Expressions for integrals involving general Gaussian (s, p, d, …) basis Bloch functions are presented. Applying the Poisson transformation and the Ewald-type partitioning scheme, all lattice sums appearing in these expressions lead to fast convergence in both direct and Fourier spaces. Numerical results produced for selected test cases show that a limited number of terms in the lattice sums are necessary to get convergence in the two spaces.
REFERENCES
1.
S.
Suhai
and J.
Ladik
, J. Phys. C
15
, 4327
(1982
).2.
S.
Suhai
, Phys. Rev. B
27
, 3506
(1983
).3.
J. -Q.
Sun
and R. J.
Bartlett
, J. Chem. Phys.
104
, 8553
(1996
).4.
J. G.
Fripiat
, J.
Delhalle
, and F. E.
Harris
, Chem. Phys. Lett.
422
, 11
(2006
).5.
J. G.
Fripiat
, J.
Delhalle
, and F. E.
Harris
, in Computation in Modern Science and Engineering
, edited by T. E.
Simos
and G.
Maroulis
(American Institute of Physics
, Melville, NY
, 2007
), Vol. 2
, Pt. A, pp. 179
–182
;J. G.
Fripiat
, J.
Delhalle
, and F. E.
Harris
, AIP Conf. Proc.
963
, 179
(2007
).6.
M. D.
Segall
, P. L. D.
Lindan
, M. J.
Probert
, C. J.
Pickard
, P. J.
Hasnip
, S. J.
Clark
, and M. C.
Payne
, J. Phys.: Condens. Matter
14
, 2717
(2002
).7.
J. M.
André
, D. H.
Mosley
, B.
Champagne
, J.
Delhalle
, J. G.
Fripiat
, J. L.
Brédas
, D. J.
Vanderveken
, and D. P.
Vercauteren
, in Methods and Techniques in Computational Chemistry, (METECC-94)
, edited by E.
Clementi
(Stef
, Cagliari
, 1993
), Vol. B
, pp. 423
–480
.8.
C.
Pisani
, R.
Dovesi
, and C.
Roetti
, Hartree-Fock Ab-Initio Treatment of Crystalline Systems, Lecture Notes in Chemistry
(Springer
, Berlin
, 1988
), Vol. 48
.9.
F. E.
Harris
, in Theoretical Chemistry, Advances and Perspectives
, edited by D.
Henderson
and H.
Eyring
(Academic
, New York
, 1975
), Vol. 1
, pp. 147
–218
.10.
J. M.
André
, J. G.
Fripiat
, Ch.
Demanet
, J. L.
Brédas
, and J.
Delhalle
, Int. J. Quantum Chem.
S12
, 233
(1978
).11.
L.
Piela
, J. M.
André
, J. G.
Fripiat
, and J.
Delhalle
, Chem. Phys. Lett.
77
, 143
(1981
).12.
H. J.
Monkhorst
and M.
Kertesz
, Phys. Rev. B
24
, 3015
(1981
).13.
J.
Delhalle
, M. H.
Delvaux
, J. G.
Fripiat
, J. M.
André
, and J. L.
Calais
, J. Chem. Phys.
88
, 3141
(1988
).14.
D.
Jacquemin
, J. G.
Fripiat
, and B.
Champagne
, Int. J. Quantum Chem.
89
, 452
(2002
).15.
J.
Delhalle
, J. G.
Fripiat
, and F. E.
Harris
, Int. J. Quantum Chem.
90
, 587
(2002
).16.
J.
Delhalle
, J. G.
Fripiat
, and F. E.
Harris
, Int. J. Quantum Chem.
90
, 1326
(2002
).17.
K. N.
Kudin
and G. E.
Scuseria
, Chem. Phys. Lett.
289
, 611
(1998
).18.
V. R.
Saunders
, C.
Freyria-Fava
, R.
Dovesi
, and C.
Roetti
, Comput. Phys. Commun.
84
, 156
(1994
).19.
J. M.
Soler
, E.
