Franck-Condon principle
The generalization that the transition from one energy state of a molecular system to
another occurs so nearly instantaneously that the nuclei of the atoms involved can be
considered as stationary during the process. The Franck-Condon principle is closely
related to the Born-Oppenheimer approximation, in which the various motions
(electronic, nuclear vibrations and rotations) are considered to be separable, and in which
the electrons respond to the instantaneous vibrations of the system whereas the system
responds only to the average position of the electrons. The principle, proposed by J.
Franck in 1925 and developed quantum-mechanically by E. U. Condon in 1928, is
important in discussing systems of more than one atom. It is therefore valuable in
molecular spectroscopy and in the interpretation of the optical properties of liquids and
solids. See below Molecular Structure and Spectra
Molecular structure and spectra
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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)
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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 hyperfinestructure 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
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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)
Article on the Franck-Condon Principle
http://www.life.illinois.edu/govindjee/biochem494/Abs.html
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