[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/coulson-fischer-theory-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki24\/coulson-fischer-theory-wikipedia\/","headline":"Coulson\u2013Fischer theory – Wikipedia","name":"Coulson\u2013Fischer theory – Wikipedia","description":"From Wikipedia, the free encyclopedia In theoretical chemistry and molecular physics, Coulson\u2013Fischer theory provides a quantum mechanical description of the","datePublished":"2014-12-03","dateModified":"2014-12-03","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki24\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/521d2b69ff65c0b2947ef84812afacf99b4692a5","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/521d2b69ff65c0b2947ef84812afacf99b4692a5","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/en\/wiki24\/coulson-fischer-theory-wikipedia\/","about":["Wiki"],"wordCount":2287,"articleBody":"From Wikipedia, the free encyclopediaIn theoretical chemistry and molecular physics, Coulson\u2013Fischer theory provides a quantum mechanical description of the electronic structure of molecules. The 1949 seminal work of Coulson and Fischer[1] 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 – valence bond theory and molecular orbital theory, whilst avoiding many of their weaknesses. For example, unlike the widely used Hartree\u2013Fock molecular orbital method, Coulson\u2013Fischer theory provides a qualitatively correct description of molecular dissociative processes.[2] The Coulson\u2013Fischer wave function has been said to provide a third way in quantum chemistry.[3]Modern valence bond theory is often seen as an extension of the Coulson\u2013Fischer method.Coulson-Fischer theory is an extension of modern valence bond theory that uses localized atomic orbitals as the basis for VBT structures.[4] In Coulson-Fischer Theory, orbitals are delocalized towards nearby atoms. This is described for H2 as follows:[1]\u03d51=a+\u03bbb{displaystyle phi _{1}=a+lambda b}\u03d52=b+\u03bba{displaystyle phi _{2}=b+lambda a}where a and b are atomic 1s orbitals, that are used as the basis functions for VBT, and \u03bb is a delocalization parameter from 0 to 1. The VB structures then use \u03d51{displaystyle phi _{1}} and \u03d52{displaystyle phi _{2}} as the basis functions to describe the total electronic wavefunction as\u03a6CF=|\u03d51\u03d52\u00af|\u2212|\u03d51\u00af\u03d52|{displaystyle Phi _{CF}=leftvert phi _{1}{overline {phi _{2}}}rightvert -leftvert {overline {phi _{1}}}phi _{2}rightvert }in obvious analogy to the Heitler-London wavefunction.[5] However, an expansion of the Coulson-Fischer description of the wavefunction in terms of a and b gives:\u03a6CF=(1+\u03bb2)(|ab\u00af|\u2212|a\u00afb|)+(2\u03bb)(|aa\u00af|\u2212|bb\u00af|){displaystyle Phi _{CF}=(1+lambda ^{2})(leftvert a{overline {b}}rightvert -leftvert {overline {a}}brightvert )+(2lambda )(leftvert a{overline {a}}rightvert -leftvert b{overline {b}}rightvert )}A full VBT description of H2 that includes both ionic and covalent contributions is\u03a6VBT=\u03f5(|ab\u00af|\u2212|a\u00afb|)+\u03bc(|aa\u00af|\u2212|bb\u00af|){displaystyle Phi _{VBT}=epsilon (leftvert a{overline {b}}rightvert -leftvert {overline {a}}brightvert )+mu (leftvert a{overline {a}}rightvert -leftvert b{overline {b}}rightvert )}where \u03b5 and \u03bc 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.[4]References[edit]^ a b C.A. Coulson and I. Fischer, Notes on the Molecular Orbital Treatment of the Hydrogen Molecule, Phil. Mag. 40, 386 (1949)^ S. Wilson and J. Gerratt, Calculation of potential energy curves for the ground state of the hydrogen molecule, Molec. Phys. 30, 777 (1975) https:\/\/doi.org\/10.1080\/14786444908521726 ^ S. Wilson, On the Wave Function of Coulson and Fischer: A Third Way in Quantum Chemistry, in Advances in the Theory of Atomic and Molecular Systems, ed. P. Piecuch, J. Maruani, G. Delgado-Barrio and S. Wilson, Progress in Theoretical Chemistry and Physics 19, Springer (2009)^ a b Shaik, Sason; Hiberty, Philippe C. (2007-11-16). A Chemist’s Guide to Valence Bond Theory. Hoboken, NJ, USA: John Wiley & Sons, Inc. doi:10.1002\/9780470192597. ISBN\u00a0978-0-470-19259-7.^ “Heitler, W., & London, F. (1927). Wechselwirkung neutraler Atome und homopolare Bindung nach der Quantenmechanik. Zeitschrift f\u00fcr Physik, 44, 455-472. – References – Scientific Research Publishing”External link[edit]  "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/coulson-fischer-theory-wikipedia\/#breadcrumbitem","name":"Coulson\u2013Fischer theory – Wikipedia"}}]}]