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Some non-relativistic many electron theories: single reference case

  • Hüseyin Aksu EMAIL logo
From the journal Open Chemistry

Abstract

There has been substantial progress in the development of electron correlation methods with some benefits and drawbacks. In this paper, we give a review of electron correlation effects on many body particles system. We focus more on atoms and molecules rather than solid state and take into account single reference case only. We mainly discuss perturbation theory, coupled electron many electron theory and a few versions of coupled electron pair approximations with comparison configuration interaction and some coupled cluster methods in which coupled cluster method is crucially important for the crystalline solids, the electron gas and the heat of the reaction. We also show some results, reported by several authors, to fairly compare and judge the methods’ feasibility mentioned above.

[1] E. Clementi, Proc. Nat. Acad. Sci. 69, 2942 (1972) http://dx.doi.org/10.1073/pnas.69.10.294210.1073/pnas.69.10.2942Search in Google Scholar

[2] E.R. Davidson, In: R. Daudel, B. Pullman (Eds.), The world of quantum chemistry (Reidel, Dordrecht, 1974) 17 http://dx.doi.org/10.1007/978-94-010-2156-2_210.1007/978-94-010-2156-2_2Search in Google Scholar

[3] R. Langhoff, R.E. Davidson, Int. J. Quantum Chem. 8, 61 (1974) http://dx.doi.org/10.1002/qua.56008010610.1002/qua.560080106Search in Google Scholar

[4] E.R. Davidson, D.W. Silver, Chem. Phys. Lett. 52, 403 (1977) http://dx.doi.org/10.1016/0009-2614(77)80475-210.1016/0009-2614(77)80475-2Search in Google Scholar

[5] P.E.M. Siegbahn, Chem. Phys. Lett. 55, 386 (1978) http://dx.doi.org/10.1016/0009-2614(78)87046-810.1016/0009-2614(78)87046-8Search in Google Scholar

[6] J.A. Pople, R. Seeger, R. Krishnan, Int. J. Quantum Chem. S11, 149, (1977) Search in Google Scholar

[7] L. Meissner, Chem. Phys. Lett. 146, 204 (1988) http://dx.doi.org/10.1016/0009-2614(88)87431-110.1016/0009-2614(88)87431-1Search in Google Scholar

[8] W. Duch, G.H. Diercksen, J. Chem. Phys. 101, 3018 (1994) http://dx.doi.org/10.1063/1.46761510.1063/1.467615Search in Google Scholar

[9] K.A. Brueckner, Phys. Rev. 97, 1353 (1955) http://dx.doi.org/10.1103/PhysRev.97.135310.1103/PhysRev.97.1353Search in Google Scholar

[10] P.-O. Löwdin, Int. J. Quantum Chem. 2, 867 (1968) http://dx.doi.org/10.1002/qua.56002061210.1002/qua.560020612Search in Google Scholar

[11] R. Krishnan, J.A. Pople, Int. J. Quantum Chem. 14, 91 (1978) http://dx.doi.org/10.1002/qua.56014010910.1002/qua.560140109Search in Google Scholar

[12] R. Krishnan, M.J. Frisch, J.A. Pople, J. Chem. Phys. 72, 4244 (1980) http://dx.doi.org/10.1063/1.43965710.1063/1.439657Search in Google Scholar

[13] M.J. Frisch, R. Krishnan, J.A. Pople, Chem. Phys. Lett. 75, 66 (1980) http://dx.doi.org/10.1016/0009-2614(80)80465-910.1016/0009-2614(80)80465-9Search in Google Scholar

[14] J. Cížek, J. Chem. Phys. 45, 4256 (1966) http://dx.doi.org/10.1063/1.172748410.1063/1.1727484Search in Google Scholar

[15] J. Cížek, Adv. Chem. Phys. 14, 35 (1969) http://dx.doi.org/10.1002/9780470143599.ch210.1002/9780470143599.ch2Search in Google Scholar

