# CCL: incremental and nonincremental Fock matrix

*From*: Jussi Lehtola <jussi.lehtola(0)helsinki.fi>
*Subject*: CCL: incremental and nonincremental Fock matrix
*Date*: Thu, 8 Mar 2012 18:27:36 +0200

Sent to CCL by: Jussi Lehtola [jussi.lehtola- -helsinki.fi]
On Thu, 08 Mar 2012 15:26:00 +0200
"Heribert Reis hreis]![eie.gr" <owner-chemistry^^^ccl.net>
wrote:
> Sent to CCL by: Heribert Reis [hreis###eie.gr]
> Dear Reza,
>
> NoIncFock calculates the Fock-matrix from scratch at each SCF step,
> which is expensive, but accurate.
> IncFock approximates the Fock-matrix by adding up the changes due to
> the density matrix change from consecutive steps of the SCF:
>
> F(P_i) = F(P_i-1) + F(P_i - P_i-1), where P is the density.
>
> This is faster than NoIncFock, and the approximation is a good one, if
> the density changes are small, e.g. close to convergence, but may also
> fail.
Well, it's not really an approximation, since in Hartree-Fock theory
the Fock matrix is linear in the density matrix, and you should get the
same result in both cases.
When you form the matrix from scratch as
G(i,j) = sum_{k,l} P(k,l) [2(ij|kl) - (ik|lj)]
you screen out the elements for which the product of the density matrix
elements and integrals (estimated, e.g., with the Schwarz inequality),
are small.
If you do incremental formation, the formation becomes much more
effective as the elements that haven't changed are screened out.
--
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Mr. Jussi Lehtola, M. Sc. Doctoral Student
jussi.lehtola^^^helsinki.fi Department of Physics
http://www.helsinki.fi/~jzlehtol University of Helsinki
Office phone: +358 9 191 50 632 Finland
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Jussi Lehtola, FM Tohtorikoulutettava
jussi.lehtola^^^helsinki.fi Fysiikan laitos
http://www.helsinki.fi/~jzlehtol Helsingin Yliopisto
TyÃpuhelin: (0)9 191 50 632
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