Introduction

In chemistry, valence bond theory is one of 2 essential theories, along via molecular orbital theory that was expanded to utilize the process of quantum mechanics to clarify chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms join on molecular formation to provide individual chemical bonds. In contrast, molecular orbital theory has orbitals that cover the whole molecule. In the year 1916, G.N. Lewis proposed that a chemical bond forms via the interaction of 2 shared bonding electrons, through the illustration of molecules as Lewis structures. In the year 1927 the Heitler-London theory was formulated which for the 1^st time enabled the computation of bonding properties of the hydrogen molecule H₂ depend on quantum mechanical considerations. Particularly, Walter Heitler determined how to utilize Schrödinger's wave equation (1925) to illustrate how 2 hydrogen atom wave functions join together, by plus, minus, and exchange terms, to form a covalent bond.

Definition of Valence Bond Theory

The valence-bond approach considers the overlap of the atomic orbitals (AO) of the participation atoms to form a chemical bond. Due to the overlapping, electrons are localized in the bond region. The overlapping AOs can be of different kinds, for instance, a sigma bond might be shaped through the overlapping the subsequent AOs (Waterloo, 2009).

Chemical bonds shaped due to overlap of atomic orbitals

Though, the atomic orbitals for linking might not be 'pure' atomic orbitals straight from the solution of the Schrodinger equation. Frequently, the linking atomic orbitals contain a character of numerous possible kinds of orbitals. The processes to obtain an AO through the proper   character for the linking are termed hybridisation. The consequential atomic orbitals are termed hybridised atomic orbitals or merely hybrid orbitals.

We shall appear at the shapes of several hybrid orbitals first, since such shapes find out the forms of the molecules.

Hybridisation of Atomic Orbitals

The solution to the Schrodinger Equation provides the wave functions for the following atomic orbitals:

1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, and so on.

For atoms enclosing 2 or more electrons, the energy levels are transferred through respect to those of the H atom. An atomic orbital is in fact the energy state of an electron bound to an atomic nucleus. The energy state transforms when one atom is linked to another atom.

Quantum mechanical approaches through combining the wave functions to provide new wave functions are termed hybridisation of atomic orbitals. Hybridisation has a sound mathematical foundation, but it is a little as well complicated to illustrate the details here. Leaving out the jargons, we can say that a fantasy mixing procedure changes a set of atomic orbitals to a new set of hybrid atomic orbitals or hybrid orbitals.

At this level, we consider the subsequent hybrid orbitals:

sp sp² sp³ sp³d sp³d²

The sp Hybrid Atomic Orbitals

The sp hybrid atomic orbitals are possible states of electron in an atom, especially when it is bonded to others. These electron states have half 2s and half 2p characters. From a mathematical view point, there are two ways to combine the 2s and 2p atomic orbitals:

sp₁ = 2s + 2p

sp₂ = 2s - 2p

Such energy states (sp₁ and sp₂) have a region of high electron probability each, and the two atomic orbitals are located opposite to each other, centered on the atom. The sp hybrid orbitals are represented by this photograph.

For instance, the  molecule  H-Be-H  is formed due to the overlapping of two 1s orbitals of 2 H  atoms and the 2 sp hybridised orbitals of Be. Therefore, the H-

               1s            1s 

H-Be-H H sp¹ Be sp² H

             1s            1s

Be-H molecule is linear. The diagram here illustrates the overlapping of AOs in the molecule H-Be-H.

The ground state electronic configuration of Be is 1s²2s², and one may think of the electronic configuration 'before' bonding as 1s²sp². The two electrons in the sp hybrid orbitals have the same energy.

 Linear molecules ClBeCl

                              HCCH

                              HCN

                             O=C=O

We might say that the concept of hybridizing AOs for the bonding is just a story made up to explain the molecular shape of Cl-Be-Cl. We are right! The story is lovely and interesting, though.

In common, when 2 and only 2 atoms bond to a third atom and the third atom makes utilize of the sp hybridised orbitals, the 3 atoms are on a straight line. For instance, sp hybrid orbitals are utilized in the central atoms in the molecules revealed on the right.

