Some non-relativistic many electron theories: single reference case

• Authors: Hüseyin Aksu
• Languages of publication: EN

Abstracts

EN

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. [...]

Keywords

EN

Many Body Particles; Davidson Type Corrections; Many Body Perturbation Theory and Coupled Electron Many Electron Theory; Coupled Electron Pair Approximations; Coupled Cluster

• Publisher: De Gruyter Open
• Journal: Open Chemistry
• Year: 2012
• Volume: 10
• Issue: 5
• Pages: 1383-1390

Dates

published

1 - 10 - 2012

online

21 - 7 - 2012

Contributors

author

Hüseyin Aksu

• Institute of Physics, Nicolaus Copernicus University, 87-100, Torun, Poland

References

• [1] E. Clementi, Proc. Nat. Acad. Sci. 69, 2942 (1972) http://dx.doi.org/10.1073/pnas.69.10.2942[Crossref]
• [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_2[Crossref]
• [3] R. Langhoff, R.E. Davidson, Int. J. Quantum Chem. 8, 61 (1974) http://dx.doi.org/10.1002/qua.560080106[Crossref]
• [4] E.R. Davidson, D.W. Silver, Chem. Phys. Lett. 52, 403 (1977) http://dx.doi.org/10.1016/0009-2614(77)80475-2[Crossref]
• [5] P.E.M. Siegbahn, Chem. Phys. Lett. 55, 386 (1978) http://dx.doi.org/10.1016/0009-2614(78)87046-8[Crossref]
• [6] J.A. Pople, R. Seeger, R. Krishnan, Int. J. Quantum Chem. S11, 149, (1977)
• [7] L. Meissner, Chem. Phys. Lett. 146, 204 (1988) http://dx.doi.org/10.1016/0009-2614(88)87431-1[Crossref]
• [8] W. Duch, G.H. Diercksen, J. Chem. Phys. 101, 3018 (1994) http://dx.doi.org/10.1063/1.467615[Crossref]
• [9] K.A. Brueckner, Phys. Rev. 97, 1353 (1955) http://dx.doi.org/10.1103/PhysRev.97.1353[Crossref]
• [10] P.-O. Löwdin, Int. J. Quantum Chem. 2, 867 (1968) http://dx.doi.org/10.1002/qua.560020612[Crossref]
• [11] R. Krishnan, J.A. Pople, Int. J. Quantum Chem. 14, 91 (1978) http://dx.doi.org/10.1002/qua.560140109[Crossref]
• [12] R. Krishnan, M.J. Frisch, J.A. Pople, J. Chem. Phys. 72, 4244 (1980) http://dx.doi.org/10.1063/1.439657[Crossref]
• [13] M.J. Frisch, R. Krishnan, J.A. Pople, Chem. Phys. Lett. 75, 66 (1980) http://dx.doi.org/10.1016/0009-2614(80)80465-9[Crossref]
• [14] J. Cížek, J. Chem. Phys. 45, 4256 (1966) http://dx.doi.org/10.1063/1.1727484[Crossref]
• [15] J. Cížek, Adv. Chem. Phys. 14, 35 (1969) http://dx.doi.org/10.1002/9780470143599.ch2[Crossref]
• [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)85390-0[Crossref]
• [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.560140503[Crossref]
• [18] R.J. Bartlett, G.D. Purvis, Int. J. Quantum Chem. 14, 561 (1978) http://dx.doi.org/10.1002/qua.560140504[Crossref]
• [19] R.A. Chiles, C.E. Dykstra, J. Chem. Phys. 74, 4544 (1981) http://dx.doi.org/10.1063/1.441643[Crossref]
• [20] J. Paldus, J. Cizek, I. Shavitt, Phys. ReV. A 5, 50 (1972) http://dx.doi.org/10.1103/PhysRevA.5.50[Crossref]
• [21] F. Coester, Nucl. Phys. 1, 421 (1958)
• [22] F. Coester, H. Kümmel, Nucl. Phys. 17, 477 (1960) http://dx.doi.org/10.1016/0029-5582(60)90140-1[Crossref]
• [23] Cížek, J. Paldus, Phys. Scr. 21, 251 (1980) http://dx.doi.org/10.1088/0031-8949/21/3-4/012[Crossref]
• [24] A.C. Hurley, Electronic Correlation in Small Molecules (Academic Press, New York, 1976)
