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Semi-empirical quantum chemistry method
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<h2 id="type-of-simplifications-used">Type of simplifications used</h2> <p>Semi-empirical methods follow what are often called empirical methods where the two-electron part of the <a href="/facts/Hamiltonian_(quantum_mechanics)/5XwK2HmD">Hamiltonian</a> is not explicitly included. For π-electron systems, this was the <a href="/facts/H%C3%BCckel_method/2F8acMEn">Hückel method</a> proposed by <a href="/facts/Erich_H%C3%BCckel/EmM42Vtp">Erich Hückel</a>.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a><a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> For all valence electron systems, the <a href="/facts/Extended_H%C3%BCckel_method/8KVbSsGI">extended Hückel method</a> was proposed by <a href="/facts/Roald_Hoffmann/DHMcXIff">Roald Hoffmann</a>.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p><p>Semi-empirical calculations are much faster than their <i>ab initio</i> counterparts, mostly due to the use of the <a href="/facts/Zero_differential_overlap/tFJtKF4F">zero differential overlap</a> approximation. Their results, however, can be very wrong if the molecule being computed is not similar enough to the molecules in the database used to parametrize the method. </p> <h2 id="preferred-application-domains">Preferred application domains</h2> <h3>Methods restricted to π-electrons</h3> <p>These methods exist for the calculation of electronically excited states of polyenes, both cyclic and linear. These methods, such as the <a href="/facts/Pariser%E2%80%93Parr%E2%80%93Pople_method/wzyeX8zg">Pariser–Parr–Pople method</a> (PPP), can provide good estimates of the π-electronic excited states, when parameterized well.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a><a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> For many years, the PPP method outperformed ab initio excited state calculations. </p> <h3>Methods restricted to all valence electrons.</h3> <p>These methods can be grouped into several groups: </p> <ul><li>Methods such as <a href="/facts/CNDO/2/4fXfeCaR">CNDO/2</a>, <a href="/facts/INDO/tU9qDFQc">INDO</a> and <a href="/facts/NDDO/sRyFkhHz">NDDO</a> that were introduced by <a href="/facts/John_Pople/1UmPknsL">John Pople</a>.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a><a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> The implementations aimed to fit, not experiment, but ab initio minimum basis set results. These methods are now rarely used but the methodology is often the basis of later methods.</li></ul> <ul><li>Methods that are in the <a href="/facts/MOPAC/L2kpo4Yf">MOPAC</a>, <a href="/facts/AMPAC/qszSJDhe">AMPAC</a>, <a href="/facts/Spartan_(chemistry_software)/5I4PGBTa">SPARTAN</a> and/or <a href="/facts/CP2K/g84Xktgq">CP2K</a> computer programs originally from the group of <a href="/facts/Michael_J._S._Dewar/mTUEsYvf">Michael Dewar</a>.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> These are <a href="/facts/MINDO/dFGVlFAs">MINDO</a>, <a href="/facts/MNDO/aFtBqEbW">MNDO</a>,<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> <a href="/facts/Austin_Model_1/PS7g3BMh">AM1</a>,<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> <a href="/facts/PM3_(chemistry)/o5ktA2Rm">PM3</a>,<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> PM6,<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> PM7<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> and <a href="/facts/SAM1/474Dzmy2">SAM1</a>. Here the objective is to use parameters to fit experimental heats of formation, dipole moments, ionization potentials, and geometries. This is by far the largest group of semiempirical methods.</li></ul> <ul><li>Methods whose primary aim is to calculate excited states and hence predict electronic spectra. These include <a href="/facts/ZINDO/47LzJxrv">ZINDO</a> and <a href="/facts/SINDO/aWMRhHwg">SINDO</a>.<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a><a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> The OMx (x=1,2,3) methods<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a> can also be viewed as belonging to this class, although they are also suitable for ground-state applications; in particular, the combination of OM2 and <a href="/facts/Multireference_configuration_interaction/Kqydgd5s">MRCI</a><a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a> is an important tool for excited state molecular dynamics.