The sp² Hybrid Orbitals

The energy states of the valence electrons in atoms of the 2^nd period are in the 2s and 2p orbitals. If we combine two of the 2p orbitals through a 2s orbital, we end up by three sp² hybridised orbitals. Such three orbitals lie on a plane, and they point to the vertices of an equilateral triangle. When the central atom makes employ of sp² hybridised orbitals, the compound so formed has a trigonal shape. BF₃ is this molecule:

Not all three sp² hybridised orbitals have to be utilized in bonding. One of the orbitals might be occupied via a pair or a single electron. If we don't count the unshared electrons, such molecules are bent, rather than linear. The 3 molecules exposed mutually through the BF₃ molecule are such molecules (Waterloo, 2009). Carbon atoms as well makes utilize of the sp² hybrid orbitals in the compound H₂C=CH₂. In this molecule, the residual p orbital from each of the carbon overlap to form the additional pi, bond.

Other ions these as CO₃^2-, and NO^-, can as well be described in the similar way.

The sp³ Hybrid Orbitals

Mixing one s and all three p atomic orbitals produces a set of four equivalent sp³ hybrid atomic orbitals. The four sp³ hybrid orbitals points towards the vertices of a tetrahedron. When sp³ hybrid orbitals are utilized for the central atom in the formation of molecule, the molecule is said to have the shape of a tetrahedron. The typical molecule is CH₄, in that the 1s orbital of an H atom overlap by one of the sp3 hybrid orbitals to form a C-H bond. Four H atoms form four such bonds, and they are all equivalent. The CH₄ molecule is the most cited molecule to have a tetrahedral shape. Other molecules and ions having tetrahedral shapes are SiO₄^4-, SO₄^2-, as are the cases by sp², hybrid orbitals, one or two of the sp³ hybrid orbitals might be occupied via non-bonding electrons (Waterloo, 2009). Water and ammonia are such molecules.

The C, N and O atoms in CH₄, NH₃, OH₂ (or H₂O) molecules utilize the sp³ hybrid orbitals, though, a lone pair occupies one of the orbitals in NH₃, and 2 lone pairs occupy 2 of the sp³ hybrid orbitals in OH₂. The lone pairs must be believed in the VSEPR model, and we can represent a lone pair through E, and two lone pairs by E₂. Therefore, we have NH₃E and OH₂E₂ respectively.

The VSEPR number is equal to the number of bonds plus the number of lone pair electrons. Does not matter what is the order of the bond, any bonded pair is considered on bond. Therefore, the VSEPR number is 4 for all of CH₄,:NH₃,::OH₂. According the VSEPR theory, the lone electron pairs need more space, and the H-O-H angle is 105 degrees, less than the model tetrahedral angle of 109.5 degrees.

The dsp³ Hybrid Orbitals

The five dsp³ hybrid orbitals resulted when one 3d, one 3s, and three 3p atomic orbitals are mixed.  When an atom makes use of fice dsp3 hybrid orbitals to link to five other atoms, the geometry of the molecule is frequently a trigonal bipyramidal. For instance, the molecule PClF₄ displayed here forms these structures. In this diagram, the Cl atom takes up an axial position of the trigonal bipyramid. There are structures in that the Cl atom might take up the equatorial position. The transform in arrangement is completed via merely modify the bond angles. This connection discusses this kind of configuration transforms of this molecule.

Several of the dsp³ hybrid orbitals might be occupied through electron pairs. The shapes of such molecules are interesting. In TeCl₄, only one of the hybrid dsp³ orbitals is occupied through a lone pair. This structure might be symbolized through TeCl₄E, where E signifies a lone pair of electrons. Two lone pairs occupy 2 such orbitals in the molecule BrF₃, or BrF₃E₂. The compound SF₄ is another AX₄E type, and many interhalogen compounds ClF₃ and IF₃ are AX₃E₂ type. The ion I₃^- is of the type AX₂E₃.

