Molecular spectroscopy probes energy levels and dynamics in atoms and molecules using light.Molecular spectroscopy is the study of how molecules absorb, emit, or scatter electromagnetic radiation, revealing their internal energy levels. Because molecules can rotate, vibrate, and undergo electronic transitions, their spectra are far richer than those of atoms, with bands of closely spaced lines. This technique is the primary tool for identifying chemical compounds and understanding molecular structure and dynamics.
The field began in the late 19th century with studies of infrared absorption by gases. The first high-resolution infrared spectra were obtained in the 1930s, and the technique became widely used after World War II with commercial instruments.
When light of a specific frequency matches the energy difference between two molecular states, the molecule can absorb or emit a photon. Infrared spectroscopy probes vibrational transitions, microwave spectroscopy probes rotations, and ultraviolet-visible spectroscopy probes electronic transitions. By analyzing the pattern of absorption or emission lines, scientists can deduce bond lengths, bond angles, and the forces between atoms.
Used in chemistry to identify unknown substances, in atmospheric science to monitor greenhouse gases, and in astronomy to detect molecules in interstellar clouds.
The same molecular spectroscopy technique that identifies pollutants in the air is used by forensic scientists to analyze trace evidence like paint chips or fibers.
| A(ω) | variable | spectral function value at energy ω — spectral function |
| ω | variable | energy variable (frequency) — energy joule |
| n | variable | index labeling excited eigenstates |
| |n⟩ | variable | excited eigenstate of the system — quantum state |
| |0⟩ | variable | ground state of the system — quantum state |
| O | variable | operator whose excitations are probed — operator |
| E_n | variable | energy of excited state n — energy joule |
| E_0 | variable | energy of ground state — energy joule |
| ⟨n|O|0⟩ | operator | inner product of states with operator applied — matrix element |
| δ(...) | operator | selects only contributions at exact energy difference — dirac delta |
| ∑_n | operator | adds contributions from all possible excitations — summation |
