The Vithoba Temple, officially known as Shri Vitthal-Rukmini Mandir (), is a Hindu temple in Pandharpur, in the Indian state of Maharashtra. It is the main centre of worship for Vithoba, a form of the god Vishnu or Krishna, and his consort Rakhumai. It is Classified one among the 108 Abhimana Kshethram of Vaishnavate tradition. The temple was built by King Vishnuvardhana of Hoysala Empire between 1108–1152 CE upon being convinced by the historical figure Pundalik. Also, there is an inscription in the temple, of a Hoysala King Vira Someshwara dating back to 1237 CE, which grants the temple a village for its upkeep. It is the most visited temple in Maharashtra. The Warkaris start marching from their homes to the temple of Pandharpur in groups called Dindi (procession) to reach on Aashadhi Ekadashi and Kartiki Ekadashi. A dip in the holy river Chandrabhaga, on whose banks Pandharpur resides, is believed to have power to wash all sins. All the devotees are allowed to touch the feet of the idol of Vithoba. In May 2014, the temple became the first in India to invite women and people from backward classes as priests.

Although parts of the temple date to the 12th or 13th century, the existing structure mainly dates to the 17th century or later, and reflects the later Deccan style, with dome motifs and lobed arches. Attempts were made to destroy the temple by Afzal Khan, however the original central figure of the shrine was protected by the Brahmin priests Badve while Afzalkhan destroyed a similar idol.

Legend of Pundalik

The saga of Pundalik is one of the most important Mahima legends about Vithoba. How Vithoba came to Pandharpur is a story in which Pundalik is vital. Pundalik is a devoted son to his parents Janudev and Satyavati, who lived in a forest called Dandirvan. But after his wedding, Pundalik begins ill-treating his parents. Tired with their son's misbehavior and ill treatment, the elderly couple decide to leave for Kashi. Legend holds that people who die in the city of Kashi attain salvation and emancipation from the cycle of birth and death; so, many pious Hindus in the bygone era would relocate to Kashi as their end drew near.

However, the elderly couple are not destined to escape their suffering so easily. Upon hearing his parents' plans, Pundalik and his wife decide to join them on pilgrimage. The ill treatment continues. While the youthful son and his wife ride on horseback, the frail old couple walk in bad weather. Pundalik even makes his old parents work to make his own journey comfortable. Every evening, when the party camps for the night, the son forces his parents to groom the horses and do other jobs.

On the way to Kashi, the group reached the ashram (hermitage) of a pious and venerable sage, Kukkutswami. Exhausted, the family decides to spend a few days there. That night, when all were asleep, Pundalik by chance is awake and sees a remarkable vision. Just before dawn, a group of beautiful young women, dressed in soiled clothes, enter the ashram; they clean the floor, fetch water and wash the venerable sage's clothes. After finishing their chores, they go to the prayer-room. When they reappear after prayer, their clothes are spotlessly clean. Then, they vanish as inexplicably as they had appeared.

Pundalik was not moved to raise an alarm, but feels a deep sense of peace witnessing the scene. It remains on his mind the whole day and he resolves to remain awake the next night, and confirm it was not merely a dream. This time, however, Pundalik is very curious. He approaches the beautiful women and asks details. They reply, they are the Ganga (Ganges), Yamuna and other holy rivers of India—revered for their holiness. Pilgrims wish to take a dip in their holy waters to wash away their sins, which in fact are soiling their clothes. Then, the women say: "But O Pundalik, you, with your ill-treatment of your parents, are the greatest sinner of them all!" Pundalik is utterly shocked and his consciousness transforms. He realizes his misdeeds, becomes entirely devoted to his parents and ensures their comfort, even risking his own.

Devotion in any form reaches God swiftly. Impressed by Pundalik's devotion to his parents, Krishna planned to bless Pundalik immediately. So, he left (His abode) for Pundalik's ashram. Krishna knocks at Pundalik's door, when he is busy serving his parents food. Pundalik does realize God is at his door. But such was his devotion to his parents, he wants to complete his duties and only then attend the visitor. Then, Pundalik does something strange but out of real devotion. He throws a brick outside for God to stand on and wait for him until he finishes attending to his parents. It is the first day of monsoon so it is wet and muddy outside.  If Lord Krishna stands upon a brick his feet will remain clean and dry.

Seeing this act, Krishna was extremely impressed and the ever-loving God waited for his devotee. When Pundalik came out, he begged for pardon but far from being displeased, Krishna was taken over by Pundalik's love for his parents and granted a boon. Pundalik requested Krishna to stay back on Earth and bless all his true devotees. He agreed to take the form of Vithoba, or God who stood upon a brick, and a temple came up there. Along with Vithoba, Rukmini (Mother Rukmini, the consort of Krishna) is also worshipped here.

