Aarushhh/wikipedia-simple-splitted huggingface dataset:
Brown was placed on paid administrative leave for 15 days.

Investigations
In March 2011, Congress announced an investigation into the hiring of Brown.

In April and May 2011, the DC City Council issued a subpeona to get Brown to testify.  Brown hid from the people trying to give him the subpeona and went to court to fight having to testify. On May 31, 2011, the D.C. Superior Court order Brown to testify before the D.C. Council committee that was investigating this matter. On June 6, 2011, Brown testified under oath that Gray had paid him cash to keep in as a candidate in the primary race and had promised him a job. Brown claimed that Gray himself had ordered one of the payoffs. The City Council probe showed that Green, Gray's chief of staff Gerri Mason Hall and Gray's personnel director Judy Banks gave Gray's political allies city jobs. They did it in a way that did not pay attention to qualifications or laws.
Brown was required to report the money that he got as campaign contributions. On June 5, Brown gave the press copies of money orders payable to "Sulaimon Brown for Mayor" from relatives of Howard Brooks, including Brook's son (Peyton Brooks), the son's girlfriend, and a cousin of Brook's wife. The last two denied ever making the contributions. Peyton Brooks was also hired as a $110,000-a-year special assistant in the Office of the Deputy Mayor for Planning and Economic Development. Peyton Brooks was one of several children of Gray's campaign workers to be fired after the press printed stories about the jobs. Brown said that he received additional money orders from Howard Brooks, but that those did not have names on them.

The United States Attorney's Office is also investigating. Brown said that the Federal Bureau of Investigation asked Brown about the payments from Brooks, Green and Gray.

References
References

Other websites
Sulaimon Brown Resume distributed at Feb. 24 press conference
Campaign website from Internet Archive

Democratic Party (United States) politicians
1970 births
Living people
People from Charleston, South Carolina
Accountants
The 2011 Norway attacks were two attacks in Norway on 22 July 2011. The first attack was a car bombing near government buildings in Oslo. The second attack was a mass shooting at a summer youth camp on an island northwest of Oslo. Of the total 77 deaths, 55 were teenagers, and another 96 people were injured. The car bomb also shattered many windows of buildings in the government quarter of downtown Oslo.

The bomb explosion was near the office of Prime Minister Jens Stoltenberg at 15:26. It killed eight people and injured several others. The second attack happened about 90 minutes later, at a youth camp organized by the youth group (AUF) of the Norwegian Labour Party (AP) at the island of Utøya in Tyrifjorden, Buskerud. A gunman disguised as a policeman opened fire at the campers, killing 69 people.
The police arrested several suspects, but most were released. Anders Behring Breivik, a 32-year-old Norwegian Protestant man, committed both attacks. He was later charged with both attacks. Records show he had planned the attacks for years, as an act of anti-immigration ideology and against multiculturalism.

The European Union, NATO and countries around the world have expressed their support for Norway and condemned the attacks.

Oslo bombing

On 22 July 2011 at 15:26 (CEST) a powerful explosion went off near the offices of the Prime Minister of Norway (H-blokka) and several other government buildings, such as the Ministry of Petroleum and Energy (R4) and Ministry of Finance. (See map)

The nearby street was filled with glass and debris following the explosion. The wreckage of a car was sighted near one of the affected buildings. A giant cloud of white smoke was seen as a fire burned at the Ministry of Petroleum. The blast was heard at least seven kilometres away.
Following the explosion, police cleared the area and searched for more explosive devices. The police asked people to leave central Oslo.

Casualties

Eight people are known to have been killed in the explosion, with fifteen injured, eleven seriously. A doctor at the Oslo University Hospital said the hospital staff were treating head, chest and abdominal injuries.

Prime Minister Jens Stoltenberg was not hurt in the blast. Norway’s finance minister, Sigbjørn Johnsen, was on holiday in Denmark at the time.

Because July is the main holiday time in Norway, and that attacks took place during the weekend, there were not as many people in the area as usual, which may saved many lives.

Impact on transportation
All roads into Oslo's downtown area were closed as police moved people from the area and warned Oslo residents to stay away from the city center. They were also told to limit their usage of mobile phones due to concerns of another possible terrorist attack. Public transport into and out of the city was stopped. The police checked cars on the road to Oslo airport, which remained open as the police conducted searches in cars at the site.

The Gardermoen railway line between Lillestrøm and Oslo airport was shut down after a suspicious package was found close to the tracks. The same happened at the offices of TV 2, which were evacuated after a suspicious package was found outside the building.
Utøya shooting
About 90 minutes after the Oslo explosion, a gunman in police uniform, believed to be Anders Behring Breivik, got on a ferry about 40 kilometres (25 miles) northwest of Oslo. The ferry went to the island of Utøya in lake Tyrifjorden. The island was the site of the Labour Party's annual Workers' Youth League (AUF) youth summer camp. Once on the island, the gunman began to shoot the mainly adolescent campers, before finally being captured.
The shooter was dressed as a police officer, and said he had come over for a routine check following the bombing event in Oslo. He signalled and asked people to gather around him before firing his weapons, killing and injuring many people. He first shot people on the island and later started shooting at people who were trying to escape by swimming across the lake. The police reported that most of the casualties were youths of about 15 and 16 years old. People on the island were reported to have hidden in lavatories or undergrowth, communicating by text message to avoid giving their positions away to the gunman.