</li></ul> <ul><li><a href="/facts/Tight_binding/1Iq7SSzo">Tight-binding methods</a>, e.g. a large family of methods known as <a href="/facts/DFTB/CW0tJcKz">DFTB</a>,<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a> are sometimes classified as semiempirical methods as well. More recent examples include the semiempirical quantum mechanical methods GFNn-xTB (n=0,1,2), which are particularly suited for the geometry, vibrational frequencies, and non-covalent interactions of large molecules.<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a></li></ul> <ul><li>The NOTCH method<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a> includes many new, physically-motivated terms compared to the NDDO family of methods, is much less empirical than the other semi-empirical methods (almost all of its parameters are determined non-empirically), provides robust accuracy for bonds between uncommon element combinations, and is applicable to ground and excited states.</li></ul> <h2 id="see-also">See also</h2> <ul><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></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Hückel, Erich (1931). "Quantentheoretische Beiträge zum Benzolproblem I". Zeitschrift für Physik (in German). 70 (3–4). Springer Science and Business Media LLC: 204–286. Bibcode:1931ZPhy...70..204H. doi:10.1007/bf01339530. ISSN 1434-6001. S2CID 186218131. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Hückel, Erich (1931). "Quanstentheoretische Beiträge zum Benzolproblem II". Zeitschrift für Physik (in German). 72 (5–6). Springer Science and Business Media LLC: 310–337. Bibcode:1931ZPhy...72..310H. doi:10.1007/bf01341953. ISSN 1434-6001. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Hückel, Erich (1932). "Quantentheoretische Beiträge zum Problem der aromatischen und ungesättigten Verbindungen. III". Zeitschrift für Physik (in German). 76 (9–10). Springer Science and Business Media LLC: 628–648. Bibcode:1932ZPhy...76..628H. doi:10.1007/bf01341936. ISSN 1434-6001. S2CID 121787219. <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>Hückel, Erich (1933). "Die freien Radikale der organischen Chemie IV". Zeitschrift für Physik (in German). 83 (9–10). Springer Science and Business Media LLC: 632–668. Bibcode:1933ZPhy...83..632H. doi:10.1007/bf01330865. ISSN 1434-6001. S2CID 121710615. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Hückel Theory for Organic Chemists, C. A. Coulson, B. O'Leary and R. B. Mallion, Academic Press, 1978. <a href="/wiki/Charles_A._Coulson" target="_blank">/wiki/Charles_A._Coulson</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Andrew Streitwieser, Molecular Orbital Theory for Organic Chemists, Wiley, New York, (1961) <a href="/wiki/Andrew_Streitwieser" target="_blank">/wiki/Andrew_Streitwieser</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Hoffmann, Roald (1963-09-15). "An Extended Hückel Theory. I. Hydrocarbons". The Journal of Chemical Physics. 39 (6). AIP Publishing: 1397–1412. Bibcode:1963JChPh..39.1397H. doi:10.1063/1.1734456. ISSN 0021-9606. <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>Pariser, Rudolph; Parr, Robert G. (1953). "A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I.". The Journal of Chemical Physics. 21 (3). AIP Publishing: 466–471. Bibcode:1953JChPh..21..466P. doi:10.1063/1.1698929. ISSN 0021-9606. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Pariser, Rudolph; Parr, Robert G. (1953). "A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. II". The Journal of Chemical Physics. 21 (5). AIP Publishing: 767–776. Bibcode:1953JChPh..21..767P. doi:10.1063/1.1699030. ISSN 0021-9606. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Pople, J. A. (1953). "Electron interaction in unsaturated hydrocarbons". Transactions of the Faraday Society. 49. Royal Society of Chemistry (RSC): 1375. doi:10.1039/tf9534901375. ISSN 0014-7672. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>J. Pople and D. Beveridge, Approximate Molecular Orbital Theory, McGraw–Hill, 1970. <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Ira Levine, Quantum Chemistry, Prentice Hall, 4th edition, (1991), pg 579–580 <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>C. J. Cramer, Essentials of Computational Chemistry, Wiley, Chichester, (2002), pg 126–131 <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>J. J. P. Stewart, Reviews in Computational Chemistry, Volume 1, Eds. K. B. Lipkowitz and D. B. Boyd, VCH, New York, 45, (1990) <a href="/w/index.php?title=Reviews_in_Computational_Chemistry&action=edit&redlink=1" target="_blank">/w/index.php?title=Reviews_in_Computational_Chemistry&action=edit&redlink=1</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Michael J. S. Dewar & Walter Thiel (1977). "Ground states of molecules. 