Efficient and accurate electron propagator methods and algorithms

Practical Aspects of Computational Chemistry: Methods, Concepts and Applications

Volumn , Issue , 2010, Pages 1-17

  Flores Moreno, Roberto ^a   Ortiz, J V ^b  

^a UNIVERSITY OF GUANAJUATO   (Mexico)

^b AUBURN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84890185764     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-90-481-2687-3_1     Document Type: Chapter

References (62)

1. J. Linderberg, Y. Öhrn, Propagators in Quantum Chemistry, 2nd edn. (Wiley, Hoboken, 2004)
2. B.T. Pickup, O. Goscinski, Direct calculation of ionization energies. Mol. Phys. 26, 1013-1035 (1973)
3. Y. Öhrn, G. Born, Molecular electron propagator theory and calculations. Adv. Quantum Chem. 13, 1-88 (1981)
4. J.V. Ortiz, Toward an exact one-electron picture of chemical bonding. Adv. Quantum Chem. 35, 33-52 (1999)
5. L.S. Cederbaum, W. Domcke, Theoretical aspects of ionization potentials of photoelectron spectroscopy: A many-body approach, Adv. Chem. Phys. 36, 205-344 (1977)
6. W. von Niessen et al., Computational methods for the one-particle Green's function. Comp. Phys. Rep. 1, 57-125 (1984)
7. J. Simons, in Theoretical Studies of Negative Molecular Ions, ed. by H. Eyring and D. Henderson Theoretical Chemistry: Advances and Perspectives, Vol. 3 (Academic, New York, 1978)
8. M.F. Herman et al., Theoretical studies of the equations of motion-Green's function methods and configuration interaction methods: Analysis of methods and applications. Adv. Chem. Phys. 48, 1-69 (1981)
9. J.V. Ortiz, Partial third order quasiparticle theory: Comparisons for closed-shell ionization energies and an application to the borazine photoelectron spectrum. J. Chem. Phys. 104, 7599-7605 (1996)
10. A.M. Ferreira et al., in Application and Testing of Diagonal, Partial Third-Order Electron Propagator Approximations, ed. by J. Cioslowski Understanding Chemical Reactivity, Vol. 22, Quantum-Mechanical Prediction of Thermochemical Data (Kluwer, Dordrecht, 2001), pp. 131-160
11. J.V. Ortiz, in The electron propagator picture of molecular electronic structure, ed. by J. Leszczynski Computational Chemistry: Reviews of Current Trends, Vol. 2 (World Scientific, Singapore, 1997), pp. 1-61
12. V.V. Zakjevskii et al., Base and phosphate electron detachment energies of deoxyribonu-cleotide anions. J. Am. Chem. Soc. 128, 13350-13351 (2006)
13. V.V. Zakjevskii et al., Electron propagator studies of vertical electron detachment energies and isomerism in purinic deoxyribonucleotides. Int. J. Quantum Chem. 107, 2266-2273 (2007)
14. O. Dolgounitcheva et al., Electron propagator calculations show that alkyl substituents alter porphyrin ionization energies. J. Am. Chem. Soc. 127, 8240-8241 (2005)
15. O. Dolgounitcheva et al., Ab initio electron propagator calculations on the ionization energies of free base porphyrin, magnesium porphyrin and zinc porphyrin. J. Phys. Chem. 109, 11596-11601 (2005)
16. J.V. Ortiz et al., in One-Electron Pictures of Electronic Structure: Propagator Calculations on Photoelectron Spectra of Aromatic Molecules, ed. by J.-L. Calais, E. Kryachko Conceptual Perspectives in Quantum Chemistry, Vol. 3 (Kluwer, Dordrecht, 1997), pp. 465-517
17. C.CJ. Roothaan, Self-consistent field theory for open-shells of electronic systems. Rev. Mod. Phys. 32, 179-185 (1960)
18. G.G. Hall, The molecular orbital theory of chemical valency. VIII-A method of calculating ionization potentials. Proc. Roy. Soc. Ser. A 205, 541-552 (1951)
19. D.R. Hartree, The Calculation of Atomic Structures. (Wiley, London, 1957)
20. V.A. Fock, Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Z. Phys. 61, 126-148 (1930)
21. V.G. Zakrzewski, J.V. Ortiz, Semidirect algorithms in electron propagator calculations. Int. J. Quantum Chem. Symp. 28, 23-27 (1994)
22. V.G. Zakrzewski, J.V. Ortiz, Semidirect algorithms for third order electron propagator calculations. Int. J. Quantum Chem. 53, 583-590 (1995)
23. J.C. Slater, J.H. Wood, Statistical exchange and the total energy of a crystal. Int. J. Quantum Chem. (Suppl.) 4, 3-34 (1971)
24. J.C. Slater, Statistical exchange-correlation in the self-consistent field. Adv. Quantum Chem. 6, 1-91 (1972)
25. J.F. Janak, Proof that dE jdn, D s, in density-functional theory. Phys. Rev. B 18, 7165-7168 (1978)
26. R. Flores-Moreno et al., Assessment of transition operator reference states in electron propagator calculations. J. Chem. Phys. 127, 134106/1-8 (2007)
27. R. Flores-Moreno, J.V. Ortiz, Quasiparticle virtual orbitals in electron propagator calculations, J. Chem. Phys. 128, 164105/1-6 (2008)