The shooting supposedly lasted for 90 minutes. The police were informed about the shooting at 17:27, and at 18:27 the gunman had been arrested. When the police arrived at the scene, they were confronted with a scene of survivors begging the officers to throw away their weapons. They were afraid that the men in uniforms would again open fire on them.
At about 03:50 (CEST) on 23 July 2011, the National Police Commissioner Øystein Mæland thought the number of deaths at Utøya was "at least 80" with the count expected to increase. Sixty-nine people died.

Perpetrator
The attacker is Anders Behring Breivik. He was arrested on Utøya for the shootings and also linked to the Oslo bombings. He has been charged and convicted of carrying out both attacks. He is in prison.
Political views
Acting national police chief Sveinung Sponheim said that the suspected gunman's Internet postings "suggest that he has some political traits directed toward the right, and anti-Muslim views, but whether that was a motivation for the actual act remains to be seen". Police have described Breivik as being a right-wing extremist. Breivik described himself as a conservative nationalist. He has been described as a Christian fundamentalist by news sources. He is reported to have written many posts on the website "document.no", described by Aftenposten as "Islam-critical and Israel-friendly". He went to meetings of "Documents venner" (Friends of Document), linked with the website. He is was also once a member of the right-wing Progress Party (FrP) and its youth wing FpU. FpU leader Ove Vanebo said Breivik was active early in the 2000s, but he left the party as his viewpoints became more extreme.
Beliefs that there were other perpetrator(s)
Several witnesses at the youth camp, believe (as of 23 July 2011) that there was more than one shooter. The police have received descriptions of a second gunman, and are currently checking this information. Due to the uncertainty surrounding these witness descriptions and the chaotic nature of the events the police have, as a matter of precaution, yet to make an official comment on the matter. Acting Police Chief Sveinung Sponheim has said that "It's very difficult at this point to say whether he was acting alone or whether he was acting as part of a larger network".

Reactions

Domestic
At a press conference on the morning after the attacks, prime minister Jens Stoltenberg called the attack a "national tragedy" and the worst atrocity since World War II. Stoltenberg said that the attack would not hurt the Norwegian democracy, and said the proper answer to the violence was "more democracy, more openness, but not naivety".
Eskil Pedersen of the Workers' Youth League vowed to "return to Utøya" and urged Norway to continue its tradition of openness and tolerance.

King Harald sent his condolences to the victims and their families, and urged unity.

Svein Østerud (no:), professor emeritus, said that before we can analyze the trauma of the nation, we have to acknowledge that Breivik and [some] other terrorists, are youths that lost their way, when going thru institutions ... while struggling to find one's identity, and at the same time (and everyday) being forced to [ conform to the] norms set by school, parents, and social media.

International
The European Union, NATO, the United Nations Security Council, governments and leaders from around the world expressed their condemnation of the attack, condolences, and solidarity with Norway.

Memorials
Memorials

At Utøya, the place of memorial is called ["the clearing"] "Lysninga"; a part of it is ["the ring"] "Ringen" - a "ring of steel [that] hangs between trees and here the names and age of the majority of those 69 killed are engraved"; "it lies at the highest point of the island"; It was unveiled during the summer of 2015. Hegnhuset was inaugurated in 2016.

A temporary national monument in Oslo was unveiled on 22 July 2016. 

One monolith stands in each municipality.

At 53 [places] in Norway, are statues by Nico Widerberg that were anonymously financed.

One monolith was put at Utsikten - a roadside rest area with a view of Utøya; it is located on E16 at Nes in Hole (municipality).

National memorial in Hole municipality
In June 2017 the government decided that one of the national memorials, should be placed at Utøya-kaia, in Hole municipality; the memorial will not [be a work of art, or] have an artistic expression. KORO (no), an agency under the Ministry of Culture, will no longer formally be tied to the process in regard to the memorial in Hole.

In popular culture
Jan Kjærstad (en) published in 2017, Berge, a novel that is about  the attacks and a triple homicide in 1999, in Norway (en).

References

Other websites
 Stor eksplosjon i Oslo sentrum, Aftenposten, news report in Norwegian, with pictures.
 Allvarligt bombattentat skakar Oslo, Sveriges Radio, news report in Swedish, with pictures.
 LIVE: Oslo explosion, BBC News, live news broadcast on the bombing in Oslo.
 Oslo Attacks: A Bloody Aftermath  — slideshow by Life magazine
 Norway Massacre: Island Under Siege  — slideshow by Life magazine
2011 in Europe
2010s building bombings
2010s explosions in Europe
2011 attacks
2010s mass shootings in Europe
21st century in Oslo
Attacks on buildings and structures in the 2010s
Building bombings in Europe
Car and truck bombings in Europe
Christian terrorism

Islamophobic attacks and incidents
July 2011 events
Mass murder in the 2010s
2011 attacks
Murder in 2011

Terrorist incidents in Europe in the 2010s
Harald Cerny (born 13 September 1973) is a former Austrian football midfielder. He played mostly for TSV 1860 München.