[16] P.R. Taylor, G.B. Bacskay, N.S. Hush, A.C. Hurley, Chem.Phys. Lett. 41, 444 (1976) http://dx.doi.org/10.1016/0009-2614(76)85390-010.1016/0009-2614(76)85390-0Search in Google Scholar

[17] J.A. Pople, R. Krishnan, H.B. Schlegel, J.S. Binkley, Int. J. Quantum Chem. 12, 545 (1978) http://dx.doi.org/10.1002/qua.56014050310.1002/qua.560140503Search in Google Scholar

[18] R.J. Bartlett, G.D. Purvis, Int. J. Quantum Chem. 14, 561 (1978) http://dx.doi.org/10.1002/qua.56014050410.1002/qua.560140504Search in Google Scholar

[19] R.A. Chiles, C.E. Dykstra, J. Chem. Phys. 74, 4544 (1981) http://dx.doi.org/10.1063/1.44164310.1063/1.441643Search in Google Scholar

[20] J. Paldus, J. Cizek, I. Shavitt, Phys. ReV. A 5, 50 (1972) http://dx.doi.org/10.1103/PhysRevA.5.5010.1103/PhysRevA.5.50Search in Google Scholar

[21] F. Coester, Nucl. Phys. 1, 421 (1958) 10.1016/0029-5582(58)90280-3Search in Google Scholar

[22] F. Coester, H. Kümmel, Nucl. Phys. 17, 477 (1960) http://dx.doi.org/10.1016/0029-5582(60)90140-110.1016/0029-5582(60)90140-1Search in Google Scholar

[23] Cížek, J. Paldus, Phys. Scr. 21, 251 (1980) http://dx.doi.org/10.1088/0031-8949/21/3-4/01210.1088/0031-8949/21/3-4/012Search in Google Scholar

[24] A.C. Hurley, Electronic Correlation in Small Molecules (Academic Press, New York, 1976) Search in Google Scholar

[25] W. Kutzelnigg, In: H.F. Schaefer III (Ed.), Methods of Electronic Structure Theory (Plenum, New York, 1977) 129 10.1007/978-1-4757-0887-5_5Search in Google Scholar

[26] R.J. Bartlett, G.D. Purvis, Phys. Scr. 21, 255 (1980) http://dx.doi.org/10.1088/0031-8949/21/3-4/00710.1088/0031-8949/21/3-4/007Search in Google Scholar

[27] R. Ahlrichs, Comput. Phys. Commun. 17, 31 (1979) http://dx.doi.org/10.1016/0010-4655(79)90067-510.1016/0010-4655(79)90067-5Search in Google Scholar

[28] J. Paldus, J. Chem. Phys. 67, 303 (1977) http://dx.doi.org/10.1063/1.43452610.1063/1.434526Search in Google Scholar

[29] J. Cížek, J. Paldus, Int. Quantum Chem. 5, 359 (1971) http://dx.doi.org/10.1002/qua.56005040210.1002/qua.560050402Search in Google Scholar

[30] G.D. Purvis, R.J. Bartlett, J. Chem. Phys. 76, 1910 (1982) http://dx.doi.org/10.1063/1.44316410.1063/1.443164Search in Google Scholar

[31] R.J. Bartlett, I. Shavitt, Chem. Phys. Lett. 50, 190 (1977) http://dx.doi.org/10.1016/0009-2614(77)80161-910.1016/0009-2614(77)80161-9Search in Google Scholar

[32] T.J. Lee, G.E. Scuseria, In: S.R. Langhoff (Ed.), Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy (Kluwer, Dordrecht, 1995) 47 http://dx.doi.org/10.1007/978-94-011-0193-6_210.1007/978-94-011-0193-6_2Search in Google Scholar

[33] R.J. Bartlett, Annu. Rev. Phys. Chem. 32, 359 (1981) http://dx.doi.org/10.1146/annurev.pc.32.100181.00204310.1146/annurev.pc.32.100181.002043Search in Google Scholar

[34] R.J. Bartlett, J. Phys. Chem. 93, 1697 (1989) http://dx.doi.org/10.1021/j100342a00810.1021/j100342a008Search in Google Scholar

