vibrational transitions that are observed in IR spectroscopy are not observed in Raman spectroscopy, and vice versa. RR spectroscopy is an extension of conventional Raman spectroscopy that can provide increased sensitivity to specific (colored) compounds that are present at low concentrations (micro to millimolar) in an otherwise complex mixture of compounds. An advantage of resonance Raman spectroscopy over (normal) Raman spectroscopy is that the intensity of bands can be increased by several orders of magnitude. An application that illustrates this advantage is the study of the dioxygen unit in cytochrome c oxidase. Identification of the band associated with the O–O stretching vibration was confirmed by using 18O–16O and 16O–16O isotopologues. Basic theory The frequencies of molecular vibrations range from less than 1012 to approximately 1014 Hz. These frequencies correspond to radiation in the infrared (IR) region of the electromagnetic spectrum. At any given instant, each molecule in a sample has a certain amount of vibrational energy. However, the amount of vibrational energy that a molecule has continually changes due to collisions and other interactions with other molecules in the sample. At room temperature, most molecules are in the lowest energy state—known as the ground state. A few molecules are in higher energy states—known as excited states. The fraction of molecules occupying a given vibrational mode at a given temperature can be calculated using the Boltzmann distribution. Performing such a calculation shows that, for relatively low temperatures (such as those used for most routine spectroscopy), most of the molecules occupy the ground vibrational state (except in the case of low-frequency modes). Such a molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy. This is the mechanism by which IR spectroscopy operates: infrared radiation is passed through the sample, and the intensity of the transmitted light is compared with that of the incident light. A reduction in intensity at a given wavelength of light indicates the absorption of energy by a vibrational transition. The energy, , of a photon is where is Planck's constant and is the frequency of the radiation. Thus, the energy required for such transition may be calculated if the frequency of the incident radiation is known. It is also possible to observe molecular vibrations by an inelastic scattering process, Stokes Raman scattering being one such process. A photon is absorbed and then re-emitted (scattered) with lower energy.