fbpx
Wikipedia

Semi-empirical quantum chemistry method

February 16, 2024

Semi-empirical quantum chemistry methods are based on the Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data. They are very important in computational chemistry for treating large molecules where the full Hartree–Fock method without the approximations is too expensive. The use of empirical parameters appears to allow some inclusion of electron correlation effects into the methods.

Within the framework of Hartree–Fock calculations, some pieces of information (such as two-electron integrals) are sometimes approximated or completely omitted. In order to correct for this loss, semi-empirical methods are parametrized, that is their results are fitted by a set of parameters, normally in such a way as to produce results that best agree with experimental data, but sometimes to agree with ab initio results.

Type of simplifications used edit

Semi-empirical methods follow what are often called empirical methods where the two-electron part of the Hamiltonian is not explicitly included. For π-electron systems, this was the Hückel method proposed by Erich Hückel.[1][2][3][4][5][6] For all valence electron systems, the extended Hückel method was proposed by Roald Hoffmann.[7]

Semi-empirical calculations are much faster than their ab initio counterparts, mostly due to the use of the zero differential overlap 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.

Preferred application domains edit

Methods restricted to π-electrons edit

These methods exist for the calculation of electronically excited states of polyenes, both cyclic and linear. These methods, such as the Pariser–Parr–Pople method (PPP), can provide good estimates of the π-electronic excited states, when parameterized well.[8][9][10] For many years, the PPP method outperformed ab initio excited state calculations.

Methods restricted to all valence electrons. edit

These methods can be grouped into several groups:

  • Methods such as CNDO/2, INDO and NDDO that were introduced by John Pople.[11][12][13] 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.
  • Methods that are in the MOPAC, AMPAC, SPARTAN and/or CP2K computer programs originally from the group of Michael Dewar.[14] These are MINDO, MNDO,[15] AM1,[16] PM3,[17] PM6,[18] PM7[19] and SAM1. 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.
  • Methods whose primary aim is to calculate excited states and hence predict electronic spectra. These include ZINDO and SINDO.[20][21] The OMx (x=1,2,3) methods[22] 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 MRCI[23] is an important tool for excited state molecular dynamics.
  • Tight-binding methods, e.g. a large family of methods known as DFTB,[24] 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.[25]
  • The NOTCH method[26] 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.

