We propose a simple scheme for decomposition of molecular functions into single‐center components. The problem of three‐dimensional integration in molecular systems thus reduces to a sum of one‐center, atomic‐like integrations which are treated using standard numerical techniques in spherical polar coordinates. The resulting method is tested on representative diatomic and polyatomic systems for which we obtain five‐ or six‐figure accuracy using a few thousand integration points per atom.
REFERENCES
1.
A. D. Becke, Ph.D. dissertation, McMaster University, Hamilton, Canada (1981);
78
, 4787
(1983
)., J. Chem. Phys.
2.
J. C. Slater, The Self‐Consistent Field for Molecules and Solids (McGraw‐Hill, New York, 1974).
3.
4.
5.
L.
Laaksonen
, D.
Sundholm
, and P.
Pyykkö
, Int. J. Quantum Chem.
27
, 601
(1985
).6.
L.
Laaksonen
, P.
Pyykkö
, and D.
Sundholm
, Comput. Phys. Rep.
4
, 315
(1986
).7.
S. A.
Alexander
and H. J.
Monkhorst
, Int. J. Quantum Chem.
32
, 361
(1987
).8.
T.
Ziegler
, V.
Tschinke
, and A.
Becke
, J. Am. Chem. Soc.
109
, 1351
(1987
).9.
10.
Local Density Approximations in Quantum Chemistry and Solid State Physics, edited by J. P. Dahl and J. Avery (Plenum, New York, 1984);
Density Functional Methods in Physics, edited by R. M. Dreizler and J. da Providencia (Plenum, New York, 1985);
Density Matrices and Density Functionals, edited by R. Erdahl and V. H. Smith, Jr. (Reidel, Dordrecht, 1987).
11.
S.
Dhar
, A.
Ziegler
, D. G.
Kanhere
, and J.
Callaway
, J. Chem. Phys.
82
, 868
(1985
).12.
G. B. Arfken, Mathematical Methods for Physicists, 2nd ed. (Academic, New York, 1970).
13.
P. M. Boerrigter, G. te Velde, and E. J. Baerends, Int. J. Quantum Chem. (to be published).
14.
R. F. W.
Bader
and T. T.
Nguyen‐Dang
, Adv. Quantum Chem.
14
, 63
(1981
).15.
F. W.
Biegler‐Koenig
, T. T.
Nguyen‐Dang
, Y.
Tal
, R. F. W.
Bader
, and A. J.
Duke
, J. Phys. B
14
, 2739
(1981
);F. W.
Biegler‐Koenig
, R. F. W.
Bader
, and Ting‐Hua
Tang
, J. Comput. Chem.
3
, 317
(1982
).16.
D. E.
Ellis
, Int. J. Quantum Chem. Quantum Chem. Symp.
2
, 35
(1968
);17.
18.
19.
20.
21.
22.
A. H. Stroud, Approximate Calculation of Multiple Integrals (Prentice‐Hall, Englewood Cliffs, 1971).
23.
S. L.
Sobolev
, Sibirsk. Mat. Zh.
3
, 769
(1962
). References 23 to 28 are in Russian. English translations are available in Siberian Math. J. (Sibirsk. Mat. Zh.), U.S.S.R. Comput. Math, and Math. Phys. (Zh. Vychisl. Mat. Mat. Fiz.), and Math. Notes (Mat. Zametki).24.
V. I.
Lebedev
, Zh. Vychisl. Mat. Mat. Fiz.
15
, 48
(1975
), also note erratum in Ref. 25.25.
26.
27.
V. I. Lebedev, Proc. Conf. Novosibirsk (1978), edited by S. L. Sobolev (Nauka Sibirsk. Otdel., Novosibirsk, 1980).
28.
29.
Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1970).
30.
J. C. Slater, Quantum Theory of Molecules and Solids (McGraw‐Hill, New York, 1965), Vol. 2.
31.
E.
Clementi
and C.
Roetti
, At. Data Nucl. Data Tables
14
, 177
(1974
).32.
B. I.
Dunlap
, J. W. D.
Connolly
, and J. R.
Sabin
, J. Chem. Phys.
71
, 3396
, 4993
(1979
).
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