[[_TOC_]]

Introduction
============

This guide covers the usage of the `CP` package, version 6.6, a core
component of the Quantum ESPRESSO distribution. Further documentation,
beyond what is provided in this guide, can be found in the directory
`CPV/Doc/`, containing a copy of this guide.

*Important notice: due to the lack of time and of manpower, this manual
is only partially updated and may contain outdated information.*

This guide assumes that you know the physics that `CP` describes and the
methods it implements. It also assumes that you have already installed,
or know how to install, Quantum ESPRESSO. If not, please read the
general User's Guide for Quantum ESPRESSO, found in directory `Doc/` two
levels above the one containing this guide; or consult the web site:\
`http://www.quantum-espresso.org`.

People who want to modify or contribute to `CP` should read the
Developer Manual:\
`Doc/developer_man.pdf`.

`CP` can perform Car-Parrinello molecular dynamics, including
variable-cell dynamics, and free-energy surface calculation at fixed
cell through meta-dynamics, if patched with PLUMED.

The `CP` package is based on the original code written by Roberto Car
and Michele Parrinello. `CP` was developed by Alfredo Pasquarello (EPF
Lausanne), Kari Laasonen (Oulu), Andrea Trave, Roberto Car (Princeton),
Nicola Marzari (EPF Lausanne), Paolo Giannozzi, and others. FPMD, later
merged with `CP`, was developed by Carlo Cavazzoni, Gerardo Ballabio
(CINECA), Sandro Scandolo (ICTP), Guido Chiarotti, Paolo Focher, and
others. We quote in particular:

-   Federico Grasselli and Riccardo Bertossa (SISSA) for bug fixes,
    extensions to Autopilot;

-   Biswajit Santra, Hsin-Yu Ko, Marcus Calegari Andrade (Princeton) for
    SCAN functional;

-   Robert DiStasio (Cornell)), Biswajit Santra, and Hsin-Yu Ko for
    hybrid functionals with MLWF; (maximally localized Wannier
    functions);

-   Manu Sharma (Princeton) and Yudong Wu (Princeton) for dynamics with
    MLWF;

-   Paolo Umari (Univ. Padua) for finite electric fields and conjugate
    gradients;

-   Paolo Umari and Ismaila Dabo for ensemble-DFT;

-   Xiaofei Wang (Princeton) for META-GGA;

-   The Autopilot feature was implemented by Targacept, Inc.

This guide has been mostly writen by Gerardo Ballabio and Carlo
Cavazzoni.

`CP` is free software, released under the GNU General Public License.\
See `http://www.gnu.org/licenses/old-licenses/gpl-2.0.txt`, or the file
License in the distribution).

We shall greatly appreciate if scientific work done using the Quantum
ESPRESSO distribution will contain an acknowledgment to the following
references:

> P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni,
> D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S.
> Fabris, G. Fratesi, S. de Gironcoli, R. Gebauer, U. Gerstmann, C.
> Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F.
> Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C.
> Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P.
> Umari, R. M. Wentzcovitch, J.Phys.: Condens.Matter 21, 395502 (2009)

and

> P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno
> Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M.
> Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P.
> Delugas, R. A. DiStasio Jr, A. Ferretti, A. Floris, G. Fratesi, G.
> Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J Jia, M.
> Kawamura, H.-Y. Ko, A. Kokalj, E. Küçükbenli, M .Lazzeri, M. Marsili,
> N. Marzari, F. Mauri, N. L. Nguyen, H.-V. Nguyen, A. Otero-de-la-Roza,
> L. Paulatto, S. Poncé, D. Rocca, R. Sabatini, B. Santra, M. Schlipf,
> A. P. Seitsonen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari, N.
> Vast, X. Wu, S. Baroni, J.Phys.: Condens.Matter 29, 465901 (2017)

Users of the GPU-enabled version should also cite the following paper:

> P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo,
> C. Cavazzoni, S. de Gironcoli, P. Delugas, F. Ferrari Ruffino, A.
> Ferretti, N. Marzari, I. Timrov, A. Urru, S. Baroni, J. Chem. Phys.
> 152, 154105 (2020)

Note the form Quantum ESPRESSO for textual citations of the code. Please
also see package-specific documentation for further recommended
citations. Pseudopotentials should be cited as (for instance)

> \[ \] We used the pseudopotentials C.pbe-rrjkus.UPF and O.pbe-vbc.UPF
> from\
> `http://www.quantum-espresso.org`.

