Molecular physics

Molecular structure

In a molecule, both the electrons and nuclei experience similar-scale forces from the Coulomb interaction. However, the nuclei remain at nearly fixed locations in the molecule while the electrons move significantly. This picture of a molecule is based on the idea that nucleons are much heavier than electrons, so will move much less in response to the same force. Neutron scattering experiments on molecules have been used to verify this description.

Molecular energy levels and spectra

When atoms join into molecules, their inner electrons remain bound to their original nucleus while the outer valence electrons are distributed around the molecule. The charge distribution of these valence electrons determines the electronic energy level of a molecule, and can be described by molecular orbital theory, which closely follows the atomic orbital theory used for single atoms. Assuming that the momenta of the electrons are on the order of ħ/a (where ħ is the reduced Planck constant and a is the average internuclear distance within a molecule, ~ 1 Å), the magnitude of the energy spacing for electronic states can be estimated at a few electron volts. This is the case for most low-lying molecular energy states, and corresponds to transitions in the visible and ultraviolet regions of the electromagnetic spectrum.

In addition to the electronic energy levels shared with atoms, molecules have additional quantized energy levels corresponding to vibrational and rotational states. Vibrational energy levels refer to motion of the nuclei about their equilibrium positions in the molecule. The approximate energy spacing of these levels can be estimated by treating each nucleus as a quantum harmonic oscillator in the potential produced by the molecule, and comparing its associated frequency to that of an electron experiencing the same potential. The result is an energy spacing about 100× smaller than that for electronic levels. In agreement with this estimate, vibrational spectra show transitions in the near infrared (about 1–5 μm). Finally, rotational energy states describe semi-rigid rotation of the entire molecule and produce transition wavelengths in the far infrared and microwave regions (about 100-10,000 μm in wavelength). These are the smallest energy spacings, and their size can be understood by comparing the energy of a diatomic molecule with internuclear spacing ~ 1 Å to the energy of a valence electron (estimated above as ~ ħ/a).

Actual molecular spectra also show transitions which simultaneously couple electronic, vibrational, and rotational states. For example, transitions involving both rotational and vibrational states are often referred to as rotational-vibrational or rovibrational transitions. Vibronic transitions combine electronic and vibrational transitions, and rovibronic transitions combine electronic, rotational, and vibrational transitions. Due to the very different frequencies associated with each type of transition, the wavelengths associated with these mixed transitions vary across the electromagnetic spectrum.