• [25] W. Kutzelnigg, In: H.F. Schaefer III (Ed.), Methods of Electronic Structure Theory (Plenum, New York, 1977) 129
• [26] R.J. Bartlett, G.D. Purvis, Phys. Scr. 21, 255 (1980) http://dx.doi.org/10.1088/0031-8949/21/3-4/007[Crossref]
• [27] R. Ahlrichs, Comput. Phys. Commun. 17, 31 (1979) http://dx.doi.org/10.1016/0010-4655(79)90067-5[Crossref]
• [28] J. Paldus, J. Chem. Phys. 67, 303 (1977) http://dx.doi.org/10.1063/1.434526[Crossref]
• [29] J. Cížek, J. Paldus, Int. Quantum Chem. 5, 359 (1971) http://dx.doi.org/10.1002/qua.560050402[Crossref]
• [30] G.D. Purvis, R.J. Bartlett, J. Chem. Phys. 76, 1910 (1982) http://dx.doi.org/10.1063/1.443164[Crossref]
• [31] R.J. Bartlett, I. Shavitt, Chem. Phys. Lett. 50, 190 (1977) http://dx.doi.org/10.1016/0009-2614(77)80161-9[Crossref]
• [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_2[Crossref]
• [33] R.J. Bartlett, Annu. Rev. Phys. Chem. 32, 359 (1981) http://dx.doi.org/10.1146/annurev.pc.32.100181.002043[Crossref]
• [34] R.J. Bartlett, J. Phys. Chem. 93, 1697 (1989) http://dx.doi.org/10.1021/j100342a008[Crossref]
• [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
• [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
• [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
• [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
• [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_0005[Crossref]
• [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)87395-6[Crossref]
• [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/10.1063/1.2920482[Crossref]
• [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.20573[Crossref]
• [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.540141112[Crossref]
• [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/CBO9780511596834[Crossref]
• [45] R.J. Bartlett, M. Musial, Rev. Modern Phys. 79, 291 (2007) http://dx.doi.org/10.1103/RevModPhys.79.291[Crossref]
• [46] K. Raghavachari, J.B. Anderson, J. Phys. Chem. 100, 12960 (1996) http://dx.doi.org/10.1021/jp953749i[Crossref]
• [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/B978-044451719-7/50085-8[Crossref]
• [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/B978-044451719-7/50050-0[Crossref]
• [49] R.J. Bartlett, I. Shavitt, Int. Qauntum Chem. Symp, 11, 165 (1977)
• [50] W.L. Luken, Chem. Phys. Lett. 58, 421 (1978) http://dx.doi.org/10.1016/0009-2614(78)85066-0[Crossref]
• [51] K. Jankowski, L. Meissner, J. Wasilewski, Int. Qauntum Chem. 28, 931 (1985) http://dx.doi.org/10.1002/qua.560280622[Crossref]
• [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
• [53] S. Koch, W. Kutzelnigg, Theoret. Chim. Acta (Berl.) 59, 387 (1981) http://dx.doi.org/10.1007/BF02402402[Crossref]
• [54] H.P. Kelly, A.M. Sessler, Phys. Rev. 132, 2091 (1963) http://dx.doi.org/10.1103/PhysRev.132.2091[Crossref]
• [55] H.P. Kelly, Phys. Rev. A. 134, 1450 (1964)
• [56] W. Meyer, J. Chem. Phys. 58, 1017 (1973) http://dx.doi.org/10.1063/1.1679283[Crossref]
• [57] W. Meyer, Theor. Chim. Acta 35, 277 (1974) http://dx.doi.org/10.1007/BF00548478[Crossref]
