Walsh model

The Walsh model is a model first developed by Arthur Donald Walsh for cyclopropane , which is based on the molecular orbital concept of chemical bonding .

prehistory

The geometry and reactivity of cyclopropane could be approximately explained by the Baeyer model and the model of the curved bonds ( banana bonds ). However, these models have weak points; the electrophilic addition reactions characteristic of cyclopropane cannot be interpreted satisfactorily in this way. Therefore, in 1947, Walsh proposed a different explanation.

Creation and energy levels

Walsh's cyclopropane model is constructed by bringing three trigonal CH ₂ groups together in such a way that the plane formed by the two hydrogen atoms and the carbon atom of the methylene groups is perpendicular to the plane of the three-membered ring. In the plane of the three ring then the 2p are _such atomic orbitals (2p _z -AO) of the sp ² -hybridized CH ₂ group and a "flap" of sp ² - hybrid orbital .

Construction of the orbitals of the cyclopropane molecule from the orbitals of the three CH ₂ groups.
Above: sp ² -hybridized CH ₂ group.
Below: the CC bonds in cyclopropane

The molecular orbitals (MOs) of the cyclopropane are formed from the orbitals of the segments (–CH ₂ -) by linear combination . Three MOs of cyclopropane are obtained by linear combination of the three lobes of the sp ² hybrid orbitals (φ ₁ , φ ₂ and φ ₃ ) pointing into the interior of the three-membered ring . Three more molecular orbitals are obtained by linear combination of the 2p _z -AOs (Φ ₁ , Φ ₂ and Φ ₃ ).

From these two sets of the base orbitals φ ₁ , φ ₂ and φ ₃ (sp ² type), as well as Φ ₁ , Φ ₂ and Φ ₃ (2p type), one obtains the following wave functions of the three by linear combination (secular determinant 3rd order) MOs:

${\displaystyle \psi _{1}={\frac {1}{\sqrt {3}}}(\varphi _{1}+\varphi _{2}+\varphi _{3})}$

${\displaystyle \psi _{2}={\frac {1}{\sqrt {2}}}(\varphi _{1}-\varphi _{2})}$

${\displaystyle \psi _{3}={\frac {1}{\sqrt {6}}}(\varphi _{1}+\varphi _{2}-2\varphi _{3})}$

such as

${\displaystyle \Psi _{1}={\frac {1}{\sqrt {3}}}(\Phi _{1}+\Phi _{2}+\Phi _{3})}$

${\displaystyle \Psi _{2}={\frac {1}{\sqrt {2}}}(\Phi _{1}-\Phi _{2})}$

${\displaystyle \Psi _{3}={\frac {1}{\sqrt {6}}}(\Phi _{1}+\Phi _{2}-2\Phi _{3})}$

Three schematic molecular orbitals of cyclopropane, first set (within the edges of the hypothetical triangle). From left to right: ψ ₁ , ψ ₂ and ψ ₃ . The red filling means positive sign (+), unfilled negative (-)

Three schematic molecular orbitals of cyclopropane, second set (outside the edges of the hypothetical triangle). From left to right: Ψ ₁ , Ψ ₂ and Ψ ₃ . Blue: positive, green: negative sign

With the simplified representations customary in organic chemistry - the "expansion" of the orbitals is not taken into account - these molecular orbitals can be made clear.

Energies of the MOs according to the Walsh model (relative, no scale).
Below the lower energy bonding MOs that are occupied, above the antibonding MOs

The molecular orbitals Ψ ₂ and Ψ ₃ , as well as ψ ₂ and ψ ₃ are each of the same energy ( "degenerate" , see adjacent picture). Of the six introduced electrons, two electrons occupy the MO ψ ₁ . The probability of your presence is the “three-lobed area” inside the cyclopropane ring. These electrons are most firmly bound. MOs ψ ₂ and ψ ₃ are not occupied; they are quite strongly antibonding (along the CC bonds the number of nodes is greater than the number of bonding interactions). With the set of MOs Ψ ₁ , Ψ _2, and Ψ ₃ , the situation is exactly the opposite of that for the MOs just discussed: Ψ ₁ is antibonding (three changes of sign along the CC bonds), while Ψ ₂ and Ψ _{3 are} overall binding. Ψ ₂ and Ψ ₃ are therefore of the lowest energy; these two MOs are occupied by 4 electrons. The probability of these electrons being located at the periphery of the three-membered ring is particularly high; these are the more reactive “valence electrons” of cyclopropane. The bonds in the molecular orbitals Ψ ₂ and Ψ ₃ are somewhat similar to the π bonds in ethene . They have both σ and π character. The size of the overlap lies between the low value for the pure p-π-overlap in ethene and the strong σ-overlap of the sp ³ -orbitals in “saturated” hydrocarbons.

