Semi-rigid Molecule
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In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
and
molecular physics Molecular physics is the study of the physical properties of molecules and molecular dynamics. The field overlaps significantly with physical chemistry, chemical physics, and quantum chemistry. It is often considered as a sub-field of atomic, mo ...
, fluxional (or non-rigid) molecules are
molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...
s that undergo dynamics such that some or all of their
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s interchange between symmetry-equivalent positions. Because virtually all molecules are fluxional in some respects, e.g. bond rotations in most
organic compound Some chemical authorities define an organic compound as a chemical compound that contains a carbon–hydrogen or carbon–carbon bond; others consider an organic compound to be any chemical compound that contains carbon. For example, carbon-co ...
s, the term fluxional depends on the context and the method used to assess the dynamics. Often, a molecule is considered fluxional if its spectroscopic signature exhibits line-broadening (beyond that dictated by the
Heisenberg uncertainty principle The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position a ...
) due to chemical exchange. In some cases, where the rates are slow, fluxionality is not detected spectroscopically, but by
isotopic labeling Isotopic labeling (or isotopic labelling) is a technique used to track the passage of an isotope (an atom with a detectable variation in neutron count) through chemical reaction, metabolic pathway, or a biological cell. The reactant is 'labeled' ...
and other methods.


Spectroscopic studies

Many
organometallic compound Organometallic chemistry is the study of organometallic compounds, chemical compounds containing at least one chemical bond between a carbon atom of an organic molecule and a metal, including alkali, alkaline earth, and transition metals, and ...
s exhibit fluxionality. Fluxionality is, however, pervasive.


NMR spectroscopy

Temperature dependent changes in the NMR spectra result from dynamics associated with the fluxional molecules when those dynamics proceed at rates comparable to the frequency differences observed by NMR. The experiment is called DNMR and typically involves recording spectra at various temperatures. In the ideal case, low temperature spectra can be assigned to the "slow exchange limit", whereas spectra recorded at higher temperatures correspond to molecules at "fast exchange limit". Typically, high temperature spectra are simpler than those recorded at low temperatures, since at high temperatures, equivalent sites are averaged out. Prior to the advent of DNMR, kinetics of reactions were measured on non-equilibrium mixtures, monitoring the approach to equilibrium. Many molecular processes exhibit fluxionality that can be probed on the NMR time scale. Beyond the examples highlighted below, other classic examples include the Cope rearrangement in bullvalene and the chair inversion in
cyclohexane Cyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colourless, flammable liquid with a distinctive detergent-like odor, reminiscent of cleaning products (in which it is sometimes used). Cyclohexan ...
. For processes that are too slow for traditional DNMR analysis, the technique spin saturation transfer (SST, also called EXSY for exchange spectroscopy) is applicable. This magnetization transfer technique gives rate information, provided that the rates exceed 1/''T''1.


IR spectroscopy

Although less common, some dynamics are also observable on the time-scale of
IR spectroscopy Infrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functio ...
. One example is
electron transfer Electron transfer (ET) occurs when an electron relocates from an atom, ion, or molecule, to another such chemical entity. ET describes the mechanism by which electrons are transferred in redox reactions. Electrochemical processes are ET reactio ...
in a mixed-valence dimer of metal clusters. Application of the equation for coalescence of two signals separated by 10 cm−1 gives the following result: : k \sim \Delta \nu_0 \sim 2(10~\text^) (300 \cdot 10^8~\text) \sim 6 \times 10^~\text^. Clearly, processes that induce line-broadening on the IR time-scale must be much more rapid than the cases that exchange on the NMR time scale.


Examples


Cyclohexane and related rings

The interconversion of equivalent chair conformers of
cyclohexane Cyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colourless, flammable liquid with a distinctive detergent-like odor, reminiscent of cleaning products (in which it is sometimes used). Cyclohexan ...
(and many other cyclic compounds) is called ring flipping. Carbon–hydrogen bonds that are axial in one configuration become equatorial in the other, and vice versa. At room temperature the two chair conformations rapidly equilibrate. The proton- and carbon-13 NMR spectra of cyclohexane show each only singlets near room temperature. At low temperatures, the singlet in the 1H NMR spectrum decoalesces but the 13C NMR spectrum remains unchanged.