[35] R.J. Bartlett, C.E. Dykstra, J. Paldus, In: C.E. Dykstra (Ed.), Advanced Theories, Computational Approaches to the Electronic Structure of Molecules (Reidel, Dordrecht, 1984) 127 10.1007/978-94-009-6451-8_8Search in Google Scholar

[36] M. Urban, I. Cernusak, V. Kellö, J. Noga, In: S. Wilson (Ed.), Methods in Computational Chemsitry, Vol. 1: Electron Correlation in Atoms, Molecules (Plenum, New York, 1987) 117 Search in Google Scholar

[37] J. Paldus, In: S. Wilson, G.H.F. Diercksen (Eds.), Methods in Computational Molecular Physics, Vol. 293, NATO Advanced Study Institute, Series B: Physics (Plenum, New York, 1992) 99 Search in Google Scholar

[38] J. Paldus, In: G.L. Malli (Ed.), Relativistic, Electron Correlation Effects in Molecules, Solids, Vol. 318, NATO Advanced Study Institute, Series B: Physics (Plenum, New York, 1994) 207 Search in Google Scholar

[39] R.J. Bartlett, In: D.R. Yarkony (Ed.), Modern Electronic Structure Theory (World Scientific, Singapore, 1995) Part I, 1047 http://dx.doi.org/10.1142/9789812832115_000510.1142/9789812832115_0005Search in Google Scholar

[40] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157, 479 (1989) http://dx.doi.org/10.1016/S0009-2614(89)87395-610.1016/S0009-2614(89)87395-6Search in Google Scholar

[41] V. Lotrich, N. Flocke, M. Ponton, A. Yau, A. Perera, E. Deumens, R.J. Bartlett, J. Chem. Phys. 128, 194104 (2008) http://dx.doi.org/10.1063/1.292048210.1063/1.2920482Search in Google Scholar PubMed

[42] T.D. Crawford, C.D. Sherrill, E.F. Valeev, J.T. Fermann, R.A. King, M L. Leininger, S.T. Brown, C.L. Janssen, E.T. Seidl, J.P. Kenny, W.D. Allen, J. Comput. Chem. 28, 1610 (2007) http://dx.doi.org/10.1002/jcc.2057310.1002/jcc.20573Search in Google Scholar PubMed

[43] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14, 1347 (1993) http://dx.doi.org/10.1002/jcc.54014111210.1002/jcc.540141112Search in Google Scholar

[44] I. Shavitt, R.J. Bartlett, Many-Body Methods in Chemistry, Physics: MBBT, Coupled Cluster Theory (Cambridge University Press, Cambridge, 2009) http://dx.doi.org/10.1017/CBO978051159683410.1017/CBO9780511596834Search in Google Scholar

[45] R.J. Bartlett, M. Musial, Rev. Modern Phys. 79, 291 (2007) http://dx.doi.org/10.1103/RevModPhys.79.29110.1103/RevModPhys.79.291Search in Google Scholar

[46] K. Raghavachari, J.B. Anderson, J. Phys. Chem. 100, 12960 (1996) http://dx.doi.org/10.1021/jp953749i10.1021/jp953749iSearch in Google Scholar

[47] R.J. Bartlett, In: C.E. Dykstra, G. Frenking, K.S. Kim, G.E. Scuseria (Eds.), Theory, Apllications of Computational Chemistry: The First Forty Years (Elsevier, Amsterdam 2005) 1191–1221 http://dx.doi.org/10.1016/B978-044451719-7/50085-810.1016/B978-044451719-7/50085-8Search in Google Scholar

[48] J. Paldus In: C.E. Dykstra, G. Frenking, K.S. Kim, G.E. Scuseria (Eds.), Theory, Apllications of Computational Chemistry: The First Forty Years (Elsevier, Amsterdam 2005) 115–147 http://dx.doi.org/10.1016/B978-044451719-7/50050-010.1016/B978-044451719-7/50050-0Search in Google Scholar

[49] R.J. Bartlett, I. Shavitt, Int. Qauntum Chem. Symp, 11, 165 (1977) Search in Google Scholar

