Visualize rovibrational energy levels and calculate transition frequencies for diatomic molecules.

• This app allows you to calculate energy levels, transition frequencies and a sample spectrum for a linear diatomic molecule undergoing rovibrational transitions. You must enter masses for the two atoms of the molcule, and you may then enter either a spring constant or frequency, and a bond length or vibrational constant. You may then "draw the energy level diagram" including calculated frequencies.
• Vibrational energies are calculated by E_v = hcν̄(v+½) where ν̄ is the vibrational frequency, ν̄ = (k/μ)^½/(2πc), in wavenumbers (cm^-1).
• Rotational energies are calculated by E_J = hcB̄J(J+1) where B̄ is the rotational constant given in wavenumbers (cm^-1), B̄ = ℏ² / (2hcμr²) and r is the bond length.
• The total energy for a rovibrational level is the sum of vibrational and rotational energies. This may then be converted to wavenumbers by dividing by hc. The "energy" levels and the transition frequencies in the figure below are give in wavenumbers, as is standard.
• The temperature is needed to calculate the peak intensities on the spectrum; intensities depend on the number of molecules in each rotational state, N_J, which obeys a Boltmann distribution: N_J/N_o = (2J+1)e^{-B̄J(J+1)/kT}.
• If peaks on the spectrum are too close together or too far apart, use the slider at the bottom to adjust the spacing, then clear the spectrum and redraw the peaks (you do not need to re-enter all of the data).
• Press here for sample values.
• For ¹H³⁵Cl, use a k of 480 ks^-2 and r of 1.27 Å. Press here to populate values.
• Press here to hide.