The d²sp³ Hybrid Orbitals

The six d²sp³ hybrid orbitals effected whenever two 3d, one 3s, and three 3p atomic orbitals are blended. When an atom makes utilize of six d²sp³ hybrid orbitals to bond to 6 other atoms, the molecule obtains the shape of an octahedron, in terms of molecular geometry. The gas compound SF₆ is a typical these structure. This link gives other shapes also. There are as well cases that several of the d²sp³ hybrid orbitals are occupied via lone pair electrons leading to the structures of the subsequent kinds:

AX₆, AX₅E, AX₄E₂ AX₃E₃ and AX₂E4

 IOF₅, IF₅E, XeF₄E₂

No known compounds of AX₃E₃ and AX₂E₄ are identified or recognized, since they are predicted to have a T shape and linear shape respectively when the lone pairs of electrons are ignored (Waterloo, 2009).

Molecular Shapes of Compounds

While the hybridised orbitals were introduced, in the foregoing conversation, Valence-shell electron-pair repulsion (VSEPR) model was contained to suggest the shapes of diverse molecules. Specifically, the VSEPR model counts unshared electron pairs and the bonded atoms as the VSEPR number. A single-, double- and tripple-bond is considered as

1. After having considered the hybridised orbitals and the VSEPR model, we cannot take a systematic approach to rationalize the shapes of many molecules depend on the number of valence electrons.

A summary in the form of a table is specified here to account for the concepts of hybrid orbitals, valence bond theory, VSEPR, resonance structures, and octet rule. In this table, the geometric shapes of the molecules are explained via linear, trigonal planar, tetrahedral, trigonal through pyramidal, and octahedral. The hybrids orbitals utilize are sp, sp², sp³, dsp³, and d²sp³.The VSEPR number is the similar for all molecules of each group. Instead of using NH₃E, and OH₂E₂, we use: NH₃:OH₂ to emphasize the unshared (or lone) electron pairs.

Table: A Summary of Hybrid Orbitals, Valence Bond Theory, VSEPR, Resonance Structures, and Octet Rule

This table correlates lots of interesting chemical ideas in order to comprehend the molecular structures of these compounds or ions. There are several intriguing chemical connections among the molecules in each column for us to ponder (Waterloo, 2009). Only Be and C atoms are included in linear molecules. In gas phase, BeH₂ and BeF₂ are stable, and such molecules don't satisfy the octet rule. The element C makes utilize of sp hybridised orbitals and it has the capability to form double and triple bonds in such linear molecules.

Carbon complexes are present in trigonal planar and tetrahedral molecules, using dissimilar hybrid orbitals. The extra electron in nitrogen for its compounds in such groups appears as lone unpaired electron or lone electron pairs. More electrons in O and S lead to compounds through lone electron pairs. The 5-atom anions are tetrahedral, and many resonance structures can be written for them (Waterloo, 2009).

Trigonal bipyramidal and octahedral molecules have 5 and 6 VSEPR pairs. When the central atoms enclose more than 5 or 6 electrons, the extra electrons form lone pairs. The number of lone pairs can simply be derived using Lewis dot structures for the valence electrons.

In describing the shapes of such molecules, we frequently ignore the lone pairs. Thus, •NO₂, N₃-, :OO₂ (O₃), and :SO₂ are bent molecules whereas :NH₃, :PF₃, and :SOF₂ are pyramidal. We already know that: OH₂ (water) and: SF₂ are bent molecules.

The lone electron pair takes up the equatorial location in: SF4, that has the same structure as:TeF₄ described earlier. If we lay a model of this molecule on the side, it looks like a butterfly. By the similar reason, ::ClF₃ and ::BrF₃  have a T shape, and :::XeF₂, :::I3-, and :::ICl₂^- are linear. Similarly,:BrF₅  and :IF₅  are square pyramidal whereas ::XeF₄ is square planar.

The centre atom

Usually, the atom in the centre is more electropositive than the terminal atoms. Though, the H and halogen atoms are generally at the terminal positions since they shape only one bond. Take a look at the chemical formulas in the table, and see if the above statement is true.

