Quantum chemistry

<h2 id="history">History</h2>
Some view the birth of quantum chemistry as starting with the discovery of the <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> and its application to the hydrogen atom. However, a 1927 article of <a href="/facts/Walter_Heitler/nhLXAQQ4">Walter Heitler</a> (1904–1981) and <a href="/facts/Fritz_London/9NvJ4MR7">Fritz London</a> is often recognized as the first milestone in the history of quantum chemistry.<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a> This was the first application of quantum mechanics to the diatomic <a href="/facts/Hydrogen_molecule/BoYHjl0J">hydrogen molecule</a>, and thus to the phenomenon of the chemical bond.<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a> However, prior to this a critical conceptual framework was provided by <a href="/facts/Gilbert_N._Lewis/wWnV6QXL">Gilbert N. Lewis</a> in his 1916 paper The Atom and the Molecule,<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a> wherein Lewis developed the first working model of <a href="/facts/Valence_electron/mXPA15VP">valence electrons</a>. Important contributions were also made by Yoshikatsu Sugiura<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a><a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> and S.C. Wang.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> A series of articles by <a href="/facts/Linus_Pauling/cBNBzs5c">Linus Pauling</a>, written throughout the 1930s, integrated the work of Heitler, London, Sugiura, Wang, Lewis, and <a href="/facts/John_C._Slater/nfqa6fbn">John C. Slater</a> on the concept of valence and its quantum-mechanical basis into a new theoretical framework.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> Many chemists were introduced to the field of quantum chemistry by Pauling's 1939 text The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry, wherein he summarized this work (referred to widely now as <a href="/facts/Valence_bond_theory/F04YPkfJ">valence bond theory</a>) and explained quantum mechanics in a way which could be followed by chemists.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> The text soon became a standard text at many universities. <a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> In 1937, <a href="/facts/Hans_Hellmann/9dSIWSMc">Hans Hellmann</a> appears to have been the first to publish a book on quantum chemistry, in the Russian <a class="footnote-ref" id="fnref:11" href="#fn:11">11</a> and German languages.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> 
In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding. In addition to the investigators mentioned above, important progress and critical contributions were made in the early years of this field by <a href="/facts/Irving_Langmuir/mPt8xwUp">Irving Langmuir</a>, <a href="/facts/Robert_S._Mulliken/l17P0TBQ">Robert S. Mulliken</a>, <a href="/facts/Max_Born/6VnUDWhA">Max Born</a>, <a href="/facts/J._Robert_Oppenheimer/qvgElLRC">J. Robert Oppenheimer</a>, <a href="/facts/Hans_Hellmann/9dSIWSMc">Hans Hellmann</a>, <a href="/facts/Maria_Goeppert_Mayer/Ung0ch6E">Maria Goeppert Mayer</a>, <a href="/facts/Erich_H%C3%BCckel/EmM42Vtp">Erich Hückel</a>, <a href="/facts/Douglas_Hartree/WKeyXHnK">Douglas Hartree</a>, <a href="/facts/John_Lennard-Jones/bIPYBATH">John Lennard-Jones</a>, and <a href="/facts/Vladimir_Fock/IeLmHFxd">Vladimir Fock</a>.

<h2 id="electronic-structure">Electronic structure</h2>
The electronic structure of an atom or molecule is the <a href="/facts/Quantum_state/7jbxd7Dx">quantum state</a> of its electrons.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a> The first step in solving a quantum chemical problem is usually solving the <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> (or <a href="/facts/Dirac_equation/DzFaXS4p">Dirac equation</a> in <a href="/facts/Relativistic_quantum_chemistry/8A1se1CS">relativistic quantum chemistry</a>) with the <a href="/facts/Electronic_molecular_Hamiltonian/JljaHd2d">electronic molecular Hamiltonian</a>, usually making use of the Born–Oppenheimer (B–O) approximation. This is called determining the electronic structure of the molecule.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a> An exact solution for the non-relativistic Schrödinger equation can only be obtained for the hydrogen atom (though exact solutions for the bound state energies of the <a href="/facts/Dihydrogen_cation/MWh6WYVG">hydrogen molecular ion</a> within the B-O approximation have been identified in terms of the <a href="/facts/Lambert_W_function/NG1wd71f">generalized Lambert W function</a>). Since all other atomic and molecular systems involve the motions of three or more "particles", their Schrödinger equations cannot be solved analytically and so approximate and/or computational solutions must be sought. The process of seeking computational solutions to these problems is part of the field known as <a href="/facts/Computational_chemistry/KyuCgRV3">computational chemistry</a>.

