Molecular structure and spectra

Molecular structure and spectra

Until the advent of quantum theory, ideas about the structure of molecules evolved gradually from analysis and interpretation of the facts of chemistry. Chemists developed the concept of molecules as built from atoms in definite proportions, and identified and constructed (synthesized) a great variety of molecules. Later, when the structure of atoms as built from nuclei and electrons began to be understood with the help of quantum theory, a beginning was made in seeing why atoms can combine in definite ways to form molecules; also, infrared spectra began to be used to obtain information about the dimensions and the nuclear motions (vibrations) in molecules. However, a fundamental understanding of chemical bonding and molecular structure became possible only by application of the present form of quantum theory, called quantum mechanics. This theory makes it possible to obtain from the spectra of molecules a great deal of information about the nature of molecules in their normal as well as excited states, and about dissociation energies and other characteristics of molecules.

Molecular sizes

The size of a molecule varies approximately in proportion to the numbers and sizes of the atoms in the molecule. Simplest are diatomic molecules. These may be thought of as built of two spherical atoms of radii r and r, flattened where they are joined. The equilibrium value Re of the distance R between their nuclei is then smaller than the sum of the atomic radii. However, the nuclei of atoms in two different molecules cannot normally approach more closely than a distance r + r; r and r are called the van der Waals radii of the atoms.

To describe a polyatomic molecule, one must specify not merely its size but also its shape or configuration. For example, carbon dioxide (CO2) is a linear symmetrical molecule, the O—C—O angle being 180°. The H—O—H angle in the nonlinear water (H2O) molecule is 105°. Many molecules which are essential for life contain thousands or even millions of atoms. Proteins are often coiled or twisted and cross-linked in ways which are important for their biological functioning.

Dipole moments

Most molecules have an electric dipole moment. In atoms, the electron cloud surrounds the nucleus so symmetrically that its electrical center coincides with the nucleus, giving zero dipole moment; in a molecule, however, these coincidences are disturbed, and a dipole moment usually results.

Thus, when the atoms of HCl come together, there is some shifting of the H-atom electron toward the Cl. A complete shift would give H+Cl-, which would constitute an electric dipole of magnitude eRe, where e is the electronic charge. But in fact the dipole moment is only 0. 17 eRe. This is because the actual electronic shift is only fractional.

Molecular polarizability

In the preceding consideration of dipole moments, the discussion has been in terms of atoms and molecules free from external forces. An electric field pulls the electrons of an atom or molecule toward it and pushes the nuclei away, or vice versa. This action creates a small induced dipole moment, whose magnitude per unit strength of the field is called the polarizability.

Molecular energy levels

The states of motion of nuclei and electrons in a molecule, or of electrons in an atom, are restricted by quantum mechanics to special forms with definite energies. The state of lowest energy is called the ground state; all others are excited states. In analogy to water levels, one speaks of energy levels. Excited states exist only momentarily, following an electrical or other stimulus.

Excitation of an atom consists of a change in the state of motion of its electrons. Electronic excitation of molecules can also occur, but alternatively or additionally, molecules can be excited to discrete states of vibration and rotation.

The total energy of any molecule can be written as Eq. (1).

(1) 
Both the electronic energy Eel and vibration energy Ev can be discrete or continuous. The quantities Er,�break Efs, and Ehfs denote rotational, fine-structure, and hyperfine-structure energies. The last two appear as small or minute splittings of the rotation levels. The spacings ΔE of adjacent discrete levels of each type are usually in the order given in notation
(2) 
(2). The Eext term in Eq. (1) refers to additional fine structure which appears on subjecting molecules to external magnetic fields (Zeeman effect) or electric fields (Stark effect). See Fine structure (spectral lines), Hyperfine structure, Stark effect, Zeeman effect

Polyatomic molecules have much more complicated patterns of vibrational and (usually) rotational energy levels than diatomic molecules.

Molecular spectra

The frequencies cv (c = speed of light) of electromagnetic spectra obey the Einstein-Bohr equation (3),

(3) 
where h is Planck's constant. Molecular emission spectra accompany jumps in energy from higher to lower levels; absorption spectra accompany jumps from lower to higher levels.

Molecular spectra can be classified as fine-structure or low-frequency spectra, rotation spectra, vibration-rotation spectra, and electronic spectra. See Magnetic resonance, Microwave spectroscopy, Molecular beams, Spectroscopy

Transitions between energy levels differing only in rotational state give rise to pure rotation spectra. These typically consist of a sequence of lines spaced almost equidistantly, and lying in the far infrared or the microwave region.

Spectra involving only vibrational and rotational state changes consist of bands which lie mainly in the infrared. Each band consists of two sets of closely spaced rotational lines, one on each side of a central frequency. Vibration-rotation absorption bands of liquids and solutions are widely used in chemical analysis. Here the rotational structure is blurred out, and only an “envelope” is seen. See Infrared spectroscopy

Electronic band spectra are the most general type of molecular spectra. For any one electronic transition, the spectrum consists typically of many bands. See Atomic structure and spectra, Intermolecular forces, Molecular weight, Raman effect, Scattering experiments (atoms and molecules)

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