Nevertheless, the application of VSEPR theory can be expanded to complicated molecules such as

By applying the VSEPR theory, one deduces the following results:

H-C-C bond angle = 109^o

H-C=C bond angle = 120^o, geometry around C trigonal planar

C=C=C bond angle = 180^o, in other words linear

H-N-C bond angle = 109^o, tetrahedral around N

C-O-H bond angle = 105 or 109^o, 2 lone electron pairs around O

Valence bond theory today

Valence bond theory now complements Molecular Orbital Theory (MO theory), 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 orbitals which can extend over the entire molecule. MO theory can forecast magnetic properties in a straightforward manner, while valence bond theory provides similar consequences but is more complicated. Valence bond theory visions aromatic properties of molecules as due to resonance between Kekule, Dewar and possibly ionic formations whilst molecular orbital theory analysis it as delocalization of the π-electrons. The underlying mathematics is also more complicated limiting VB treatment to relatively small molecules. On the other hand, VB theory gives a much more precise picture of the reorganization of electronic charge that occurs when bonds are broken and formed during the course of a chemical reaction. In particular, valence bond theory properly predicts the dissociation of homonuclear diatomic molecules into divide atoms, while easy molecular orbital theory predicts dissociation into a mixture of atoms and ions.

More lately, numerous groups have expanded what is often termed modern valence bond theory.  This replaces the overlapping atomic orbitals via overlapping valence bond orbitals that are expanded over a huge number of essential functions; either centered each on one atom to provide a classical valence bond picture, or centered on all atoms in the molecule. The consequential energies are more competitive through energies from calculations where electron correlation is introduced depend on a Hartree- Fock reference wavefunction. The most recent text is via Shaik and Hiberty.

Modern valence bond theory is the term utilized to explain applications of valence bond theory by computer programmers that are competitive in accurateness and economy by programmers for the Hartree-Fock method and other molecular orbital based methods. The latter process dominated quantum chemistry from the advent of digital computers since they were easier to programme. The early popularity of valence bond methods therefore declined. It is simply recently that the programming of valence bond methods has progressed. Such developments are due to and explained via Gerratt, Cooper, Karadakov and Raimondi (1997); Li and

McWeeny (2002); Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004). In its simplest form the overlapping atomic orbitals are replaced via orbitals that are expanded as linear combinations of the atom-based basis functions. This expansion is optimized to provide the lowest energy. This process gives good energies without including ionic structures.

For instance, in the hydrogen molecule, classic valence bond theory utilizes two 1s atomic orbitals (a and b) on the two hydrogen atoms correspondingly and then constructs a covalent structure:

Φ_C  = ((a(1)b(2) + b(1)a(2)) ((α(1)β(2) - β(1)α(2))

and then an ionic structure:

Φ_I  = ((a(1)a(2) + b(1)b(2)) ((α(1)β(2) - β(1)α(2))

The final wave function is a linear combination of such 2 functions. Coulson and Fischer pointed out that a totally equivalent function is:

Φ_CF = ((a+kb)(1)(b+ka)(2) + (b+ka)(1)(a+kb)(2)) ((α(1)β(2) - β(1)α(2))

As expanding this out provides a linear combination of the covalent and ionic structures. Modern valence bond theory replaces the easy linear combination of the 2 atomic orbitals by a linear combination of all orbitals in a larger basis set. The 2 consequential valence bond orbitals look like an atomic orbital on one hydrogen atom faintly distorted towards the other hydrogen atom. Modern valence bond theory is therefore an extension of the Coulson-Fischer technique

There are a huge number of dissimilar valence bond processes. Most utilize n valence bond orbitals for n electrons. If a single set of such orbitals is joined through all linear independent mixtures of the spin functions, we have spin-coupled valence bond theory. The total wave function is optimized using the variation principle via fluctuating the coefficients of the essential functions in the valence bond orbitals and the coefficients of the dissimilar spin functions. In other cases only a sub-set of all possible spin functions is utilized. Many valence bond processes utilize numerous sets of the valence bond orbitals. Be notified that different authors utilize different names for these different valence bond methods.

Application of Valence Bond Theory

A significant feature of the VB theory is the condition of maximum overlap that leads to the formation of the strongest possible bonds. This theory is employed to clarify the covalent bond formation in many molecules. For Example in the case of F₂ molecule the F - F bond is formed by the overlap of pz orbitals of the 2F atoms each containing an unpaired electron. Since the nature of the overlapping orbitals are different in H₂ and F₂ molecules, the bond strength and bond lengths differ between H₂ and F₂ molecules. In a HF molecule the covalent bond is shaped via the overlap of 1s orbital of H and 2pz orbital of F each enclosing an unpaired electron. Mutual sharing of electrons between H and F consequences in a covalent bond between HF.

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