<h3>Valence bond theory</h3>
Main article: <a href="/facts/Valence_bond_theory/F04YPkfJ">Valence bond theory</a>
As mentioned above, Heitler and London's method was extended by Slater and Pauling to become the valence-bond (VB) 
method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of <a href="/facts/Chemical_bond/ArNUMnIB">bonds</a>. It focuses on how the atomic orbitals of an atom combine to give individual chemical bonds when a molecule is formed, incorporating the two key concepts of <a href="/facts/Orbital_hybridization/Fl7sz8Jm">orbital hybridization</a> and <a href="/facts/Resonance_(chemistry)/5tymwoIP">resonance</a>.<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a>

<h3>Molecular orbital theory</h3>

Main article: <a href="/facts/Molecular_orbital_theory/VJ6Kg8bI">Molecular orbital theory</a>
An alternative approach to valence bond theory was developed in 1929 by <a href="/facts/Friedrich_Hund/b7AjzGVG">Friedrich Hund</a> and <a href="/facts/Robert_S._Mulliken/l17P0TBQ">Robert S. Mulliken</a>, in which <a href="/facts/Electron/L0KBo5cW">electrons</a> are described by mathematical functions delocalized over an entire <a href="/facts/Molecule/N9ljSfFq">molecule</a>. The Hund–Mulliken approach or molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting <a href="/facts/Spectroscopy/mj71FuNK">spectroscopic properties</a> better than the VB method. This approach is the conceptual basis of the <a href="/facts/Hartree%E2%80%93Fock_method/U9mlRWVR">Hartree–Fock method</a> and further <a href="/facts/Post%E2%80%93Hartree%E2%80%93Fock/SEG7bvRn">post-Hartree–Fock</a> methods.

<h3>Density functional theory</h3>
Main article: <a href="/facts/Density_functional_theory/wwz4Gqdg">Density functional theory</a>
The <a href="/facts/Gas_in_a_box/Rt6rexfo">Thomas–Fermi model</a> was developed independently by <a href="/facts/L._H._Thomas/cAzzHNCg">Thomas</a> and <a href="/facts/Enrico_Fermi/cmYcY15H">Fermi</a> in 1927. This was the first attempt to describe many-electron systems on the basis of <a href="/facts/Electronic_density/L5yDsk6j">electronic density</a> instead of <a href="/facts/Wave_function/KgM5ykjY">wave functions</a>, although it was not very successful in the treatment of entire molecules. The method did provide the basis for what is now known as density functional theory (DFT). Modern day DFT uses the <a href="/facts/Kohn%E2%80%93Sham_equations/mz2BklaC">Kohn–Sham method</a>, where the density functional is split into four terms; the Kohn–Sham kinetic energy, an external potential, exchange and correlation energies. A large part of the focus on developing DFT is on improving the exchange and correlation terms. Though this method is less developed than post Hartree–Fock methods, its significantly lower computational requirements (scaling typically no worse than n3 with respect to n basis functions, for the pure functionals) allow it to tackle larger <a href="/facts/Polyatomic_molecule/N9ljSfFq">polyatomic molecules</a> and even <a href="/facts/Macromolecule/039ULSLg">macromolecules</a>. This computational affordability and often comparable accuracy to <a href="/facts/M%C3%B8ller%E2%80%93Plesset_perturbation_theory/AuKWfsI2">MP2</a> and <a href="/facts/Coupled_cluster/VAdquKSJ">CCSD(T)</a> (post-Hartree–Fock methods) has made it one of the most popular methods in <a href="/facts/Computational_chemistry/KyuCgRV3">computational chemistry</a>.

