The Coulomb three-body problem in Jacobi coordinates was solved by treating the distance of the particles having equal charge as a parameter. This method allows computation of electronic energies with finite nuclear masses while maintaining the notion of a potential energy curve. The rotationless ground-state electronic and the so-called adiabatic Jacobi correction (AJC) energies are presented for H2+, D2+, and HD+ at fixed internuclear separations. The AJCs are defined as the difference between the results obtained from calculations using proper finite and infinite nuclear masses. Except at the united atom limit, the AJCs are smaller than the traditional first-order diagonal Born-Oppenheimer corrections. Expectation values of proton-electron, p-e, and deuteron-electron, d-e, distances for HD+ have been computed as a function of internuclear separation. Similarly to the fully nonadiabatic approach, the present method is able to follow the symmetry breaking in HD+. Exact and approximate analytical and numerical results are given for counterfactual systems as well. In these cases changes are allowed for the values of the electron rest mass or the elementary charge, as well as for the mass or charge of the unique particle (electron).

1.
E. A. G.
Armour
,
J.-M.
Richard
, and
K.
Varga
,
Phys. Rep.
413
,
1
(
2005
).
2.
F. E.
Harris
,
Adv. Quantum Chem.
47
,
129
(
2004
).
3.
G. W. F.
Drake
,
Phys. Scr., T
T83
,
83
(
1999
).
4.
F. W.
King
,
J. Mol. Struct.: THEOCHEM
400
,
7
(
1997
).
6.
B. T.
Sutcliffe
and
J.
Tennyson
,
Int. J. Quantum Chem.
39
,
183
(
1991
).
7.
T.
Kato
,
Trans. Am. Math. Soc.
70
,
212
(
1951
).
8.
W.
Thirring
, in
Schrödinger, Centenary Celebrations of a Polymath
, edited by
C. W.
Kilminster
(
Cambridge University Press
,
Cambridge
,
1987
), p.
65
.
9.
M.
Reed
and
B.
Simon
,
Methods of Modern Mathematical Physics
,
Analysis of Operators
Vol.
IV
(
Academic
,
New York
,
1978
).
10.
A. M.
Frolov
,
Phys. Rev. A
59
,
4270
(
1999
).
11.
S.
Takahashi
and
K.
Takatsuka
,
J. Chem. Phys.
124
,
144101
(
2006
).
12.
J.-M.
Combes
and
R.
Seiler
, in
Quantum Dynamics of Molecules
, edited by
R. G.
Woolley
(
Plenum
,
New York
,
1980
), p.
435
.
13.
L.
Wolniewicz
and
J.
Poll
,
Mol. Phys.
59
,
953
(
1986
).
14.
L.
Hilico
,
N.
Billy
,
B.
Grémaud
, and
D.
Delande
,
Eur. Phys. J. D
12
,
449
(
2000
).
15.
A. M.
Frolov
,
Phys. Rev. A
67
,
064501
(
2003
).
16.
D.
Baye
,
M.
Hesse
, and
M.
Vincke
,
Phys. Rev. E
65
,
026701
(
2002
).
17.
N. C.
Handy
,
Y.
Yamaguchi
, and
H. F.
Schaefer
 III
,
J. Chem. Phys.
84
,
4481
(
1986
).
18.
W.
Kutzelnigg
,
Mol. Phys.
90
,
909
(
1997
).
19.
P. R.
Bunker
and
R. E.
Moss
,
Mol. Phys.
33
,
417
(
1977
).
20.
E. F.
Valeev
and
C. D.
Sherrill
,
J. Chem. Phys.
118
,
3921
(
2003
).
21.
D. W.
Schwenke
,
J. Phys. Chem. A
105
,
2352
(
2001
).
22.
J.
Gauss
,
A.
Tajti
,
M.
Kállay
,
J. F.
Stanton
, and
P. G.
Szalay
,
J. Chem. Phys.
125
,
144111
(
2006
).
23.
M.
Born
and
K.
Huang
,
Dynamical Theory of Crystal Lattices
(
Oxford University Press
,
New York
,
1955
), Appendix 8.
24.
S.
Bubin
,
E.
Bednarz
, and
L.
Adamowicz
,
J. Chem. Phys.
122
,
041102
(
2005
).
25.
H. A.
Mavromatis
and
R. S.
Alassar
,
Appl. Math. Lett.
12
,
101
(
1999
).
26.
MATHEMATICA, Version 2.2, Wolfram Research, Inc., Champaign, IL,
1994
.
27.
I. M.
Mills
,
T.
Cvitas
,
K.
Homann
,
N.
Kallay
, and
K.
Kuchitsu
,
Quantities, Units and Symbols in Physical Chemistry
(
Blackwell Science
,
Oxford
,
1993
).
28.
T. D.
Crawford
,
C. D.
Sherrill
,
E. F.
Valeev
 et al, PSI 3.2,
2003
.
29.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
30.
A.
Karton
and
J. M. L.
Martin
,
Theor. Chem. Acc.
115
,
330
(
2006
).
31.
D.
Feller
,
J. Chem. Phys.
96
,
6104
(
1992
).
32.
G. M.
Zhislin
,
Trudy Mosk. Mat. Obsc.
9
,
81
(
1960
).
33.
I.
Ben-Itzhak
,
E.
Wells
,
K. D.
Carnes
,
V.
Krishnamurthi
,
O. L.
Weaver
, and
B. D.
Esry
,
Phys. Rev. Lett.
85
,
58
(
2000
).
34.
B. T.
Sutcliffe
,
Adv. Chem. Phys.
114
,
1
(
2000
).
You do not currently have access to this content.