[50] W.L. Luken, Chem. Phys. Lett. 58, 421 (1978) http://dx.doi.org/10.1016/0009-2614(78)85066-010.1016/0009-2614(78)85066-0Search in Google Scholar

[51] K. Jankowski, L. Meissner, J. Wasilewski, Int. Qauntum Chem. 28, 931 (1985) http://dx.doi.org/10.1002/qua.56028062210.1002/qua.560280622Search in Google Scholar

[52] P.G. Szalay, In: P. von Ragué Schleyer, H.F. Schaefer III, P.R. Schreiner, W.L. Jorgensen, W. Thiel, R.C. Glen (Eds.), Configuration Interaction: Correction for Size-Consistency (Wiley, Chichester, 2005) cn0066 Search in Google Scholar

[53] S. Koch, W. Kutzelnigg, Theoret. Chim. Acta (Berl.) 59, 387 (1981) http://dx.doi.org/10.1007/BF0240240210.1007/BF02402402Search in Google Scholar

[54] H.P. Kelly, A.M. Sessler, Phys. Rev. 132, 2091 (1963) http://dx.doi.org/10.1103/PhysRev.132.209110.1103/PhysRev.132.2091Search in Google Scholar

[55] H.P. Kelly, Phys. Rev. A. 134, 1450 (1964) 10.1103/PhysRev.134.A1450Search in Google Scholar

[56] W. Meyer, J. Chem. Phys. 58, 1017 (1973) http://dx.doi.org/10.1063/1.167928310.1063/1.1679283Search in Google Scholar

[57] W. Meyer, Theor. Chim. Acta 35, 277 (1974) http://dx.doi.org/10.1007/BF0054847810.1007/BF00548478Search in Google Scholar

[58] M. Urban, J. Noga, S.J. Cole, R.J. Bartlett, J. Chem. Phys. 83, 4041 (1985) http://dx.doi.org/10.1063/1.44906710.1063/1.449067Search in Google Scholar

[59] Y.S. Lee, S.A. Kucharski, R.J. Bartlett, J. Chem. Phys. 81, 5906 (1984) http://dx.doi.org/10.1063/1.44759110.1063/1.447591Search in Google Scholar

[60] Y.S. Lee, S.A. Kucharski, R.J. Bartlett, J. Chem. Phys. 82, 5761 (1984) http://dx.doi.org/10.1063/1.44899010.1063/1.448990Search in Google Scholar

[61] J. Noga, R.J. Bartlett, M. Urban, Chem. Phys. Lett. 134, 126 (1987) http://dx.doi.org/10.1016/0009-2614(87)87107-510.1016/0009-2614(87)87107-5Search in Google Scholar

[62] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157, 479 (1989) http://dx.doi.org/10.1016/S0009-2614(89)87395-610.1016/S0009-2614(89)87395-6Search in Google Scholar

[63] S. Hirata, J. Phys. Chem. A 107, 10154 (2003) http://dx.doi.org/10.1021/jp035667x10.1021/jp035667xSearch in Google Scholar

[64] J. Olsen, J. Chem. Phys. 113, 7140 (2000) http://dx.doi.org/10.1063/1.129000510.1063/1.1290005Search in Google Scholar

[65] M. Kallay, P. Surjan, J. Chem. Phys. 115, 2945 (2001) http://dx.doi.org/10.1063/1.138329010.1063/1.1383290Search in Google Scholar

[66] M. Kallay, J. Gauss, J. Chem. Phys. 120, 6841 (2004) http://dx.doi.org/10.1063/1.166863210.1063/1.1668632Search in Google Scholar PubMed

[67] T.J. Lee, G.E. Scuseria, In: S.R. Langhoff (Ed.), Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy (Kluwer, Dordrecht, 1995) 47 http://dx.doi.org/10.1007/978-94-011-0193-6_210.1007/978-94-011-0193-6_2Search in Google Scholar

