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title="Quantum Monte Carlo">Quantum Monte Carlo</a></td> </tr><tr><th class="sidebar-heading" style="background-color: #ddd"> <a href="/wiki/Density_functional_theory" title="Density functional theory">Density functional theory</a></th></tr><tr><td class="sidebar-content"> <a href="/wiki/Time-dependent_density_functional_theory" title="Time-dependent density functional theory">Time-dependent density functional theory</a><br /><a href="/wiki/Thomas%E2%80%93Fermi_model" title="Thomas–Fermi model">Thomas–Fermi model</a><br /><a href="/wiki/Orbital-free_density_functional_theory" title="Orbital-free density functional theory">Orbital-free density functional theory</a><br /><a href="/wiki/Linearized_augmented-plane-wave_method" title="Linearized augmented-plane-wave method">Linearized augmented-plane-wave method</a><br /><a href="/wiki/Projector_augmented_wave_method" title="Projector augmented wave method">Projector augmented wave method</a></td> </tr><tr><th class="sidebar-heading" style="background-color: #ddd"> <a href="/wiki/Electronic_band_structure" title="Electronic band structure">Electronic band structure</a></th></tr><tr><td class="sidebar-content"> <a href="/wiki/Nearly_free_electron_model" title="Nearly free electron model">Nearly free electron model</a><br /><a href="/wiki/Tight_binding" title="Tight binding">Tight binding</a><br /><a href="/wiki/Muffin-tin_approximation" title="Muffin-tin approximation">Muffin-tin approximation</a><br /><a href="/wiki/K%C2%B7p_perturbation_theory" title="K·p perturbation theory">k·p perturbation theory</a><br /><a href="/wiki/Empty_lattice_approximation" title="Empty lattice approximation">Empty lattice approximation</a><br /><a href="/wiki/GW_approximation" title="GW approximation">GW approximation</a><br /><a href="/wiki/Korringa%E2%80%93Kohn%E2%80%93Rostoker_method" title="Korringa–Kohn–Rostoker method">Korringa–Kohn–Rostoker method</a></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electronic_structure_methods" title="Template:Electronic structure methods"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electronic_structure_methods" title="Template talk:Electronic structure methods"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electronic_structure_methods" title="Special:EditPage/Template:Electronic structure methods"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Theoretical_chemistry" title="Theoretical chemistry">theoretical chemistry</a> and <a href="/wiki/Molecular_physics" title="Molecular physics">molecular physics</a>, <b>Coulson–Fischer theory</b> provides a quantum mechanical description of the electronic structure of molecules. The 1949 seminal work of <a href="/wiki/Charles_Coulson" title="Charles Coulson">Coulson</a> and <a href="/wiki/Inga_Fischer-Hjalmars" title="Inga Fischer-Hjalmars">Fischer</a><sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> established a theory of molecular electronic structure which combines the strengths of the two rival theories which emerged soon after the advent of <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a> - <a href="/wiki/Valence_bond_theory" title="Valence bond theory">valence bond theory</a> and <a href="/wiki/Molecular_orbital_theory" title="Molecular orbital theory">molecular orbital theory</a>, whilst avoiding many of their weaknesses. For example, unlike the widely used <a href="/wiki/Hartree%E2%80%93Fock_method" title="Hartree–Fock method">Hartree–Fock</a> molecular orbital method, Coulson–Fischer theory provides a qualitatively correct description of molecular dissociative processes.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The Coulson–Fischer wave function has been said to provide a <i>third way</i> in quantum chemistry.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Modern_valence_bond_theory" title="Modern valence bond theory">Modern valence bond theory</a> is often seen as an extension of the Coulson–Fischer method. </p> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulson%E2%80%93Fischer_theory&action=edit&section=1" title="Edit section: Theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Coulson–Fischer theory is an extension of <a href="/wiki/Modern_valence_bond_theory" title="Modern valence bond theory">modern valence bond theory</a> that uses localized atomic orbitals as the basis for VBT structures.<sup id="cite_ref-:1_4-0" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In Coulson-Fischer Theory, orbitals are delocalized towards nearby atoms. This is described for H<sub>2</sub> as follows:<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{1}=a+\lambda b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>λ</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi _{1}=a+\lambda b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/521d2b69ff65c0b2947ef84812afacf99b4692a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.961ex; height:2.509ex;" alt="{\displaystyle \phi _{1}=a+\lambda b}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{2}=b+\lambda a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mi>b</mi> <mo>+</mo> <mi>λ</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi _{2}=b+\lambda a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bce8d8de29505f0da7a0a79f9709a7b97a8278e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.961ex; height:2.509ex;" alt="{\displaystyle \phi _{2}=b+\lambda a}"></span></dd></dl> <p>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 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cf64c7dccd0c826bec4f0df13d467daf64ccf06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.44ex; height:2.509ex;" alt="{\displaystyle \phi _{1}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60e1171ff278ebe52a46956ba3e04f4df0acc97b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.44ex; height:2.509ex;" alt="{\displaystyle \phi _{2}}"></span> as the basis functions to describe the total electronic wavefunction as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi _{CF}=\left\vert \phi _{1}{\overline {\phi _{2}}}\right\vert -\left\vert {\overline {\phi _{1}}}\phi _{2}\right\vert }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>|</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{CF}=\left\vert \phi _{1}{\overline {\phi _{2}}}\right\vert -\left\vert {\overline {\phi _{1}}}\phi _{2}\right\vert }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d181ea1b77982324e0d18aad2d8e6036c8f66226" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:22.905ex; height:4.176ex;" alt="{\displaystyle \Phi _{CF}=\left\vert \phi _{1}{\overline {\phi _{2}}}\right\vert -\left\vert {\overline {\phi _{1}}}\phi _{2}\right\vert }"></span></dd></dl> <p>in obvious analogy to the Heitler-London wavefunction.