Career
He started his career  with ASV Hinterbrühl and FC Admira/Wacker where he played in the different youth teams. At the age of 19 he went to Bayern München where he started the professional career. The first two years he played for the second squad but in the 1992/93 he played in the first team giving his debut versus Eintracht Frankfurt. 1993 he went back to Austria playing with  FC Admira/Wacker . After Wacker Innsbruck in the 1994/95 season he went back to Munich but played for Bayerns rival TSV 1860 München. With 268 matches, 238 of them in the Bundesliga, for 1860 he is the record holder of the club. Due to injuries, he ended his career in 2007.
International
Cerny made his debut for Austria in  March 1993 against Greece. He played 47 matches and  scored four goals.His last international was an April 2004 against Luxembourg. He was also in the squad for the  1998 FIFA World Cup in France. There he played two matches versus Cameroon and Chile.

National team statistics

|-
|1993||4||0
|-
|1994||6||0
|-
|1995||2||0
|-
|1996||1||0
|-
|1997||7||0
|-
|1998||8||3
|-
|1999||6||0
|-
|2000||4||0
|-
|2001||2||0
|-
|2002||4||0
|-
|2003||2||1
|-
|2004||1||0
|-
!Total||47||4
|}

References

Austrian footballers
1973 births
Austrian football managers
Players of the Austrian national football team
Living people
Franz Bernhard Wohlfahrt (born 1 July 1964 in Sankt Veit an der Glan, Austria) is a former Austrian goalkeeper.

Career
He started with the local club SV St.Veit and turned professional with F.K. Austria Wien. He came together with his older brother Mario, who soon went back to St. Veit. Franz Wohlfahrt played then 20 years or 496 matches for this club divided in two sections. With Austria Wien he became 6 times Austrian Champion and four times Austrian cup winner. He became widely known during a UEFA Cup match versus Ajax Amsterdam when he was injured by a bar thrown by an Ajax supporter. Following this Ajax was banned for one year in European football. From 1996 till 2000 he played for the German team VfB Stuttgart, with the club he played in the 1997/98 UEFA Cup final versus Chelsea (0:1). 2000 he went back to Austria Wien. 2002 he ended his career but in 2007 he started again playing for ASK Hirm, whose goalkeeper was injured.
International
In 1983 he played in the 1983 FIFA World Youth Championship. His first match in the senior team was in August 1987 in a match versus Switzerland. His last match was  a qualification match for the 2002 FIFA World Cup versus Turkey. He was also a goalkeeper in the 1998 FIFA World Cup squad. In 1999 he was goalkeeper during the 0:9 defeat versus Spain in Valencia. All in all he played 59 matches for Austria.

Honours
Austrian League: 1983–84, 1984–85, 1985–86, 1990–91, 1991–92, 1992–93
Austrian Cup: 1985–86, 1989–90, 1991–92, 1993–94
German Cup: 1996–97
UEFA Cup Winners' Cup: Runner-up 1997–98
Austrian Footballer of the Year: 1993

References

1964 births
Austrian footballers
Austrian football managers
Players of the Austrian national football team
Living people
Austrian football champions
Exchange of gases or gas exchange is carried out by organisms. 

Animals breathe out carbon dioxide and breathe in oxygen. Plants use carbon dioxide to carry out photosynthesis, which makes oxygen. Plants only do this out during the day, when there is sunlight. Plants respire all day and night.

In the human respiratory system, gas exchange happens in the alveolus (alveoli for plural). These are in the lungs and help with diffusion. Oxygen diffuses into the bloodstream, from the air. Oxygen is used in aerobic respiration. Carbon dioxide diffuses out of the bloodstream, into the air. Carbon dioxide is a waste product made by respiration.

References 

Physiology
Pentene is the name of alkenes with the formula C5H10. They are hydrocarbons. In total, there are five different pentenes. Pentens occur in cracking processes and in natural gas. Pentenes are used for polymerization, and for the synthesis of isoprene, amyl alcohols and Alkylphenols. Amyl alcohols are used as stabilizers in the production of Chloroform and Dichloromethane to stop phosgene from being made.

5
Paul Edmund de Strzelecki (20 July 1797 — October 1873) was a Polish man who taught himself geology. He became famous for his explorations in Australia.

He was born in Gluszyna, near Poznan, Western Poland in 1797 and later served briefly with the Prussian army. He tried unsuccessfully to marry a young girl, and then was accused of stealing money from his employer. He moved to London and gave himself the title of Count Strzelecki. In 1834 he went to North America and spent time visiting mineral areas and exploring for minerals. He is said to be the first person to find copper in Canada. In 1836 he travelled along the west coast from Chile to California.

In 1839 he visited the Hawaii, Tahiti, New Zealand and finally landed in Sydney, Australia. He wanted to make a geological map, and explored large parts of New South Wales and Victoria, including the Australian Alps. He climbed Australia's highest mountain, and named it Mount Kosciuszko, after the Polish leader, Tadeusz Kosciuszko.
He spent several years in Tasmania before going back to Sydney. He went back to London in 1843. He wrote a book on his discoveries in Australia called Physical Description of New South Wales and Van Diemen's Land. He was given the Founder's Medal by the Royal Geographical Society.

In 1847—8 he was put in charge of the giving out money in Ireland during the Great Famine for the British Relief Association. He established standards for giving out assistance that are still being used.

