polarizability is compatible with preservation of the center of symmetry. Thus, in a centrosymmetric molecule, asymmetrical stretching and bending are IR active and Raman inactive, while symmetrical stretching and bending is Raman active and IR inactive. Hence, in a centrosymmetric molecule, IR and Raman spectroscopy are mutually exclusive. For molecules without a center of symmetry, each vibrational mode may be IR active, Raman active, both, or neither. Symmetrical stretches and bends, however, tend to be Raman active. Theory of resonance Raman scattering In resonance Raman spectroscopy, the wavelength of the incoming photons coincides with an electronic transition of the molecule or material. Electronic excitation of a molecule results in structural changes which are reflected in the enhancement of Raman scattering of certain vibrational modes. Vibrational modes that undergo a change in bond length and/or force constant during the electronic excitation can show a large increase in polarizability and hence Raman intensity. This is known as Tsuboi's rule, which gives a qualitative relationship between the nature of an electronic transition and the enhancement pattern in resonance Raman spectroscopy. The enhancement factor can be by a factor of 10 to > 100,000 and is most apparent in the case of π-π* transitions and least for metal centered (d–d) transitions. There are two primary methods used to quantitatively understand resonance Raman enhancement. These are the transform theory, developed by Albrecht and the time-dependent theory developed by Heller. Applications The selective enhancement of the Raman scattering from specific modes under resonance conditions means that resonance Raman spectroscopy is especially useful for large biomolecules with chromophores embedded in their structure. In such chromophores, the resonance scattering from charge-transfer (CT) electronic transitions of the metal complex generally result in enhancement of metal-ligand stretching modes, as well as some of the modes associated with the ligands alone. Hence, in a biomolecule such as hemoglobin, tuning the laser to near the charge-transfer electronic transition of the iron center results in a spectrum reflecting only the stretching and bending modes associated with the tetrapyrrole-iron group. Consequently, in a molecule with thousands of vibrational modes, RR spectroscopy allows us to look at relatively few vibrational modes at a time. The Raman spectrum of a protein containing perhaps hundreds of peptide bonds but only a single porphyrin molecule may show only the vibrations associated with the porphyrin. This reduces the complexity of the spectrum and allows for easier identification of an