Frost Musulin Circle

Do not confuse this article with Frost Diagram

The frost circle is a simple graphical aid for recognizing or illustrating the aromatic character of an unsaturated monocycle . It was developed by the American chemist Arthur A. Frost and Boris Musulin , and named after Frost ( English Frost’s Circle ). He estimates the relative orbital energies for planar, monocyclic and fully conjugated molecules.

Hückel rule

With the beginning of quantum chemistry in the first half of the 20th century, some aromaticity criteria were developed. Erich Hückel found an important result of his theoretical work in the 1930s. According to the Hückel rule :

• Monocyclic planar molecules with (4n + 2) π electrons are aromatic.
• The π electrons are characterized by the fact that they are located above and below, but not in the molecular plane of the planar aromatic .

The experimentally observed special stability of benzene (empirical formula: C ₆ H ₆ ), the prototype of an aromatic compound, explained Hückel with the double occupation of all available binding molecular orbitals with (4 · 1 + 2 = 6) π electrons. According to the LCAO method, the atomic orbitals of the atoms involved are "mixed" (mathematical linear combinations of the solutions to the Schrödinger equation ). They split up into binding, non-binding and antibonding molecular orbitals, which are then filled up according to Hund's rules as the energy increases .

Construction of the Frost Circle

A circle is drawn around the n-cycle, drawn with a point downwards. Frost calls the radius of this circle 2β. The relative orbital energies of the orbitals m = 0 - n result from the formula sin ( m  · 360 ° / n  - 90 °) · 2β or sin ( m  · 2 π / n  - π / 2) · 2β.

Example cyclopropenyl cation / anion

Starting with an energy diagram, a circle with the radius 2β is drawn around the abscissa . The n-cycle, one point downwards, is inscribed in this circle. The points of contact between the n-cycle and the circle reflect the relative energy of the molecular orbitals:

According to Hückel, such a system should be aromatic if all available bonding orbitals are doubly occupied (see above).

The cyclopropenyl cation C ₃ H ₃ ⁺ should be aromatic. The energy gain ΔE due to the delocalization is 2e ^- · (−2β) = −4β. For the cyclopropenyl anion C ₃ H ₃ ^- , because of the single occupancy of the top two orbitals, according to Hund's rule, a diradical structure results , ΔE = β + β - 2β = 0.

Example cyclobutadiene

Delocalization of the π electrons would result in a diradical structure; Cyclobutadiene is not aromatic, see also other references.

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1. ↑ Arthur A. Frost, Boris Musulin: A Mnemonic Device for Molecular Orbital Energies . In: The Journal of Chemical Physics . tape 21 , no. 3 , December 20, 2004, p. 572-573 , doi : 10.1063 / 1.1698970 .
2. ^ Nguyên Trong Anh: The Woodward-Hofmann rule and its application . Verlag Chemie, Weinheim 1972, ISBN 3-527-25430-7 .
3. ↑ Aromatic Compounds (Overview) . Chemgapedia.
4. ^ Hückel-MO: aromatics, Hückel rule . Chemgapedia.