To use all functions of this page, please activate cookies in your browser.
my.chemeurope.com
With an accout for my.chemeurope.com you can always see everything at a glance – and you can configure your own website and individual newsletter.
 My watch list
 My saved searches
 My saved topics
 My newsletter
Semirigid moleculeA semirigid molecule is a molecule which has a potential energy surface with a welldefined minimum corresponding to a stable structure of the molecule. The only (quantum mechanical) motions that a semirigid molecule makes are (small) internal vibrations around its equilibrium geometry and overall translations and rotations. Additional recommended knowledge
Potential energy surfaceA molecule consists of atoms held together by chemical bonding forces. The potential, derived from these forces, is a function of the Cartesian nuclear coordinates R_{1}, ..., R_{N}. These coordinates are expressed with respect to a frame attached to the molecule. The potential function is known as force field or potential energy surface written as V(R_{1}, ..., R_{N}). Often a more accurate representation of the potential V is obtained by the use of internal curvilinear coordinates, socalled valence coordinates. We mention bond stretch, valence angle bending, outofplanerotation angles, and dihedral(torsion) angles. Although the curvilinear internal coordinates can give a good description of the molecular potential, it is difficult to express the kinetic energy of nuclear vibrations in these coordinates. Identical nucleiWhen a molecule contains identical nuclei—which is commonly the case—there are a number of minima related by the permutations of the identical nuclei. The minima, distinguished by different numberings of identical nuclei, can be partitioned in equivalent classes. Two minima are equivalent if they can be transformed into one other by rotating the molecule, that is, without surmounting any energy barrier (bond breaking or bond twisting). The molecules with minima in different equivalent classes are called versions. To transform one version into another version an energy barrier must be overcome. ExampleTake for instance the pyramidal ammonia (NH_{3}) molecule. There are 3!=6 permutations of the hydrogen atoms. If we count the hydrogens looking down from the nitrogen onto the plane of the hydrogens, then we see that
forms one equivalence class, (class I), because the members can be transformed into each other by simply rotating around the 3fold axis without overcoming an energy barrier. The other equivalence class (class II) consists of
To transform a member (version) of class I to class II, an energy barrier has to be overcome. (The lowest path on the potential energy surface is actually via the flipping of the ammonia "umbrella". The umbrella up and the umbrella down are separated by an energy barrier of height of ca. 1000 cm^{1}). In a semirigid molecule all the barriers between different versions are so high that the tunneling though the barriers may be neglected. Under these conditions identical nuclei may be seen as distinguishable particles to which the Pauli principle does not apply. This is a very common point of view in chemistry. Floppy moleculeIn a nonrigid (floppy) molecule (some of) the potential barriers between the different versions are so low that tunneling through the barrier is appreciable, or, in other words, that splittings due to tunneling are spectroscopically observable. Under these conditions one must take care that the identical nuclei obey the Pauli principle (are described by either a symmetric or antisymmetric wavefunction).
References


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Semirigid_molecule". A list of authors is available in Wikipedia. 