Möbius aromaticity
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In
organic chemistry Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
, Möbius aromaticity is a special type of
aromaticity In chemistry, aromaticity is a chemical property of cyclic ( ring-shaped), ''typically'' planar (flat) molecular structures with pi bonds in resonance (those containing delocalized electrons) that gives increased stability compared to saturate ...
believed to exist in a number of
organic molecule 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 ...
s. In terms of
molecular orbital theory In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. In molecular orbital theory, electrons in a molecule ...
these compounds have in common a monocyclic array of
molecular orbital In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding ...
s in which there is an odd number of out-of-phase overlaps, the opposite pattern compared to the aromatic character to Hückel systems. The nodal plane of the orbitals, viewed as a ribbon, is a
Möbius strip In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and Augu ...
, rather than a cylinder, hence the name. The pattern of orbital energies is given by a rotated Frost circle (with the edge of the polygon on the bottom instead of a vertex), so systems with 4''n'' electrons are aromatic, while those with 4''n'' + 2 electrons are anti-aromatic/non-aromatic. Due to incrementally twisted nature of the orbitals of a Möbius aromatic system, stable Möbius aromatic molecules need to contain at least 8 electrons, although 4 electron Möbius aromatic transition states are well known in the context of the Dewar-Zimmerman framework for
pericyclic reaction In organic chemistry, a pericyclic reaction is the type of organic reaction wherein the transition state of the molecule has a cyclic geometry, the reaction progresses in a concerted fashion, and the bond orbitals involved in the reaction overlap ...
s. Möbius molecular systems were considered in 1964 by
Edgar Heilbronner Edgar Heilbronner (13 May 1921 – 28 August 2006) was a Swiss German chemist. In 1964 he published the concept of Möbius cyclic annulenes, but the first Möbius aromatic was not synthesized until 2003.On Molecular Orbital Correlation Dia ...
by application of the
Hückel method The Hückel method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear combinations of atomic orbitals. The theory predicts the molecular orbitals for π-electro ...
, but the first such isolable compound was not synthesized until 2003 by the group of Rainer Herges. However, the fleeting ''trans-''C9H9+ cation, one conformation of which is shown on the right, was proposed to be a Möbius aromatic reactive intermediate in 1998 based on computational and experimental evidence.


