quantum-espresso/examples/example29

This example shows how to perform Born-Oppeheimer molecular dynamics
using the conjugate-gradient minimization of the electronic states.
It uses also the ensemble DFT  for dealing with partial occupations
of the electronic states.
The example shows a simple Silicon dimer.
The systems has 8 valence electrons, described by 8 states (nspin=1).
For every ionic step, it fully minimized the electronic enthalpy
(electronic energy if ensemble-DFT is not used)
The conjugate-gradient algorith REQUIRES Gram-Schmidt orho-normalization.

Ensemble-DFT is implemented only for conjugate gradient minimization
of the electronic states and Born-Oppenheimer molecular dynamics
(NOT FOR Car-Parrinello), it supports Ultrasoft pseudopotentials.
For Ensemble DFT see:
N. Marzari, D. Vanderbilt, and M. C. Payne
"Ensemble Density-Functional Theory for Ab Initio 
Molecular Dynamics of Metals and Finite-Temperature Insulators"
Phys. Rev. Lett. 79, 1337-1340 (1997)


Note that here we start a conjugate gradient minimizatio from
scratch, directly with preconditioning on the electron masses
(emass=1000.d0,emass_cutoff = 4.d0). This should not be done
for larger systems (Just use maxiter=5 for doing some c.g. 
iteration with no mass preconditioning and then do restart
with mass preconditioning)

The concerned parameters are:

FOR CONJUGATE GRADIENT:

tcg            LOGICAL ( default = .FALSE. )
               if .TRUE. perform a conjugate gradient minimization of the
               electronic states for every ionic step.
               It requires Gram-Schmidt orthogonalization of the electronic
               states.
 
maxiter        INTEGER ( default = 100 )
               maximum number of conjugate gradient iterations for
               conjugate gradient minimizations of electronic states
 
conv_thr         REAL ( default = 1.D-6 )
               convergence criterion for energy in the case of
               conjugate gradient minimization of the electronic states
                
passop         REAL ( default =  0.3D0 )
               small step used in the  conjugate gradient minimization
               of the electronic states.


FOR ENSEMBLE-DFT


occupations    CHARACTER
               a string describing the occupation of the electronic states.
               In the case of conjugate gradient style of minimization
               of the electronic states, if occupations is set to 'ensemble',
               this allows ensemble dft calculations for metallic systems
                                                                                                                             
smearing       CHARACTER
               a string describing the kind of occupations for electronic states
               in the case of ensemble dft (occupations == 'ensemble' );
               now only Fermi-Dirac ('fd') case is implemented
                                                                                                                             
degauss        REAL ( default = 0.D0 )
               parameter for the smearing function, only used for ensemble dft
               calculations

 
n_inner        INTEGER ( default = 2 )
               number of internal cycles for every conjugate gradient
               iteration only for ensemble dft


The output file is slightly different from the Car-Parrinello case:

It reports Kohn-Sham eigenstates energies and occupancies:

    eigenvalues at k-point:  0.000 0.000 0.000
         -10.79   -9.16   -4.57   -3.85   -3.85   -2.54   -2.54   -0.25
  
    Occupations  :
       1.999925 1.999182 1.484846 1.000959 1.000959 0.252111 0.252111 0.009907

At every steps, it reports:

        nfi   tempp            E -T.S-mu.nbsp         +K_p #Iter
   Step    10      13     -7.57738     -7.71516     -7.71504     9
   Step    11      15     -7.57743     -7.71519     -7.71504    10
   Step    12      19     -7.57748     -7.71522     -7.71504     6
   Step    13      22     -7.57754     -7.71525     -7.71504     6


where nfi is a counter of the ionic steps, tempp is the ionic temperature,
E is the electronic energy at the minimum of the electronic enthalpy,
-T.S-mu.nbsp is the electronic enthalpy (electronic energy -TS , S=entropy)
, and +K_p  is the electronic enthalpy plus the ionic kinetic energy,
#Iter is the number of iterations which were needed to minimized
the electronic enthalpy with the conjugate gradient algorithm.

NB: from one ionic step to the following, a linear extrapolation is 
used to provide an estimate for the electronic wave-functions,
every 10 steps, this procedure is restarted.
A more powerful scheme will be implemented in the future.