Sant Namdeva Maharaj Payari

An interesting tale is that of the temple's first step called "Sant Namdev Maharaj Pāyari" (step of Sant Namdev Maharaj). The child and future saint, Namdev was an ardent devotee of Vithoba. One day his mother asks him to complete the ritual of "naivedya" (any food made in the house is first offered to God, the ritual comprises placing the offering plate before the deity and sprinkling water around the plate and with a prayer to God). Namdev faithfully does "naivedya" and waits for God to appear and take the offering. But he is disheartened. He keeps praying and requests God to come in person and accept the offering. With no answer, the child starts banging his head at the feet of God. Seeing this utmost devotion and innocence of a child, God appears, eats the offering and blesses Namdev. Namdev asks for being present in the "first step" at His temple, so that he could innumerable devotees will touch him before having the "darshan" (view). So, this first step is called "Sant Namdev Maharaj  Pāyari".

Sant Tukaram
It is also believed that Tukaram - a 17th-century devotee of Krishna in the form of Vithoba - spent his last days in the temple.

The Temple

The main entrance of Lord Vittala's Temple is facing towards the Chandrabhaga or Bhima river. Samadhi of Namadev and Chokamela is at the entrance. Pilgrims will first pray to the Devotees and then enter the temple. A small Ganesh Shrine is present inside the temple as first Shrine. Then, a small hall where bhajans are performed.

A small Shrine for Garuda and Hanuman. Then, after climbing a few steps, we can see the face of Lord Vittala. We can have this Mukha Darshan any time without standing in Queue.
For, Padha Darshan (To touch the Lotus Feet of Lord), there is an entrance which leads to the queue complex outside the temple. It will lead to many small shrines of Bhaktas, then towards the Lord Panduranga. We can touch the feet of Lord. We feel best when we touch the Lord's Lotus feet.
There are Shrines for Rukmini Devi, Satyabhama Devi, Radhika Devi (Rahi), Lord Narasimha, Lord Venkateshwara, Goddess Mahalakshmi, Nagaraj, Ganesha, Annapoorna Devi. There is another mandap where all devotees play like Krishna had played with Gopikas.
It is a great experience.

See also
Rukmini
Rahi (goddess)
Avatars of Vishnu
Chokhamela

References

External links
 Vithoba Temple's daily schedule
 Vithoba Temple Pandharpur - The Divine India

Hindu temples in Maharashtra
Warkari
Haridasa
Vishnu temples
Tourist attractions in Solapur district
Krishna temples
Abhimana temples of Vishnu

Vithoba Temple


Thorn (;  or Thoear) is a village in the municipality of Maasgouw, in the Dutch province of Limburg. It lies on the rivers Meuse and Witbeek. It is known as 'the white village' for its white-washed brick houses in the centre of town. It used to be part of the Imperial Abbey of Thorn.

History
First, the region of Thorn was a swamp nearby the Roman road between Maastricht and Nijmegen. But the region had been drained and about 975, Bishop Ansfried of Utrecht founded a Benedictine nunnery. This monastery
developed since the 12th century into a secular stift or convent. The principal of the stift was the abbess. She was assisted by a chapter of at most twenty ladies of the highest nobility.

Previously the abbess and the chapter were endowed with religious tasks but, since the 12th century, they served secular matters and formed the government of a truly sovereign miniature principality, the smallest independent state in the German Holy Roman Empire, approximately 250 x 250 metres. Besides Thorn, Ittervoort, Grathem, Baexem, Stramproy, Ell, Haler and Molenbeersel belonged to this principality.  After the French invasion in the winter of 1794–95 and the formal abolition in 1797 made an end to the existence of the abbey and the principality of Thorn; Thorn was first part of the department of Meuse-Inférieure, and after the Vienna Congress it became a municipality of the United Kingdom of the Netherlands.

Gallery

See also
 Thorn Abbey

References

States and territories established in 1292
States and territories disestablished in 1797
Municipalities of the Netherlands disestablished in 2007
Populated places in Limburg (Netherlands)
Former municipalities of Limburg (Netherlands)
Maasgouw

Thorn, Netherlands


The Arab Orchestra of Nazareth is an Israeli orchestra that plays Arab and Mediterranean music. It was founded in 1991 by conductor and musicologist Suhil Radwan.

The Nazareth Orchestra performs in Israel and abroad. It has performed in world music festivals as well as Jazz festivals in New York's Central Park, in many European capitals and in the Pas Festival in Morocco. The orchestra's soloists took part in The Samarkand International Oriental Music Competition, winning third prize; in the Earth Festival in Kenya and have also performed in the successful Israeli film The Orchestra Visit. The orchestra has been part of the Israel Festival, the Carmiel Dance Festival, Jaffa Festival, Oud Festival of Tel Aviv and the Culture Of Peace Festival.

