Chemistry
How Molecular Symmetry Determines Infrared and Raman Activity of Vibrations
Quick fact
In carbon dioxide (CO2), the symmetric stretch vibration (both C=O bonds lengthening and shortening together) is Raman-active but infrared-inactive, while the asymmetric stretch and bending vibrations are IR-active but Raman-inactive. This happens because of the molecule's high symmetry.
Why this is interesting
You might think that every molecular vibration appears in an infrared spectrum, but some vibrations are invisible to IR and only show up in Raman. Why does molecular symmetry decide which vibrations you can see?
Read the full explanation
Understanding How Molecular Symmetry Determines Infrared and Raman Activity of Vibrations
When a molecule vibrates, each normal mode involves all atoms moving in a coordinated way. Infrared (IR) spectroscopy works by passing infrared light through a sample; a vibration is IR-active if it causes a change in the molecule's dipole moment. A dipole moment is a measure of charge separation, and if the vibration alters the distribution of electrons and nuclei so that the dipole moment changes, the vibration can absorb infrared radiation. Raman spectroscopy, on the other hand, involves scattering of light and depends on a change in polarizability—the ease with which the electron cloud can be distorted. A vibration is Raman-active if it changes the molecule's polarizability. Molecular symmetry plays a crucial role because it determines whether a particular vibration can produce a change in dipole moment or polarizability. For symmetric molecules, some vibrations are symmetrical and do not disturb the dipole moment, while others are asymmetrical and do. Conversely, symmetric vibrations often change the polarizability because the electron cloud expands and contracts symmetrically, whereas asymmetric vibrations may not. Thus, the point group of the molecule—its set of symmetry operations—directly dictates which vibrations are allowed in each spectrum. For example, water (H2O) has a bent shape with permanent dipole moment. Its symmetric O–H stretch changes the dipole moment that lies along the bisector of the H–O–H angle, and it also changes polarizability, so it is both IR and Raman active. But in a linear molecule like CO2, the symmetric stretch leaves the dipole moment zero because the two bond dipoles cancel exactly, so it is IR-inactive; yet this vibration greatly distorts the electron cloud, making it Raman-active. The asymmetric stretch creates a net dipole moment, so it is IR-active, but it does not change polarizability in a way that yields Raman scattering. The key insight is symmetry: a vibration is IR-active if its symmetry matches that of a component of the dipole moment vector (x, y, or z). A vibration is Raman-active if its symmetry matches that of a component of the polarizability tensor (the quadratic forms x², y², z², xy, etc.). In group theory, each normal mode belongs to an irreducible representation (symmetry species). The selection rules state that a mode is IR-active if its representation is the same as that of a translation in x, y, or z, and Raman-active if it matches a quadratic function. This formal classification lets you predict the number and type of IR and Raman bands from the molecule's point group.
A deeper explanation
The underlying principle is that the interaction of a molecule with electromagnetic radiation depends on the change in its charge distribution. For IR absorption, the transition dipole moment integral over the vibrational states must be nonzero. This integral is governed by the symmetry of the vibrational mode. The dipole moment operator transforms as the coordinates x, y, and z (i.e., along the molecular axes). Therefore, a vibration is IR-active only if its irreducible representation is the same as that of one of the Cartesian coordinates. This is a direct consequence of group theory: the integral vanishes unless the direct product of the representations of the initial state, the dipole operator, and the final state contains the totally symmetric representation. Since the initial and final vibrational states have the same symmetry (vibrational ground state is totally symmetric), the condition reduces to the mode's representation having a component of the dipole operator. Similarly, Raman scattering involves the polarizability tensor, which transforms as the second-rank tensor components (x², y², z², xy, xz, yz). A vibration is Raman-active if its irreducible representation matches one of these quadratic forms. For a heteronuclear diatomic molecule like HCl, all vibrations are both IR and Raman active because the molecule lacks an inversion center. In contrast, homonuclear diatomic molecules like N2 have an inversion center; they have only one vibration (the stretch) which is symmetric, so it is Raman-active but IR-inactive. For polyatomic molecules, the point group determines which modes are active. The mutual exclusion rule states that for centrosymmetric molecules, a mode cannot be both IR and Raman active: if it is symmetric with respect to inversion, it is Raman-active; if antisymmetric, it is IR-active. For example, in CO2 (linear, centrosymmetric), the symmetric stretch is totally symmetric (σg+), thus Raman-active but IR-inactive. The antisymmetric stretch (σu+) is IR-active, and the bending modes (πu) are also IR-active (they produce a perpendicular dipole change) and are Raman-inactive because they do not have the correct symmetry for polarizability components. This symmetry-based selection is not just theoretical: it is central to determining molecular structure from spectra. By knowing the point group, one can predict how many IR and Raman bands a molecule should exhibit, and conversely, by observing the spectra, one can infer symmetry. In the laboratory, complementary IR and Raman spectroscopy together provide a full picture of a molecule's vibrational modes. Moreover, these principles carry over into solid-state physics, where phonon modes follow similar selection rules based on crystal symmetry, enabling the study of lattice dynamics. Understanding symmetry and activity is essential for choosing experimental techniques and interpreting spectral data in chemistry and materials science.