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Conical intersection
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<h2 id="experimental-observation">Experimental observation</h2> <p>In order to be able to observe it, the process would need to be slowed down from femtoseconds to milliseconds. A novel 2023 quantum experiment, involving trapped-ion quantum computer, slowed down interference pattern of a single atom (caused by a conical intersection) by a factor of 100 billion, making a direct observation possible.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p> <h2 id="local-characterization">Local characterization</h2> <p>Conical intersections are ubiquitous in both trivial and non-trivial chemical systems. In an ideal system of two dimensionalities, this can occur at one <a href="/facts/Molecular_geometry/7USG5zDn">molecular geometry</a>. If the potential energy surfaces are plotted as functions of the two coordinates, they form a <a href="/facts/Cone_(geometry)/2c9GIzYD">cone</a> centered at the degeneracy point. This is shown in the adjacent picture, where the upper and lower potential energy surfaces are plotted in different colors. The name conical intersection comes from this observation. </p><p>In <a href="/facts/Diatomic_molecule/hkfKAC7m">diatomic molecules</a>, the number of vibrational <a href="/facts/Degrees_of_freedom_(physics_and_chemistry)/Rrjl0lnq">degrees of freedom</a> is 1. Without the necessary two dimensions required to form the cone shape, conical intersections cannot exist in these molecules. Instead, the potential energy curves experience <a href="/facts/Avoided_crossing/7VtKlQkC">avoided crossings</a> if they have the same point group symmetry, otherwise they can cross. </p><p>In molecules with three or more atoms, the number of degrees of freedom for <a href="/facts/Molecular_vibration/Y0ovRukI">molecular vibrations</a> is at least 3. In these systems, when <a href="/facts/Spin%25E2%2580%2593orbit_interaction/Pv6maL1S">spin–orbit interaction</a> is ignored, the degeneracy of conical intersection is lifted through first order by displacements in a two dimensional subspace of the nuclear coordinate space. </p><p>The two-dimensional degeneracy lifting subspace is referred to as the branching space or branching plane. This space is spanned by two vectors, the difference of energy gradient vectors of the two intersecting electronic states (the <i>g vector</i>), and the non-adiabatic coupling vector between these two states (the <i>h vector</i>). Because the electronic states are degenerate, the wave functions of the two electronic states are subject to an arbitrary <a href="/facts/Rotation_(mathematics)/6gtkkcy0">rotation</a>. Therefore, the <i>g</i> and <i>h</i> vectors are also subject to a related arbitrary rotation, despite the fact that the space spanned by the two vectors is invariant. To enable a consistent representation of the branching space, the set of wave functions that makes the <i>g</i> and <i>h</i> vectors orthogonal is usually chosen. This choice is unique up to the signs and switchings of the two vectors, and allows these two vectors to have proper symmetry when the molecular geometry is symmetric. </p><p>The degeneracy is preserved through first order by differential displacements that are perpendicular to the branching space. The space of non-degeneracy-lifting displacements, which is the <a href="/facts/Orthogonal_complement/a13oQBsz">orthogonal complement</a> of the branching space, is termed the seam space. Movement within the seam space will take the molecule from one point of conical intersection to an adjacent point of conical intersection. The degeneracy space connecting different conical intersections can be explored and characterised using band and <a href="/facts/Molecular_dynamics/yR3DNt6U">molecular dynamics</a> methods.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> </p><p>For an <a href="/facts/Open_shell/4khSKXPV">open shell</a> molecule, when spin-orbit interaction is added to the, the dimensionality of seam space is reduced.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p><p>The presence of conical intersections can be detected experimentally.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> It has been proposed that two-dimensional spectroscopy can be used to detect their presence through the modulation of the frequency of the vibrational coupling mode.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> A more direct spectroscopy of conical intersections, based on ultrafast X-ray transient absorption spectroscopy, was proposed, offering new approaches to their study.