The orchestra's manager and international agent is Eli Grunfeld. Its conductor is Dr. Nizar Raduwan. He has released a personal album entitled Haifa (Magda). Among the orchestra's singers are Lubna Salama, Hiba Battihish, Alias Attalla and Maamun Zayud. The orchestra has also performed in special concerts alongside Zehava Ben, David D'or, Dikla, Yasmin Levi and Galit Giat. The orchestra has collaborated in the past with the singer Sapho (France), Omar Faruk Tekbilek (Turkey), Thom Yorke of Radiohead (UK), Radiodervish (Lebanon/Italy), London Sinfonietta (UK), Hind Laroussi (Netherlands) and even the Israeli Oriental Metal band Orphaned Land, as well as Finnish Melodic Death/Progressive Folk Metal band Amorphis (credited as "The Orphaned Land Oriental Orchestra).

Discography
 Inta Umri with Zehava Ben (Helicon Records)
 Live in Nazareth (Magda)
 100 years to Umm Kulthum (Magda)

See also
Music of Israel
Culture of Israel

References

Arabic music
Israeli orchestras
Nazareth

Arab Orchestra of Nazareth


An aglet, or aiglet, is the small tip on the end of a shoelace or rope. It can be plastic or metal. It keeps the fibres from fraying or unwinding. This makes it easier to hold, and easier to feed through a hole, such as a grommmet, eyelet, or lacing guides.

The word aglet (or aiglet) comes from the Old French word, aguillette (or aiguillette), which means needle. This in turn comes from acus, Latin for needle. An aglet is like a small needle at the end of a cord.

Types
There are two main types of aglets. Some are purely functional, that is to simply stop fraying, while others can also be decorative. Decorative aglets are on the end of decorative cords, such as bolo ties, or on the aiguillettes of military dress uniforms.

Aglets today are most often made of plastic; they also have been made of metal, glass, and stone. Many were highly ornamental and made of metals such as silver. Before the invention of buttons, they were used on the ends of ribbons to hold clothing together. Sometimes they were formed into small figures. Shakespeare called these an "aglet baby" in The Taming of the Shrew.

Homemade aglets can be made out of adhesive tape, wax, resin, glue, thread, heat shrink or metal tubing, and by simply knotting or melting the end of a lace or cord. During the Great Depression, aglets were made out of paper and glue.

References

Other websites
Aglets on Ian's Shoelace Site

Footwear

Aglet


Rádio BandNews FM is a Brazilian all news radio network. It first started in 20 March 2005. It is owned by Grupo Bandeirantes de Comunicação.

The network started broadcasting at exactly midnight in 20 March 2005, after at 23:59, Rádio Cidade said goodbye to its listeners after 25 years and played the last top 3 songs. The first on-air journalist was Carlos Nascimento.

Currently, it serves ten cities: Brasilia, Rio de Janeiro, São Paulo, Belo Horizonte, Porto Alegre, Curitiba, Fortaleza, Vitoria, Joao Pessoa and Salvador. The first 4 cities carry the network's de facto flagship stations.

Campinas and Ribeirao Preto (in 106.7 FM and 96.7 FM) stopped carrying BandNews FM programming in 2014. They are now branded as Band FM.

BandNews FM is well known for its slogan Em 20 minutos, tudo pode mudar (In 20 minutes, everything can happen), which refers to how the news is updated every 20 minutes. This format (that allows listeners to tune in at any time of the day to get the leading stories of the moment) is inspired by 1010 WINS, America's most well-known news station.

From 6:00 to 23:00, on these news blocks, 6 minutes of them being given to each individual affiliate for providing local stories, read by a local announcer. Normally there's a local-only news programme from 9:00 to 11:00. Overnights feature live national announcers, broadcast by all affiliates.

The network also broadcasts selected Brazilian football matches, alongside Bandeirantes and CBN, two likewise-formatted radio networks.

Frequencies
 96.9 MHz (São Paulo)
 90.3 MHz (Rio de Janeiro)
 89.5 MHz (Belo Horizonte)
 90.5 MHz (Brasília)
 96.3 MHz (Curitiba)
 99.1 MHz (Salvador)
 99.3 MHz (Porto Alegre)
 101.7 MHz (Fortaleza)
 103.3 MHz (João Pessoa)
 90.1 MHz (Vitória)

Brazilian culture
Radio
2005 establishments in South America
2000s establishments in Brazil

BandNews FM


Pyotr Petrovich Vershigora (first name also Petr) () or Petro Petrovych Vershyhora () ( – 23 March 1963) was one of the leaders of the Soviet partisan movement in Ukraine, Belarus and Poland and later a writer.

