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chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
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 held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s that undergo dynamics such that some or all of their
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s interchange between symmetry-equivalent positions. Because virtually all molecules are fluxional in some respects, e.g. bond rotations in most
organic compound In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The ...
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 Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
signature exhibits line-broadening (beyond that dictated by the
Heisenberg uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
) 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 a reaction, metabolic pathway, or cell. The reactant is 'labeled' by replacing specific ...
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 ...
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 The Cope rearrangement is an extensively studied organic reaction involving the ,3sigmatropic rearrangement of 1,5-dienes. It was developed by Arthur C. Cope and Elizabeth Hardy. For example, 3-methyl-hexa-1,5-diene heated to 300 °C yield ...
in
bullvalene Bullvalene is a hydrocarbon with the chemical formula . The molecule has a cage-like structure formed by the fusion of one cyclopropane and three cyclohepta-1,4-diene rings. Bullvalene is unusual as an organic molecule due to the and bonds fo ...
and the chair inversion in
cyclohexane Cyclohexane is a cycloalkane with the molecular formula . Cyclohexane is non-polar. Cyclohexane is a colorless, 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 functiona ...
. One example is
electron transfer Electron transfer (ET) occurs when an electron relocates from an atom or molecule to another such chemical entity. ET is a mechanistic description of certain kinds of redox reactions involving transfer of electrons. Electrochemical processes ar ...
in a mixed-valence dimer of
metal cluster In chemistry, an atom cluster (or simply cluster) is an ensemble of bound atoms or molecules that is intermediate in size between a simple molecule and a nanoparticle; that is, up to a few nanometers (nm) in diameter. The term ''microcluster ...
s. Application of the equation for coalescence of two signals separated by 10 cm−1 gives the following result: :k \sim \Delta \nu_\circ \sim 2(10 \mathrm^) (300 \cdot 10^8 \mathrm) \sim 6 \times 10^ \mathrm^ \cdot 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 colorless, 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 Phosphorus pentafluoride, P F5, is a phosphorus halide. It is a colourless, toxic gas that fumes in air. Preparation Phosphorus pentafluoride was first prepared in 1876 by the fluorination of phosphorus pentachloride using arsenic trifluoride, w ...
. 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 In chemistry, a pseudorotation is a set of intramolecular movements of attached groups (i.e., ligands) on a highly symmetric molecule, leading to a molecule indistinguishable from the initial one. The International Union of Pure and Applied Chem ...
via the
Berry mechanism The Berry mechanism, or Berry pseudorotation mechanism, is a type of vibration causing molecules of certain geometries to isomerize by exchanging the two axial ligands (see Figure at right) for two of the equatorial ones. It is the most widely ac ...
, 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 to ...
(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 the chemical compound with the formula S F4. It is a colorless corrosive gas that releases dangerous HF upon exposure to water or moisture. Despite these unwelcome characteristics, this compound is a useful reagent for t ...
(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 []+, namely a molecule with one carbon atom covalent bond, bonded to three hydrogen atoms and one hydrogen molecule, bearing a +1 electric charge. It is a superacid and one of the ...
ion, which is protonated methane, . In this unusual species, whose IR spectrum was experimentally observed and understood, the barriers to proton exchange are lower than the
zero-point energy Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly Quantum fluctuation, fluctuate in their lowest energy state as described by the Heisen ...
. Thus, even at
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
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 oc ...
, 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 The Bailar twist is a mechanism proposed for the racemization of octahedral complexes containing three bidentate chelate rings. Such complexes typically adopt an octahedral molecular geometry, in which case they possess helical chirality. One p ...
, 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 is an organic compound with the formula ( CH3)2NC(O)H. Commonly abbreviated as DMF (although this initialism is sometimes used for dimethylfuran, or dimethyl fumarate), this colourless liquid is miscible with water and the majo ...
(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_\circ where Δνo is the difference in Hz between the frequencies 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 Δνo = 1ppm @ 500 MHz :k \sim 2(500) = 1000 \mathrm^ (ca. 0.5 millisecond
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
)


"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

*
Bullvalene Bullvalene is a hydrocarbon with the chemical formula . The molecule has a cage-like structure formed by the fusion of one cyclopropane and three cyclohepta-1,4-diene rings. Bullvalene is unusual as an organic molecule due to the and bonds fo ...
, a fluxional molecule * * *
Pseudorotation In chemistry, a pseudorotation is a set of intramolecular movements of attached groups (i.e., ligands) on a highly symmetric molecule, leading to a molecule indistinguishable from the initial one. The International Union of Pure and Applied Chem ...
**
Bailar twist The Bailar twist is a mechanism proposed for the racemization of octahedral complexes containing three bidentate chelate rings. Such complexes typically adopt an octahedral molecular geometry, in which case they possess helical chirality. One p ...
**
Bartell mechanism The Bartell mechanism is a pseudorotational mechanism similar to the Berry mechanism. It occurs only in molecules with a pentagonal bipyramidal molecular geometry, such as IF7. This mechanism was first predicted by H. B. Bartell. The mechanism exch ...
**
Berry mechanism The Berry mechanism, or Berry pseudorotation mechanism, is a type of vibration causing molecules of certain geometries to isomerize by exchanging the two axial ligands (see Figure at right) for two of the equatorial ones. It is the most widely ac ...
**
Ray–Dutt twist The Ray–Dutt twist is a mechanism proposed for the racemization of octahedral complexes containing three bidentate chelate rings. Such complexes typically adopt an octahedral molecular geometry in their ground states, in which case they posses ...


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''. *Philip R. Bunker and Per Jensen, ''Molecular Symmetry and Spectroscopy'', 2nd edition, NRC Research Press, Ottawa, 199

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References

{{Reflist Chemical bond properties