Summary
The error in the energy of the traditional coupled-cluster (TCC) approach and of several variants is analyzed in terms of the error δ of the cluster operatorS. A key feature of this analysis is that TCC can be based on an energy functional (asymmetric inS andS †) that is made stationary with respect to variation ofS †. The error of TCC scales with the particle numbern, but it is not quadratic in δ. An improved coupled-cluster method (ICC) is presented that is the next step in a hierarchy from TCC to an exact variational theory. An alternative hierarchy is possible that leads to the extended coupled-cluster (ECC) method of Arponen. Variational (VCC) and unitary (UCC) coupled cluster theories and their stationary conditions and errors are analyzed along similar lines and practicable VCC or UCC approaches are presented. An infinite summation of certain terms in the VCC expectation value is shown to lead to a coupled-pair functional of the type proposed by Ahlrichs. The various CC schemes discussed here are compared on the CC-D, CC-SD and CC-SDT levels and beyond this. Special aspects referring to properties are also discussed.
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References
Coester F (1958) Nucl Phys 7:421
Coester F, Kümmel H (1960) Nucl Phys 17:477
Kümmel H (1961) Nucl Phys 22:177
Kümmel H, Lührmann H (1972) Nucl Phys A 191:525; A 194:225
Bishop RF, Kümmel H (1987) Physics Today 40:52
Čižek J (1966) J Chem Phys 45:4256
Čižek J (1969) Adv Chem Phys 14:35
Paldus J, Čižek J, Shavitt I (1972) Phys Rev A 5:50
Lindgren I (1974) J Phys B 7:2441; (1978) Int J Quantum Chem Symp 12:33
Lindgren I, Morrison J Atomic many-body theory, Springer, Berlin Heidelberg New York, 1982
Lindgren I, Salomonsen S (1980) Phys Scr 21:335
Taylor PR, Backsay GB, Hurley AC, Hush NS (1978) J Chem Phys 69:1971
Bartlett RJ, Purvis GD (1978) Int J Quantum Chem 14:561; (1980) Phys Scr 21:251
Bartlett RJ (1981) Ann Rev Phys Chem 32:359
Purvis GD, Bartlett RJ (1982) J Chem Phys 76:1910
Lee YS, Bartlett RJ (1984) J Chem Phys 80:4371
Laidig W, Bartlett RJ (1984) Chem Phys Lett 104:424
Lee YS, Kucharski SA, Bartlett RJ (1984) J Chem Phys 81:5906; (1985) 82:5761
Urban M, Noga J, Cole SJ, Bartlett RJ (1985) J Chem Phys 83:4041
Cole SJ, Bartlett RJ (1987) J Chem Phys 86:7041; (1987) 86:873
Noga J, Bartlett RJ, Urban M (1987) Chem Phys Lett 134:128
Noga J, Bartlett RJ (1987) J Chem Phys 86:7024; (1988) 89:3401
Sosa C, Noga J, Bartlett RJ (1988) J Chem Phys 88:5974
Bartlett RJ, Noga J (1988) Chem Phys Lett 150:29
Geertsen J, Rittby M, Bartlett RJ (1989) Chem Phys Lett 164:57
Watts JD, Trucks GW, Bartlett RJ (1989) Chem Phys Lett 164:502
Bartlett RJ, Watts JD, Kucharski SA, Noga J (1990) Chem Phys Lett 165:519; (1990) 167:609
Pople JA, Krishnan R, Schlegel HB, Binkley JS (1978) Int J Quantum Chem 14:545
Paldus J (1977) J Chem Phys 67:303
Jankowski K, Paldus J (1980) Int J Quantum Chem 18:1243; (1981) Phys Rev A 24:2316, 2330
Paldus J, Boyle MJ (1982) Int J Quantum Chem 22:1281
Paldus J, Čižek J, Takahashi M (1984) Phys Rev A 30:2193
Kvasnička V, Laurinc V, Biskupič S (1982) Phys Rep 90:159
Pal S, Prasad MD, Mukherjee D (1983) Theor Chim Acta 62:523
Szalewicz K, Zabolitzky J, Jeziorski B, Monkhorst H (1984) J Chem Phys 81:2723
Scuseria G, Sheiner A, Lee TJ, Rice JE, Schaefer III HF (1987) J Chem Phys 86:2881
Adamowicz L (1989) J Comput Chem 10:928
Bartlett RJ, Dykstra CE, Paldus J In: Dykstra CE (ed) Advanced theories and computational approaches to the electronic structure of molecules. Reidel, Dordrecht, 1984
Hoffmann MR, Schaefer III HF (1986) Adv Quantum Chem 18:207
Kucharski SA, Bartlett RJ (1986) Adv Quantum Chem 18:281
Urban M, Kellö V, Černušák I, Noga J In: Wilson S (ed) Methods in computational chemistry, Vol. 1, New York, Plenum, 1987
Jankowski K ibid In:
Bartlett RJ (1989) J Phys Chem 93:1697
Meyer W (1973) J Chem Phys 58:1017
Ahlrichs R, Lischka H, Staemmler V, Kutzelnigg W (1975) J Chem Phys 62:1225
Kutzelnigg W In: Schaefer III HF (ed) Modern theoretical chemistry, Vol. 3a, Plenum, New York, 1977
Ahlrichs R (1979) Comp Phys Commun 17:31
