Name: frost circle for pi orbital energies
Uploaded: 2023-04-30T10:31:15.000Z
Duration: 1 min 8 s
Channel: JoVE

Die Methode des Frostkreises oder des eingeschriebenen Polygons ist ein grafisches Verfahren, das auf der Hückelschen Regel basiert, um die Anzahl und die relativen Energien der π Molekülorbitale von planaren, monozyklischen und konjugierten Systemen zu bestimmen.
Ein Frostkreis wird gezeichnet, indem ein Polygon, das die zyklische Verbindung darstellt, in einen Kreis eingeschrieben wird, wobei einer der Eckpunkte nach unten zeigt.
Die Schnittpunkte, an denen der Kreis das Polygon berührt, sind durch kurze horizontale Linien markiert, die die Anzahl und die relativen Energien π Molekülorbitale darstellen.
Als Nächstes wird eine gestrichelte horizontale Linie durch den Mittelpunkt des Kreises gezogen, die das Polygon halbiert. Diese Linie stellt die Energie der beteiligten p-Orbitale dar.
Alle Molekülorbitale mit Energien unterhalb dieser Linie sind bindend, die oberhalb der Linie sind antibindend und die Molekülorbitale auf der Linie sind nicht bindende Molekülorbitale.
Zuletzt werden die π Elektronen nach der Hundschen Regel und dem Pauli-Ausschlussprinzip zu den Energieniveaus addiert.

hückels regeldiagramm von π mos: frostkreis

H&uuml;ckel's Rule Diagram of &pi; MOs: Frost Circle

Die Frostkreis- oder Inskriptionspolygon-Methode ist eine grafische Methode zur Bestimmung der relativen Energien von π-Molekülorbitalen (MOs) für planare, vollständig konjugierte und monocyclische Verbindungen. Diese Methode wurde erstmals von A. A. Frost und Boris Musulin im Jahr 1953 beschrieben.

Ein Frostkreis wird konstruiert, indem ein Polygon gezeichnet wird, dessen Anzahl der Kanten der Anzahl der Kohlensubstanzen des gegebenen cyclischen Systems entspricht, wobei einer der Scheitelpunkte nach unten zeigt. Dann wird ein Kreis gezeichnet, der das Polygon so umschließt, dass alle Eckpunkte des Polygons den Kreis berühren. Die Punkte, an denen der Kreis das Polygon berührt, werden mit kurzen horizontalen Linien markiert, die die Energieniveaus von π-Molekülorbitalen darstellen.

<img alt="Figure1" src="/files/ftp_upload/12454/12454_PT-Figure_1.png" style="text-align: center; height: 250px;">

Anschließend wird eine gestrichelte horizontale Linie durch den Mittelpunkt des Kreises gezogen, die das Polygon halbiert. Die Energieniveaus unterhalb dieser Linie stehen für bindende Molekülorbitale, die oberhalb dieser Linie für antibindende Molekülorbitale. Die Energieniveaus auf der Linie stellen nichtbindende Molekülorbitale dar, wobei die Energie den p-Orbitalen entspricht, aus denen die Molekülorbitale gebildet werden.

Schließlich werden die π-Elektronen zu den Energieniveaus hinzugefügt, beginnend mit dem niedrigsten und aufsteigend. Die entarteten Orbitale werden zunächst mit einem einzelnen Elektron aufgefüllt und dann mit einem anderen Elektron gepaart, sofern verfügbar, wobei das Pauli-Ausschlussprinzip und die Hund'schen Regeln beachtet werden.

Hückels Regeldiagramm von π MOs: Frostkreis

Die Frostkreis- oder Inscribed-Polygon-Methode ist eine grafische Methode zur Bestimmung der relativen Energien von π Molekülorbitalen (MOs) für ...

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frost circle for pi orbital energies

The Frost circle is a graphical method for showing the relative energies of pi molecular orbitals in planar, fully conjugated, monocyclic compounds. It is also called the inscribed polygon method. A. A. Frost and Boris Musulin first described this method in 1953.

To build a Frost circle, draw a polygon with the same number of edges as the number of carbons in the cyclic system. Place one vertex pointing downward. Then draw a circle around the polygon so that every vertex touches the circle. Mark the touch points with short horizontal lines. These lines show the energy levels of the pi molecular orbitals.

Next, draw a dashed horizontal line through the center of the circle. This line divides the energy levels into bonding, non-bonding, and antibonding orbitals. Levels below the line are bonding molecular orbitals. Levels above the line are antibonding molecular orbitals. The levels on the line are non-bonding molecular orbitals, and they have the same energy as the p orbitals that form them.

Finally, place the pi electrons into the energy levels from lowest to highest. If two orbitals have the same energy, they are degenerate orbitals. Fill each degenerate orbital with one electron first, then pair the electrons if more are available. This follows Pauli’s exclusion principle and Hund’s rules.

Frost Circle for Pi Orbital Energies

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h&uuml;ckel's rule diagram of &pi; mos: frost circle

The Frost circle is a graphical method for showing the relative energies of pi molecular orbitals in planar, fully conjugated, monocyclic compounds. It is also called the inscribed polygon method. A. A. Frost and Boris Musulin first described this method in 1953. To build a Frost circle, draw a polygon with the same number of edges as the number of carbons in the cyclic system. Place one vertex pointing downward. Then draw a circle around the polygon so that every vertex touches the circle.

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Learn how the Frost circle maps pi molecular orbital energies in planar conjugated rings, from drawing the polygon to filling bonding, non-bonding, and antibonding levels.

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Frost Circle for Pi Orbital Energies

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