Petro Vershigora was born in the village of Severinovca near the Transnistrian town of Rybnitsa. His parents were ethnic Ukrainian teachers at the local rural school, who died during his childhood. As a young orphan he worked at various jobs, including shepherd, miller, and librarian, as well as amateur actor and musician in his native village. In 1927, after completing his conscript military service, he enrolled in the Odessa Fine Arts Academy and upon graduation worked as an actor and stage manager.

In 1936 Vershigora completed his studies at cinema school and worked on several documentary films with the Kiev cinematographic company. Following the German invasion of the Soviet Union, he joined the Red Army. On 23 June 1942 he was air dropped on a reconnaissance mission in the German-occupied Oryol region with orders to join the underground resistance movement there.

Within a few months Vershigora joined the partisan units led by Sydir Kovpak in northeastern Ukraine. After the death of Semyon Rudnev in the summer of 1943, he became Kovpak's right-hand man and the head of his scouting and reconnaissance elements. Under his leadership, the 1st Ukrainian Partisan Division raided German-occupied western Belarus and eastern Poland, harassing the German rear. On 3 July 1944 they joined the regular Soviet army that was fighting to expel German forces from Belarus. In August 1944, after three years of fighting, Vershigora was promoted to the rank of major general.

After the war Vershigora taught at the military academy in Moscow and wrote a number of books, including Lyudi s chistoi sovestyu (People with a Clear Conscience, 1947), his memoirs about the war.

Honours and awards
 Hero of the Soviet Union
 Two Orders of Lenin
 Order of the Red Banner
 Order of Bogdan Khmelnitsky 1st class
 Medal "Partisan of the Patriotic War" 1st class
 Medal "For the Victory over Germany in the Great Patriotic War 1941–1945"

References
 War Hero Pyotr Vershigora
 People with a Clear Conscience — Pyotr Petrovich Vershigora's Memoirs

1905 births
1963 deaths
People from Camenca District
People from Olgopolsky Uyezd
Transnistrian people of Ukrainian descent
Soviet major generals
Soviet military personnel of World War II
Soviet partisans in Ukraine
Soviet writers
Ukrainian male writers
Ukrainian people of World War II
Recipients of the Stalin Prize
Heroes of the Soviet Union
Recipients of the Order of Lenin
Recipients of the Order of the Red Banner
Recipients of the Order of Bogdan Khmelnitsky (Soviet Union), 1st class
Ukrainian anti-fascists

Pyotr Vershigora


The terrainability of a machine or robot is defined as its ability to negotiate terrain irregularities.

Terrainability is a term coined in the research community and related to locomotion in the field of mobile robotics. Its various definitions generically describe the ability of the robot to handle various terrains in terms of their ground support, obstacle sizes and spacing, passive/dynamic stability, etc.

References

Robotics

Terrainability


Angie Be (born 1977) pseudonym of Élodie Bouche, is a French singer and former candidate of Secret Story 2009 (France). Her single "Soundwaves" reached number 17 on the French charts in 2009 and remained on the chart for almost one year. In December 2009, a French version of Soundwaves was available digitally. This version was in the musical programming of Fun Radio during October 2009 – March 2010.

She created and directed a manicure company at home from 2007 to 2009 in Southern France. She was especially known for her television appearances as model for the muscle stimulator Sport-Elec brand and her performances as Jenny on the automoto.fr site after her participation in the TV reality show.

She is the mother of a little girl, Manon, and is now separated from the father of this one. She dated another candidate of the TV show, Romain Chavent, and was to marry him, but announced two months later that the marriage was annulled.

In 2009, she won the Eurodanceweb Award with her single "Soundwaves". Her next single will be "Forever".

Awards and nominations

References

1977 births
Living people
French female models
Big Brother (France) participants
21st-century French singers
21st-century French women singers

Angie Be


In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures (or forms, also variously known as resonance structures or canonical structures) into a resonance hybrid (or hybrid structure) in valence bond theory. It has particular value for analyzing delocalized electrons where the bonding cannot be expressed by one single Lewis structure.
It is considered as the accurate structure for a compound.

Overview
Under the framework of valence bond theory, resonance is an extension of the idea that the bonding in a chemical species can be described by a Lewis structure.  For many chemical species, a single Lewis structure, consisting of atoms obeying the octet rule, possibly bearing formal charges, and connected by bonds of positive integer order, is sufficient for describing the chemical bonding and rationalizing experimentally determined molecular properties like bond lengths, angles, and dipole moment. However, in some cases, more than one Lewis structure could be drawn, and experimental properties are inconsistent with any one structure.  In order to address this type of situation, several contributing structures are considered together as an average, and the molecule is said to be represented by a resonance hybrid in which several Lewis structures are used collectively to describe its true structure.  For instance, in NO2–, nitrite anion, the two N–O bond lengths are equal, even though no single Lewis structure has two N–O bonds with the same formal bond order. However, its measured structure is consistent with a description as a resonance hybrid of the two major contributing structures shown above: it has two equal N–O bonds of 125 pm, intermediate in length between a typical N–O single bond (145 pm in hydroxylamine, H2N–OH) and N–O double bond (115 pm in nitronium ion, [O=N=O]+).  According to the contributing structures, each N–O bond is an average of a formal single and formal double bond, leading to a true bond order of 1.5.  By virtue of this averaging, the Lewis description of the bonding in NO2– is reconciled with the experimental fact that the anion has equivalent N–O bonds.