He was made a Fellow of the Royal Geographic Society and the Royal Society. He was awarded the K.C.M.G. in 1869. He died from cancer in 1873. He left instructions that after his death his papers were to be burnt and his body buried in an unmarked grave.
A road from Lyndhurst to Innamincka was named the Strzelecki Track after Paul Strzelecki. It was used until the 1930's to move cattle to Adelaide, and now is the main road to Moomba, a huge natural gas field which supplies Adelaide and Sydney. The Strzelecki Ranges in Victoria are also named after him. A large national park on Flinders Island, the Strzelecki National Park, was named after Strzelecki who climbed the mountains there in 1842.

References

1797 births
1873 deaths

Explorers
Exploration of Australia
Polish scientists
Stress is the force per unit area on a body that tends to cause it to change shape.

Stress is a measure of the internal forces in a body between its particles. These internal forces are a reaction to the external forces applied on the body that cause it to separate, compress or slide. External forces are either surface forces or body forces. Stress is the average force per unit area that a particle of a body exerts on an adjacent particle, across an imaginary surface that separates them.

The formula for uniaxial normal stress is:

where σ is the stress, F is the force and A is the surface area.

In SI units, force is measured in newtons and area in square metres. This means stress is newtons per square meter, or N/m2. However, stress has its own SI unit, called the pascal. 1 pascal (symbol Pa) is equal to 1 N/m2. In Imperial units, stress is measured in pound-force per square inch, which is often shortened to "psi". The dimension of stress is the same as that of pressure.
In continuum mechanics, the loaded deformable body behaves as a continuum. So, these internal forces are distributed continually within the volume of the material body. (This means that the stress distribution in the body is expressed as a piecewise continuous function of space and time.) The forces cause deformation of the body's shape. The deformation can lead to a permanent shape change or structural failure if the material is not strong enough.

Some models of continuum mechanics treat force as something that can change. Other models look at the deformation of matter and solid bodies, because the characteristics of matter and solids are three dimensional. Each approach can give different results. Classical models of continuum mechanics assume an average force and do not properly include  "geometrical factors". (The geometry of the body can be important to how stress is shared out and how energy builds up during the application of the external force.)

Shear stress
Shear stress

Simple stresses
In some situations, the stress within an object can be described by a single number, or by a single vector (a number and a direction). Three such simple stress situations are the uniaxial normal stress, the simple shear stress, and the isotropic normal stress.

Uniaxial normal stress
Tensile stress (or tension) is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. The volume of the material stays constant. When equal and opposite forces are applied on a body, then the stress due to this force is called tensile stress.

Therefore in a uniaxial material the length increases in the tensile stress direction and the other two directions will decrease in size. In the uniaxial manner of tension, tensile stress is induced by pulling forces. Tensile stress is the opposite of compressive stress.
Structural members in direct tension are ropes, soil anchors and nails, bolts, etc. Beams subjected to bending moments may include tensile stress as well as compressive stress and/or shear stress.

Tensile stress may be increased until the reach of tensile strength, namely the limit state of stress.

Stress in one-dimensional bodies
All real objects occupy three-dimensional space. However, if two dimensions are very large or very small compared to the others, the object may be modelled as one-dimensional. This simplifies the mathematical modelling of the object. One-dimensional objects include a piece of wire loaded at the ends and viewed from the side, and a metal sheet loaded on the face and viewed up close and through the cross section.

Related pages
 Tension
 Bending
 Stress–strain curve

References

Bibliography

Other websites 
 Stress analysis, Wolfram Research 
 ESDU Stress Analysis Methods
 True stress and true strain 
 Stress-Strain Curve for Ductile Material 
 Encyclopædia Britannica article
Materials science
Elasticity (physics)
Solid mechanics
Engineering
In organic chemistry, a pericyclic reaction is a type of chemical reaction between organic compounds. In the case of pericyclic reactions, the transition state of the molecule is a ring (has a cyclic geometry), and the reaction goes forward in a concerted way. Pericyclic reactions are usually rearrangement reactions. The most important groups of pericyclic reactions are:

 Electrocyclic reactions
 Cycloadditions
 Sigmatropic reactions
 Group transfer reactions
 Cheletropic reactions
 Dyotropic reactions

In general, pericyclic reactions are equilibrium processes. However, it is possible to push the reaction in one direction if the product is at a significantly lower energy level. This is applying Le Chatelier's principle to a reaction involving a single molecule.
Many pericyclic reactions have similar stepwise radical processes connected with them. Chemists disagree whether some reactions are pericyclic reactions. For example, it is not definitively known whether the [2+2] cycloaddition mechanism is concerted (or may depend on the reactive system). Many pericyclic reactions have similar reactions that are metal-catalyzed. But these metal-catalyzed reactions are also not really pericyclic. The metal catalysts stabilize the reaction intermediates. So the reaction is not concerted, but rather metal-stabilized.

A large photoinduced hydrogen sigmatropic shift was utilized in a corrin synthesis performed by Albert Eschenmoser containing a 16π system.  

Due to the principle of microscopic reversibility, there is a parallel set of "retro" pericyclic reactions, which perform the reverse reaction.