Hückel-Möbius aromaticity

The Herges compound (6 in the image below) was synthesized in several
photochemical Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400  nm), visible light (400–7 ...
cycloaddition In organic chemistry, a cycloaddition is a chemical reaction in which "two or more Unsaturated hydrocarbon, unsaturated molecules (or parts of the same molecule) combine with the formation of a cyclic adduct in which there is a net reduction of th ...
reactions from tetradehydrodianthracene 1 and the
ladderane In chemistry, a ladderane is an organic molecule containing two or more fused cyclobutane rings. The name arises from the resemblance of a series of fused cyclobutane rings to a ladder. Numerous synthetic approaches have been developed for the synt ...
syn-tricyclooctadiene 2 as a substitute for
cyclooctatetraene 1,3,5,7-Cyclooctatetraene (COT) is an unsaturated derivative of cyclooctane, with the formula C8H8. It is also known as nnulene. This polyunsaturated hydrocarbon is a colorless to light yellow flammable liquid at room temperature. Because of ...
. : Intermediate 5 was a mixture of 2
isomer In chemistry, isomers are molecules or polyatomic ions with identical molecular formulae – that is, same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism is existence or possibility of isomers. Iso ...
s and the final product 6 a mixture of 5 isomers with different cis and trans configurations. One of them was found to have a C2
molecular symmetry Molecular symmetry in chemistry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain m ...
corresponding to a Möbius aromatic and another Hückel isomer was found with Cs symmetry. Despite having 16 electrons in its pi system (making it a 4n
antiaromatic Antiaromaticity is a chemical property of a cyclic molecule with a π electron system that has higher energy, i.e., it is less stable due to the presence of 4n delocalised (π or lone pair) electrons in it, as opposed to aromaticity. Unlike aroma ...
compound) the Heilbronner prediction was borne out because according to Herges the Möbius compound was found to have aromatic properties. With
bond length In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of ...
s deduced from
X-ray crystallography X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
a
HOMA Homa may refer to: Places Ethiopia * Homa (woreda), a district in Oromia Region, Ethiopia Kenya * Homa Bay, a town and a bay on the shore of Lake Victoria in Kenya * Homa Mountain, a volcano near Homa Bay, Kenya Iran * Chal Homa, Mark ...
value was obtained of 0.50 (for the
polyene In organic chemistry, polyenes are poly- unsaturated, organic compounds that contain at least three alternating double () and single () carbon–carbon bonds. These carbon–carbon double bonds interact in a process known as conjugation, resultin ...
part alone) and 0.35 for the whole compound which qualifies it as a moderate aromat. It was pointed out by
Henry Rzepa Henry Stephen Rzepa (born 1950) is a chemist and Emeritus Professor of Computational chemistry at Imperial College London. Education Rzepa was born in London in 1950, was educated at Wandsworth Comprehensive School, and then entered the chemi ...
that the conversion of intermediate 5 to 6 can proceed by either a Hückel or a Möbius
transition state In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked wi ...
. : The difference was demonstrated in a hypothetical
pericyclic In organic chemistry, a pericyclic reaction is the type of organic reaction wherein the transition state of the molecule has a cyclic geometry, the reaction progresses in a concerted fashion, and the bond orbitals involved in the reaction overlap ...
ring opening reaction to
cyclododecahexaene Cyclododecahexaene or 2nnulene () is a member of the series of annulenes with some interest in organic chemistry with regard to the study of aromaticity. Cyclododecahexaene is non-aromatic due to the lack of planarity of the structure. On the ot ...
. The Hückel TS (left) involves 6 electrons (arrow pushing in red) with Cs
molecular symmetry Molecular symmetry in chemistry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain m ...
conserved throughout the reaction. The ring opening is
disrotatory An electrocyclic reaction can either be classified as conrotatory or disrotatory based on the rotation at each end of the molecule. In conrotatory mode, both atomic orbitals of the end groups turn in the same direction (such as both atomic orbital ...
and
suprafacial Antarafacial ( Woodward-Hoffmann symbol a) and suprafacial (s) are two topological concepts in organic chemistry describing the relationship between two simultaneous chemical bond making and/or bond breaking processes in or around a reaction center ...
and both
bond length In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of ...
alternation and NICS values indicate that the 6 membered ring is aromatic. The Möbius TS with 8 electrons on the other hand has lower computed
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
and is characterized by C2 symmetry, a
conrotatory An electrocyclic reaction can either be classified as conrotatory or disrotatory based on the rotation at each end of the molecule. In conrotatory mode, both atomic orbitals of the end groups turn in the same direction (such as both atomic orbital ...
and
antarafacial Antarafacial ( Woodward-Hoffmann symbol a) and suprafacial (s) are two topological concepts in organic chemistry describing the relationship between two simultaneous chemical bond making and/or bond breaking processes in or around a reaction center ...
ring opening and 8-membered ring aromaticity. Another interesting system is the cyclononatetraenyl cation explored for over 30 years by Paul v. R. Schleyer et al. This
reactive intermediate In chemistry, a reactive intermediate or an intermediate is a short-lived, high-energy, highly reactive molecule. When generated in a chemical reaction, it will quickly convert into a more stable molecule. Only in exceptional cases can these comp ...
is implied in the
solvolysis In chemistry, solvolysis is a type of nucleophilic substitution (S1/S2) or elimination where the nucleophile is a solvent molecule. Characteristic of S1 reactions, solvolysis of a chiral reactant affords the racemate. Sometimes however, the ster ...
of the
bicyclic In chemistry, a bicyclic molecule () is a molecule that features two joined rings. Bicyclic structures occur widely, for example in many biologically important molecules like α-thujene and camphor. A bicyclic compound can be carbocyclic (all o ...
chloride The chloride ion is the anion (negatively charged ion) Cl−. It is formed when the element chlorine (a halogen) gains an electron or when a compound such as hydrogen chloride is dissolved in water or other polar solvents. Chloride salts ...
9-deutero-9'-chlorobicyclo .1.0nonatriene 1 to the
indene Indene is a flammable polycyclic hydrocarbon with chemical formula . It is composed of a benzene ring fused with a cyclopentene ring. This aromatic liquid is colorless although samples often are pale yellow. The principal industrial use of in ...
dihydroindenol 4. The starting chloride is
deuterated 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 ...
in only one position but in the final product deuterium is distributed at every available position. This observation is explained by invoking a twisted 8-electron cyclononatetraenyl cation 2 for which a NICS value of -13.4 (outsmarting
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms, ...
) is calculated. A more recent study, however, suggests that the stability of ''trans''-C9H9+ is not much different in energy compared to a Hückel topology isomer. The same study suggested that for 3nnulenyl cation, the Möbius topology penta-''trans''-C13H13+ is a global energy minimum and predicts that it may be directly observable. : In 2005 the same P. v. R. Schleyer questioned the 2003 Herges claim: he analyzed the same crystallographic data and concluded that there was indeed a large degree of bond length alternation resulting in a HOMA value of -0.02, a computed NICS value of -3.4 ppm also did not point towards aromaticity and (also inferred from a computer model)
steric strain Van der Waals strain is strain resulting from Van der Waals repulsion when two substituents in a molecule approach each other with a distance less than the sum of their Van der Waals radii. Van der Waals strain is also called Van der Waals repuls ...
would prevent effective pi-orbital overlap. A Hückel-Möbius aromaticity switch (2007) has been described based on a 28 pi-electron
porphyrin Porphyrins ( ) are a group of heterocyclic macrocycle organic compounds, composed of four modified pyrrole subunits interconnected at their α carbon atoms via methine bridges (=CH−). The parent of porphyrin is porphine, a rare chemical com ...
system: : The
phenylene In organic chemistry, the phenylene group () is based on a di-substituted benzene ring ( arylene). For example, poly(''p''-phenylene) is a polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material cons ...
rings in this molecule are free to rotate forming a set of
conformers In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds (refer to figure on single bond rotation). While any two arrangements of atoms in a molec ...
: one with a Möbius half-twist and another with a Hückel double-twist (a figure-eight configuration) of roughly equal energy. In 2014, Zhu and Xia (with the help of Schleyer) synthesized a planar Möbius system that consisted of two pentene rings connected with an osmium atom. They formed derivatives where osmium had 16 and 18 electrons and determined that Craig–Möbius aromaticity is more important for the stabilization of the molecule than the metal's electron count.