See also edit

References edit

  1. ^ Hückel, Erich (1931). "Quantentheoretische Beiträge zum Benzolproblem I". Zeitschrift für Physik (in German). Springer Science and Business Media LLC. 70 (3–4): 204–286. Bibcode:1931ZPhy...70..204H. doi:10.1007/bf01339530. ISSN 1434-6001. S2CID 186218131.
  2. ^ Hückel, Erich (1931). "Quanstentheoretische Beiträge zum Benzolproblem II". Zeitschrift für Physik (in German). Springer Science and Business Media LLC. 72 (5–6): 310–337. Bibcode:1931ZPhy...72..310H. doi:10.1007/bf01341953. ISSN 1434-6001.
  3. ^ Hückel, Erich (1932). "Quantentheoretische Beiträge zum Problem der aromatischen und ungesättigten Verbindungen. III". Zeitschrift für Physik (in German). Springer Science and Business Media LLC. 76 (9–10): 628–648. Bibcode:1932ZPhy...76..628H. doi:10.1007/bf01341936. ISSN 1434-6001. S2CID 121787219.
  4. ^ Hückel, Erich (1933). "Die freien Radikale der organischen Chemie IV". Zeitschrift für Physik (in German). Springer Science and Business Media LLC. 83 (9–10): 632–668. Bibcode:1933ZPhy...83..632H. doi:10.1007/bf01330865. ISSN 1434-6001. S2CID 121710615.
  5. ^ Hückel Theory for Organic Chemists, C. A. Coulson, B. O'Leary and R. B. Mallion, Academic Press, 1978.
  6. ^ Andrew Streitwieser, Molecular Orbital Theory for Organic Chemists, Wiley, New York, (1961)
  7. ^ Hoffmann, Roald (1963-09-15). "An Extended Hückel Theory. I. Hydrocarbons". The Journal of Chemical Physics. AIP Publishing. 39 (6): 1397–1412. Bibcode:1963JChPh..39.1397H. doi:10.1063/1.1734456. ISSN 0021-9606.
  8. ^ 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. AIP Publishing. 21 (3): 466–471. Bibcode:1953JChPh..21..466P. doi:10.1063/1.1698929. ISSN 0021-9606.
  9. ^ 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. AIP Publishing. 21 (5): 767–776. Bibcode:1953JChPh..21..767P. doi:10.1063/1.1699030. ISSN 0021-9606.
  10. ^ Pople, J. A. (1953). "Electron interaction in unsaturated hydrocarbons". Transactions of the Faraday Society. Royal Society of Chemistry (RSC). 49: 1375. doi:10.1039/tf9534901375. ISSN 0014-7672.
  11. ^ J. Pople and D. Beveridge, Approximate Molecular Orbital Theory, McGraw–Hill, 1970.
  12. ^ Ira Levine, Quantum Chemistry, Prentice Hall, 4th edition, (1991), pg 579–580
  13. ^ C. J. Cramer, Essentials of Computational Chemistry, Wiley, Chichester, (2002), pg 126–131
  14. ^ J. J. P. Stewart, Reviews in Computational Chemistry, Volume 1, Eds. K. B. Lipkowitz and D. B. Boyd, VCH, New York, 45, (1990)
  15. ^ 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.
  16. ^ 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.
  17. ^ 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.
  18. ^ 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.
  19. ^ 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.
  20. ^ M. Zerner, Reviews in Computational Chemistry, Volume 2, Eds. K. B. Lipkowitz and D. B. Boyd, VCH, New York, 313, (1991)
  21. ^ 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. Springer Science and Business Media LLC. 57 (2): 95–106. doi:10.1007/bf00574898. ISSN 0040-5744. S2CID 98468383.
  22. ^ 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.
  23. ^ 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.
  24. ^ 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.
  25. ^ 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.
  26. ^ 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.