The resonance hybrid represents the actual molecule as the "average" of the contributing structures, with bond lengths and partial charges taking on intermediate values compared to those expected for the individual Lewis structures of the contributors, were they to exist as "real" chemical entities. The contributing structures differ only in the formal apportionment of electrons to the atoms, and not in the actual physically and chemically significant electron or spin density.  While contributing structures may differ in formal bond orders and in formal charge assignments, all contributing structures must have the same number of valence electrons and the same spin multiplicity.

Because electron delocalization lowers the potential energy of a system, any species represented by a resonance hybrid is more stable than any of the (hypothetical) contributing structures. Electron delocalization stabilizes a molecule because the electrons are more evenly spread out over the molecule, decreasing electron-electron repulsion. The difference in potential energy between the actual species and the (computed) energy of the contributing structure with the lowest potential energy is called the resonance energy or delocalization energy.  The magnitude of the resonance energy depends on assumptions made about the hypothetical "non-stabilized" species and the computational methods used and does not represent a measurable physical quantity, although comparisons of resonance energies computed under similar assumptions and conditions may be chemically meaningful.

Molecules with an extended π system such as linear polyenes and polyaromatic compounds are well described by resonance hybrids as well as by delocalised orbitals in molecular orbital theory.

Resonance vs isomerism
Resonance is to be distinguished from isomerism. Isomers are molecules with the same chemical formula but are distinct chemical species with different arrangements of atomic nuclei in space.  Resonance contributors of a molecule, on the other hand, can only differ in the way electrons are formally assigned to atoms in the Lewis structure depictions of the molecule.  Specifically, when a molecular structure is said to be represented by a resonance hybrid, it does not mean that electrons of the molecule are "resonating" or shifting back and forth between several sets of positions, each one represented by a Lewis structure.  Rather, it means that the set of contributing structures represents an intermediate structure (a weighted average of the contributors), with a single, well-defined geometry and distribution of electrons.  It is incorrect to regard resonance hybrids as rapidly interconverting isomers, even though the term "resonance" might evoke such an image.  (As described below, the term "resonance" originated as a classical physics analogy for a quantum mechanical phenomenon, so it should not be construed too literally.) Symbolically, the double headed arrow A<->B is used to indicate that A and B are contributing forms of a single chemical species (as opposed to an equilibrium arrow, e.g., A <=> B; see below for details on usage).

A non-chemical analogy is illustrative: one can describe the characteristics of a real animal, the narwhal, in terms of the characteristics of two mythical creatures: the unicorn, a creature with a single horn on its head, and the leviathan, a large, whale-like creature.  The narwhal is not a creature that goes back and forth between being a unicorn and being a leviathan, nor do the unicorn and leviathan have any physical existence outside the collective human imagination.  Nevertheless, describing the narwhal in terms of these imaginary creatures provides a reasonably good description of its physical characteristics.

Due to confusion with the physical meaning of the word resonance, as no entities actually physically "resonate", it has been suggested that the term resonance be abandoned in favor of delocalization and resonance energy abandoned in favor of delocalization energy. A resonance structure becomes a contributing structure and the resonance hybrid becomes the hybrid structure. The double headed arrows would be replaced by commas to illustrate a set of structures, as arrows of any type may suggest to beginning students that a chemical change is taking place.

Representation in diagrams

In diagrams, contributing structures are typically separated by double-headed arrows (↔). The arrow should not be confused with the right and left pointing equilibrium arrow (). All structures together may be enclosed in large square brackets, to indicate they picture one single molecule or ion, not different species in a chemical equilibrium.

Alternatively to the use of contributing structures in diagrams, a hybrid structure can be used. In a hybrid structure, pi bonds that are involved in resonance are usually pictured as curves or dashed lines, indicating that these are partial rather than normal complete pi bonds. In benzene and other aromatic rings, the delocalized pi-electrons are sometimes pictured as a solid circle.

History
The concept first appeared in 1899 in Johannes Thiele's "Partial Valence Hypothesis" to explain the unusual stability of benzene which would not be expected from August Kekulé's structure proposed in 1865 with alternating single and double bonds. Benzene undergoes substitution reactions, rather than addition reactions as typical for alkenes. He proposed that the carbon-carbon bond in benzene is intermediate of a single and double bond.

