In
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, fluxional (or non-rigid) molecules are
molecules that undergo dynamics such that some or all of their
atoms interchange between symmetry-equivalent positions. Because virtually all molecules are fluxional in some respects, e.g.
bond rotations in most
organic compounds, 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
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 and other methods.
Spectroscopic studies
Many
organometallic compounds 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 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. One example is
electron transfer 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:
:
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. 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, by which the axial and equatorial fluorine atoms rapidly exchange positions.
Iron pentacarbonyl (Fe(CO)
5) follows the pattern set for PF
5: 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 ...
(SF
4), a similar pattern is observed even though this compound has only four ligands.
A well-studied fluxional ion is the
methanium ion, which is protonated methane, .
In this unusual species, whose
IR spectrum
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 function ...
was experimentally observed
and understood, the barriers to proton exchange are lower than the
zero-point energy. 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 CH
4, 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, 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(SiMe
3)
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 (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:
:
where Δν
o 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 Δν
o = 1ppm @ 500 MHz
:
(ca. 0.5 millisecond
half-life)
"Ring whizzing"
The compound Fe(η
5-C
5H
5)(η
1-C
5H
5)(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 η
5-C
5H
5 and the other assigned η
1-C
5H
5. The singlet assigned to the η
1-C
5H
5 ligand splits at low temperatures owing to the slow hopping of the Fe center from carbon to carbon in the η
1-C
5H
5 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, a fluxional molecule
*
*
*
Pseudorotation
**
Bailar twist
**
Bartell mechanism
**
Berry mechanism
**
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 possess ...
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