Pericyclic reactions in biochemistry 

Pericyclic reactions also happen in several biological processes:
Claisen rearrangement of chorismate to prephenate in almost all prototrophic organisms.
[1,5]-sigmatropic shift when precorrin-8x is being changed into hydrogenobyrinic acid
non-enzymatic, photochemical electrocyclic ring opening and a (1,7) sigmatropic hydride shift in vitamin D synthesis.
a conversion of Isochorismate into salicylate and Pyruvate in a catalyzed, true pericyclic reaction.

Related pages
Woodward–Hoffmann rules

References 

Pericyclic reactions
Rearrangement reactions
Organic Chemistry
The 2011–12 season is Manchester United's 20th season in the Premier League.

Manchester United signed a £40 million four-year deal with DHL.

In November, Sir Alex Ferguson celebrated 25 years in charge of the club.

Pre-season 

Manchester United started their season with a tour in the United States. United finishing the tour with a game against Barcelona in Washington on 30 July.

Community Shield

Transfers

Squad

Premier League

Stats

Champions League 

Manchester United will face Benfica, Basel and Otelul Galati in Group C.

League Cup and FA Cup

League Cup 
Manchester United were drawn against Crystal Palace in the quarter-finals of the League Cup.

References 

Football seasons
2011 in association football
2012 in association football
2011 in England
2012 in England
2010s in Manchester
Annoying Orange is a live action/animated comedy web series created by Dane Boedigheimer. The main character is an orange who annoys other fruits. The episodes are uploaded to the YouTube channel realannoyingorange weekly. As of 2022 there were over 700 videos. The channel had over 11 million subscribers.

Television series
In 2012, Cartoon Network made a 2012-2014 television series, The High Fructose Adventures of Annoying Orange, based on the YouTube series.

References

Other websites

YouTube
Internet memes
A cycloaddition is a chemical reaction between reactants with double bonds that get replaced by a ring structure.  It is a pericyclic chemical reaction where "two or more unsaturated molecules (or parts of the same molecule) combine with the formation of a cyclic adduct in which there is a net reduction of the bond multiplicity." It is a cyclization reaction: it makes new ring of atoms.

Cycloadditions are named by the basic size of the molecules that are being brought together. This would make the Diels–Alder reaction a [4 + 2]cycloaddition, and the 1,3-dipolar cycloaddition a [3 + 2]cycloaddition. This type of reaction is a non-polar addition reaction.
Reaction mechanism
Heat can cause the double bonds to form a ring. Thermal cycloadditions usually have (4n + 2) π electrons participating in the starting material, for some whole number n.  Because of orbital symmetry, most cycloadditions are suprafacial-suprafacial. Rarely, they are antarafacial-antarafacial.  There are a few examples of thermal cycloadditions which have 4n π electrons (for example the [2 + 2] cycloaddition). These proceed in a suprafacial-antarafacial sense. For example, the dimerisation of ketene has a orthogonal set of p orbitals. Those p orbitals allow the reaction to proceed using a crossed transition state.
Light can also cause the double bonds to form a ring. Cycloadditions in which 4n π electrons participate can also occur as a result of photochemical activation. Here, one component makes an electron move from the  highest occupied molecular orbital (HOMO) (π bonding) to the lowest unoccupied molecular orbital (LUMO) (π* antibonding). After the electron is promoted to the higher orbital, orbital symmetry allows the reaction to proceed in a suprafacial-suprafacial manner. An example is the DeMayo reaction. Another example is shown below, the photochemical dimerization of cinnamic acid.

Note that not all photochemical (2+2) cyclizations are cycloadditions; some are known to operate by radical mechanisms.

Some cycloadditions instead of π bonds operate through strained cyclopropane rings; as these have significant π character. For example, an analog for the Diels–Alder reaction is the quadricyclane-DMAD reaction:
In the (i+j+...) cycloaddition notation i and j refer to the number of atoms involved in the cycloaddition. In this notation a Diels-Alder reaction is a (4+2)cycloaddition and a 1,3-dipolar addition such as the first step in ozonolysis is a (3+2)cycloaddition. This notation uses parenthesis. The IUPAC preferred notation however,  with [i+j+...] counts electrons and not atoms. It uses square brackets. In this notation, the Diels–Alder reaction and the dipolar reaction both become a [4+2]cycloaddition. The reaction between norbornadiene and an activated alkyne is a [2+2+2]cycloaddition.

Types of cycloaddition

Diels-Alder reactions
The Diels–Alder reaction is a [4+2]cycloaddition reaction.

Huisgen cycloadditions
The Huisgen cycloaddition reaction is a [2+3]cycloaddition.

Nitrone-olefin cycloaddition
The Nitrone-olefin cycloaddition is a [3+2]cycloaddition.
Formal cycloadditions
Cycloadditions often have metal-catalyzed and stepwise radical analogs, however these are not strictly speaking pericyclic reactions. When charged or radical intermediates are involved in a cycloaddition, or when the cycloaddition result is found in a series of reaction steps, they are sometimes called formal cycloadditions to make a difference from true pericyclic cycloadditions. 

One example of a formal [3+3]cycloaddition between a cyclic enone and an enamine catalyzed by n-butyllithium is a Stork enamine / 1,2-addition cascade reaction:

References

Chemical reactions
Cheletropic reactions are a subclass of cycloadditions. What sets cheletropic reactions apart is that on one of the reagents, both new bonds are being made to the same atom.<ref name="Fleming">Ian Fleming. Frontier Orbitals and Organic Chemistry Reactions. Wiley, 1976.</ref>  A few examples are shown to the right in Figure 1. In the first case, the single atom is the carbon atom in the carbonyl group. That carbon atom ends up in carbon monoxide. The end result is making two new bonds to one atom. The first two examples are known as "cheletropic extrusions" because a small stable molecule is given off in the reaction. The driving force for these reactions is often the entropic benefit of releasing a gas (e.g. CO or N2).

