The Hooke model for the two‐electron atom replaces the electron–nuclear interaction by a harmonic oscillator potential, but retains the Coulomb repulsion of the electrons. The first‐order perturbation equation for the electron repulsion is solved analytically, and the exact first‐, second‐, and third‐order perturbation energies are obtained. A similar Z−1 perturbation treatment is carried out for the Hartree–Fock equation and other variational approximations. The Z−1 expansion of the correlation energy is compared with that for heliumlike atoms and found to be similar.

1.
J. O. Hirschfelder, W. B. Brown, and S. T. Epstein in Advances in Quantum Chemistry, edited by P.‐O. Löwdin (Academic, New York, 1964), Vol. 1, p. 256.
2.
R. J.
White
and
W. B.
Brown
,
Intern. J. Quantum Chem.
1S
,
61
(
1967
).
3.
N. R.
Kestner
and
O.
Sinanoğlu
,
Phys. Rev.
128
,
2687
(
1962
).
4.
D. F.
Tuan
,
J. Chem. Phys.
50
,
2740
(
1969
).
5.
T.
Kato
,
Commun. Pure Appl. Math.
10
,
151
(
1957
).
6.
R. T.
Pack
and
W. B.
Brown
,
J. Chem. Phys.
45
,
556
(
1966
).
7.
Reference 1, p. 270.
8.
More details are presented in R. J. White and W. B. Brown, Wisc. Theoret. Chem. Inst. Tech. Rept. WIS‐TCI‐116 (1965).
9.
Reference 1, p. 271.
10.
A.
Dalgarno
,
Proc. Phys. Soc. (London)
75
,
439
(
1960
).
11.
A.
Fröman
,
Phys. Rev.
112
,
870
(
1958
).
12.
L. Lewin, Dilogarithms and Associated Functions (Macdonald, London, 1958).
13.
E. A.
Hylleraas
,
Z. Physik
65
,
209
(
1930
).
14.
W. B. Brown (unpublished work).
An account of the two‐electron delta model atom is given in an appendix to
R. J.
White
and
F. H.
Stillinger
,
J. Chem. Phys.
52
,
5800
(
1970
).
15.
F. W.
Byron
and
C. J.
Joachain
,
Phys. Rev.
157
,
1
(
1967
).
16.
C. W.
Scherr
and
R. E.
Knight
,
Revs. Mod. Phys.
35
,
436
(
1963
).
17.
R. J.
White
,
Phys. Rev.
154
,
116
(
1967
).
18.
J. M.
Benson
and
W. B.
Brown
,
J. Chem. Phys.
53
,
3880
(
1970
), following paper.
19.
F. H.
Stillinger
,
J. Chem. Phys.
45
,
3623
(
1966
).
20.
J.
Linderberg
,
Phys. Rev.
121
,
816
(
1961
).
21.
N. R.
Kestner
,
J. Chem. Phys.
45
,
3121
(
1966
).
22.
W. Gröbner and N. Hofreiter, Integraltafel (Springer, Vienna, 1966).
This content is only available via PDF.
You do not currently have access to this content.