<h2 id="chemical-dynamics">Chemical dynamics</h2>
A further step can consist of solving the <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> with the total <a href="/facts/Molecular_Hamiltonian/JljaHd2d">molecular Hamiltonian</a> in order to study the motion of molecules. Direct solution of the Schrödinger equation is called <a href="/facts/Quantum_dynamics/dmCGsg6B">quantum dynamics</a>, whereas its solution within the <a href="/facts/Semiclassical_physics/8v1CG3RP">semiclassical</a> approximation is called semiclassical dynamics. Purely <a href="/facts/Classical_mechanics/ykG8upsN">classical</a> simulations of molecular motion are referred to as <a href="/facts/Molecular_dynamics/yR3DNt6U">molecular dynamics</a> (MD). Another approach to dynamics is a hybrid framework known as <a href="/facts/Mixed_quantum-classical_dynamics/b1RdoHkJ">mixed quantum-classical dynamics</a>; yet another hybrid framework uses the <a href="/facts/Path_integral_formulation/6lt2MHkW">Feynman path integral</a> formulation to add quantum corrections to molecular dynamics, which is called <a href="/facts/Path_integral_molecular_dynamics/1aLo41sR">path integral molecular dynamics</a>. Statistical approaches, using for example classical and quantum <a href="/facts/Monte_Carlo_method/AkHjY7jc">Monte Carlo methods</a>, are also possible and are particularly useful for describing equilibrium distributions of states.

<h3>Adiabatic chemical dynamics</h3>
Main article: <a href="/facts/Born%E2%80%93Oppenheimer_approximation/hxlUcBrX">Born–Oppenheimer approximation</a>
In adiabatic dynamics, interatomic interactions are represented by single <a href="/facts/Scalar_(physics)/05uvvP8N">scalar</a> <a href="/facts/Potential/8Fcbtnt9">potentials</a> called <a href="/facts/Potential_energy_surface/YDUNcSM8">potential energy surfaces</a>. This is the <a href="/facts/Born%E2%80%93Oppenheimer_approximation/hxlUcBrX">Born–Oppenheimer approximation</a> introduced by <a href="/facts/Max_Born/6VnUDWhA">Born</a> and <a href="/facts/Robert_Oppenheimer/qvgElLRC">Oppenheimer</a> in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into the <a href="/facts/RRKM/CQ73dVhE">RRKM</a> theory in 1952 by <a href="/facts/Rudolph_A._Marcus/uBAqcJyv">Marcus</a> who took the <a href="/facts/Transition_state/34PsdqRd">transition state</a> theory developed by <a href="/facts/Henry_Eyring_(chemist)/9nU3NFN8">Eyring</a> in 1935 into account. These methods enable simple estimates of unimolecular <a href="/facts/Reaction_rates/Prwvxq0y">reaction rates</a> from a few characteristics of the potential surface.

<h3>Non-adiabatic chemical dynamics</h3>
Main article: <a href="/facts/Vibronic_coupling/IDmq1G4J">Vibronic coupling</a>
Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surfaces (corresponding to different electronic <a href="/facts/Quantum_state/7jbxd7Dx">quantum states</a> of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done by <a href="/facts/Ernst_Stueckelberg/T6vw38Sq">Stueckelberg</a>, <a href="/facts/Lev_Davidovich_Landau/lNXQTC49">Landau</a>, and <a href="/facts/Clarence_Zener/wLHoYt84">Zener</a> in the 1930s, in their work on what is now known as the <a href="/facts/Landau%E2%80%93Zener_transition/JkgAw34u">Landau–Zener transition</a>. Their formula allows the transition probability between two <a href="/facts/Adiabatic/rJj42U5h">adiabatic</a> potential curves in the neighborhood of an <a href="/facts/Avoided_crossing/7VtKlQkC">avoided crossing</a> to be calculated. <a href="/facts/Spin_forbidden_reactions/WJVIEu4w">Spin-forbidden reactions</a> are one type of non-adiabatic reactions where at least one change in <a href="/facts/Spin_states_(d_electrons)/QDMbT06M">spin state</a> occurs when progressing from <a href="/facts/Reagent/c3GLInCu">reactant</a> to <a href="/facts/Product_(chemistry)/8uCoDUdv">product</a>.

<h2 id="see-also">See also</h2>
<ul>
<li>Chemistry portal</li><li>Physics portal</li></ul>

