Frontier Molecular Orbital Theory
Encyclopedia
In chemistry
, frontier molecular orbital theory is an application of MO theory describing HOMO
/ LUMO
interactions.
published a paper in the Journal of Chemical Physics titled "A molecular theory of reactivity in aromatic hydrocarbons." Though widely criticized at the time, he later shared the Nobel Prize in Chemistry with Roald Hoffmann
for his work on reaction mechanisms. Hoffman's work focused on creating a set of four pericyclic reactions in organic chemistry, based on orbital symmetry, which he coauthored with Robert Burns Woodward
entitled, "The Conservation of Orbital Symmetry."
Fukui's own work looked at the frontier orbitals, and in particular the effects of the Highest Occupied Molecular Orbital (HOMO
) and the Lowest Unoccupied Molecular Orbital (LUMO
) on reaction mechanisms, which led to it being called Frontier Molecular Orbital Theory (FMO Theory). He used these interactions to better understand the conclusions of the Woodward–Hoffmann rules.
). This was based on three main observations of molecular orbital theory as two molecules interact:
From these observations, frontier molecular orbital (FMO) theory simplifies reactivity to interactions between the HOMO of one species and the LUMO of the
other. This helps to explain the predictions of the Woodward–Hoffmann rules for thermal pericyclic reactions, which are summarized in the following statement:
(4q+2)s refers to the number of aromatic, suprafacial electron systems; likewise, (4r)a refers to antiaromatic, antarafacial systems. It can be shown that if the total number of these systems is odd then the reaction is thermally allowed.
is a reaction that simultaneously forms at least two new bonds, and in doing so, converts two or more open-chain molecules into rings. The transition state
s for these reactions typically involves the electrons of the molecules moving in continuous rings, making it a pericyclic reaction
. These reactions can be predicted by the Woodward–Hoffmann rules and thus are closely approximated by FMO Theory.
The Diels–Alder reaction between maleic anhydride
and cyclopentadiene
is allowed by the Woodward–Hoffmann rules because there are six electrons moving suprafacially and no electrons moving antarafacially. Thus, there is one (4q + 2)s component and no (4r)a component, which means the reaction is allowed thermally.
FMO theory also finds that this reaction is allowed and goes even further by predicting its stereoselectivity
, which is unknown under the Woodward-Hoffmann rules. Since this is a [4 + 2], the reaction can be simplified by considering the reaction between butadiene and ethene. The HOMO of butadiene and the LUMO of ethene are both antisymmetric (rotationally symmetric), meaning the reaction is allowed.*
In terms of the stereoselectivity of the reaction between maleic anhydride and cyclopentadiene, the endo
-product is favored, a result best explained through FMO theory. The maleic anhydride is an electron-withdrawing species that makes the dieneophile electron deficient, forcing the regular Diels–Alder reaction. Thus, only the reaction between the HOMO of cyclopentadiene and the LUMO of maleic anhydride is allowed. Furthermore, though the exo
-product is the more thermodynamically stable isomer, there are secondary (non-bonding) orbital interactions in the endo- transition state, lowering its energy and making the reaction towards the endo- product faster, and therefore more kinetically favorable. Since the exo-product has primary (bonding) orbital interactions it can still form, but since the endo-product forms faster it is the major product.
*Note: The LUMO of ethene and the HOMO of butadiene are both symmetric, meaning the reaction between these species is allowed as well. This is referred to as the "inverse electron demand Diels–Alder."
is a reaction in which a sigma bond moves across a conjugated pi system with a concomitant shift in the pi bonds. The shift in the sigma bond may be antarafacial or suprafacial. In the example of a [1,5] shift in pentadiene, if there is a suprafacial shift, there is 6 e− moving suprafacially and none moving antarafacially, implying this reaction is allowed by the Woodward–Hoffmann rules. For an antarafacial shift, the reaction is not allowed.
