# [Pw_forum] multiplicity in lsda calculation

Nicola Marzari marzari at MIT.EDU
Wed Feb 23 15:30:23 CET 2005

```Dear Massimiliano,

using Gamma-sampling only (as appropriate in this case) there
should be a fixed-occupations option described somewhere in the
docs (it would be trivial but not terribly useful to expand the
input flags to have this option imposed at every k-point).

Sometimes it is difficult (or impossible) to converge some of
these simple systems (atoms, molecules, or clusters in vacuum);
I presume this is due to level-crossings instabilities, that
affect iterative selfconsistent approaches (as is the case with
PWSCF). We have experienced quite a few of these problems in
recent weeks.

A finite electronic temperature would help smooth the level-crossing
instabilities, and thus aid convergence, but then you are not
anymore guaranteed to converge to the state of definite S_z you
were originally looking for. (Note: finite electronic T approaches
should be used to improve k-point sampling accuracy, more than
ground-state convergence; e.g. in direct-minimization approaches
convergence to the ground state is reached variationally irrespectively
of the electronic T, but in iterative scf approaches a finite T
helps out. See http://nnn.mit.edu/phd for a detailed explanation).

A simple solution to this problem that I have been mulling
would be introducing two Fermi energies - i.e. combining an
electronic temperature with a constraint of fixed n_up-n_down
(and, given that nelec is fixed -> fixed n_up and fixed n_down). It
should be very easy to implement, and we might give it a try in the
next few weeks (but you'd be also welcome to try, or interact with
one of my students on this - Heather Kulik).

Any comments ? (By the way, it would be helpful to have in the
docs a note that says that for finite temperature calculations
the "total energy" printed by the code is actually

nicola

PS: note that in DFT you have states of definite S_z, but not S^2, so
the notation singlet or triplet is only approximate. E.g. a real
triplet has S = 1 and S_z = 1, 0 or -1 in hbar units.

Massimiliano Bonomi wrote:

> Dear users,
> I'm doing a lsda calculation with a gold cluster of 8 atoms using both
> CPMD and espresso 2.1.2 package.
> With the first one  I can specify the multiplicity of the state
> (singolet, triplet...), but it's very slow in reaching convergence.
> How can i specify the multiplicity with pwscf (which is much faster)??
>