The resonance proposal also helped explain the number of isomers of benzene derivatives. For example, Kekulé's structure would predict four dibromobenzene isomers, including two ortho isomers with the brominated carbon atoms joined by either a single or a double bond. In reality there are only three dibromobenzene isomers and only one is ortho, in agreement with the idea that there is only one type of carbon-carbon bond, intermediate between a single and a double bond.

The mechanism of resonance was introduced into quantum mechanics by Werner Heisenberg in 1926 in a discussion of the quantum states of the helium atom. He compared the structure of the helium atom with the classical system of resonating coupled harmonic oscillators. In the classical system, the coupling produces two modes, one of which is lower in frequency than either of the uncoupled vibrations; quantum mechanically, this lower frequency is interpreted as a lower energy. Linus Pauling used this mechanism to explain the partial valence of molecules in 1928, and developed it further in a series of papers in 1931-1933. The alternative term mesomerism popular in German and French publications with the same meaning was introduced by C. K. Ingold in 1938, but did not catch on in the English literature. The current concept of mesomeric effect has taken on a related but different meaning. The double headed arrow was introduced by the German chemist Fritz Arndt who preferred the German phrase zwischenstufe or intermediate stage.

Resonance theory dominated over competing Hückel method for two decades thanks to being relatively easier to understand for chemists without fundamental physics background, even if they couldn't grasp the concept of quantum superposition and confused it with tautomerism. Pauling and Wheland themselves characterized Erich Hückel's approach as "cumbersome" at the time, and his lack of communication skills contributed: when Robert Robinson sent him a friendly request, he responded arrogantly that he is not interested in organic chemistry.

In the Soviet Union, resonance theory – especially as developed by Pauling – was attacked in the early 1950s as being contrary to the Marxist principles of dialectical materialism, and in June 1951 the Soviet Academy of Sciences under the leadership of Alexander Nesmeyanov convened a conference on the chemical structure of organic compounds, attended by 400 physicists, chemists, and philosophers, where "the pseudo-scientific essence of the theory of resonance was exposed and unmasked".

Major and minor contributors

One contributing structure may resemble the actual molecule more than another (in the sense of energy and stability). Structures with a low value of potential energy are more stable than those with high values and resemble the actual structure more. The most stable contributing structures are called major contributors. Energetically unfavourable and therefore less favorable structures are minor contributors. With rules listed in rough order of diminishing importance, major contributors are generally structures that

obey as much as possible the octet rule (8 valence electrons around each atom rather than having deficiencies or surplus, or 2 electrons for Period 1 elements);
have a maximum number of covalent bonds;
carry a minimum of formally charged atoms, with the separation for unlike and like charges minimized and maximized, respectively;
place negative charge, if any, on the most electronegative atoms and positive charge, if any, on the most electropositive;
do not deviate substantially from idealized bond lengths and angles (e.g., the relative unimportance of Dewar-type resonance contributors for benzene);
maintain aromatic substructures locally while avoiding anti-aromatic ones (see Clar sextet and biphenylene).

A maximum of eight valence electrons is strict for the Period 2 elements Be, B, C, N, O, and F, as is a maximum of two for H and He and effectively for Li as well.  The issue of expansion of the valence shell of third period and heavier main group elements is controversial.  A Lewis structure in which a central atom has a valence electron count greater than eight traditionally implies the participation of d orbitals in bonding.  However, the consensus opinion is that while they may make a marginal contribution, the participation of d orbitals is unimportant, and the bonding of so-called hypervalent molecules are, for the most part, better explained by charge-separated contributing forms that depict three-center four-electron bonding.  Nevertheless, by tradition, expanded octet structures are still commonly drawn for functional groups like sulfoxides, sulfones, and phosphorus ylides, for example.  Regarded as a formalism that does not necessarily reflect the true electronic structure, such depictions are preferred by the IUPAC over structures featuring partial bonds, charge separation, or dative bonds.

Equivalent contributors contribute equally to the actual structure, while the importance of nonequivalent contributors is determined by the extent to which they conform to the properties listed above.  A larger number of significant contributing structures and a more voluminous space available for delocalized electrons lead to stabilization (lowering of the energy) of the molecule.

Examples

Aromatic molecules

In benzene the two cyclohexatriene Kekulé structures, first proposed by Kekulé, are taken together as contributing structures to represent the total structure. In the hybrid structure on the right, the dashed hexagon replaces three double bonds, and represents six electrons in a set of three molecular orbitals of π symmetry, with a nodal plane in the plane of the molecule.

In furan a lone pair of the oxygen atom interacts with the π orbitals of the carbon atoms. The curved arrows depict the permutation of delocalized π electrons, which results in different contributors.

Electron-rich molecules
The ozone molecule is represented by two contributing structures. In reality the two terminal oxygen atoms are equivalent and the hybrid structure is drawn on the right with a charge of − on both oxygen atoms and partial double bonds with a full and dashed line and bond order .