• [58] M. Urban, J. Noga, S.J. Cole, R.J. Bartlett, J. Chem. Phys. 83, 4041 (1985) http://dx.doi.org/10.1063/1.449067[Crossref]
• [59] Y.S. Lee, S.A. Kucharski, R.J. Bartlett, J. Chem. Phys. 81, 5906 (1984) http://dx.doi.org/10.1063/1.447591[Crossref]
• [60] Y.S. Lee, S.A. Kucharski, R.J. Bartlett, J. Chem. Phys. 82, 5761 (1984) http://dx.doi.org/10.1063/1.448990[Crossref]
• [61] J. Noga, R.J. Bartlett, M. Urban, Chem. Phys. Lett. 134, 126 (1987) http://dx.doi.org/10.1016/0009-2614(87)87107-5[Crossref]
• [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)87395-6[Crossref]
• [63] S. Hirata, J. Phys. Chem. A 107, 10154 (2003) http://dx.doi.org/10.1021/jp035667x[Crossref]
• [64] J. Olsen, J. Chem. Phys. 113, 7140 (2000) http://dx.doi.org/10.1063/1.1290005[Crossref]
• [65] M. Kallay, P. Surjan, J. Chem. Phys. 115, 2945 (2001) http://dx.doi.org/10.1063/1.1383290[Crossref]
• [66] M. Kallay, J. Gauss, J. Chem. Phys. 120, 6841 (2004) http://dx.doi.org/10.1063/1.1668632[Crossref]
• [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_2[Crossref]
• [68] T.J. Lee, G.E. Scuseria, J. Chem. Phys. 93, 489 (1990) http://dx.doi.org/10.1063/1.459548[Crossref]
• [69] G.E. Scuseria, T.J. Lee, J. Chem. Phys. 93, 5851 (1990) http://dx.doi.org/10.1063/1.459684[Crossref]
• [70] S.R. Gwaltney, M. Head-Gordon, J. Chem. Phys. 115, 2014 (2001) http://dx.doi.org/10.1063/1.1383589[Crossref]
• [71] S. Hirata, M. Nooijen, I. Grabowski, R.J. Bartlett, J. Chem. Phys. 114, 3919 (2001) http://dx.doi.org/10.1063/1.1346578[Crossref]
• [72] S. Hirata, P.-D. Fan, A.A. Auer, M. Nooijen, P. Piecuch, J. Chem. Phys. 121, 12197 (2004) http://dx.doi.org/10.1063/1.1814932[Crossref]
• [73] Y.J. Bomble, J.F. Stanton, M. Kallay, J. Gauss, J. Chem. Phys. 123, 054101 (2005)
• [74] J. Paldus, P.E.S. Wormer, F. Visser, A. van der Avoird, J Chem. Phys. 76, 2485 (1982) http://dx.doi.org/10.1063/1.443275[Crossref]
• [75] G.A. van der Velde, Ph.D. Thesis, University of Groningen (University of Groningen, Groningen, 1974)
• [76] C.W. Bauschlicher, P.R. Taylor, J. Chem. Phys. 85, 2779 (1986) http://dx.doi.org/10.1063/1.451034[Crossref]
• [77] C.W. Bauschlicher, P.R. Taylor, J. Chem. Phys. 86, 1420 (1987) http://dx.doi.org/10.1063/1.452229[Crossref]
• [78] C.W. Bauschlicher, P.R. Taylor, J. Chem. Phys. 86, 2844 (1987) http://dx.doi.org/10.1063/1.452035[Crossref]
• [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/10.1063/1.451238[Crossref]
• [80] S.A. Kucharski, R.J. Bartlett, Chem. Phys. Lett. 206, 574 (1993) http://dx.doi.org/10.1016/0009-2614(93)80186-S[Crossref]
• [81] O. Christiansen, H. Koch, P. Jörgensen, J. Chem. Phys. 103, 7429 (1995) http://dx.doi.org/10.1063/1.470315[Crossref]
• [82] S.A. Kucharski, R.J. Bartlett, J. Chem. Phys. 108, 5243 (1998) http://dx.doi.org/10.1063/1.475961[Crossref]
• [83] M. Musiał, S.A. Kucharski, R. J. Bartlett, J. Chem. Phys. 116, 4382 (2002) http://dx.doi.org/10.1063/1.1445744[Crossref]
• [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)00897-1[Crossref]
• [85] S. Hirata, R. Podeszwa, M. Tobita, R.J. Bartlett, J. Chem. Phys. 120, 2581 (2004) http://dx.doi.org/10.1063/1.1637577[Crossref]

Identifiers

DOI

10.2478/s11532-012-0097-z