<ul><li><a href="/facts/Atomic_physics/7Jlm4I7k">Atomic physics</a></li>
<li><a href="/facts/Computational_chemistry/KyuCgRV3">Computational chemistry</a></li>
<li><a href="/facts/Condensed_matter_physics/EBVI5nmL">Condensed matter physics</a></li>
<li><a href="/facts/Car%E2%80%93Parrinello_molecular_dynamics/IhUdV435">Car–Parrinello molecular dynamics</a></li>
<li><a href="/facts/Electron_localization_function/B0gzVycW">Electron localization function</a></li>
<li><a href="/facts/International_Academy_of_Quantum_Molecular_Science/ms3s6RQP">International Academy of Quantum Molecular Science</a></li>
<li><a href="/facts/Molecular_modelling/bc80hbtm">Molecular modelling</a></li>
<li><a href="/facts/Physical_chemistry/WqwnJjRM">Physical chemistry</a></li>
<li><a href="/facts/Quantum_computational_chemistry/mXD08RNJ">Quantum computational chemistry </a></li>
<li><a href="/facts/List_of_quantum_chemistry_and_solid-state_physics_software/WpF4uoKD">List of quantum chemistry and solid-state physics software</a></li>
<li><a href="/facts/QMC@Home/32QwUm2H">QMC@Home</a></li>
<li><a href="/facts/Quantum_Aspects_of_Life/WLMwC8Lv">Quantum Aspects of Life</a></li>
<li><a href="/facts/Quantum_electrochemistry/E3w8nGKx">Quantum electrochemistry</a></li>
<li><a href="/facts/Relativistic_quantum_chemistry/8A1se1CS">Relativistic quantum chemistry</a></li>
<li><a href="/facts/Theoretical_physics/Cs2Y12rQ">Theoretical physics</a></li>
<li><a href="/facts/Spin_forbidden_reactions/WJVIEu4w">Spin forbidden reactions</a></li></ul>

