does a monatomic system show zero vibrational modes?
A single atom has no internal bond stretching or bending. It can translate in space, but it cannot support internal molecular vibration by itself.
4. What is the force constant?
The force constant describes bond stiffness. Larger values usually increase frequency and wavenumber, because the restoring force becomes stronger for the same atomic displacement.
5. What is reduced mass?
Reduced mass combines the masses involved in a vibration into one effective value. Higher reduced mass usually lowers the estimated vibrational frequency.
6. Is the plotted spectrum exact?
No. The mode count is exact for the chosen geometry, but the plotted mode distribution is an estimate built from your frequency inputs and spread setting.
7. Why include a scaling factor?
Scaling factors help align simple harmonic estimates with corrected or reference values. They are useful when you want faster approximation tuning without changing the structural inputs.
8. When should I export CSV or PDF?
Use CSV for spreadsheet work, sorting, or bulk records. Use PDF for reports, reviews, sharing, or keeping a clean printable summary of your results.