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> </p> <h2 id="categorization-by-symmetry-of-intersecting-electronic-states">Categorization by symmetry of intersecting electronic states</h2> <p>Conical intersections can occur between electronic states with the same or different point group symmetry, with the same or different spin symmetry. When restricted to a non-relativistic Coulomb Hamiltonian, conical intersections can be classified as symmetry-required, accidental symmetry-allowed, or accidental same-symmetry, according to the symmetry of the intersecting states. </p><p>A symmetry-required conical intersection is an intersection between two electronic states carrying the same multidimensional irreducible representation. For example, intersections between a pair of E states at a geometry that has a non-abelian group symmetry (e.g. C3h, C3v or D3h). It is named symmetry-required because these electronic states will always be degenerate as long as the symmetry is present. Symmetry-required intersections are often associated with <a href="/facts/Jahn%25E2%2580%2593Teller_effect/9M5WFCsA">Jahn–Teller effect</a>. </p><p>An accidental symmetry-allowed conical intersection is an intersection between two electronic states that carry different point group symmetry. It is called accidental because the states may or may not be degenerate when the symmetry is present. Movement along one of the dimensions along which the degeneracy is lifted, the direction of the difference of the energy gradients of the two electronic states, will preserve the symmetry while displacements along the other degeneracy lifting dimension, the direction of the non-adiabatic couplings, will break the symmetry of the molecule. Thus, by enforcing the symmetry of the molecule, the degeneracy lifting effect caused by inter-state couplings is prevented. Therefore, the search for a symmetry-allowed intersection becomes a one-dimensional problem and does not require knowledge of the non-adiabatic couplings, significantly simplifying the effort. As a result, all the conical intersections found through quantum mechanical calculations during the early years of quantum chemistry were symmetry-allowed intersections. </p><p>An accidental same-symmetry conical intersection is an intersection between two electronic states that carry the same point group symmetry. While this type of intersection was traditionally more difficult to locate, a number of efficient searching algorithms and methods to compute non-adiabatic couplings have emerged in the past decade. It is now understood that same-symmetry intersections play as important a role in non-adiabatic processes as symmetry-allowed intersections. </p> <h2 id="see-also">See also</h2> <ul><li>Yarkony, David (1996). "Diabolical Conical Intersections". <i>Reviews of Modern Physics</i>. 68 (4): 985–1013. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1996RvMP...68..985Y">1996RvMP...68..985Y</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1103%2FRevModPhys.68.985">10.1103/RevModPhys.68.985</a>.</li> <li>Baer, Michael (2006). <a href="https://onlinelibrary.wiley.com/doi/book/10.1002/0471780081"><i>Beyond Born–Oppenheimer: Electronic Nonadiabatic Coupling Terms and Conical Intersections</i></a>. Wiley-Interscience. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1002%2F0471780081">10.1002/0471780081</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-471-77891-2.</li> <li>Domcke, Wolfgang; Yarkony, David R.; Köppel, Horst (2004). <a href="https://www.worldscientific.com/worldscibooks/10.1142/5406"><i>Conical Intersections: Electronic Structure, Dynamics and Spectroscopy</i></a>. Advanced Series in Physical Chemistry. Vol. 15. World Scientific. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1142%2F5406">10.1142/5406</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-981-256-546-4.</li> <li>Domcke, Wolfgang; Yarkony, David R.; Köppel, Horst (2011). <a href="https://www.worldscientific.com/worldscibooks/10.1142/7803"><i>Conical Intersections: Theory, Computation and Experiment</i></a>. Advanced Series in Physical Chemistry. Vol. 17. World Scientific. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1142%2F7803">10.1142/7803</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-981-4313-45-2.