A direct inversion iterative subspace version of the relaxed constrained algorithm is found to be a very powerful convergence acceleration technique for the solution of the self-consistent field equations found in the Hartree–Fock method and Kohn–Sham-based density functional theory (KS-DFT). The present algorithm, abbreviated EDIIS, is benchmarked against the direct inversion iterative subspace method based on the commutator of the density and Fock matrices developed by Pulay (DIIS). Our findings indicate that while EDIIS is able to rapidly bring the density matrix from any initial guess to a solution region, the DIIS method is faster when the density matrix is close to convergence. Consequently, we propose a combination of EDIIS and DIIS methods, which is both very robust and highly efficient. We also show how EDIIS can detect the presence and determine the value of fractional occupations in KS-DFT.

1.
P.
Pulay
,
Chem. Phys. Lett.
73
,
393
(
1980
).
2.
P.
Pulay
,
J. Comput. Chem.
3
,
556
(
1982
).
3.
V. R.
Saunders
and
I. H.
Hillier
,
Int. J. Quantum Chem.
7
,
699
(
1973
).
4.
A. D.
Rabuck
and
G. E.
Scuseria
,
J. Chem. Phys.
110
,
695
(
1999
).
5.
G.
Vacek
,
J. K.
Perry
, and
J.-M.
Langlois
,
Chem. Phys. Lett.
310
,
189
(
1999
).
6.
M. A.
Natiello
and
G. E.
Scuseria
,
Int. J. Quantum Chem.
26
,
1039
(
1984
).
7.
E.
Cancès
and
C.
Le Bris
,
Int. J. Quantum Chem.
79
,
82
(
2000
).
8.
E. Cancès, in Mathematical Models and Methods for ab initio Quantum Chemistry, edited by M. Defranceschi and C. Le Bris, Lecture Notes in Chemistry, Vol. 74 (Springer, Berlin, 2000).
9.
E.
Cancès
and
C.
Le Bris
,
Math. Modell. Numer. Anal.
34
,
749
(
2000
).
10.
E.
Cancès
,
J. Chem. Phys.
114
,
10616
(
2001
).
11.
E. R. Davidson (private communication, 2002).
12.
H.
Hsu
,
E. R.
Davidson
, and
R. M.
Pitzer
,
J. Chem. Phys.
65
,
609
(
1976
).
13.
R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer, Berlin, 1990).
14.
M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 01, Development Version (Revision B.01), Gaussian, Inc., Pittsburgh, PA, 2001.
15.
D. G. Luenberger, Introduction to Linear and Nonlinear Programming (Addison-Wesley, Reading, MA, 1984).
16.
P. R. T.
Schipper
,
O. V.
Gritsenko
, and
E. J.
Baerends
,
Theor. Chem. Acc.
99
,
329
(
1998
).
17.
A. D.
Daniels
and
G. E.
Scuseria
,
Phys. Chem. Chem. Phys.
2
,
2173
(
2000
).
18.
F. W.
Averill
and
G. S.
Painter
,
Phys. Rev. B
46
,
2498
(
1992
).
19.
E. Cancès (unpublished).
This content is only available via PDF.
You do not currently have access to this content.