Theoretical analysis
Because of the geometry of the molecules involved in cheletropic reactions, they confirm a number of predictions made by theoretical chemists. Cheletropic reactions confirm the conservation of molecular orbital symmetry.
In the pericyclic transition state, a small molecule donates two electrons to the ring. Two possible geometries can explain the reaction.  The small molecule can approach in either a linear or non-linear way. In the linear approach, the electrons in the orbital of the small molecule are pointed directly at the π system of the big molecule. In the non-linear approach, the orbital approaches at a slightly off angle. The π-systems ability to rotate as the small molecule approaches is crucial in forming new bonds. The direction of rotation will be different depending on how many π-electrons are in the system. A diagram of a two-electron fragment approaching a four-electron π-system using frontier molecular orbitals is shown below. The rotation will be disrotatory if the small molecule approaches linearly and conrotatory if the molecule approaches non-linearly. Disrotatory and conrotatory tell how the bonds in the π-system are rotating
.  Disrotatory means opposite directions while conrotatory means the same direction. This is also shown in the diagram below.
Cheletropic Reactions Involving SO2
Thermodynamics
When sulfur dioxide reacts with butadiene and isoprene, two different products result. The reaction mechanism will control what gets made.  A kinetic product and a thermodynamic product are both possible. More of the thermodynamic product gets made than the kinetic product. The kinetic product comes from a Diels–Alder reaction, while a cheletropic reaction makes a more thermodynamically stable product. The cheletropic pathway is used more because it makes to a more stable five-membered ring adduct. The scheme below shows the difference between the two products. The path to the left shows the thermodynamic product, while the path to the right shows the kinetic product. Suarez and Sordo showed this in 1995. They showed this both with experiments and using Gaussian calculations.
Monnat, Vogel, and Sordo, in 2002, measured the kinetics of addition of sulfur dioxide to 1,2-dimethylidenecycloalkanes. They wrote that the reaction of 1,2-dimethylidenecyclohexane with sulfur dioxide can give two different products depending on reaction conditions. The reaction makes the corresponding sultine through a hetero-Diels-Alder reaction under kinetic control (≤ -60 °C), but, under thermodynamic control (≥ -40 °C), the reaction makes the corresponding sulfolene through a cheletropic reaction. The activation enthalpy for the hetero-Diels-Alder reaction is about 2 kcal/mol smaller than that for the corresponding cheletropic reaction.  The sulfolene is about 10 kcal/mol more stable than the isometric sultine in CH2Cl2/SO2 solution. Similar results were found in an 1995 study by Suarez, Sordo, and Sordo which used ab initio calculations to study the kinetic and thermodynamic control of the reaction of sulfur dioxide with 1,3-dienes.

 Solvent effects
Solvent effects 

The effect of the solvent of the cheletropic reaction of 3,4-dimethyl-2,5-dihydrothiophen-1,1-dioxide (shown at right) was kinetically investigated in 14 solvents. The reaction rate constants of the forward and reverse reaction in addition to the equilibrium constants were found to be linearly correlated with the ET(30) solvent polarity scale.
Reactions were done at 120 °C and were studied by 1H-NMR spectroscopy of the reaction mixture. The forward rate k1 was found to decrease by a factor of 4.5 going from cyclohexane to methanol. The reverse rate k-1 was found to increase by a factor of 53 going from cyclohexane to methanol, while the equilibrium constant Keq decreased by a factor of 140. It is suggested that there is a change of the polarity during the activation process as evidenced by relationships between the equilibrium and kinetic data. The authors say that the reaction appears to be influenced by the polarity of the solvent, and this can be shown by the change in the dipole moments when going from reactant to transition state to product. The authors also state that the cheletropic reaction doesn’t seem to be influenced by either solvent acidity or basicity. 

The results of this study lead the authors to expect the following behaviors: 

1. The change in the solvent polarity will influence the rate less than the equilibrium.
2. The rate constants will be characterized by opposite effect on the polarity: k1 will slightly decrease with the increase of ET(30), and k-1 will increase under the same conditions.

3. The effect on k-1 will be larger than on k1.

Carbene Additions to Alkenes

One of the most synthetically important cheletropic reactions is the addition of a singlet carbene to an alkene to make a cyclopropane (see figure at left). A carbene is a neutral molecule containing a divalent carbon with six electrons in its valence shell. Because of this, carbenes are highly reactive electrophiles and generated as reaction intermediates.
Interaction of the filled carbene orbital with the alkene π system creates a four-electron system and favors a non-linear approach. It is also favorable to mix the carbene empty p'' orbital with the filled alkene π orbital. Favorable mixing occurs through a non-linear approach (see figure 2 at right). However, while theory clearly favors a non-linear approach, there are no obvious experimental implications for a linear vs. non-linear approach.