[68] T.J. Lee, G.E. Scuseria, J. Chem. Phys. 93, 489 (1990) http://dx.doi.org/10.1063/1.45954810.1063/1.459548Search in Google Scholar

[69] G.E. Scuseria, T.J. Lee, J. Chem. Phys. 93, 5851 (1990) http://dx.doi.org/10.1063/1.45968410.1063/1.459684Search in Google Scholar

[70] S.R. Gwaltney, M. Head-Gordon, J. Chem. Phys. 115, 2014 (2001) http://dx.doi.org/10.1063/1.138358910.1063/1.1383589Search in Google Scholar

[71] S. Hirata, M. Nooijen, I. Grabowski, R.J. Bartlett, J. Chem. Phys. 114, 3919 (2001) http://dx.doi.org/10.1063/1.134657810.1063/1.1346578Search in Google Scholar

[72] S. Hirata, P.-D. Fan, A.A. Auer, M. Nooijen, P. Piecuch, J. Chem. Phys. 121, 12197 (2004) http://dx.doi.org/10.1063/1.181493210.1063/1.1814932Search in Google Scholar PubMed

[73] Y.J. Bomble, J.F. Stanton, M. Kallay, J. Gauss, J. Chem. Phys. 123, 054101 (2005) 10.1063/1.1950567Search in Google Scholar PubMed

[74] J. Paldus, P.E.S. Wormer, F. Visser, A. van der Avoird, J Chem. Phys. 76, 2485 (1982) http://dx.doi.org/10.1063/1.44327510.1063/1.443275Search in Google Scholar

[75] G.A. van der Velde, Ph.D. Thesis, University of Groningen (University of Groningen, Groningen, 1974) Search in Google Scholar

[76] C.W. Bauschlicher, P.R. Taylor, J. Chem. Phys. 85, 2779 (1986) http://dx.doi.org/10.1063/1.45103410.1063/1.451034Search in Google Scholar

[77] C.W. Bauschlicher, P.R. Taylor, J. Chem. Phys. 86, 1420 (1987) http://dx.doi.org/10.1063/1.45222910.1063/1.452229Search in Google Scholar

[78] C.W. Bauschlicher, P.R. Taylor, J. Chem. Phys. 86, 2844 (1987) http://dx.doi.org/10.1063/1.45203510.1063/1.452035Search in Google Scholar

[79] C. W. Bauschlicher, S.R. Langhoff, P.R. Taylor, N.C. Handy, P.J. Knowles, J. Chem. Phys. 85, 1469 (1986) http://dx.doi.org/10.1063/1.45123810.1063/1.451238Search in Google Scholar

[80] S.A. Kucharski, R.J. Bartlett, Chem. Phys. Lett. 206, 574 (1993) http://dx.doi.org/10.1016/0009-2614(93)80186-S10.1016/0009-2614(93)80186-SSearch in Google Scholar

[81] O. Christiansen, H. Koch, P. Jörgensen, J. Chem. Phys. 103, 7429 (1995) http://dx.doi.org/10.1063/1.47031510.1063/1.470315Search in Google Scholar

[82] S.A. Kucharski, R.J. Bartlett, J. Chem. Phys. 108, 5243 (1998) http://dx.doi.org/10.1063/1.47596110.1063/1.475961Search in Google Scholar

[83] M. Musiał, S.A. Kucharski, R. J. Bartlett, J. Chem. Phys. 116, 4382 (2002) http://dx.doi.org/10.1063/1.144574410.1063/1.1445744Search in Google Scholar

[84] S. Hirata, I. Grabowski, M. Tobita, R.J. Bartlett, Chem. Phys. Lett. 345, 475 (2001) http://dx.doi.org/10.1016/S0009-2614(01)00897-110.1016/S0009-2614(01)00897-1Search in Google Scholar

[85] S. Hirata, R. Podeszwa, M. Tobita, R.J. Bartlett, J. Chem. Phys. 120, 2581 (2004) http://dx.doi.org/10.1063/1.163757710.1063/1.1637577Search in Google Scholar PubMed

Published Online: 2012-7-21
Published in Print: 2012-10-1

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