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> However, an expansion of the Coulson-Fischer description of the wavefunction in terms of a and b gives: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi _{CF}=(1+\lambda ^{2})(\left\vert a{\overline {b}}\right\vert -\left\vert {\overline {a}}b\right\vert )+(2\lambda )(\left\vert a{\overline {a}}\right\vert -\left\vert b{\overline {b}}\right\vert )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mrow> <mo>|</mo> <mrow> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>|</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo accent="false">¯</mo> </mover> </mrow> <mi>b</mi> </mrow> <mo>|</mo> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>λ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mrow> <mo>|</mo> <mrow> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>|</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>|</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{CF}=(1+\lambda ^{2})(\left\vert a{\overline {b}}\right\vert -\left\vert {\overline {a}}b\right\vert )+(2\lambda )(\left\vert a{\overline {a}}\right\vert -\left\vert b{\overline {b}}\right\vert )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d56e2ef1ce22b99d238edefc0f9c73564479b0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:46.721ex; height:4.176ex;" alt="{\displaystyle \Phi _{CF}=(1+\lambda ^{2})(\left\vert a{\overline {b}}\right\vert -\left\vert {\overline {a}}b\right\vert )+(2\lambda )(\left\vert a{\overline {a}}\right\vert -\left\vert b{\overline {b}}\right\vert )}"></span></dd></dl> <p>A full VBT description of H<sub>2</sub> that includes both ionic and covalent contributions is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi _{VBT}=\epsilon (\left\vert a{\overline {b}}\right\vert -\left\vert {\overline {a}}b\right\vert )+\mu (\left\vert a{\overline {a}}\right\vert -\left\vert b{\overline {b}}\right\vert )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mi>B</mi> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>ϵ</mi> <mo stretchy="false">(</mo> <mrow> <mo>|</mo> <mrow> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>|</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo accent="false">¯</mo> </mover> </mrow> <mi>b</mi> </mrow> <mo>|</mo> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mi>μ</mi> <mo stretchy="false">(</mo> <mrow> <mo>|</mo> <mrow> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>|</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>|</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{VBT}=\epsilon (\left\vert a{\overline {b}}\right\vert -\left\vert {\overline {a}}b\right\vert )+\mu (\left\vert a{\overline {a}}\right\vert -\left\vert b{\overline {b}}\right\vert )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d06938919a725e87075b0cca89ebf177452a7e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:37.707ex; height:4.176ex;" alt="{\displaystyle \Phi _{VBT}=\epsilon (\left\vert a{\overline {b}}\right\vert -\left\vert {\overline {a}}b\right\vert )+\mu (\left\vert a{\overline {a}}\right\vert -\left\vert b{\overline {b}}\right\vert )}"></span></dd></dl> <p>where ε and μ are constants between 0 and 1. </p><p>As a result, the CF description gives the same description as a full valence bond description, but with just one VB structure.<sup id="cite_ref-:1_4-1" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulson%E2%80%93Fischer_theory&action=edit&section=2" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-:0-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">C.A. Coulson and I. Fischer, <i>Notes on the Molecular Orbital Treatment of the Hydrogen Molecule</i>, Phil. Mag. <b>40</b>, 386 (1949)</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">S. Wilson and J. Gerratt, <i>Calculation of potential energy curves for the ground state of the hydrogen molecule</i>, Molec. Phys. <b>30</b>, 777 (1975) <a rel="nofollow" class="external free" href="https://doi.org/10.1080/14786444908521726">https://doi.org/10.1080/14786444908521726</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">S. Wilson, <i>On the Wave Function of Coulson and Fischer: A Third Way in Quantum Chemistry</i>, in <i>Advances in the Theory of Atomic and Molecular Systems</i>, ed. P. Piecuch, J. Maruani, G. Delgado-Barrio and S. Wilson, <i>Progress in Theoretical Chemistry and Physics</i> <b>19</b>, Springer (2009)</span> </li> <li id="cite_note-:1-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFShaikHiberty2007" class="citation book cs1">Shaik, Sason; Hiberty, Philippe C. (2007-11-16). <a rel="nofollow" class="external text" href="http://doi.wiley.com/10.1002/9780470192597"><i>A Chemist's Guide to Valence Bond Theory</i></a>. Hoboken, NJ, USA: John Wiley & Sons, Inc. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9780470192597">10.1002/9780470192597</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-19259-7" title="Special:BookSources/978-0-470-19259-7"><bdi>978-0-470-19259-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Chemist%27s+Guide+to+Valence+Bond+Theory&rft.place=Hoboken%2C+NJ%2C+USA&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=2007-11-16&rft_id=info%3Adoi%2F10.1002%2F9780470192597&rft.isbn=978-0-470-19259-7&rft.aulast=Shaik&rft.aufirst=Sason&rft.au=Hiberty%2C+Philippe+C.&rft_id=http%3A%2F%2Fdoi.wiley.com%2F10.1002%2F9780470192597&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoulson%E2%80%93Fischer+theory" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">"Heitler, W., & London, F. (1927). Wechselwirkung neutraler Atome und homopolare Bindung nach der Quantenmechanik. Zeitschrift für Physik, 44, 455-472. - References - Scientific Research Publishing"</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulson%E2%80%93Fischer_theory&action=edit&section=3" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStephen_Wilson" class="citation web cs1">Stephen Wilson. <a rel="nofollow" class="external text" href="https://sites.google.com/site/coulsonfischertheory/">"The Coulson-Fischer theory of molecular electronic structure"</a><span class="reference-accessdate">. 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