The calculated energies of the molecular orbitals and their occupation by electrons can be shown in a schematic picture.

In the context of the frontier orbital concept of chemical reactivity ( HOMO / LUMO ), the molecular orbitals Ψ ₂ and Ψ _{3 of} cyclopropane are the energetically highest occupied orbitals (HOMOs). They interact with protons and the LUMOs of electrophilic reagents.

The Walsh model thus allows both a π bond , which holds the small ring molecule together despite the unfavorable angle, and an occupied p orbital, which is relatively less energetic, which explains the reactivity of the ring molecule.

Weak points

Although the Walsh model was / is very popular among organic chemists, it has weaknesses that have been pointed out several times. The orbitals according to Walsh are not equivalent to the orbitals according to the Förster-Coulson-Moffitt model . For detailed criticism, reference must be made to the original literature.

Further development

Hückel approximation , Möbius aromatics and Hellmann-Feynman theorem are further concepts that have been incorporated into the topic and the further development of this model. It was not until 1986 that Dewar, when looking at the molecular orbital, pointed out the σ-component typical of aromatics with their delocalized double bonds , which can nevertheless justify an anomaly in the tension energy of cyclopropane, which is not an aromatic. Calculations of the Laplace distribution of the electrons confirmed their higher density in the middle of the three atomic nuclei.

literature

• Martin Klessinger: Electronic structure of organic molecules. Verlag Chemie, Weinheim u. a. 1982, ISBN 3-527-25925-2 , pp. 101ff, pp. 264-266.
• AD Walsh: Structures of Ethylene Oxide and Cyclopropane . In: Nature . tape 159 , no. 4031 , 1947, pp. 165-165 , doi : 10.1038 / 159165a0 .

Individual evidence

1. ^ AD Walsh: The structures of ethylene oxide, cyclopropane, and related molecules . In: Transactions of the Faraday Society . 45, 1949, pp. 179-190, doi: 10.1039 / TF9494500179 .
2. ↑ See e.g. BHR Christen, F. Vögtle: Organic Chemistry - From the Basics to Research. Vol. 2, 1st edition. Otto Salle Verlag, Frankfurt a. Main 1990, ISBN 3-7935-5398-1 , pp. 284-285.
3. ↑ E. Honegger, E. Heilbronner, A. Schmelzer In: Nouveau Journal de Chimie. 6: 519 (1982).
4. ^ KB Wiberg: Structures, energies and spectra of cyclopropanes . In: Zvi Rappoport (Ed.): Patai's Chemistry of Functional Groups. The Chemistry of the Cyclopropyl Group. Wiley, Chichester et al. 1987, pp. 1-4.
5. ↑ D. Cremer, E. Kraka, KJ Szabo: General and Theoretical Aspects of the Cyclopropyl Group . In: Zvi Rappoport (Ed.): Patai's Chemistry of Functional Groups. The chemistry of the cyclopropyl group. Volume 2, Wiley, Chichester 1995, ISBN 0-471-94074-7 . doi: 10.1002 / 9780470682531.pat0028 .
6. ↑ Wolfgang W. Schoeller, Thomas Dabisch: Substituent effects on the bonding properties in cyclotriphosphanes and related compounds. Polarization of Hückel versus Möbius orbitals . In: Journal of the Chemical Society, Dalton Transactions . tape 0 , no. 11 , 1983, pp. 2411-2413 , doi : 10.1039 / DT9830002411 .
7. ↑ Vincenzo Barone, Sándor Fliszár: Theoretical energies of representative carbon-carbon bonds. In: International Journal of Quantum Chemistry. Volume 55, No. 6, 1995, pp. 469-476, doi: 10.1002 / qua.560550605 .
8. ^ Francis A. Carey, Richard J. Sundberg: Advanced Organic Chemistry: Reactions and synthesis. 2005, p. 85ff ( limited preview in Google Book Search).