Transition states

In contrast to the rarity of Möbius aromatic ''ground state'' molecular systems, there are many examples of
pericyclic In organic chemistry, a pericyclic reaction is the type of organic reaction wherein the transition state of the molecule has a cyclic geometry, the reaction progresses in a concerted fashion, and the bond orbitals involved in the reaction overlap ...
''transition states'' that exhibit Möbius aromaticity. The classification of a pericyclic transition state as either Möbius or Hückel topology determines whether 4''N'' or 4''N'' + 2 electrons are required to make the transition state aromatic or antiaromatic, and therefore, allowed or forbidden, respectively. Based on the energy level diagrams derived from Hückel MO theory, (4''N'' + 2)-electron Hückel and (4''N'')-electron Möbius transition states are aromatic and allowed, while (4''N'' + 2)-electron Möbius and (4''N'')-electron Hückel transition states are antiaromatic and forbidden. This is the basic premise of the Möbius-Hückel concept.


Derivation of Hückel MO theory energy levels for Möbius topology

From the figure above, it can also be seen that the interaction between two consecutive p_z AOs is attenuated by the incremental twisting between orbitals by \cos\omega, where \omega=\pi/N is the angle of twisting between consecutive orbitals, compared to the usual Hückel system. For this reason resonance integral \beta^\prime is given by :\beta^\prime=\beta\cos(\pi/N), where \beta is the standard Hückel resonance integral value (with completely parallel orbitals). Nevertheless, after going all the way around, the ''N''th and 1st orbitals are almost completely out of phase. (If the twisting were to continue after the Nth orbital, the (N+1)st orbital would be exactly phase-inverted compared to the 1st orbital). For this reason, in the Hückel matrix the resonance integral between carbon 1 and N is -\beta^\prime.
For the generic N carbon Möbius system, the Hamiltonian matrix \mathbf is: : \mathbf= \begin \alpha& \beta' & 0 &\cdots& -\beta' \\ \beta' & \alpha& \beta' & \cdots & 0 \\ 0 & \beta' & \alpha & \cdots & 0 \\ \vdots &\vdots &\vdots &\ddots &\vdots \\ -\beta' &0& 0 & \cdots & \alpha \end . Eigenvalues for this matrix can now be found, which correspond to the energy levels of the Möbius system. Since \mathbf is a N\times N matrix, we will have N eigenvalues E_k and N MOs. Defining the variable :x_k=\frac, we have: : \begin x_k& 1 & 0 &\cdots& -1 \\ 1 & x_k& 1 & \cdots & 0 \\ 0 & 1 & x_k & \cdots & 0 \\ \vdots &\vdots &\vdots &\ddots &\vdots \\ -1 &0& 0 & \cdots & x_k \end \cdot \begin c_1^ \\ c_2^ \\ c_3^ \\ \vdots\\ c_N^ \\ \end=0 . To find nontrivial solutions to this equation, we set the determinant of this matrix to zero to obtain : x_k=-2\cos . Hence, we find the energy levels for a cyclic system with Möbius topology, : E_k=\alpha+2\beta^\prime\cos\quad (k=0,1,\ldots, \lceil N/2 \rceil-1) . In contrast, recall the energy levels for a cyclic system with Hückel topology, : E_k=\alpha+2\beta\cos\quad (k=0,1,\ldots, \lfloor N/2 \rfloor) .


See also

*
Barrelene Barrelene is a bicyclic organic compound with chemical formula C8H8 and systematic name bicyclo .2.2cta-2,5,7-triene. First synthesized and described by Howard Zimmerman in 1960, the name derives from the resemblance to a barrel, with the staves b ...
*
Baird's rule In organic chemistry, Baird's rule estimates whether the lowest triplet state of planar, cyclic structures will have aromatic properties or not. The quantum mechanical basis for its formulation was first worked out by physical chemist N. Colin Bai ...
* Bicycloaromaticity


References

{{DEFAULTSORT:Mobius Aromaticity Physical organic chemistry