28. R. Flores-Moreno, J.V. Ortiz, Resolution of the identity for electron propagator calculations. unpublished results.
29. J.V. Ortiz, Energy gradients and effective density differences in electron propagator theory. J. Chem. Phys. 112, 56-68 (2000)
30. P.-O. Löwdin, Studies in perturbation theory. IX. Connection between various approaches in the recent development-evaluation of upper bounds to energy eigenvalues in Schrödinger's perturbation theory. J. Math. Phys. 6, 1341-1353 (1965)
31. C. Møller, M.S. Plesset, Note on an approximation treatment for many-electron systems. Phys. Rev. 46, 618-622 (1934)
32. P.-O. Löwdin, Studies in perturbation theory. X. Lower bounds to energy eigenvalues in perturbation-theory ground state. Phys. Rev. 139, A357-A372 (1965)
33. C4. J. Chem. Phys. 99, 6716-6726 (1993)
34. J. Baker, B.T. Pickup, A molecular method for ionization potentials. Chem. Phys. Lett. 76, 537-541 (1980)
35. S.F. Abdulnur et al., Atomic central-field models for open shells with application to transition metals. Phys. Rev. A 6, 889-898 (1972)
36. P. Bagus, Self-consistent-field wave functions for hole states of some Ne-like and Ar-like ions. Phys. Rev. 139, A619-634 (1965)
37. GD. Purvis, Y. Öhrn, The transition state, the electron propagator, and the equation of motion method. J. Chem. Phys. 65, 917-922 (1976)
38. G. Born et al., Elementary finite order perturbation theory for vertical ionization energies. J. Chem. Phys. 68, 74-85 (1978)
39. G. Born et al., On the calculation of electron binding energies. J. Chem. Phys. 69, 1162-1167 (1978)
40. J.V. Ortiz et al., Electron propagator calculations with a transition operator reference state. Chem. Phys. Lett. 103, 29-34 (1983)
41. MJ. Frisch et al., Gaussian 2003 (Gaussian, Inc., Pittsburgh, PA, 2003)
42. J. Cioslowski, J.V. Ortiz, One-electron density matrices and energy gradients in second-order electron propagator theory. J. Chem. Phys. 96, 8379-8389 (1992)
43. A. Köster, Hermite gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods. J. Chem. Phys. 118, 9943-9951 (2003)
44. N.H.F. Beebe, J. Linderberg, Simplifications in the generation and transformation of two-electron integrals in molecular calculations. Int. J. Quantum Chem. 12, 683-705 (1977)
45. B.I. Dunlap et al., On some approximations in applications of X? theory. J. Chem. Phys. 71, 3396-3402 (1979)
46. J.W. Mintmire, B.I. Dunlap, Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations. Phys. Rev. A 25, 88-95 (1982)
47. O. Vahtras et al., Integral approximations for LCAO-SCF calculations. Chem. Phys. Lett. 213, 514-518 (1993)
48. E.J. Baerends et al., Self-consistent molecular Hartree-Fock-Slater calculations I. The computational procedure. Chem. Phys. 2, 41-51 (1973)
49. C.-K. Skylaris et al., On the resolution of identity Coulomb energy approximation in density functional theory. J. Mol. Struct.: Theochem. 501, 229-239 (2000)
50. A.P Rendell, T.J. Lee, Coupled-cluster theory employing approximate integrals: An approach to avoid the input/output and storage bottlenecks. J. Chem. Phys. 101, 400-408 (1994)
51. S. Hamel et al., Assessment of the quality of orbital energies in resolution-of-the-identity Hartree-Fock calculations using deMon auxiliary basis sets. J. Chem. Phys. 114, 7342-7350 (2001)
52. W. Kohn, L.J. Sham, Quantum density oscillations in an inhomogeneous electron gas. Phys. Rev. 137, A1697-A1705 (1965)
53. P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136, B864-B871 (1964)
54. Y. Shigeta et al., Electron propagator calculations with Kohn-Sham reference states. Int. J. Quantum. Chem. 85, 411-420 (2001)
55. A.M. Köster et al., deMon developers, (2006), http://www.demon- software.com
56. L. Hedin, New method for calculating the one-particle Green's function with application to the electron-gas problem. Phys. Rev. 139, A796-A823 (1965)
57. Ionization potentials for atoms were taken from NIST tables (2007), http://physics.nist.gov/PhysRefData/IonEnergy/tblNew.html
58. W.L. Jolly et al., Core-electron binding energies for gaseous atoms and molecules. At. Data Nucl. Data Tables 31, 433-493 (1984)
59. T.H. Dunning, Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007-1023 (1989)
60. R.C. Morrison, G. Liu, Extended Koopmans' theorem: Approximate ionization energies from MSCF wave functions. J. Comput. Chem. 13, 1004-1010 (1992)
61. 3O and Ta3O~. Comput. Lett. 1, 164-171 (2005)
62. P. Calaminici et al., Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems. J. Chem. Phys. 126, 044108/1-10 (2007)