theoretical chemistry Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface ...

and

molecular physics Molecular physics is the study of the physical properties of molecules and molecular dynamics. The field overlaps significantly with physical chemistry, chemical physics, and quantum chemistry. It is often considered as a sub-field of atomic, mo ...

, Coulson–Fischer theory provides a quantum mechanical description of the electronic structure of molecules. The 1949 seminal work of Coulson and FischerC.A. Coulson and I. Fischer, ''Notes on the Molecular Orbital Treatment of the Hydrogen Molecule'', Phil. Mag. 40, 386 (1949) established a theory of molecular electronic structure which combines the strengths of the two rival theories which emerged soon after the advent of

quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contribution ...

valence bond theory In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of ...

and

molecular orbital theory In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. In molecular orbital theory, electrons in a molec ...

, whilst avoiding many of their weaknesses. For example, unlike the widely used Hartree–Fock molecular orbital method, Coulson–Fischer theory provides a qualitatively correct description of molecular dissociative processes. The Coulson–Fischer wave function has been said to provide a ''third way'' in quantum chemistry. Modern valence bond theory is often seen as an extension of the Coulson–Fischer method.

Theory

Coulson-Fischer theory is an extension of modern valence bond theory that uses localized atomic orbitals as the basis for VBT structures. In Coulson-Fischer Theory, orbitals are delocalized towards nearby atoms. This is described for H₂ as follows: :

\phi_1 = a + \lambda b

\phi_2 = b + \lambda a

where a and b are atomic 1s orbitals, that are used as the basis functions for VBT, and λ is a delocalization parameter from 0 to 1. The VB structures then use

\phi_1

and

\phi_2

as the basis functions to describe the total electronic wavefunction as :

\Phi_ = \left\vert \phi_1\overline \right\vert - \left\vert \overline\phi_2 \right\vert

in obvious analogy to the Heitler-London wavefunction. However, an expansion of the Coulson-Fischer description of the wavefunction in terms of a and b gives: :

\Phi_ = (1 + \lambda^2)(\left\vert a\overline \right\vert - \left\vert \overlineb \right\vert) + (2\lambda)(\left\vert a\overline \right\vert - \left\vert b\overline \right\vert)

A full VBT description of H₂ that includes both ionic and covalent contributions is :

\Phi_ = \epsilon(\left\vert a\overline \right\vert - \left\vert \overlineb \right\vert) + \mu(\left\vert a\overline \right\vert - \left\vert b\overline \right\vert)

where ε and μ are constants between 0 and 1. As a result, the CF description gives the same description as a full valence bond description, but with just one VB structure.

References

External link

* Theoretical chemistry Molecular physics Electronic structure methods {{AMO-physics-stub