Summary
A novel formulation of MP2 theory is presented which starts from the Laplace transform MP2 ansatz, and subsequently moves from a molecular orbital (MO) representation to an atomic orbital (AO) representation. Consequently, the new formulation is denoted AO-MP2. As in traditional MP2 approaches electron repulsion integrals still need to be transformed. Strict bounds on the individual MP2 energy contribution of each intermediate four-index quantity allow to screen off numerically insignificant integrals with a single threshold parameter. Implicit in our formulation is a bound to two-particle density matrix elements. For small molecules the computational cost for AO-MP2 calculations is about a factor of 100 higher than for traditional MO-based approaches, but due to screening the computational effort in larger systems will only grow with the fourth power of the size of the system (or less) as is demonstrated both in theory and in application. MP2 calculations on (non-metallic) crystalline systems seem to be a feasible extension of the Laplace transform approach. In large molecules the AO-MP2 ansatz allows massively parallel MP2 calculations without input/output of four-index quantities provided that each processor has in-core memory for a limited number of two-index quantities. Energy gradient formulas for the AO-MP2 approach are derived.
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References
Møller C, Plesset MS (1934) Phys Rev 46:618
Hehre WJ, Radom L, Schleyer PvR, Pople JA (1986) Ab initio molecular orbital theory. Wiley, NY
Gauss J (1992) Chem Phys Lett 191:614
Häser M, Almlöf J, Scuseria GE (1991) Chem Phys Lett 181:497
Häser M, Almlöf J, Feyereisen MW (1991) Theoret Chim Acta 79:115
Ahlrichs R, Bär M, Häser M, Horn H, Kölmel C (1989) Chem Phys Lett 162:165
Dyczmons V (1973) Theoret Chim Acta 28:307
Almlöf J, Faegri Jr K, Korsell K (1982) J Comput Chem 3:385
Head-Gordon M, Pople JA, Frisch MJ (1988) Chem Phys Lett 153:503
Edmiston C, Krauss M (1965) J Chem Phys 42:1119; (1966) 45:1833
Jungen M, Ahlrichs R (1970) Theoret Chim Acta 17:339
Meyer W (1977) in: Schaefer HF III (ed) Methods of electronic structure theory. Plenum, NY, p 413
Pulay P (1983) Chem Phys Lett 100:151; Saebø S, Pulay P (1985) Chem Phys Lett 113:13; Saebø S, Pulay P (1987) J Chem Phys 86:914
Saebø S, Pulay P (1988) J Chem Phys 88:1884
Pulay P, Saebø S (1986) Theoret Chim Acta 69:357
Stollhoff G, Fulde P (1977) Z Physik B26:257
Stollhoff G, Vasilopoulos P (1986) J Chem Phys 84:2744
Stollhoff G, Fulde P (1980) J Chem Phys 73:4548
Almlöf J (1991) Chem Phys Lett 176:319
Häser M, Almlöf J (1992) J Chem Phys 96:489
Whitten JL (1973) J Chem Phys 58:4496
Häser M, Ahlrichs R (1989) J Comput Chem 10:104
Saebø S, Almlöf J (1989) Chem Phys Lett 154:83
Dupuis M, Rys J, King HF (1976) J Chem Phys 65:111
des Cloizeaux J (1964) Phys Rev 135:A685
These results most likely also hold for crystals with degenerate band structure; proofs, however, become significantly more technical and involved. The reader may want to consult the paper by Lix B (1971) Phys Stat Sol B44:411
Pisani C, Dovesi R, Roetti C (1988) Hartree Fock ab initio treatment of crystalline systems. Springer, Berlin
Bulyanitsa DS, Svetlov YE (1962) Soviet Phys-Solid State 4:981 (the proof given is for a one-electron operator with local potential)
Monkhorst HJ (1979) Phys Rev B20:1504
Bary NK (1964) Treatise on trigonometric series. Pergamon, Oxford
Pitzer RM (1973) J Chem Phys 59:3308;
Davidson ER (1975) J Chem Phys 62:400
Heinzmann R, Ahlrichs R (1976) Theoret Chim Acta 42:33;
Ehrhardt C, Ahlrichs R (1985) Theoret Chim Acta 68:231
Raffenetti RC (1973) J Chem Phys 58:4452
Almlöf J, Taylor PR (1987) J Chem Phys 86:4070
Van Alsenoy C (1988) J Comput Chem 9:620
see, for example, Ringnalda MN, Belhadj M, Friesner RA (1990) J Chem Phys 93:3397
Pople JA, Krishnan R, Schlegel HB, Binkley JS (1979) Int J Quant Chem Quant Chem Symp 13:225
Pulay P (1987) Adv Chem Phys 69:241, and references therein
Handy NC, Schaefer HF III (1984) J Chem Phys 81:5031
Frisch MJ, Head-Gordon M, Pople JA (1990) Chem Phys Lett 166:275
Head-Gordon M, Trucks GW, Frisch MJ (1992) Chem Phys Lett 196:624 and references therein.
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Dedicated to Prof. W. Kutzelnigg whose books on theoretical chemistry aroused my interest in this field
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Häser, M. Møller-Plesset (MP2) perturbation theory for large molecules. Theoret. Chim. Acta 87, 147–173 (1993). https://doi.org/10.1007/BF01113535
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DOI: https://doi.org/10.1007/BF01113535