Compilation
===========

`CP` is included in the core Quantum ESPRESSO distribution. Instruction
on how to install it can be found in the general documentation (User's
Guide) for Quantum ESPRESSO.

Typing `make cp` from the main Quantum ESPRESSO directory or `make` from
the `CPV/` subdirectory produces the following codes in `CPV/src`:

-   `cp.x`: Car-Parrinello Molecular Dynamics code

-   `cppp.x`: postprocessing code for `cp.x`. See `Doc/INPUT_CPPP.*` for
    input variables.

-   `wfdd.x`: utility code for finding maximally localized Wannier
    functions using damped dynamics.

Symlinks to executable programs will be placed in the `bin/`
subdirectory.

As a final check that compilation was successful, you may want to run
some or all of the tests and examples. Automated tests for `cp.x` are in
directory `test-suite/` and can be run via the `Makefile` found there.
Please see the general User's Guide for their setup.

You may take the tests and examples distributed with `CP` as templates
for writing your own input files. Input files for tests are contained in
subdirectories `test-suite/cp_` with file type `*.in1`, `*.in2`, \... .
Input files for examples are produced, if you run the examples, in the
`results/` subdirectories, with names ending with `.in`.

For general information on parallelism and how to run in parallel
execution, please see the general User's Guide. `CP` currently can take
advantage of both MPI and OpenMP parallelization. The "plane-wave",
"linear-algebra" and "task-group" parallelization levels are
implemented.

Input data
==========

Input data for `cp.x` is organized into several namelists, followed by
other fields ("cards") introduced by keywords. The namelists are

  ------------------- ----------------------------------------------------------
  &CONTROL:           general variables controlling the run
  &SYSTEM:            structural information on the system under investigation
  &ELECTRONS:         electronic variables, electron dynamics
  &IONS :             ionic variables, ionic dynamics
  &CELL (optional):   variable-cell dynamics
  ------------------- ----------------------------------------------------------

\
The `&CELL` namelist may be omitted for fixed-cell calculations. This
depends on the value of variable `calculation` in namelist &CONTROL.
Most variables in namelists have default values. Only the following
variables in &SYSTEM must always be specified:

  ----------- --------------------- -----------------------------------------------
  `ibrav`     (integer)             Bravais-lattice index
  `celldm`    (real, dimension 6)   crystallographic constants
  `nat`       (integer)             number of atoms in the unit cell
  `ntyp`      (integer)             number of types of atoms in the unit cell
  `ecutwfc`   (real)                kinetic energy cutoff (Ry) for wavefunctions.
  ----------- --------------------- -----------------------------------------------

\
).

Explanations for the meaning of variables `ibrav` and `celldm`, as well
as on alternative ways to input structural data, are contained in files
`Doc/INPUT_CP.*`. These files are the reference for input data and
describe a large number of other variables as well. Almost all variables
have default values, which may or may not fit your needs.

Comment lines in namelists can be introduced by a \"!\", exactly as in
fortran code.

After the namelists, you have several fields ("cards") introduced by
keywords with self-explanatory names:

> ATOMIC\_SPECIES\
> ATOMIC\_POSITIONS\
> CELL\_PARAMETERS (optional)\
> OCCUPATIONS (optional)\

The keywords may be followed on the same line by an option. Unknown
fields are ignored. See the files mentioned above for details on the
available "cards".

Comments lines in "cards" can be introduced by either a "!" or a "\#"
character in the first position of a line.

Data files
----------

The output data files are written in the directory specified by variable
`outdir`, with names specified by variable `prefix` (a string that is
prepended to all file names, whose default value is: `prefix=’pwscf’`).
The `iotk` toolkit is used to write the file in a XML format, whose
definition can be found in the Developer Manual. In order to use the
data directory on a different machine, you need to convert the binary
files to formatted and back, using the `bin/iotk` script.

