What it does
The infrared spectrum of a gas such as HCl or CO is a comb of lines either side of a gap. Each line is a change of vibration plus a change of rotation, and from their positions you can read the bond’s stiffness, its length and how it breaks. This tool goes the other way too: from the standard spectroscopic constants it predicts the spectrum, the energy levels and the potential curve.
- Vibration: levels G(v) = ωe(v + ½) − ωexe(v + ½)², the fundamental and overtones, the zero-point energy and the force constant k = μ(2πcωe)².
- Morse potential: well depth De = ωe²/4ωexe, D0, the number of bound levels and a plot of the curve with its levels between the classical turning points, beside the harmonic parabola.
- Rotation: B for v = 0 and v = 1, the bond length from Be, the line spacing, the most populated J at your temperature, and the first pure rotational line in cm⁻¹ and GHz.
- IR spectrum: P and R branch line positions with Boltzmann intensities at any temperature, as a picture and a table. The missing line at the centre (no Q branch) and the closing-up of the R branch come out naturally.
- Isotopes: type 2H, 37Cl or 13C and the constants are rescaled with the reduced mass, so you can see the shift from HCl to DCl.
- Fit: paste band origins (fundamental and overtones) to get ωe and ωexe with their standard errors and a Birge–Sponer estimate of the dissociation energy.
How to use it
- Choose a molecule. The constants (Huber and Herzberg, via the NIST Chemistry WebBook) fill in.
- Change an atom to another isotope if you want, or type your own constants.
- Set the temperature for the line intensities.
- Read the results, the spectrum, the line table and the potential curve. Download them as a PNG, PDF or Word file.
Worked example
For H³⁵Cl (μ = 0.97959 u), ωe = 2990.95 and ωexe = 52.82 cm⁻¹ give a fundamental at 2885.3 cm⁻¹ (measured: 2886.0) and a force constant of 516 N/m. Be = 10.5934 cm⁻¹ gives a bond length of 1.2746 Å. At 298 K the strongest lines come from J = 3, and R(0) and P(1) sit at 2905.6 and 2864.4 cm⁻¹. Changing ¹H to ²H moves the fundamental to 2090.8 cm⁻¹, close to the ratio √(μ/μ′) ≈ 0.72.
The four measured HCl bands 2885.9, 5668.0, 8346.8 and 10923.1 cm⁻¹ fit to ωe = 2989.2 and ωexe = 51.71 cm⁻¹.
Questions
Why is the Morse D0 larger than the measured one? A Morse curve is only an approximation; real levels crowd together faster near dissociation. The tool shows both where the measured value is known.
Why does the calculated line differ from the measured one by about 1 cm⁻¹? Only the first anharmonic and rotation–vibration terms are used. That is enough for teaching and for assigning lines, not for high-resolution work.
Is anything sent anywhere? No. Everything is worked out in your browser.
Where the numbers come from
- Spectroscopic constants: Huber and Herzberg (1979) as given in the NIST Chemistry WebBook.
- Isotope masses and abundances: the chemical-elements data set by cheminfo (MIT licence), compiled from NIST and IUPAC data.
- Physical constants: CODATA recommended values (NIST).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.