Max von Laue (1879-1960) recognized that the regularly spaced planes of atoms and molecules in crystals resemble a diffraction grating. He and his coworkers, W. Friedrich and P. Knipping, showed in 1912 that a beam of x rays, with a wavelength comparable to the magnitude of crystal spacings, is diffracted when passed through crystalline substances. The observed diffraction patterns can be explained by considering the beam of x rays to be scattered by the atoms of the molecule in the crystal.

The solutions of the Schrödinger wave equation for atoms and molecules are sets of wave functions. Each of these wave functions corresponds to a stationary state in which the atom or molecule is allowed to be, and each of these allowed states has energy associated with it. There are two major types of interactions that molecules may have with electromagnetic radiation. In the first...