February 16, 2024
semi, empirical, quantum, chemistry, method, based, hartree, fock, formalism, make, many, approximations, obtain, some, parameters, from, empirical, data, they, very, important, computational, chemistry, treating, large, molecules, where, full, hartree, fock, . Semi empirical quantum chemistry methods are based on the Hartree Fock formalism but make many approximations and obtain some parameters from empirical data They are very important in computational chemistry for treating large molecules where the full Hartree Fock method without the approximations is too expensive The use of empirical parameters appears to allow some inclusion of electron correlation effects into the methods Within the framework of Hartree Fock calculations some pieces of information such as two electron integrals are sometimes approximated or completely omitted In order to correct for this loss semi empirical methods are parametrized that is their results are fitted by a set of parameters normally in such a way as to produce results that best agree with experimental data but sometimes to agree with ab initio results Contents 1 Type of simplifications used 2 Preferred application domains 2 1 Methods restricted to p electrons 2 2 Methods restricted to all valence electrons 3 See also 4 ReferencesType of simplifications used editSemi empirical methods follow what are often called empirical methods where the two electron part of the Hamiltonian is not explicitly included For p electron systems this was the Huckel method proposed by Erich Huckel 1 2 3 4 5 6 For all valence electron systems the extended Huckel method was proposed by Roald Hoffmann 7 Semi empirical calculations are much faster than their ab initio counterparts mostly due to the use of the zero differential overlap 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 Preferred application domains editMethods restricted to p electrons edit These methods exist for the calculation of electronically excited states of polyenes both cyclic and linear These methods such as the Pariser Parr Pople method PPP can provide good estimates of the p electronic excited states when parameterized well 8 9 10 For many years the PPP method outperformed ab initio excited state calculations Methods restricted to all valence electrons edit These methods can be grouped into several groups Methods such as CNDO 2 INDO and NDDO that were introduced by John Pople 11 12 13 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 Methods that are in the MOPAC AMPAC SPARTAN and or CP2K computer programs originally from the group of Michael Dewar 14 These are MINDO MNDO 15 AM1 16 PM3 17 PM6 18 PM7 19 and SAM1 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 Methods whose primary aim is to calculate excited states and hence predict electronic spectra These include ZINDO and SINDO 20 21 The OMx x 1 2 3 methods 22 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 MRCI 23 is an important tool for excited state molecular dynamics Tight binding methods e g a large family of methods known as DFTB 24 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 25 The NOTCH method 26 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 See also editList of quantum chemistry and solid state physics softwareReferences edit Huckel Erich 1931 Quantentheoretische Beitrage zum Benzolproblem I Zeitschrift fur Physik in German Springer Science and Business Media LLC 70 3 4 204 286 Bibcode 1931ZPhy 70 204H doi 10 1007 bf01339530 ISSN 1434 6001 S2CID 186218131 Huckel Erich 1931 Quanstentheoretische Beitrage zum Benzolproblem II Zeitschrift fur Physik in German Springer Science and Business Media LLC 72 5 6 310 337 Bibcode 1931ZPhy 72 310H doi 10 1007 bf01341953 ISSN 1434 6001 Huckel Erich 1932 Quantentheoretische Beitrage zum Problem der aromatischen und ungesattigten Verbindungen III Zeitschrift fur Physik in German Springer Science and Business Media LLC 76 9 10 628 648 Bibcode 1932ZPhy 76 628H doi 10 1007 bf01341936 ISSN 1434 6001 S2CID 121787219 Huckel Erich 1933 Die freien Radikale der organischen Chemie IV Zeitschrift fur Physik in German Springer Science and Business Media LLC 83 9 10 632 668 Bibcode 1933ZPhy 83 632H doi 10 1007 bf01330865 ISSN 1434 6001 S2CID 121710615 Huckel Theory for Organic Chemists C A Coulson B O Leary and R B Mallion Academic Press 1978 Andrew Streitwieser Molecular Orbital Theory for Organic Chemists Wiley New York 1961 Hoffmann Roald 1963 09 15 An Extended Huckel Theory I Hydrocarbons The Journal of Chemical Physics AIP Publishing 39 6 1397 1412 Bibcode 1963JChPh 39 1397H doi 10 1063 1 1734456 ISSN 0021 9606 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 AIP Publishing 21 3 466 471 Bibcode 1953JChPh 21 466P doi 10 1063 1 1698929 ISSN 0021 9606 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 AIP Publishing 21 5 767 776 Bibcode 1953JChPh 21 767P doi 10 1063 1 1699030 ISSN 0021 9606 Pople J A 1953 Electron interaction in unsaturated hydrocarbons Transactions of the Faraday Society Royal Society of Chemistry RSC 49 1375 doi 10 1039 tf9534901375 ISSN 0014 7672 J Pople and D Beveridge Approximate Molecular Orbital Theory McGraw Hill 1970 Ira Levine Quantum Chemistry Prentice Hall 4th edition 1991 pg 579 580 C J Cramer Essentials of Computational Chemistry Wiley Chichester 2002 pg 126 131 J J P Stewart Reviews in Computational Chemistry Volume 1 Eds K B Lipkowitz and D B Boyd VCH New York 45 1990 Michael J S Dewar amp 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 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 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 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 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 M Zerner Reviews in Computational Chemistry Volume 2 Eds K B Lipkowitz and D B Boyd VCH New York 313 1991 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 Springer Science and Business Media LLC 57 2 95 106 doi 10 1007 bf00574898 ISSN 0040 5744 S2CID 98468383 Dral Pavlo O Wu Xin Sporkel 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 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 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 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 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 Retrieved from https en wikipedia org w index php title Semi empirical quantum chemistry method amp oldid 1170349826, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.