[Pw_forum] Constraint optimization: how to fix coordination

[Giovanni La Penna]

Even though be not the same thing, I would suggest
to use a dynamical approach like metadynamics for
restraining the coordination number (CN) close to a desired value,
CN(reference).
The current version of QE can use the PLUMED plugin:

M. Bonomi, D. Branduardi, G. Bussi, C. Camilloni, D. Provasi, P. Raiteri,
D. Donadio, F. Marinelli, F. Pietrucci, R.A. Broglia and M. Parrinello.
PLUMED: a portable plugin for free-energy calculations with molecular
dynamics, Comp. Phys. Comm. 2009 vol. 180 (10) pp. 1961-1972.

make plumed
makes cp and pw with metadynamics.

See the Plumed manual for its definition of coordination
number.
Using CN as a collective variable,
given values of CN can be sampled according to an added given
external weight. This latter can be constructed via
metadynamics or, alternatively, can be assigned as
a finite difference approximation to an external bias.
In this latter case, the bias can be, for instance,
harmonic and centered around the desired CN.

Here below is the input for the Plumed plugin
(plumed.dat):

## plumed.dat begins
# Metadynamics with CV=coordination number of a Cu
# ion (atom 1 in QE numbering) with O of water molecules
# (atoms 2,3,4,..., n_wat+1=19+1=20)
# d0=2 Ang, r0=0.5 Ang

NOTE atomic order: QE output (pseudo-pot. order, then input)
NOTE distance units: bohr
NOTE energy units: Ha(CP); Ry(PW)
#W_STRIDE must be larger than number of steps (no bias update)
HILLS HEIGHT 0.0 W_STRIDE 1000000
COORD LIST <solute> <solvent> NN 6 MM 12 D_0 3.779 R_0 0.945 SIGMA 0.35
solute->
1
solute<-
solvent->
LOOP 2 20 1
solvent<-
PRINT W_STRIDE 10
GRID CV 1 MIN 0. MAX 10. NBIN 20
EXTERNAL NCV 1 CV 1 FILENAME uext.dat

ENDMETA
##plumed.dat ends

One can perform dynamics (both Born-Oppenheimer and
Car-Parrinello) with the external harmonic bias uext.dat.

#uext.dat begins
#! FORCE 0
#! NVAR 1
#! TYPE 3
#! BIN 20
#! MIN 0.000000
#! MAX 10.000000
#! PBC 1
...
CN  U=K/2(CN-CN(reference))^2
...
#uext.dat ends

Choice of K and CN(reference) needs a careful calibration.
Decreasing temperature provides a relaxed configuration.
Due to the many possibilities for collective variables,
I found the implementation quite useful in different fields.

                Giovanni La Penna

============================================================
Giovanni La Penna - National research council (Cnr)
Institute for chemistry of organo-metallic compounds (Iccom)
via Madonna del Piano 10,
I-50019 Sesto Fiorentino, Firenze, Italy
tel.: +39 055 522-5264, fax: +39 055 522-5203
e-mail: glapenna at iccom.cnr.it - http://www.iccom.cnr.it/lapenna
skype: giovannilapenna
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