38. The MNDO method. Approximations and parameters". Journal of the American Chemical Society. 99 (15): 4899–4907. doi:10.1021/ja00457a004. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Michael J. S. Dewar; Eve G. Zoebisch; Eamonn F. Healy; James J. P. Stewart (1985). "Development and use of quantum molecular models. 75. Comparative tests of theoretical procedures for studying chemical reactions". Journal of the American Chemical Society. 107 (13): 3902–3909. doi:10.1021/ja00299a024. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>James J. P. Stewart (1989). "Optimization of parameters for semiempirical methods I. Method". The Journal of Computational Chemistry. 10 (2): 209–220. doi:10.1002/jcc.540100208. S2CID 36907984. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Stewart, James J. P. (2007). "Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements". Journal of Molecular Modeling. 13 (12): 1173–1213. doi:10.1007/s00894-007-0233-4. PMC 2039871. PMID 17828561. <a href="https://doi.org/10.1007/s00894-007-0233-4" target="_blank">https://doi.org/10.1007/s00894-007-0233-4</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>Stewart, James J. P. (2013). "Optimization of parameters for semiempirical methods VI: More modifications to the NDDO approximations and re-optimization of parameters". Journal of Molecular Modeling. 19 (1): 1–32. doi:10.1007/s00894-012-1667-x. PMC 3536963. PMID 23187683. <a href="https://doi.org/10.1007/s00894-012-1667-x" target="_blank">https://doi.org/10.1007/s00894-012-1667-x</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>M. Zerner, Reviews in Computational Chemistry, Volume 2, Eds. K. B. Lipkowitz and D. B. Boyd, VCH, New York, 313, (1991) <a href="/w/index.php?title=Reviews_in_Computational_Chemistry&action=edit&redlink=1" target="_blank">/w/index.php?title=Reviews_in_Computational_Chemistry&action=edit&redlink=1</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>Nanda, D. N.; Jug, Karl (1980). "SINDO1. A semiempirical SCF MO method for molecular binding energy and geometry I. Approximations and parametrization". Theoretica Chimica Acta. 57 (2). Springer Science and Business Media LLC: 95–106. doi:10.1007/bf00574898. ISSN 0040-5744. S2CID 98468383. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> <li id="fn:22"><p>Dral, Pavlo O.; Wu, Xin; Spörkel, Lasse; Koslowski, Axel; Weber, Wolfgang; Steiger, Rainer; Scholten, Mirjam; Thiel, Walter (2016). "Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters". Journal of Chemical Theory and Computation. 12 (3): 1082–1096. doi:10.1021/acs.jctc.5b01046. PMC 4785507. PMID 26771204. <a href="https://doi.org/10.1021/acs.jctc.5b01046" target="_blank">https://doi.org/10.1021/acs.jctc.5b01046</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li> <li id="fn:23"><p>Tuna, Deniz; Lu, You; Koslowski, Axel; Thiel, Walter (2016). "Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks of Electronically Excited States". Journal of Chemical Theory and Computation. 12 (9): 4400–4422. doi:10.1021/acs.jctc.6b00403. PMID 27380455. <a href="https://doi.org/10.1021%2Facs.jctc.6b00403" target="_blank">https://doi.org/10.1021%2Facs.jctc.6b00403</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li> <li id="fn:24"><p>Seifert, Gotthard; Joswig, Jan-Ole (2012). "Density-functional tight binding—an approximate density-functional theory method". WIREs Computational Molecular Science. 2 (3): 456–465. doi:10.1002/wcms.1094. S2CID 121521740. <a href="https://doi.org/10.1002/wcms.1094" target="_blank">https://doi.org/10.1002/wcms.1094</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li> <li id="fn:25"><p>Bannwarth, Christoph; Ehlert, Sebastian; Grimme, Stefan (2019-03-12). "GFN2-xTB—An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions". Journal of Chemical Theory and Computation. 15 (3): 1652–1671. doi:10.1021/acs.jctc.8b01176. ISSN 1549-9618. PMID 30741547. S2CID 73419235. <a href="https://doi.org/10.1021%2Facs.jctc.8b01176" target="_blank">https://doi.org/10.1021%2Facs.jctc.8b01176</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></p></li> <li id="fn:26"><p>Wang, Zikuan; Neese, Frank (2023). "Development of NOTCH, an all-electron, beyond-NDDO semiempirical method: Application to diatomic molecules". The Journal of Chemical Physics. 158 (18): 184102. Bibcode:2023JChPh.158r4102W. doi:10.1063/5.0141686. PMID 37154284. S2CID 258565304. <a href="https://doi.org/10.1063%2F5.0141686" target="_blank">https://doi.org/10.1063%2F5.0141686</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></p></li> </ol>