# Infrared Spectroscopy Calculators

## Wavenumber-to-wavelength converter

Wavelength (mm): Wavenumber (cm-1):

## Wavelength calculator

The calculator can be used to get an idea where absorption bands occur in the infrared spectrum and it demonstrates the effect of atom mass and bond force constant on the band position. However, the exact position of an infrared absorption band depends on a variety of parameters, like intramolecular and intermolecular chemical effects.
The frequency of molecular vibrations is calculated from the equations given below by substituting the masses of two atoms for m1 and m2; the quantity k becomes the force constant for the chemical bond, which is a measure of its stiffness (but not necessarily its strength!). Generally, k has been found to lie in the range 3*105 to 8*105 dynes/cm for most single bonds, with 5*105 serving as a reasonable average value (used in calculations). Double and triple bonds have k-values of about 2 and 3 times the value for a single bond, respectively (double bond, 1*106 dynes/cm; triple bond, 1.5*106 dynes/cm). With these values, the equation can be used to estimate the wavenumber of fundamental absorption peak (due to the transition from ground to first excited state) for a variety of bond types.

 bond order: single bond (k=5*10e5 dynes/cm) double bond (k=1*10e6 dynes/cm) triple bond (k=1.5*10e6 dynes/cm) atom 1: H C N O F Cl Br I P S atom 2: H C N O F Cl Br I P S absorption wavenumber (cm-1): and where: sigma, wavenumber (cm-1); c, speed of light (cm/s); k, bond force constant (dynes/cm); µ, reduced mass; m1, mass for atom 1 (g/atom); m2, mass for atom 2 (g/atom).

 Note that this formula only holds for a harmonic oscillator and is a simple theoretical approximation. From qualitative considerations, however, it is apparent that this description of a molecular vibration is imperfect. In fact a more quantum mechanically treatment is necessary for anharmonic oscillators. Furthermore, vibrational spectra are complicated by the fact that two different vibrations in a molecule can interact to give absorption peaks with frequencies that are approximately the sums or differences of their fundamental frequencies. For another detailed description, including an example of HCl, please click here.

 last update: augustus 11, 2007 