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Valence bond theory

Valence bond theory

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In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, valence bond (VB) theory is one of two basic theories, along with molecular orbital (MO) theory
Molecular orbital theory
In chemistry, molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule...

, that were developed to use the methods of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 to explain chemical bond
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

ing. It focuses on how the atomic orbital
Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

s of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.

History


In 1916, G.N. Lewis proposed that a chemical bond forms by the interaction of two shared bonding electrons, with the representation of molecules as Lewis structure
Lewis structure
Lewis structures are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds...

s. In 1927 the Heitler
Walter Heitler
Walter Heinrich Heitler was a German physicist who made contributions to quantum electrodynamics and quantum field theory...

London
Fritz London
Fritz Wolfgang London was a German theoretical physicist. His fundamental contributions to the theories of chemical bonding and of intermolecular forces are today considered classic and are discussed in standard textbooks of physical chemistry.With his brother Heinz, he made a significant...

 theory was formulated which for the first time enabled the calculation of bonding properties of the hydrogen molecule H2 based on quantum mechanical considerations. Specifically, Walter Heitler
Walter Heitler
Walter Heinrich Heitler was a German physicist who made contributions to quantum electrodynamics and quantum field theory...

 determined how to use Schrödinger's wave equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

 (1925) to show how two hydrogen atom wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...

s join together, with plus, minus, and exchange terms, to form a covalent bond
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....

. He then called up his associate Fritz London
Fritz London
Fritz Wolfgang London was a German theoretical physicist. His fundamental contributions to the theories of chemical bonding and of intermolecular forces are today considered classic and are discussed in standard textbooks of physical chemistry.With his brother Heinz, he made a significant...

 and they worked out the details of the theory over the course of the night. Later, Linus Pauling
Linus Pauling
Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists of the 20th century...

 used the pair bonding ideas of Lewis together with Heitler-London theory to develop two other key concepts in VB theory: resonance
Resonance (chemistry)
In chemistry, resonance or mesomerism is a way of describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis formula...

 (1928) and orbital hybridization (1930). According to Charles Coulson
Charles Coulson
Charles Alfred Coulson FRS was an applied mathematician, theoretical chemist and religious author.His major scientific work was as a pioneer of the application of the quantum theory of valency to problems of molecular structure, dynamics and reactivity...

, author of the noted 1952 book Valence, this period marks the start of "modern valence bond theory", as contrasted with older valence bond theories, which are essentially electronic theories of valence
Valence (chemistry)
In chemistry, valence, also known as valency or valence number, is a measure of the number of bonds formed by an atom of a given element. "Valence" can be defined as the number of valence bonds...

 couched in pre-wave-mechanical terms. Resonance theory was criticized as imperfect by Soviet chemists during the 1950s.

Theory


According to this theory a covalent bond is formed between the two atoms by the overlap of half filled valence atomic orbitals of each atom containing one unpaired electron. A valence bond structure is similar to a Lewis structure
Lewis structure
Lewis structures are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds...

, but where a single Lewis structure cannot be written, several valence bond structures are used. Each of these VB structures represents a specific Lewis structure. This combination of valence bond structures is the main point of resonance
Resonance (chemistry)
In chemistry, resonance or mesomerism is a way of describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis formula...

 theory. Valence bond theory considers that the overlapping atomic orbitals of the participating atoms form a chemical bond
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

. Because of the overlapping, it is most probable
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 that electrons should be in the bond region. Valence bond theory views bonds as weakly coupled orbitals (small overlap). Valence bond theory is typically easier to employ in ground state
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...

 molecules.

The overlapping atomic orbitals can differ. The two types of overlapping orbitals are sigma and pi. Sigma bond
Sigma bond
In chemistry, sigma bonds are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most clearly defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is...

s occur when the orbitals of two shared electrons overlap head-to-head. Pi bond
Pi bond
In chemistry, pi bonds are covalent chemical bonds where two lobes of one involved atomic orbital overlap two lobes of the other involved atomic orbital...

s occur when two orbitals overlap when they are parallel. For example, a bond between two s-orbital electrons is a sigma bond, because two spheres are always coaxial. In terms of bond order, single bonds have one sigma bond, double bonds consist of one sigma bond and one pi bond, and triple bonds contain one sigma bond and two pi bonds. However, the atomic orbitals for bonding may be hybrids. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an atomic orbital with the proper character for the bonding is called hybridization.

VB theory today


Valence bond theory now complements molecular orbital (MO) theory
Molecular orbital
In chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first...

, which does not adhere to the VB idea that electron pairs are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbital
Molecular orbital
In chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first...

s which can extend over the entire molecule. MO theory can predict magnetic
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...

 properties in a straightforward manner, while valence bond theory gives similar results but is more complicated. Valence bond theory views aromatic
Aromaticity
In organic chemistry, Aromaticity is a chemical property in which a conjugated ring of unsaturated bonds, lone pairs, or empty orbitals exhibit a stabilization stronger than would be expected by the stabilization of conjugation alone. The earliest use of the term was in an article by August...

 properties of molecules as due to resonance between Kekulé
Friedrich August Kekulé von Stradonitz
Friedrich August Kekule von Stradonitz was a German organic chemist. From the 1850s until his death, Kekule was one of the most prominent chemists in Europe, especially in theoretical chemistry...

, Dewar
James Dewar
Sir James Dewar FRS was a Scottish chemist and physicist. He is probably best-known today for his invention of the Dewar flask, which he used in conjunction with extensive research into the liquefaction of gases...

 and possibly ionic structures, while molecular orbital theory views it as delocalization of the π-electrons. The underlying mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 are also more complicated limiting VB treatment to relatively small molecules. On the other hand, VB theory provides a much more accurate picture of the reorganization of electronic charge that takes place when bonds are broken and formed during the course of a chemical reaction. In particular, valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple molecular orbital theory predicts dissociation into a mixture of atoms and ions.

More recently, several groups have developed what is often called modern valence bond theory. This replaces the overlapping atomic orbitals by overlapping valence bond orbitals that are expanded over a large number of basis functions
Basis set (chemistry)
A basis set in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined. Usually these functions are atomic orbitals, in that they are centered on atoms. Otherwise, the...

, either centered each on one atom to give a classical valence bond picture, or centered on all atoms in the molecule. The resulting energies are more competitive with energies from calculations where electron correlation is introduced based on a Hartree-Fock
Hartree-Fock
In computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system....

reference wavefunction. The most recent text is by Shaik and Hiberty.

Applications of VB theory


An important aspect of the VB theory is the condition of maximum overlap which leads to the formation of the strongest possible bonds. This theory is used to explain the covalent bond formation in many molecules.

For Example in the case of the F2 molecule the F - F bond is formed by the overlap of pz orbitals of the two F atoms, each containing an unpaired electron. Since the natures of the overlapping orbitals are different in H2 and F2 molecules, the bond strength and bond lengths differ between
H2 and F2 molecules.

In an HF molecule the covalent bond is formed by the overlap of the 1s orbital of H and the 2pz orbital of F, each containing an unpaired electron. Mutual sharing of electrons between H and F results in a covalent bond in HF.