Čársky P, Urban M ‘Ab initio calculations’, Lecture notes in chemistry, Vol. 16, Springer, Berlin Heidelberg New York, 1960
Primas H In: Sinanoglu O (ed) Modern quantum chemistry, Vol. 2, p. 45, Academic Press, New York, 1965
Hubbard J (1957) Proc Roy Soc London A 240:539; (1958) A 243:336; (1958) A 244:199; Hugenholtz NM (1957) Physica 23:481
Goldstone J (1957) Proc Roy Soc London A 239:267
Kutzelnigg W, Koch S (1983) J Chem Phys 79:4315
Koch S, Kutzelnigg W (1981) Theor Chim Acta 59:387
Lee TJ, Rendell AP, Taylor PR (1990) J Phys Chem 94:5463
Handy NC, Harrison RJ (1983) Chem Phys Lett 95:386; Bauschlicher CW, Taylor PR (1986) J Chem Phys 85:2779
Kutzelnigg W (1979) Chem Phys Lett 64:383; (1980) Int J Quantum Chem 18:3
Arponen J (1983) Ann Phys (NY) 151:311; Arponen DS, Bishop RF, Pajanne E (1987) Phys Rev A 36:2519, 2539; Bishop RF, Arponen J, Pajanne E In: Mukherjee D (ed) Aspects of many-body effects in molecules and extended systems, Lecture notes in chemistry, Vol. 50, p. 79, Springer, Berlin Heidelberg New York, 1989
Hurley AC Electron correlation in small molecules. New York, Academic Press, 1976
Kutzelnigg W (1975) Chem Phys Lett 35:283
Bartlett RJ, Shavitt I (1977) Chem Phys Lett 50:190; Bartlett RJ, Shavitt I, Purvis GD (1979) J Chem Phys 71:281
Pople JA, Head-Gordon M, Raghavachari K (1987) J Chem Phys 87:5968; (1989) 90:4635
Scuseria G, Schaefer III HF (1989) J Chem Phys 90:3700
Paldus J, Čižek J, Jeziorski B (1989) J Chem Phys 90:4356
Handy C, Knowles PJ, Somasundran K (1985) Theor Chim Acta 68:87
Gill PMW, Pople JA, Radom L, Nobes RH (1988) J Chem Phys 89:7307
Bartlett RJ, Noga J (1988) Chem Phys Lett 150:29
Bartlett RJ, Kucharski SA, Noga J (1989) Chem Phys Lett 155:133
Watts JD, Trucks GW, Bartlett RJ (1989) Chem Phys Lett 157:359
Reitz H, Kutzelnigg W (1979) Chem Phys Lett 66:111
Kutzelnigg W (1981) Chem Phys Lett 83:156; (1982) J Chem Phys 77:3081; (1984) 80:822; (1985) 82:4166
Yaris RJ (1964) J Chem Phys 41:2419; (1965) 42:3019
Westhaus P, Bradford EG, Hall D (1975) J Chem Phys 62:1607; Westhaus P (1980) J Chem Phys 73:5197
Baker H, Robb MA (1983) Mol Phys 50:1077
Tanaka K, Terashima H (1984) Chem Phys Lett 106:588
Hoffmann MR, Simons J (1988) J Chem Phys 88:993; (1987) Chem Phys Lett 142:451
Pal S, Prasad MD, Mukherjee D (1983) Theor Chim Acta 62:523; (1984) 66:311
Kutzelnigg W In: Kümmel H, Ristig ML (eds) Recent progress in many-body theories, Lecture notes in physics, Vol. 198, Springer, Berlin Heidelberg New York, 1984
Ahlrichs R, Scharf P, Ehrhard C (1985) J Chem Phys 82:890; Ahlrichs R, Scharf P In: Lawley KP (ed) Ab initio methods in quantum chemistry I, New York, Wiley, 1987
Kelly HP, Sessler AM (1963) Phys Rev 132:2091; Kelly HP (1964) Phys Rev 134A:1450
Kutzelnigg W (1973) Top Curr Chem 41:31
Sinanoglu O (1962) J Chem Phys 36:706, 3198
Gdanitz RJ, Ahlrichs R (1988) Chem Phys Lett 143:413
Pulay P (1983) J Mol Struct 103:57; (1983) Int J Quant Chem Symp 17:257
Chiles RA, Dykstra CE (1981) Chem Phys Lett 80:69; Bachrach SM, Chiles RA, Dykstra CE (1981) J Chem Phys 75:2270; Jasien PG, Dykstra CE (1983) Int J Quantum Chem Symp 17:289
Sadlej A (1983) Int J Quant Chem 23:147; (1982) 75:320
Kutzelnigg W (1989) J Mol Struct Theochem 202:11
Epstein ST The variation method in quantum chemistry. Academic Press, New York 1974
Monkhorst HJ (1977) Int J Quantum Chem 11:421; Dalgaard E, Monkhorst H (1983) Phys Rev A 28:1217
Mukherjee D, Pal S (1989) Adv Quantum Chem 20:292
Kutzelnigg W, Mukherjee D, Koch S (1987) J Chem Phys 87:5902; Mukherjee D, Kutzelnigg W, Koch S (1987) J Chem Phys 87:5911
Anderrson K, Malmquist DÅ, Roos BO, Sadlej AJ, Wolinski K (1990) J Phys Chem 94:5483
Landscheid U, Kutzelnigg W (1988) Coll Czech Chem Comm 53:1953
Laaksonen L, Müller-Plathe F, Diercksen GHF (1988) J Chem Phys 89:4903
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Kutzelnigg, W. Error analysis and improvements of coupled-cluster theory. Theoret. Chim. Acta 80, 349–386 (1991). https://doi.org/10.1007/BF01117418
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DOI: https://doi.org/10.1007/BF01117418