Computing singularities of perturbation series

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 83, Issue 3, 2011, Pages

  Kvaal, Simen ^a   Jarlebring, Elias ^b   Michiels, Wim ^b  

^a UNIVERSITY OF OSLO   (Norway)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

AB INITIO APPROACH; EIGENVALUES; GENERALIZED EIGENVALUE EQUATIONS; HAMILTONIAN MATRIX; ITERATIVE TECHNIQUE; MANY-BODY PROBLEMS; MODEL PROBLEMS; NUMERICAL PROCEDURES; PERTURBATION SERIES; PLESSET PERTURBATION THEORY; RADIUS OF CONVERGENCE; RAYLEIGH; RESUMMATION;

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; HELIUM;

PERTURBATION TECHNIQUES;

EID: 79952752825     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.83.032505     Document Type: Article

References (37)

1. O. Christiansen, J. Olsen, P. Jørgensen, H. Koch, and P.-Å Malmqvist, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/0009-2614(96)00974-8 261, 369 (1996). (Pubitemid 126163433)
2. J. Olsen, O. Christiansen, H. Koch, and P. Jørgensen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.472352 105, 5082 (1996).
3. T. H. Dunning Jr. and K. A. Peterson, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.476308 108, 4761 (1998).
4. F. H. Stillinger, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.481608 112, 9711 (2000).
5. M. L. Leininger, W. D. Allen, H. F. Schaefer III, and C. D. Sherrill, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.481764 112, 9213 (2000).
6. R. Roth and J. Langhammer, Phys. Lett. B PYLBAJ 0370-2693 10.1016/j.physletb.2009.12.046 683, 272 (2010).
7. R. J. Bartlett, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev.pc.32.100181.002043 32, 359 (1981).
8. E. Brändas and O. Goscinski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.1.552 1, 552 (1970).
9. D. Z. Goodson, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.481044 112, 4901 (2000).
10. D. Z. Goodson, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.10489 92, 35 (2003).
11. A. V. Sergeev and D. Z. Goodson, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2173989 124, 094111 (11) (2006). (Pubitemid 43346526)
12. L.-W. Siu, J. W. Holt, T. T. S. Kuo, and G. E. Brown, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.79.054004 79, 054004 (2009).
13. C. Hunter and B. Guerrieri, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0139022 39, 248 (1980).
14. C. J. Pearce, Adv. Phys. ADPHAH 0001-8732 10.1080/00018737800101354 27, 89 (1978).
15. J. Zamastil and F. Vinette, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/18/010 38, 4009 (2005). (Pubitemid 41237161)
16. T. Helgaker, P. Jørgensen, and J. Olsen, Molecular Electronic-Structure Theory (Wiley, New York, 2002).
17. A. V. Sergeev, D. Z. Goodson, S. E. Wheeler, and W. D. Allen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1991854 123, 064105 (2005). (Pubitemid 41231970)
18. M. Herman and G. Hagedorn, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.21763 109, 210 (2009).
19. T. H. Schucan and H. A. Weidenmüller, Ann. Phys. APNYA6 0003-4916 10.1016/0003-4916(73)90044-4 76, 483 (1973).
20. I. Lindgren and J. Morrison, Atomic Many-Body Theory (Springer, New York, 1986).
21. W. D. Laidig, G. Fitzgerald, and R. J. Bartlett, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/0009-2614(85)80934-9 113, 151 (1985).
22. N. C. Handy, P. J. Knowles, and K. Somasundram, Theor. Chim. Acta TCHAAM 0040-5744 10.1007/BF00698753 68, 87 (1985).
23. S. Patil, Eur. J. Phys. EJPHD4 0143-0807 10.1088/0143-0807/27/4/021 27, 899 (2006). (Pubitemid 43932821)
24. S. M. Reimann and M. Manninen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.1283 74, 1283 (2002). (Pubitemid 36121907)
25. T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1995).
26. E. Jarlebring, S. Kvaal, and W. Michiels, TW Report 559, Department of Computer Science, Katholieke Universiteit Leuven, Belgium (2010), submitted [http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW559.pdf].
27. A. Katz, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(62)90191-8 29, 353 (1962).
28. Z. He and D. Cremer, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/(SICI)1097-461X(1996)59:1<15::AID-QUA3>3.0.CO;2-# 59, 15 (1996);
29. Z. He and D. Cremer, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/(SICI)1097-461X(1996)59:1<31::AID-QUA4>3.0.CO;2-Y 59, 31 (1996);
30. Z. He and D. Cremer, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/(SICI)1097-461X(1996)59:1<57::AID-QUA5>3.0.CO;2-W 59, 57 (1996);
31. Z. He and D. Cremer, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/(SICI)1097-461X(1996)59:1<71::AID-QUA6>3.0.CO;2-U 59, 71 (1996).
32. G. A. Baker, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.43.479 43, 479 (1971).
33. D. Z. Goodson and A. V. Sergeev, Adv. Quantum Chem. AQCHA9 0065-3276 10.1016/S0065-3276(04)47011-7 47, 193 (2004). (Pubitemid 39752278)
34. Y. Saad, Numerical Methods for Large Eigenvalue Problems (Manchester University Press, Manchester, 1992).
35. R. Bartels and G. Stewart, Commun. ACM CACMA2 0001-0782 10.1145/361573.361582 15, 820 (1972).
36. S. G. Krantz, Handbook of Complex Variables (Birkhäuser, Boston, MA, USA, 1999).
37. R. Seydel, Practical Bifurcation and Stability Analysis (Springer, New York, 2010), 3rd ed., Vol. 5.