</li> <li><a href="/facts/Born%25E2%2580%2593Oppenheimer_approximation/hxlUcBrX">Born–Oppenheimer approximation</a></li> <li><a href="/facts/Potential_energy_surface/YDUNcSM8">Potential energy surface</a></li> <li><a href="/facts/Geometric_phase/d0QbNVdS">Geometric phase</a></li> <li><a href="/facts/Christopher_Longuet-Higgins/y3JGEVyq">Christopher Longuet-Higgins</a></li> <li><a href="/facts/Diabatic_representation/yb7hUVvM">Diabatic Representation</a></li> <li><a href="/facts/Jahn%25E2%2580%2593Teller_effect/9M5WFCsA">Jahn–Teller effect</a></li> <li><a href="/facts/Avoided_crossing/7VtKlQkC">Avoided crossing</a></li> <li><a href="/facts/Bond_softening/mgDML3cz">Bond softening</a></li> <li><a href="/facts/Bond_hardening/1zQe9pNT">Bond hardening</a></li> <li><a href="/facts/Vibronic_coupling/IDmq1G4J">Vibronic coupling</a></li> <li><a href="/facts/Surface_hopping/TdXpXUMM">Surface hopping</a></li> <li><a href="/facts/Ab_initio_multiple_spawning/Bl0TSG9L">Ab initio multiple spawning</a></li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://web.archive.org/web/20050404055458/http://ccmaol1.chim.unisi.it/comp-photochem/">Computational Organic Photochemistry</a></li> <li><a href="http://www.chm.bris.ac.uk/webprojects2002/grant/webcomp/conical.html">Potential Energy Surfaces and Conical Intersections</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Todd J. Martinez (September 2010). "Physical chemistry: Seaming is believing". Nature. 467 (7314): 412–413. Bibcode:2010Natur.467..412M. doi:10.1038/467412a. PMID 20864993. S2CID 205058988. <a href="https://doi.org/10.1038%2F467412a" target="_blank">https://doi.org/10.1038%2F467412a</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Kang, Hyuk; Kang Taek Lee; Boyong Jung; Yeon Jae Ko; Seong Keun Kim (October 2002). "Intrinsic Lifetimes of the Excited State of DNA and RNA Bases". J. Am. Chem. Soc. 124 (44): 12958–12959. doi:10.1021/ja027627x. PMID 12405817. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>H. C. Longuet Higgins; U. Öpik; M. H. L. Pryce; R. A. Sack (1958). "Studies of the Jahn-Teller effect .II. The dynamical problem". Proc. R. Soc. A. 244 (1236): 1–16. Bibcode:1958RSPSA.244....1L. doi:10.1098/rspa.1958.0022. S2CID 97141844.See page 12 <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Lluís Blancafort (November 2010). "A global picture of the S1/S0 conical intersection seam of benzene" (PDF). Chemical Physics. 377 (1): 60–65. Bibcode:2010CP....377...60L. doi:10.1016/j.chemphys.2010.08.016. hdl:10044/1/10099. <a href="http://spiral.imperial.ac.uk/bitstream/10044/1/10099/4/Bearpark%2c%20M%20-%20A%20global%20picture.pdf" target="_blank">http://spiral.imperial.ac.uk/bitstream/10044/1/10099/4/Bearpark%2c%20M%20-%20A%20global%20picture.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>C. H. Valahu, V. C. Olaya-Agudelo, R. J. MacDonell, T. Navickas, A. D. Rao, M. J. Millican, J. B. Pérez-Sánchez, J. Yuen-Zhou, M. J. Biercuk, C. Hempel, T. R. Tan, I. Kassal. "Direct observation of geometric-phase interference in dynamics around a conical intersection." Nature Chemistry, 2023; DOI: 10.1038/s41557-023-01300-3 <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Laino, T.; D. Passerone (2004). "Pseudo-dynamics and band optimizations: shedding light into conical intersection seams". Chemical Physics Letters. 389 (1–3): 1–6. doi:10.1016/j.cplett.2004.02.110. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Matsika, Spiridoula; David R Yarkony (1 August 2001). "On the effects of spin-orbit coupling on conical intersection seams in molecules with an odd number of electrons. I. Locating the seam". Journal of Chemical Physics. 115 (5): 2038. Bibcode:2001JChPh.115.2038M. doi:10.1063/1.1378324. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Stolow, Albert; Michael S. Schuurman (2018). "Dynamics at Conical Intersections". Annual Review of Physical Chemistry. 69: 427–459. doi:10.1146/annurev-physchem-052516-050721. PMID 29490199. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Farag, M. H.; T. L. C. Jansen; J. Knoester (2016). "Probing the Inter-State Coupling near a Conical Intersection by Optical Spectroscopy". Journal of Physical Chemistry Letters. 7 (17): 3328–3334. doi:10.1021/acs.jpclett.6b01463. PMID 27509384. <a href="https://research.rug.nl/en/publications/f9bd6305-00d2-44d2-aca2-167f52b256f0" target="_blank">https://research.rug.nl/en/publications/f9bd6305-00d2-44d2-aca2-167f52b256f0</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Neville, Simon P.; Majed Chergui; Albert Stolow; Michael S. Schuurman (2018). "Ultrafast X-Ray Spectroscopy of Conical Intersections". Physical Review Letters. 120 (24): 243001. arXiv:1805.05733. doi:10.1103/PhysRevLett.120.243001. PMID 29956989. S2CID 206312264. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> </ol>