For hypervalent molecules, the rationalization described above can be applied to generate contributing structures to explain the bonding in such molecules. Shown below are the contributing structures of a 3c-4e bond in xenon difluoride.
[\mathsf{F-XeF^- <-> F^-Xe-F}]

Electron-deficient molecules

The allyl cation has two contributing structures with a positive charge on the terminal carbon atoms. In the hybrid structure their charge is +. The full positive charge can also be depicted as delocalized among three carbon atoms.

The diborane molecule is described by contributing structures, each with electron-deficiency on different atoms. This reduces the electron-deficiency on each atom and stabilizes the molecule. Below are the contributing structures of an individual 3c-2e bond in diborane.

Reactive intermediates

Often, reactive intermediates such as carbocations and free radicals have more delocalized structure than their parent reactants, giving rise to unexpected products. The classical example is allylic rearrangement. When 1 mole of HCl adds to 1 mole of 1,3-butadiene, in addition to the ordinarily expected product 3-chloro-1-butene, we also find 1-chloro-2-butene. Isotope labelling experiments have shown that what happens here is that the additional double bond shifts from 1,2 position to 2,3 position in some of the product. This and other evidence (such as NMR in superacid solutions) shows that the intermediate carbocation must have a highly delocalized structure, different from its mostly classical (delocalization exists but is small) parent molecule. This cation (an allylic cation) can be represented using resonance, as shown above.

This observation of greater delocalization in less stable molecules is quite general. The excited states of conjugated dienes are stabilised more by conjugation than their ground states, causing them to become organic dyes.

A well-studied example of delocalization that does not involve π electrons (hyperconjugation) can be observed in the non-classical 2-Norbornyl cation. Another example is methanium (). These can be viewed as containing three-center two-electron bonds and are represented either by contributing structures involving rearrangement of σ electrons or by a special notation, a Y that has the three nuclei at its three points.

Delocalized electrons are important for several reasons; a major one is that an expected chemical reaction may not occur because the electrons delocalize to a more stable configuration, resulting in a reaction that happens at a different location. An example is the Friedel–Crafts alkylation of benzene with 1-chloro-2-methylpropane; the carbocation rearranges to a tert-butyl group stabilized by hyperconjugation, a particular form of delocalization. Delocalization leads to lengthening of wavelength of electron therefore decreases the energy.

Benzene

Bond lengths

Comparing the two contributing structures of benzene, all single and double bonds are interchanged. Bond lengths can be measured, for example using X-ray diffraction. The average length of a C–C single bond is 154 pm; that of a C=C double bond is 133 pm. In localized cyclohexatriene, the carbon–carbon bonds should be alternating 154 and 133 pm. Instead, all carbon–carbon bonds in benzene are found to be about 139 pm, a bond length intermediate between single and double bond. This mixed single and double bond (or triple bond) character is typical for all molecules in which bonds have a different bond order in different contributing structures. Bond lengths can be compared using bond orders. For example, in cyclohexane the bond order is 1 while that in benzene is 1 + (3 ÷ 6) = . Consequently, benzene has more double bond character and hence has a shorter bond length than cyclohexane.

Resonance energy

Resonance (or delocalization) energy is the amount of energy needed to convert the true delocalized structure into that of the most stable contributing structure. The empirical resonance energy can be estimated by comparing the enthalpy change of hydrogenation of the real substance with that estimated for the contributing structure.

The complete hydrogenation of benzene to cyclohexane via 1,3-cyclohexadiene and cyclohexene is exothermic; 1 mole of benzene delivers 208.4 kJ (49.8 kcal).

Hydrogenation of one mole of double bonds delivers 119.7 kJ (28.6 kcal), as can be deduced from the last step, the hydrogenation of cyclohexene. In benzene, however, 23.4 kJ (5.6 kcal) are needed to hydrogenate one mole of double bonds. The difference, being 143.1 kJ (34.2 kcal), is the empirical resonance energy of benzene. Because 1,3-cyclohexadiene also has a small delocalization energy (7.6 kJ or 1.8 kcal/mol) the net resonance energy, relative to the localized cyclohexatriene, is a bit higher: 151 kJ or 36 kcal/mol.

This measured resonance energy is also the difference between the hydrogenation energy of three 'non-resonance' double bonds and the measured hydrogenation energy:
(3 × 119.7) − 208.4 = 150.7 kJ/mol (36 kcal).

Regardless of its exact value, resonance energies of various related compounds provide insights into their bonding. The resonance energies for pyrrole, thiophene, and furan are, respectively, 88, 121, and
67 kJ/mol (21, 29, and 16 kcal/mol).  Thus, these heterocycles are far less aromatic than benzene, as is manifested in the lability of these rings.

