What is valence bond theory 1

The Valence structure theory, also VB theory, Electron pair theory or engl. Valence Bond Theory called, is a quantum mechanical approximation method developed by Walter Heitler and Fritz London in 1927 to describe atomic bonds in polyatomic systems.

In this model a Valence bond between two atoms in that each of these atoms provides an electron for a bond. These two electrons form an electron pair in one binding molecular orbital. The two atoms in the molecule now have a share in both electrons, in other words in their "own" electron and in "the partner's" electron. The energetic advantage that this creates for both atoms is the driving force for the formation of molecules.

Basic model

The basic model was developed for the hydrogen molecule as it allows the simplest calculations:

  • By combining the s-Orbitals of the hydrogen atoms, in which the electrons were originally located, result in molecular orbitals, a empty antibonding molecular orbital and a occupied molecular orbital, in which the two electrons are then spin-coupled as an electron pair (Pauli principle).
  • However, the wave function of the binding molecular orbital is unknown and is calculated taking various factors into account approximateduntil it is in satisfactory agreement with experimental results.
  • The two serve as the starting point for the computational approximation s-Orbitals of the originally individual hydrogen atoms.

Valence structure method for the hydrogen molecule

Hydrogen atom A has electron number 1 and the wave function ΨA (1).

Hydrogen atom B has electron number 2 and the wave function ΨB (2).

The experimentally determined distance between the hydrogen nuclei in the molecule is 74 pm, the binding energy is -458 kJ mol-1.

First approximation

In the first approximation, it is completely disregarded whether and how the two atomic nuclei and electrons influence each other when they approach each other to form a bond. The wave function Ψ for a system of two atoms that do not influence each other, one obtains from the wave functions of the individual hydrogen atoms:

The binding energy and the nuclear distance that result from this hardly agree with the experimental results.

Exchange energy according to Heitler and London

In the molecular orbital, electron 1 does not always have to be in hydrogen atom A, just as electron 2 does not always have to be in hydrogen atom B. Accordingly, a term for exchanged electrons is added:

Ψ = ΨA (1) · ΨB (2) + ΨA (2) · ΨB (1)

Here you can find a good approximation of experimental results.


The terms ΨA. and ΨB. just take into account that a Electron shields the nuclear charge of a hydrogen nucleus. In the molecule, however, there are two nuclei and two electrons in between, so that the shielding effect is greater.

Taking into account the effective nuclear charge finds in the terms for Ψ´A. and Ψ´B. instead, the above equation can in principle remain as follows:

Ψ = Ψ´A (1) · Ψ´B (2) + Ψ´A (2) · Ψ´B (1)


Theoretically, the hydrogen atoms in the compound can not only exchange their electrons, but there is also a small probability that sometimes both electrons will meet one of the hydrogen nuclei. Accordingly, ionic structures can be formulated for the hydrogen molecule H-H:

However, since the ionic structures are likely to occur rarely, their influence on the wave function Ψ with a factor λ < 1="" versehen:="">

Ψ = Ψ´A (1) · Ψ´B (2) + Ψ´A (2) · Ψ´B (1) + λΨ´H+H- + λΨ´H-H+

Here the deviation from experimental findings is already small and after applying a wave equation with 100 correction terms, results are obtained that almost agree with the experimental findings.

The basic model for hydrogen molecules was continuously refined and the problem was transferred to larger and much more complicated molecules, as well as to multiple bonds. The approach of the valence structure method, as well as the molecular orbital theory, form the basis of today's Molecular Modeling which enables predictions and interpretations of many molecular structures and properties through computer-aided calculations.

Pauling's theory of complexes

The coordinative bond is present in complexes made up of a central atom and a certain number of ligands. This type of bond does not come about because both reaction partners, i.e. the central atom and ligand, each provide one electron, but rather because the ligand alone brings two electrons and thus forms a bond to the central atom.

When a ligand provides two electrons, and n is the number of binding ligands, then gets the central atom nx2 electrons that it has to accommodate somewhere. The empty outer orbitals of the central atom are available for accommodation:

  • First period of transition metals: (outside) 4 d, 4 p, 4 s, 3 d (Inside)
  • Second period of transition metals: (outside) 5 d, 5 p, 5 s, 4 d (Inside)
  • Third period of transition metals: (outside) 6 d, 6 p, 6 s and 5 d (Inside)

inner / outer orbital complexes

Usually located in the innerd-Orbitals already have electrons of the central atom. When the orbitals are occupied by ligand-electron pairs, the "original occupation" either remains unchanged (outer orbital complex), or the electrons already present are pushed together on the inner orbitals of the central atom (inner orbital complex). Which of the two possibilities occurs depends on the ligand and influences the paramagnetic properties of the complex.

The explanation of why some ligands produce outer or inner sphere complexes was only possible with the crystal field or ligand field theory. Here the concept of high spin and low spin Complexes introduced according to the magnetic properties of such complexes.


The Fe2+-Cation has 6 electrons in the 3rdd-Orbital, i.e. a 3rdd6-Configuration.

With six water ligands there are 12 electrons. In this case, the configuration of the cation is retained: 3d6 4s2 4p6 4d4.

With six cyanide ligands there are also 12 electrons. Here the "original occupation" of the central atom changes to: 3d10 4s2 4p6 4d0.


To form bonds between the central atom and ligands, hybrid orbitals are formed by the central atom according to the VB theory, the number of which corresponds to the number of electron pairs that the ligands make available for binding.

Depending on the type and, above all, the number of ligand electron pairs are determined for hybridization d(Inside)-, s-, p- and d(outside) orbitals of the central atom are used, resulting in characteristic coordination geometries:

  • 6 ligands: 2 · d(inside) + 1 s + 3 · p = 6 · d2sp3 --> octahedron (inner orbital complex)
  • 6 ligands: 1 · s + 3 · p + 2 · d(outside) = 6 sp3d2 --> octahedron (outer orbital complex)
  • 4 ligands: 1 · d(inside) + 1 s + 2 · p = 4 · dsp2 --> planar square



The VB theory is ideal for determining complex geometries and for explaining magnetic phenomena. Many complexes are colored, which cannot be explained with the VB theory. Further theories are crystal field theory and ligand field theory.


  • C.A. Coulson; The chemical bond; S. Hirzel Verlag, 1969
  • J. Huheey, E. Keiter, R. Keiter; Inorganic chemistry; WdeG, 2003
  • A. F. Holleman, E. Wiberg; Inorganic Chemistry Textbook; WdeG, 1995

See also

Categories: Quantum Physics | Chemical bond