These results can be predicted with FMO theory by observing the interaction between the HOMO and LUMO of the species. To use FMO theory, the reaction should be considered as two separate ideas: (1) whether or not the reaction is allowed, and (2) which mechanism the reaction proceeds though. In the case of a [1,5] shift on pentadiene, the HOMO of the sigma bond (i.e. a constructive bond) and the LUMO of butadiene on the remaining 4 carbons is observed. Assuming the reaction happens suprafacially, the shift results with the HOMO of butadiene on the 4 carbons that are not involved in the sigma bond of the product. Since the pi system changed from the LUMO to the HOMO, this reaction is allowed (though it would not be allowed if the pi system went from LUMO to LUMO).
To explain why the reaction happens suprafacially, first notice that the terminal orbitals are in the same phase. For there to be a constructive sigma bond formed after the shift, the reaction would have to be suprafacial. If the species shifted antarafacially then it would form an antibonding
orbital and there would not be a constructive sigma shift.
It is worth noting that in propene the shift would have to be antarafacial, but since the molecule is very small that twist is not possible and the reaction is not allowed.
is a percyclic reaction involving the net loss of a pi bond and creation of a sigma bond with formation of a ring. This reaction proceeds through either a conrotatory or disrotatory
mechanism. In the conrotatory ring opening of cyclobutene, there are two electrons moving suprafacially (on the pi bond) and two moving antarafacially (on the sigma bond). This means there is one 4q + 2 suprafacial system and no 4r antarafacial system; thus the conrotatory process is thermally allowed by the Woodward–Hoffmann rules.
The HOMO of the sigma bond (i.e. a constructive bond) and the LUMO of the pi bond are important in the FMO theory consideration. If the ring opening uses a conrotatory process then the reaction results with the HOMO of butadiene. As in the previous examples the pi system moves from a LUMO species to a HOMO species, meaning this reaction is allowed.
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, frontier molecular orbital theory is an application of MO theory describing HOMO
Homo
Homo may refer to:*the Greek prefix ὅμο-, meaning "the same"*the Latin for man, human being*Homo, the taxonomical genus including modern humans...
/ LUMO
Lumo
Lumo is a 2007 documentary film about twenty-year-old Lumo Sinai, a woman who fell victim to "Africa's First World War." While returning home one day, Lumo and another woman were gang-raped by a group of soldiers fighting for control of the Democratic Republic of the Congo during the 1994 Rwandan...
interactions.
History
In 1952, Kenichi FukuiKenichi Fukui
Kenichi Fukui was a Japanese chemist.Kenichi Fukui was co-recipient of the Nobel Prize in Chemistry in 1981 with Roald Hoffmann, for their independent investigations into the mechanisms of chemical reactions...
published a paper in the Journal of Chemical Physics titled "A molecular theory of reactivity in aromatic hydrocarbons." Though widely criticized at the time, he later shared the Nobel Prize in Chemistry with Roald Hoffmann
Roald Hoffmann
Roald Hoffmann is an American theoretical chemist who won the 1981 Nobel Prize in Chemistry. He currently teaches at Cornell University in Ithaca, New York.-Escape from the Holocaust:...
for his work on reaction mechanisms. Hoffman's work focused on creating a set of four pericyclic reactions in organic chemistry, based on orbital symmetry, which he coauthored with Robert Burns Woodward
Robert Burns Woodward
Robert Burns Woodward was an American organic chemist, considered by many to be the preeminent organic chemist of the twentieth century...
entitled, "The Conservation of Orbital Symmetry."
Fukui's own work looked at the frontier orbitals, and in particular the effects of the Highest Occupied Molecular Orbital (HOMO
Homo
Homo may refer to:*the Greek prefix ὅμο-, meaning "the same"*the Latin for man, human being*Homo, the taxonomical genus including modern humans...
) and the Lowest Unoccupied Molecular Orbital (LUMO
Lumo
Lumo is a 2007 documentary film about twenty-year-old Lumo Sinai, a woman who fell victim to "Africa's First World War." While returning home one day, Lumo and another woman were gang-raped by a group of soldiers fighting for control of the Democratic Republic of the Congo during the 1994 Rwandan...
) on reaction mechanisms, which led to it being called Frontier Molecular Orbital Theory (FMO Theory). He used these interactions to better understand the conclusions of the Woodward–Hoffmann rules.