References

Pericyclic reactions
A sigmatropic reaction in organic chemistry is a pericyclic reaction. A sigmatropic reaction does not use a catalyst and involves a single molecule (an uncatalyzed intramolecular process). It changes one σ-bond into a different σ-bond. The name sigmatropic is the result of a compounding of the long-established "sigma" name for single carbon-carbon bonds and the Greek word tropos, meaning turn.  This is a rearrangement reaction which means that the bonds in a molecule shift between atoms without any atoms leaving or new atoms added to the molecule. In a sigmatropic reaction, a substituent moves from one part of a π-bonded system to another part in an intramolecular reaction with simultaneous rearrangement of the π system. True sigmatropic reactions usually do not need a catalyst. Some sigmatropic reactions are catalyzed by a Lewis acid.  Sigmatropic reactions often have transition-metal catalysts that form intermediates in analogous reactions
.  The most well-known of the sigmatropic rearrangements are the [3,3] Cope rearrangement, Claisen rearrangement, Carroll rearrangement and the Fischer indole synthesis.
Overview of Sigmatropic Shifts

Woodward-Hoffman Sigmatropic Shift Nomenclature
A special notation is used to describe sigmatropic shifts.  Each of the carbon atoms on the backbone of the molecule are assigned a position number.  Sigmatropic rearrangements are described by an order term [i,j]. This means the migration of a σ-bond adjacent to one or more π systems to a new position (i-1) and (j-1) atoms removed from the original location of the σ-bond.  When the sum of i and j is an even number, this is an indication of the involvement of a neutral, all C atom chain. An odd number suggests that there is a charged C atom or of a heteroatom lone pair replacing a carbon-carbon double bond. Thus, [1,5] and [3,3] shifts become [1,4] and [2,3] shifts with heteroatoms, while preserving symmetry considerations.  Hydrogens are omitted in the third example for clarity.
Here is a way to find the order of a given sigmatropic rearrangement. The first step is to give numbers to each atom starting with the atoms of the bond being broken as atom 1. Chemists count the atoms in each direction from the broken bond to the atoms that form the new σ-bond in the product.  The numbers that correspond to the atoms forming the new bond are then separated by a comma and placed within brackets. This creates the sigmatropic reaction order descriptor.

Chemists also count atoms when naming a sigmatropic shift where a hydrogen atom moves.  The carbon chain does not break in a hydrogen atom migration. So, chemists count across all atoms involved in the reaction rather than only across the closest atoms.  For example, the following hydrogen atom migration is of order [1,5], attained by counting counterclockwise through the π system, rather than the [1,3] order through the ring CH2 group that would mistakenly result if counted clockwise.

Suprafacial and Antarafacial Shifts
Chemists have studied sigmatropic reactions where the migrating group has a sterocenter. In principle, all sigmatropic shifts can occur with either the same (retention) or the opposite (inversion) geometry of the migrating group.  This depends on whether the original bonding lobe of the migrating atom or its other lobe is used to form the new bond.

In cases of stereochemical retention, the migrating group translates without rotation into the bonding position. In the case of stereochemical inversion the migrating group both rotates and translates to reach its bonded conformation.
There is another way that a sigmatropic reaction can produce products with different sterochemistry. The migrating group can stay on the original face of the π system after rebonding. Or, it can go to the opposite face of the π system.  If the migrating group remains on the same face of the π system, the shift is known as suprafacial. If the migrating group transfers to the opposite face is called an antarafacial shift. Transformations that occur within small- or medium-sized rings cannot make antarafacial shifts.

Classes of Sigmatropic Rearrangements

[1,3] Shifts

Thermal Hydride Shifts
In a thermal [1,3] hydride shift, a hydride moves three atoms.  The Woodward-Hoffmann rules dictate that it would proceed in an antarafacial shift.  Although such a shift is symmetry allowed, the Mobius topology required in the transition state prohibits such a shift. It is geometrically impossible. This is why enols do not isomerize without an acid or base catalyst.
Thermal Alkyl Shifts
Thermal alkyl [1,3] shifts, similar to [1,3] hydride shifts, must proceed antarafacially.  The geometry of the transition state is prohibitive. But an alkyl group, due to the nature of its orbitals, can invert its geometry and form a new bond with the back lobe of its sp3 orbital. This reaction will result a suprafacial shift. These reactions are still not common in open chain systems because of the highly ordered nature of the transition state. So, the reactions work better in cyclic molecules.

Photochemical [1,3] Shifts
Photochemical [1,3] shifts should be suprafacial shifts; however, most are non-concerted because they proceed through a triplet state (that is, they have a diradical mechanism, to which the Woodward-Hoffmann rules do not apply).
[1,5] Shifts
A [1,5] shift involves the shift of 1 substituent (-H, -R or -Ar) down 5 atoms of a π system.  Hydrogen has been shown to shift in both cyclic and open chain systems at temperatures at or above 200 ˚C. These reactions are predicted to proceed suprafacially, by a Huckel-topology transition state.