Quantum mechanical description in valence bond (VB) theory

Resonance has a deeper significance in the mathematical formalism of valence bond theory (VB). Quantum mechanics requires that the wavefunction of a molecule obey its observed symmetry. If a single contributing structure does not achieve this, resonance is invoked.

For example, in benzene, valence bond theory begins with the two Kekulé structures which do not individually possess the sixfold symmetry of the real molecule. The theory constructs the actual wave function as a linear superposition of the wave functions representing the two structures. As both Kekulé structures have equal energy, they are equal contributors to the overall structure – the superposition is an equally weighted average, or a 1:1 linear combination of the two in the case of benzene. The symmetric combination gives the ground state, while the antisymmetric combination gives the first excited state, as shown.

In general, the superposition is written with undetermined coefficients, which are then variationally optimized to find the lowest possible energy for the given set of basis wave functions. When more contributing structures are included, the molecular wave function becomes more accurate and more excited states can be derived from different combinations of the contributing structures.

Comparison with molecular orbital (MO) theory

In molecular orbital theory, the main alternative to valence bond theory, the molecular orbitals (MOs) are approximated as sums of all the atomic orbitals (AOs) on all the atoms; there are as many MOs as AOs. Each AOi has a weighting coefficient ci that indicates the AO's contribution to a particular MO. For example, in benzene, the MO model gives us 6 π MOs which are combinations of the 2pz AOs on each of the 6 C atoms. Thus, each π MO is delocalized over the whole benzene molecule and any electron occupying an MO will be delocalized over the whole molecule. This MO interpretation has inspired the picture of the benzene ring as a hexagon with a circle inside. When describing benzene, the VB concept of localized σ bonds and the MO concept of delocalized π orbitals are frequently combined in elementary chemistry courses.

The contributing structures in the VB model are particularly useful in predicting the effect of substituents on π systems such as benzene. They lead to the models of contributing structures for an electron-withdrawing group and electron-releasing group on benzene. The utility of MO theory is that a quantitative indication of the charge from the π system on an atom can be obtained from the squares of the weighting coefficient ci on atom Ci. Charge qi ≈ c. The reason for squaring the coefficient is that if an electron is described by an AO, then the square of the AO gives the electron density. The AOs are adjusted (normalized) so that AO2 = 1, and qi ≈ (ciAOi)2 ≈ c. In benzene, qi = 1 on each C atom. With an electron-withdrawing group qi < 1 on the ortho and para C atoms and qi > 1 for an electron-releasing group.

Coefficients

Weighting of the contributing structures in terms of their contribution to the overall structure can be calculated in multiple ways, using "Ab initio" methods derived from Valence Bond theory, or else from the Natural Bond Orbitals (NBO) approaches of Weinhold NBO5 , or finally from empirical calculations based on the Hückel method. A Hückel method-based software for teaching resonance is available on the HuLiS Web site.

Charge delocalization
In the case of ions it is common to speak about delocalized charge (charge delocalization). An example of delocalized charge in ions can be found in the carboxylate group, wherein the negative charge is centered equally on the two oxygen atoms. Charge delocalization in anions is an important factor determining their reactivity (generally: the higher the extent of delocalization the lower the reactivity) and, specifically, the acid strength of their conjugate acids. As a general rule, the better delocalized is the charge in an anion the stronger is its conjugate acid. For example, the negative charge in perchlorate anion () is evenly distributed among the symmetrically oriented oxygen atoms (and a part of it is also kept by the central chlorine atom). This excellent charge delocalization combined with the high number of oxygen atoms (four) and high electronegativity of the central chlorine atom leads to perchloric acid being one of the strongest known acids with a pKa value of −10.
The extent of charge delocalization in an anion can be quantitatively expressed via the WAPS (weighted average positive sigma) parameter parameter and an analogous WANS (weighted average negative sigma) parameter is used for cations.

WAPS and WANS values are given in e/Å4. Larger values indicate more localized charge in the corresponding ion.

See also

 Hückel molecular orbital theory
 Conjugated system
 Fluxional molecule
 Avoided crossing

External links

References

Chemical bonding
Physical chemistry
Electronic structure methods

Resonance (chemistry)


In association football, a substitute is a player who is brought on to the pitch during a match in exchange for a player who is currently playing. Substitutions can be made for many reasons. Sometimes, they are made to replace a player who has become tired or injured. Substitutes can also replace a player who is playing poorly, or can be for tactics. For example, substitute strikers can be brought on for defenders if the team needs to attack. The term "super-sub" refers to a substitution made by the manager that saves the game. This is generally done by scoring one or more late goals. The goals can equalize or win the team the match. Players who have been called "super-subs" include David Fairclough for Liverpool, Adam Le Fondre for Reading, Ole Gunnar Solskjær and Javier Hernández for Manchester United, and Edin Džeko for Manchester City  among others.

References

Football (soccer) terminology

Substitute (association football)