page_title: Rotational–vibrational spectroscopy
section_title: Appendix
hierarchical_section_title: Rotational–vibrational spectroscopy / Appendix
caption_attribution_description: English: Plot of data for carbon monoxide
context_page_description: Rotational–vibrational spectroscopy is a branch of molecular spectroscopy concerned with infrared and Raman spectra of molecules in the gas phase. Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational transitions. When such transitions emit or absorb photons, the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy. Since changes in rotational energy levels are typically much smaller than changes in vibrational energy levels, changes in rotational state are said to give fine structure to the vibrational spectrum. For a given vibrational transition, the same theoretical treatment as for pure rotational spectroscopy gives the rotational quantum numbers, energy levels, and selection rules. In linear and spherical top molecules, rotational lines are found as simple progressions at both higher and lower frequencies relative to the pure vibration frequency. In symmetric top molecules the transitions are classified as parallel when the dipole moment change is parallel to the principal axis of rotation, and perpendicular when the change is perpendicular to that axis.
context_section_description: The method of combination differences uses differences of wavenumbers in the P- and R- branches to obtain data that depend only on rotational constants in the vibrational ground or excited state. For the excited state
  This function can be fitted, using the method of least-squares to data for carbon monoxide, from Harris and Bertolucci. The data calculated with the formula
  in which centrifugal distortion is ignored, are shown in the columns labelled with (1). This formula implies that the data should lie on a straight line with slope 2B′′ and intercept zero. At first sight the data appear to conform to this model, with a root mean square residual of 0.21 cm⁻¹. However, when centrifugal distortion is included, using the formula
  the least-squares fit is improved markedly, with ms residual decreasing to 0.000086 cm⁻¹. The calculated data are shown in the columns labelled with (2).
caption: Plot of the differences R(J)-P(J) as a function of 2J+1 taken from observed data for the fundamental vibration of carbon monoxide[51]
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