Photoirradiation would require an antarafacial shift of hydrogen. Although such reactions are rare, there are examples where antarafacial shifts are favored:

 
In contrast to hydrogen [1,5] shifts, there have never been any observed [1,5] alky shifts in an open-chain system. Chemists have determined rate preferences for [1,5] alkyl shifts in cyclic systems:  carbonyl and carboxyl> hydride> phenyl and vinyl>> alkyl.
Alkyl groups undergo [1,5] shifts very poorly and usually require high temperatures. However, for cyclohexadienes, the temperature for alkyl shifts is not much higher than that for carbonyls, the best migratory group. A study showed that this is because alkyl shifts on cyclohexadienes proceed through a different mechanism.  First the ring opens, followed by a [1,7] shift, and then the ring reforms electrocyclically:

This same mechanistic process is seen below, without the final electrocyclic ring-closing reaction, in the interconversion of lumisterol to vitamin D2.

[1,7] Shifts
[1,7] sigmatropic shifts are predicted by the Woodward-Hoffmann rules to proceed in an antarafacial fashion, by a Mobius topology transition state. An antarafacial [1,7] shift is observed in the conversion of lumisterol to vitamin D2, where following an electrocyclic ring opening to previtamin D2, a methyl hydrogen shifts.
Bicyclic nonatrienes also undergo [1,7] shifts in a so called walk rearrangement, which is the shift of divalent group, as part of a three-membered ring, in a bicyclic molecule.

[3,3] Shifts

[3,3] sigmatropic shifts are well studied sigmatropic rearrangements. The Woodward-Hoffman rules predict that these six electron reactions would proceed suprafacially, using a Huckel topology transition state.

Claisen Rearrangement
Discovered in 1912 by Rainer Ludwig Claisen, the Claisen rearrangement is the first recorded example of a [3,3]-sigmatropic rearrangement. This rearrangement is a useful carbon-carbon bond-forming reaction. An example of Claisen rearrangement is the [3,3] rearrangement of an allyl vinyl ether, which upon heating yields a γ,δ-unsaturated carbonyl.  The formation of a carbonyl group makes this reaction, unlike other sigmatropic rearrangements, inherently irreversible.
Aromatic Claisen rearrangement
The ortho-Claisen rearrangement involves the [3,3] shift of an allyl phenyl ether to an intermediate which quickly tautomerizes to an ortho-substituted phenol.

When both the ortho positions on the benzene ring are blocked, a second ortho-Claisen rearrangement will occur. This para-Claisen rearrangement ends with the tautomerization to a tri-substituted phenol.

Cope Rearrangement
The Cope rearrangement is an extensively studied organic reaction involving the [3,3] sigmatropic rearrangement of 1,5-dienes. It was developed by Arthur C. Cope. For example 3,4-dimethyl-1,5-hexadiene heated to 300 °C yields 2,6-octadiene.

Oxy-Cope rearrangement
The Oxy-Cope rearrangement a hydroxyl group is added at C3 forming an enal or enone after Keto-enol tautomerism of the intermediate enol:
Carroll Rearrangement
The Carroll rearrangement is a rearrangement reaction in organic chemistry and involves the transformation of a β-keto allyl ester into a α-allyl-β-ketocarboxylic acid. This organic reaction can be followed by decarboxylation and the final product is a γ,δ-allylketone. The Carroll rearrangement is an adaptation of the Claisen rearrangement and effectively a decarboxylative allylation.

Fischer Indole Synthesis
The Fischer indole synthesis is a chemical reaction that produces the aromatic heterocycle indole from a (substituted) phenylhydrazine and an aldehyde or ketone under acidic conditions. The reaction was discovered in 1883 by Hermann Emil Fischer.

The choice of acid catalyst is very important.  Successful acid catalysts include: Bronsted acids such as HCl, H2SO4, polyphosphoric acid and p-toluenesulfonic acid. Lewis acids such as boron trifluoride, zinc chloride, iron chloride, and aluminium chloride are also useful catalysts.

Several reviews have been published.
[5,5] Shifts
Similar to [3,3] shifts, the Woodward-Hoffman rules predict that [5,5] sigmatropic shifts would proceed suprafacially, Huckel topology transition state.  These reactions are rarer than [3,3] sigmatropic shifts, but this is mainly a function of the fact that molecules that can undergo [5,5] shifts are rarer than molecules that can undergo [3,3] shifts.

Walk Rearrangements
The migration of a divalent group, such as O, S, NR or CR2, which is part of a three-membered ring in a bicyclic molecule, is commonly referred to as a walk rearrangement.  This can be formally characterized according to the Woodward-Hofmann rules as being a (1, n) sigmatropic shift. An example of such a rearrangement is the shift of substituents on tropilidenes (1,3,5-cycloheptatrienes). When heated, the pi-system goes through an electrocyclic ring closing to form bicycle[4,1,0]heptadiene (norcaradiene). Thereafter follows a [1,5] alkyl shift and an electrocyclic ring opening.
Proceeding through a [1,5] shift, the walk rearrangement of norcaradienes is expected to proceed suprafacially with a retention of stereochemistry. Experimental observations, however, show that the 1,5-shifts of norcaradienes proceed antarafacially. Theoretical calculations found the [1,5] shift to be a diradical process, but without involving any diradical minima on the potential energy surface.

Related pages
2,3-sigmatropic rearrangement
NIH shift
Frontier Molecular Orbital Theory
Woodward–Hoffmann rules

References

Rearrangement reactions
A Group transfer reaction is pericyclic reaction where one pi bond is converted to one sigma bond, at the same time that a sigma bond migrates.

The best known group transfer reaction is the ene reaction.

Chemical reactions
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References

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