Second order Møller-Plesset perturbation theory without basis set superposition error

Journal of Chemical Physics

Volumn 109, Issue 9, 1998, Pages 3360-3373

  Mayer, I ^a,b   Valiron, P ^b  

^a CTRL RES INSTITUTE FOR CHEMISTRY   (Hungary)

^b UNIV GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001675857     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.476931     Document Type: Article

References (49)

1. J. E. Del Bene, Int. J. Quantum Chem. Symp. 26, 527 (1992);
2. J. Chem. Phys. 97, 107 (1993);
3. 100, 6284 (1996).
4. H. B. Jansen and P. Ross, Chem. Phys. Lett. 3, 140 (1969).
5. S. B. Boys and F. Bernardi, Mol. Phys. 19, 553 (1970).
6. J. C. White and E. R. Davidson, J. Chem. Phys. 93, 8029 (1990).
7. P. Valiron and I. Mayer, Chem. Phys. Lett. 275, 46 (1997).
8. P. Valiron, Á. Vibók, and I. Mayer, J. Comput. Chem. 14, 401 (1993).
9. I. Mayer, Int. J. Quantum Chem. (to be published).
10. I. Mayer, Int. J. Quantum Chem. 23, 341 (1983).
11. I. Mayer and P. R. Surján, Int. J. Quantum Chem. 36, 225 (1989).
12. I. Mayer and Á. Vibók, Int. J. Quantum Chem. 40, 139 (1991);
13. Á. Vibók and I. Mayer 43, 801 (1992);
14. I. Mayer, Á. Vibók, G. Halász, and P. Valiron 57, 1049 (1996);
15. G. Halász, Á. Vibók, P. Valiron, and I. Mayer, J. Phys. Chem. 100, 6332 (1996).
16. M. Kieninger, S. Suhai, and I. Mayer, Chem. Phys. Lett. 230, 485 (1994).
17. B. Paizs and S. Suhai, J. Comput. Chem. 18, 694 (1997).
18. I. Mayer, Á. Vibók, and P. Valiron, Chem. Phys. Lett. 224, 166 (1994).
19. I. Mayer and Á. Vibók, Mol. Phys. 92, 503 (1997);
20. Á. Vibók, G. Halász, and I. Mayer, 93, 873 (1998).
21. G. Chalasiński and M. M. Szczȩśniak, Chem. Rev. 94, 1723 (1994), and references therein.
22. I. Mayer, in "Modelling of structure and properties of molecules," edited by Z. B. Maksić (Ellis Horwood, Chicester, 1987), p. 145.
23. A being the exact solution, this subspace is one-dimensional.
24. F. F. Muguet and G. W. Robinson, J. Chem. Phys. 102, 3648 (1995).
25. E. Gianinetti, M. Raimondi, and E. Tornaghi, Int. J. Quantum Chem. 60, 157 (1996).
26. In the "intramolecular" version of CHA, discussed in Refs. 8 16 both individual atoms and pairs of atoms have been considered as "subunits," depending on the term under study. Accordingly, terms containing the projector on the union of the two atomic basis sets have also appeared. However, all the results of the present paper remain valid mutatis mutandis for that formalism, too. (For the explicit expression of the CHA integrals in that case we refer to Ref. 16.)
27. I. Mayer and Á. Vibók, Chem. Phys. Lett. 140, 558 (1987).
28. I. Mayer and Á. Vibók, Chem. Phys. Lett. 136, 115 (1987).
29. i. However, any orthogonalization transformation is appropriate, and a special version of Schmidt-orthogonalization will be more adequate for the derivations presented in Sec. IIID.
30. CHA was also expressed in terms of non-orthogonal basis sets; in the present paper we shall not make any direct use of those formulae.
31. I. Mayer and L. Turi, J. Mol. Struct.: THEOCHEM 227, 43 (1991).
32. As noted in Ref. 22, complex orbitals do not cause any complications in the CHA-SCF calculations, provided that both components of each pair of complex conjugated orbitals are assigned to the same (either occupied or virtual) subspace. In that case the P-matrix remains real; instead of a complex pair of occupied orbitals one may build the P-matrix by using simply their properly normalized real and imaginary parts. The original complex orbitals should be used in the MP2 case, however.
33. if〉. Formulae of a general biorthogonal perturbation theory for arbitrary order may be found, e.g., in the Appendix B of Ref. 28.
34. P. R. Surjan and I. Mayer, J. Mol. Struct.: THEOCHEM 226, 47 (1991).
35. I. Mayer, Mol. Phys. 89, 515 (1996).
36. k〉≠0
37. HONDO-8, from MOTECC-91, contributed and documented by M. Dupuis and A. Farazdel, IBM Corporation, Center for Scientific & Engineering Computations, Kingston, New York, 1991.
38. C. Rist, M. H. Alexander, and P. Valiron, J. Chem. Phys. 98, 4662 (1993).
39. S. Green, J. Chem. Phys. 103, 1035 (1995).
40. B. J. Garrison, W. A. Lester, Jr., and H. F. Schaeffer, J. Chem. Phys. 63, 1449 (1975).
41. 2O interaction in M. Bulski, P. E. S. Wormer, and A. van der Avoird, J. Chem. Phys. 94, 8096 (1991), and references therein. Bulski et al. claimed that an even larger (13s 10p 5d 3f 3g) basis set was required for Ar to saturate the dispersion terms.
42. T. Clark, J. Chandrasekhar, G. W. Spitznagel, and P. v. R. Schleyer, J. Comput. Chem. 4, 294 (1983).
43. I. Mayer and P. R. Surján, Chem. Phys. Lett. 91, 497 (1992).
44. The BSSE correction should be performed in the supermolecule basis, while the relaxation energy of each monomer can be computed only in the basis of the respective free molecule (Refs. 7 37).
45. The same remarkable similarity has been observed in the calculations using the smaller basis sets for which full CI calculations are also available (Ref. 13), both at full-CI (Ref. 13) and MP2 levels. For saving space, we do not describe these results here, only note that for the (10/5s 2p 1d) basis for which such a comparison has been made, the present CHA-MP2 method gives results which are even slightly closer to the MP2/CP ones than those obtained by the recent monomer based BSSE-free second order perturbation theory (Ref. 14).
46. R. A. Aziz and M. J. Slaman, J. Chem. Phys. 94, 8047 (1991).
47. K. A. Peterson and T. H. Dunning, Jr., J. Chem. Phys. 102, 2032 (1995).
48. M. W. Feyereisen, D. Feller, and D. A. Dixon, J. Chem. Phys. 100, 2993 (1996).
49. We have performed about 2000 CHA-MP2 calculations on different systems with different basis sets and geometries and have only encountered two points with complex occupied orbitals; both were related to the sulphur 6-31G * basis (one with diffuse functions also added), one of them in a physically irrelevant short range. Should complex solutions appear in some cases of actual interest, they would require an analysis analogous to the considerations presented here or turning to the use of complex computer arithmetics.