Artacho
, J. D.
Gale
, A.
Garcia
, J.
Jonquera
, P.
Ordejón
, and D.
Sánchez-Portal
, J. Phys.: Condens. Matter
14
, 2745
(2002
).20.
F. E.
Harris
and H. J.
Monkhorst
, Phys. Rev. B
2
, 4400
(1970
).21.
F. E.
Harris
, J. Chem. Phys.
56
, 4422
(1972
).22.
J.
Delhalle
and F. E.
Harris
, Phys. Rev. B
31
, 6755
(1985
).23.
P. P.
Ewald
, Ann. Phys.
(Leipzig) 369
, 253
(1921
).24.
J.
Delhalle
, J.
Čížek
, I.
Flamant
, J. L.
Calais
, and J. G.
Fripiat
, J. Chem. Phys.
101
, 10717
(1994
).25.
I.
Flamant
, “Fourier space restricted Hartree-Fock method for the electronic structure calculation of stereoregular polymers
,” Ph.D. dissertation, Facultés Universitaires Notre-Dame de la Paix
, 1998
.26.
I.
Flamant
, J. G.
Fripiat
, J.
Delhalle
, and F. E.
Harris
, Theor. Chem. Acc.
104
, 350
(2000
).27.
28.
I.
Flamant
, J.
Delhalle
, and J. G.
Fripiat
, Int. J. Quantum Chem.
63
, 709
(1997
).29.
I.
Flamant
, J. G.
Fripiat
, and J.
Delhalle
, Theor. Chem. Acc.
98
, 155
(1998
).30.
I.
Flamant
, J. G.
Fripiat
, and J.
Delhalle
, Int. J. Quantum Chem.
70
, 1045
(1998
).31.
M. M.
Agrest
and M. S.
Maksimov
, Theory of Incomplete Cylindrical Functions and their Applications
(Springer-Verlag
, Berlin
, 1971
).32.
M. S.
Hantush
and C. E.
Jacob
, Trans., Am. Geophys. Union
36
, 95
(1955
).33.
G. W.
Thomas
, R. G.
Keys
, and A. C.
Reynolds
, Jr., J. Hydrol.
36
, 173
(1978
).34.
M. A.
Chaudhry
and S. M.
Zubair
, J. Comput. Appl. Math.
55
, 99
(1994
).35.
M. A.
Chaudhry
, N. M.
Temme
, and E. J. M.
Veling
, J. Comput. Appl. Math.
67
, 371
(1996
).36.
J. A.
Alford
, Comput. Phys. Commun.
173
, 1
(2005
).37.
F. E.
Harris
, J. Comput. Appl. Math.
215
, 260
(2008
).38.
F. E.
Harris
and J. G.
Fripiat
, Int. J. Quantum Chem.
109
, 1728
(2009
).39.
F. E.
Harris
, Int. J. Quantum Chem.
63
, 913
(1997
).40.
F. E.
Harris
, Int. J. Quantum Chem.
70
, 623
(1998
).41.
L. E.
McMurchie
and E. R.
Davidson
, J. Comput. Phys.
26
, 218
(1978
).42.
I.
Shavitt
, in Methods in Computational Physics
, edited by B.
Alder
, S.
Fernbach
, and M.
Rotenberg
(Academic
, New York
, 1963
), Vol. 2
, pp. 1
–45
.43.
J. G.
Fripiat
and J.
Delhalle
, Int. J. Quantum Chem.
109
, 2960
(2009
).44.
M.
Abramowitz
and I.
Stegun
, Handbook of Mathematical Functions
(Dover
, New York
, 1964
).45.
D. E.
Amos
, ACM Trans. Math. Softw.
6
, 365
(1980
).46.
D. E.
Amos
, ACM Trans. Math. Softw.
6
, 420
(1980
).47.
P. M. W.
Gill
, B. G.
Johnson
, and J. A.
Pople
, Int. J. Quantum Chem.
40
, 745
(1991
).© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.