<h2 id="sources">Sources</h2>
<ul><li>Atkins, P.W. (2002). Physical Chemistry. Oxford University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-19-879285-9.</li>
<li>Atkins, P.W.; Friedman, R. (2005). Molecular Quantum Mechanics (4th ed.). Oxford University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-19-927498-7.</li>
<li>Atkins, P.W.; Friedman, R. (2008). Quanta, Matter and Change: A Molecular Approach to Physical Change. Macmillan. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-7167-6117-4.</li>
<li><a href="/facts/Richard_Bader/XcfRAHqx">Bader, Richard</a> (1994). Atoms in Molecules: A Quantum Theory. Oxford University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-19-855865-1.</li>
<li>Cramer, Christopher J (2004). Essentials of Computational Chemistry : Theories and Models (2 ed.). Wiley. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780470091821. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/55887497">55887497</a>.</li>
<li>Gavroglu, Kostas; Ana Simões: Neither Physics nor Chemistry: A History of Quantum Chemistry, MIT Press, 2011, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-262-01618-4</li>
<li>Karplus M., Porter R.N. (1971). Atoms and Molecules. An introduction for students of physical chemistry, Benjamin–Cummings Publishing Company, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-8053-5218-4</li>
<li>Landau, L.D.; Lifshitz, E.M. (1977). Quantum Mechanics:Non-relativistic Theory. Course of Theoretical Physic. Vol. 3. Pergamon Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-08-019012-X.</li>
<li>Levine, I. (2008). Physical Chemistry (6th ed.). McGraw–Hill Science. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-07-253862-5.</li>
<li><a href="/facts/Charles_Coulson/CSKYHwBU">Coulson, Charles Alfred</a> (1991) [1979]. McWeeny, Roy (ed.). Coulson's valence (3 ed.). Oxford University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780198551454. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/468330825">468330825</a>.</li>
<li><a href="/facts/Linus_Pauling/cBNBzs5c">Pauling, L.</a> (1954). <a href="https://archive.org/details/generalchemistry00paul_0">General Chemistry</a>. Dover Publications. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-486-65622-5.</li>
<li><a href="/facts/Linus_Pauling/cBNBzs5c">Pauling, L.</a>; Wilson, E. B. (1963) [1935]. Introduction to Quantum Mechanics with Applications to Chemistry. Dover Publications. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-486-64871-0.</li>
<li>Pullman, Bernard; Pullman, Alberte (1963). Quantum Biochemistry. New York and London: Academic Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 90-277-1830-X.</li>
<li>Scerri, Eric R. (2006). <a href="https://archive.org/details/periodictableits0000scer">The Periodic Table: Its Story and Its Significance</a>. Oxford University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-19-530573-6. Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics.</li>
<li>Simon, Z. (1976). Quantum Biochemistry and Specific Interactions. Taylor & Francis. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-85626-087-2.</li>
<li>Szabo, Attila; Ostlund, Neil S. (1996). Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-486-69186-1.</li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.quantum-chemistry-history.com/">Early ideas in the history of quantum chemistry</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">McQuarrie, Donald A. (2007). Quantum Chemistry (2nd ed.). University Science Books. ISBN 978-1891389504. <a href="978-1891389504" target="_blank">978-1891389504</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Heitler, W.; London, F. (1927). "Wechselwirkung neutraler Atome und homopolare Bindung nach der Quantenmechanik". Zeitschrift für Physik. 44 (6–7): 455–472. Bibcode:1927ZPhy...44..455H. doi:10.1007/BF01397394. <a href="https://dx.doi.org/10.1007/BF01397394" target="_blank">https://dx.doi.org/10.1007/BF01397394</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Kołos, W. (1989). "The Origin, Development and Significance of the Heitler-London Approach". Perspectives in Quantum Chemistry. Académie Internationale Des Sciences Moléculaires Quantiques/International Academy of Quantum Molecular Science. Vol. 6. Dordrecht: Springer. pp. 145–159. doi:10.1007/978-94-009-0949-6_8. ISBN 978-94-010-6917-5. <a href="978-94-010-6917-5" target="_blank">978-94-010-6917-5</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Lewis, G.N. (1916). "The Atom and the Molecule". Journal of the American Chemical Society. 38 (4): 762–785. Bibcode:1916JAChS..38..762L. doi:10.1021/ja02261a002. <a href="https://dx.doi.org/10.1021/ja02261a002" target="_blank">https://dx.doi.org/10.1021/ja02261a002</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Sugiura, Y. (1927). "Über die Eigenschaften des Wasserstoffmoleküls im Grundzustande". Zeitschrift für Physik. 45 (7–8): 484–492. Bibcode:1927ZPhy...45..484S. doi:10.1007/BF01329207. <a href="https://link.springer.com/article/10.1007/BF01329207" target="_blank">https://link.springer.com/article/10.1007/BF01329207</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Nakane, Michiyo (2019). "Yoshikatsu Sugiura's Contribution to the Development of Quantum Physics in Japan". Berichte zur Wissenschaftsgeschichte. 42 (4): 338–356. doi:10.1002/bewi.201900007. PMID 31777981. <a href="https://onlinelibrary.wiley.com/doi/10.1002/bewi.201900007" target="_blank">https://onlinelibrary.wiley.com/doi/10.1002/bewi.201900007</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Wang, S. C. (1928-04-01). "The Problem of the Normal Hydrogen Molecule in the New Quantum Mechanics". Physical Review. 31 (4): 579–586. Bibcode:1928PhRv...31..579W. doi:10.1103/PhysRev.31.579. <a href="https://link.aps.org/doi/10.1103/PhysRev.31.579" target="_blank">https://link.aps.org/doi/10.1103/PhysRev.31.579</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Pauling, Linus (April 6, 1931). "The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules". Journal of the American Chemical Society. 53 (4): 1367–1400. Bibcode:1931JAChS..53.1367P. doi:10.1021/ja01355a027 – via Oregon State University Library. <a href="http://scarc.library.oregonstate.edu/coll/pauling/bond/papers/1931p.3.html" target="_blank">http://scarc.library.oregonstate.edu/coll/pauling/bond/papers/1931p.3.html</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Pauling, Linus (1939). The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry (1st ed.). Cornell University Press. <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Norman, Jeremy. "Pauling Publishes "The Nature of the Chemical Bond"". History of Information. Retrieved July 11, 2023. <a href="https://historyofinformation.com/detail.php?id=3956" target="_blank">https://historyofinformation.com/detail.php?id=3956</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Хельман, Г. (1937). Квантовая Химия. Главная Редакция Технико-Теоретической Литературы, Moscow and Leningrad. <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Hellmann, Hans (1937). Einführung in die Quantenchemie. Deuticke, Leipzig und Wien. <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Simons, Jack (2003). "Chapter 6. Electronic Structures". An introduction to theoretical chemistry (PDF). Cambridge, UK: Cambridge University Press. ISBN 0521823609. <a href="0521823609" target="_blank">0521823609</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Martin, Richard M. (2008-10-27). Electronic Structure: Basic Theory and Practical Methods. Cambridge: Cambridge University Press. ISBN 978-0-521-53440-6. <a href="978-0-521-53440-6" target="_blank">978-0-521-53440-6</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">Shaik, S.S.; Hiberty, P.C. (2007). A Chemist's Guide to Valence Bond Theory. Wiley-Interscience. ISBN 978-0470037355. <a href="978-0470037355" target="_blank">978-0470037355</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
</ol>

Quantum chemistry open-in-new

Quantum chemistry