Hostname: page-component-6bf8c574d5-2jptb Total loading time: 0 Render date: 2025-02-19T01:50:05.078Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower bound energy calculations for

Published online by Cambridge University Press:  24 October 2008

Mary Walmsley  and
C. A. Coulson
Mary Walmsley
Affiliation:
Mathematical Institute, Oxford
C. A. Coulson
Affiliation:
Mathematical Institute, Oxford
Get access Rights & Permissions [Opens in a new window]

Abstract

Two different calculations are made of lower bounds for the electronic energy of . In the first the method of truncated Hamiltonians due to Bazley and Fox is adapted in such a way that the nuclear charge rather than the energy becomes the eigenvalue. Lower bounds are calculated for the energies of the six lowest σg and six lowest σu states, as well as of the three lowest of both πg and πu symmetries. This approach gives better convergence than when the energy is used as eigenvalue. In the second calculation the method of Temple and Kato is shown to give a satisfactory value for the energy of the ground state, provided that some necessary knowledge of the energy of the first-excited state is available.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 769 - 776
Copyright
Copyright © Cambridge Philosophical Society 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bates, D. R., Ledsham, K. and Stewart, A. L.Philos. Trans. Roy. Soc. London, Ser. A 246 (1953), 215–240.Google Scholar
(2)Bazley, N. W.Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 850–853.CrossRefGoogle Scholar
(3)Bazley, N. W.Phys. Rev. 120 (1960), 144–149.CrossRefGoogle Scholar
(4)Bazley, N. W.J. Math. Mech. 10 (1961), 289–307.Google Scholar
(5)Bazley, N. W. and Fox, D. W.J. Res. Nat. Bur. Standards 65 B (1961), 105–111.CrossRefGoogle Scholar
(6)Bazley, N. W. and Fox, D. W. Phys. Rev. 124 (1961), 483–492.CrossRefGoogle Scholar
(7)Bazley, N. W. and Fox, D. W. J. Math. Phys. 3 (1962), 469–471.CrossRefGoogle Scholar
(8)Bazley, N. W. and Fox, D. W. Arch. Rational Mech. Anal. 10 (1962), 352–360.CrossRefGoogle Scholar
(9)Bazley, N. W. and Fox, D. W. Rev. Mod. Phys. 35 (1963), 712–716.CrossRefGoogle Scholar
(10)Bazley, N. W. and Fox, D. W. J. Math. Phys. 4 (1963), 1147–1153.CrossRefGoogle Scholar
(11)Caldow, G. L. and Coulson, C. A.Proc. Cambridge Philos. Soc. 57 (1961), 341–347.CrossRefGoogle Scholar
(12)Johnson, B. P. and Coulson, C. A.Proc. Phys. Soc. 84 (1964), 263–268.CrossRefGoogle Scholar
(13)Kato, T.J. Phys. Soc. Japan 4 (1949), 334–339.CrossRefGoogle Scholar
(14)Stevenson, A. F.Phys. Rev. 53 (1938), 199.CrossRefGoogle Scholar
(15)Stevenson, A. F. and Crawford, M. F.Phys. Rev. 54 (1938), 375–379.CrossRefGoogle Scholar
(16)Svartholm, N. V. Doctoral thesis, Lund (1945).Google Scholar
(17)Temple, G.Proc. London Math. Soc. 29 (1928), 257–280.Google Scholar
(18)Temple, G.Proc. Roy. Soc. London Ser. A 119 (1928), 276–293.Google Scholar
(19)Weinstein, D. H.Phys. Rev. 40 (1932), 797–799.CrossRefGoogle Scholar
(20)Weinstein, D. H.Phys. Rev. 41 (1932), 839.CrossRefGoogle Scholar
(21)Weinstein, D. H.Proc. Nat. Acad. Sci. U.S.A. 20 (1934), 529–532.CrossRefGoogle Scholar