Berry pseudorotation of pentacoordinate compounds

A prototypical fluxional molecule is phosphorus pentafluoride. Its 19F NMR spectrum consists of a 31P-coupled doublet, indicating that the equatorial and axial fluorine centers interchange rapidly on the NMR timescale. Fluorine-19 NMR spectroscopy, even at temperatures as low as −100 °C, fails to distinguish the axial from the equatorial fluorine environments. The apparent equivalency arises from the low barrier for pseudorotation via the
Berry mechanism The Berry mechanism, or Berry pseudorotation mechanism, is a type of vibration causing molecules of certain geometries to isomerization, isomerize by exchanging the two axial ligands (see the figure) for two of the equatorial ones. It is the most ...
, by which the axial and equatorial fluorine atoms rapidly exchange positions.
Iron pentacarbonyl Iron pentacarbonyl, also known as iron carbonyl, is the compound with formula . Under standard conditions Fe( CO)5 is a free-flowing, straw-colored liquid with a pungent odour. Older samples appear darker. This compound is a common precursor t ...
(Fe(CO)5) follows the pattern set for PF5: only one signal is observed in the 13C NMR spectrum near room temperature) whereas at low temperatures, two signals in a 2:3 ratio can be resolved. In
sulfur tetrafluoride Sulfur tetrafluoride is a chemical compound with the formula S F4. It is a colorless corrosive gas that releases dangerous hydrogen fluoride gas upon exposure to water or moisture. Sulfur tetrafluoride is a useful reagent for the preparation o ...
(SF4), a similar pattern is observed even though this compound has only four ligands. A well-studied fluxional ion is the
methanium In chemistry, methanium is a complex positive ion with formula (metastable transitional form, a carbon atom covalently bonded to five hydrogen atoms) or (fluxional form, namely a molecule with one carbon atom covalently bonded to three hydro ...
ion, . Even at
absolute zero Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 ° ...
there is no rigid molecular structure; the H atoms are always in motion. More precisely, the spatial distribution of protons in is many times broader than its parent molecule CH4, methane.


Six-coordinate species

While nonrigidity is common for pentacoordinate species, six-coordinate species typically adopt a more rigid
octahedral molecular geometry In chemistry, octahedral molecular geometry, also called square bipyramidal, describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The o ...
, featuring close-packed array of six ligating atoms surrounding a central atom. Such compounds do rearrange intramolecularly via the Ray-Dutt twist and the Bailar twist, but the barriers for these processes are typically high such that these processes do not lead to line broadening. For some compounds, dynamics occur via dissociation of a ligand, giving a pentacoordinate intermediate, which is subject to the mechanisms discussed above. Yet another mechanism, exhibited by Fe(CO)4(SiMe3)2 and related hydride complexes, is intramolecular scrambling of ligands over the faces of the tetrahedron defined by the four CO ligands.


Dimethylformamide

A classic example of a fluxional molecule is
dimethylformamide Dimethylformamide, DMF is an organic compound with the chemical formula . Its structure is . Commonly abbreviated as DMF (although this initialism is sometimes used for 2,5-dimethylfuran, dimethylfuran, or dimethyl fumarate), this colourless liqui ...
(DMF). At temperatures near 100 °C, the 500 MHz 1H NMR spectrum of DMF shows only one signal for the methyl groups. Near room temperature, however, separate signals are seen for the non-equivalent methyl groups. The rate of exchange can be calculated at the temperature where the two signals are just merged. This "coalescence temperature" depends on the measuring field. The relevant equation is : k = \frac \sim 2 \Delta \nu_0, where Δν0 is the difference between the frequencies (in Hz) of the exchanging sites. These frequencies are obtained from the limiting low-temperature NMR spectrum. At these lower temperatures, the dynamics continue, of course, but the contribution of the dynamics to line broadening is negligible. For example, if Δν0 = 1ppm @ 500 MHz, : k \sim 2(500) = 1000~\text^ (~0.5 millisecond
half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...
).


"Ring whizzing"

The compound Fe(η5-C5H5)(η1-C5H5)(CO)2 exhibits the phenomenon of "ring whizzing". At 30 °C, the 1H NMR spectrum shows only two peaks, one typical (δ5.6) of the η5-C5H5 and the other assigned η1-C5H5. The singlet assigned to the η1-C5H5 ligand splits at low temperatures owing to the slow hopping of the Fe center from carbon to carbon in the η1-C5H5 ligand. Two mechanisms have been proposed, with the consensus favoring the 1,2 shift pathway.Robert B. Jordan, Reaction Mechanisms of Inorganic and Organometallic Systems (''Topics in Inorganic Chemistry''), 2007.


See also

* Pyramidal inversion * Bullvalene, a fluxional molecule * * * Pseudorotation ** Bailar twist ** Bartell mechanism **
Berry mechanism The Berry mechanism, or Berry pseudorotation mechanism, is a type of vibration causing molecules of certain geometries to isomerization, isomerize by exchanging the two axial ligands (see the figure) for two of the equatorial ones. It is the most ...
** Ray–Dutt twist


Further reading

*D. Papoušek and M. R. Aliev, ''Molecular Vibrational-Rotational Spectra'' Elsevier, Amsterdam, 1982 *E. B. Wilson, J. C. Decius, and P. C. Cross, ''Molecular Vibrations'', McGraw-Hill, New York, 1955 (reprinted by Dover 1980) *: The use of permutation-inversion groups for the symmetry classification of the states of fluxional (or non-rigid) molecules. *P. R. Bunker and P. Jensen, ''Fundamentals of Molecular Symmetry'', CRC Press, 199

*H. W. Kroto, ''Molecular Rotation Spectra'', Wiley, New York, 1975 (reprinted by Dover 1992), describing the term "semi-rigid molecule". *


References

{{Reflist Chemical bond properties