Theory
Fukui realized that a good approximation for reactivity could be found by looking at the frontier orbitals (HOMO/LUMOHOMO/LUMO
HOMO and LUMO are acronyms for highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively. The energy difference between the HOMO and LUMO is termed the HOMO-LUMO gap...
). This was based on three main observations of molecular orbital theory as two molecules interact:
- The occupied orbitals of different molecules repel each other.
- Positive charges of one molecule attract the negative charges of the other.
- The occupied orbitals of one molecule and the unoccupied orbitals of the other (especially the HOMO and LUMO) interact with each other causing attraction.
From these observations, frontier molecular orbital (FMO) theory simplifies reactivity to interactions between the HOMO of one species and the LUMO of the
other. This helps to explain the predictions of the Woodward–Hoffmann rules for thermal pericyclic reactions, which are summarized in the following statement:
"A ground-state pericyclic change is symmetry-allowed when the total number of (4q+2)s and (4r)a components is odd"
(4q+2)s refers to the number of aromatic, suprafacial electron systems; likewise, (4r)a refers to antiaromatic, antarafacial systems. It can be shown that if the total number of these systems is odd then the reaction is thermally allowed.
Cycloadditions
A cycloadditionCycloaddition
A cycloaddition is a pericyclic chemical reaction, in which "two or more unsaturated molecules combine with the formation of a cyclic adduct in which there is a net reduction of the bond multiplicity." The resulting reaction is a cyclization reaction.Cycloadditions are usually described by the...
is a reaction that simultaneously forms at least two new bonds, and in doing so, converts two or more open-chain molecules into rings. The transition state
Transition state
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 energy along this reaction coordinate. At this point, assuming a perfectly irreversible reaction, colliding reactant molecules will always...
s for these reactions typically involves the electrons of the molecules moving in continuous rings, making it a pericyclic reaction
Pericyclic reaction
In organic chemistry, a pericyclic reaction is a type of organic reaction wherein the transition state of the molecule has a cyclic geometry, and the reaction progresses in a concerted fashion. Pericyclic reactions are usually rearrangement reactions...
. These reactions can be predicted by the Woodward–Hoffmann rules and thus are closely approximated by FMO Theory.
The Diels–Alder reaction between maleic anhydride
Maleic anhydride
Maleic anhydride is an organic compound with the formula C2H22O. It is the acid anhydride of maleic acid and in its pure state it is a colourless or white solid with an acrid odour....
and cyclopentadiene
Cyclopentadiene
Cyclopentadiene is an organic compound with the formula C5H6. This colorless liquid has a strong and unpleasant odor. At room temperature, this cyclic diene dimerizes over the course of hours to give dicyclopentadiene via a Diels–Alder reaction...
is allowed by the Woodward–Hoffmann rules because there are six electrons moving suprafacially and no electrons moving antarafacially. Thus, there is one (4q + 2)s component and no (4r)a component, which means the reaction is allowed thermally.
FMO theory also finds that this reaction is allowed and goes even further by predicting its stereoselectivity
Stereoselectivity
In chemistry, stereoselectivity is the property of a chemical reaction in which a single reactant forms an unequal mixture of stereoisomers during the non-stereospecific creation of a new stereocenter or during the non-stereospecific transformation of a pre-existing one...
, which is unknown under the Woodward-Hoffmann rules. Since this is a [4 + 2], the reaction can be simplified by considering the reaction between butadiene and ethene. The HOMO of butadiene and the LUMO of ethene are both antisymmetric (rotationally symmetric), meaning the reaction is allowed.*
In terms of the stereoselectivity of the reaction between maleic anhydride and cyclopentadiene, the endo
Endo-exo isomerism
Endo-exo isomerism is a special type of isomerism found in organic compounds with a substituent on a bridged ring system. The prefix endo is reserved for the isomer with the substituent located closest, or "syn," to the longest bridge. The prefix exo is reserved for the isomer with the substituent...
-product is favored, a result best explained through FMO theory. The maleic anhydride is an electron-withdrawing species that makes the dieneophile electron deficient, forcing the regular Diels–Alder reaction. Thus, only the reaction between the HOMO of cyclopentadiene and the LUMO of maleic anhydride is allowed. Furthermore, though the exo
Endo-exo isomerism
Endo-exo isomerism is a special type of isomerism found in organic compounds with a substituent on a bridged ring system. The prefix endo is reserved for the isomer with the substituent located closest, or "syn," to the longest bridge. The prefix exo is reserved for the isomer with the substituent...
-product is the more thermodynamically stable isomer, there are secondary (non-bonding) orbital interactions in the endo- transition state, lowering its energy and making the reaction towards the endo- product faster, and therefore more kinetically favorable. Since the exo-product has primary (bonding) orbital interactions it can still form, but since the endo-product forms faster it is the major product.
*Note: The LUMO of ethene and the HOMO of butadiene are both symmetric, meaning the reaction between these species is allowed as well. This is referred to as the "inverse electron demand Diels–Alder."
Sigmatropic reactions
A sigmatropic rearrangementSigmatropic reaction
A sigmatropic reaction in organic chemistry is a pericyclic reaction wherein the net result is one σ-bond is changed to another σ-bond in an uncatalyzed intramolecular process. The name sigmatropic is the result of a compounding of the long-established sigma designation from single carbon-carbon...
is a reaction in which a sigma bond moves across a conjugated pi system with a concomitant shift in the pi bonds. The shift in the sigma bond may be antarafacial or suprafacial. In the example of a [1,5] shift in pentadiene, if there is a suprafacial shift, there is 6 e− moving suprafacially and none moving antarafacially, implying this reaction is allowed by the Woodward–Hoffmann rules. For an antarafacial shift, the reaction is not allowed.
These results can be predicted with FMO theory by observing the interaction between the HOMO and LUMO of the species. To use FMO theory, the reaction should be considered as two separate ideas: (1) whether or not the reaction is allowed, and (2) which mechanism the reaction proceeds though. In the case of a [1,5] shift on pentadiene, the HOMO of the sigma bond (i.e. a constructive bond) and the LUMO of butadiene on the remaining 4 carbons is observed. Assuming the reaction happens suprafacially, the shift results with the HOMO of butadiene on the 4 carbons that are not involved in the sigma bond of the product. Since the pi system changed from the LUMO to the HOMO, this reaction is allowed (though it would not be allowed if the pi system went from LUMO to LUMO).
To explain why the reaction happens suprafacially, first notice that the terminal orbitals are in the same phase. For there to be a constructive sigma bond formed after the shift, the reaction would have to be suprafacial. If the species shifted antarafacially then it would form an antibonding
Antibonding
Antibonding is a type of chemical bonding. An antibonding orbital is a form of molecular orbital that is located outside the region of two distinct nuclei...
orbital and there would not be a constructive sigma shift.
It is worth noting that in propene the shift would have to be antarafacial, but since the molecule is very small that twist is not possible and the reaction is not allowed.
Electrocyclic reactions
An electrocyclic reactionElectrocyclic reaction
In organic chemistry, an electrocyclic reaction is a type of pericyclic rearrangement reaction where the net result is one pi bond being converted into one sigma bond or vice-versa...
is a percyclic reaction involving the net loss of a pi bond and creation of a sigma bond with formation of a ring. This reaction proceeds through either a conrotatory or disrotatory
Disrotatory
In a conrotatory mode of an electrocyclic reaction the substituents located at the termini of a conjugated double bond system move in the same direction during ring opening or ring closure...
mechanism. In the conrotatory ring opening of cyclobutene, there are two electrons moving suprafacially (on the pi bond) and two moving antarafacially (on the sigma bond). This means there is one 4q + 2 suprafacial system and no 4r antarafacial system; thus the conrotatory process is thermally allowed by the Woodward–Hoffmann rules.
The HOMO of the sigma bond (i.e. a constructive bond) and the LUMO of the pi bond are important in the FMO theory consideration. If the ring opening uses a conrotatory process then the reaction results with the HOMO of butadiene. As in the previous examples the pi system moves from a LUMO species to a HOMO species, meaning this reaction is allowed.