The execution stops if you create a file `prefix.EXIT` either in the
working directory (i.e. where the program is executed), or in the
`outdir` directory. Note that with some versions of MPI, the working
directory is the directory where the executable is! The advantage of
this procedure is that all files are properly closed, whereas just
killing the process may leave data and output files in an unusable
state.

Format of arrays containing charge density, potential, etc.
-----------------------------------------------------------

The index of arrays used to store functions defined on 3D meshes is
actually a shorthand for three indices, following the FORTRAN convention
(\"leftmost index runs faster\"). An example will explain this better.
Suppose you have a 3D array `psi(nr1x,nr2x,nr3x)`. FORTRAN compilers
store this array sequentially in the computer RAM in the following way:

            psi(   1,   1,   1)
            psi(   2,   1,   1)
            ...
            psi(nr1x,   1,   1)
            psi(   1,   2,   1)
            psi(   2,   2,   1)
            ...
            psi(nr1x,   2,   1)
            ...
            ...
            psi(nr1x,nr2x,   1)
            ...
            psi(nr1x,nr2x,nr3x)
    etc

Let `ind` be the position of the `(i,j,k)` element in the above list:
the following relation

            ind = i + (j - 1) * nr1x + (k - 1) *  nr2x * nr1x

holds. This should clarify the relation between 1D and 3D indexing. In
real space, the `(i,j,k)` point of the FFT grid with dimensions `nr1`
($\le$`nr1x`), `nr2` ($\le$`nr2x`), , `nr3` ($\le$`nr3x`), is
$$r_{ijk}=\frac{i-1}{nr1} \tau_1  +  \frac{j-1}{nr2} \tau_2 +
\frac{k-1}{nr3} \tau_3$$ where the $\tau_i$ are the basis vectors of the
Bravais lattice. The latter are stored row-wise in the `at` array:
$\tau_1 =$ `at(:, 1)`, $\tau_2 =$ `at(:, 2)`, $\tau_3 =$ `at(:, 3)`.

The distinction between the dimensions of the FFT grid, `(nr1,nr2,nr3)`
and the physical dimensions of the array, `(nr1x,nr2x,nr3x)` is done
only because it is computationally convenient in some cases that the two
sets are not the same. In particular, it is often convenient to have
`nrx1`=`nr1`+1 to reduce memory conflicts.

Using `CP`
==========

It is important to understand that a CP simulation is a sequence of
different runs, some of them used to \"prepare\" the initial state of
the system, and other performed to collect statistics, or to modify the
state of the system itself, i.e. modify the temperature or the pressure.

To prepare and run a CP simulation you should first of all define the
system:

> atomic positions\
> system cell\
> pseudopotentials\
> cut-offs\
> number of electrons and bands (optional)\
> FFT grids (optional)

An example of input file (Benzene Molecule):

             &control
                title = 'Benzene Molecule',
                calculation = 'cp',
                restart_mode = 'from_scratch',
                ndr = 51,
                ndw = 51,
                nstep = 100,
                iprint = 10,
                isave = 100,
                tstress = .TRUE.,
                tprnfor = .TRUE.,
                dt    = 5.0d0,
                etot_conv_thr = 1.d-9,
                ekin_conv_thr = 1.d-4,
                prefix = 'c6h6',
                pseudo_dir='/scratch/benzene/',
                outdir='/scratch/benzene/Out/'
             /
             &system
                ibrav = 14,
                celldm(1) = 16.0,
                celldm(2) = 1.0,
                celldm(3) = 0.5,
                celldm(4) = 0.0,
                celldm(5) = 0.0,
                celldm(6) = 0.0,
                nat = 12,
                ntyp = 2,
                nbnd = 15,
                ecutwfc = 40.0,
                nr1b= 10, nr2b = 10, nr3b = 10,
                input_dft = 'BLYP'
             /
             &electrons
                emass = 400.d0,
                emass_cutoff = 2.5d0,
                electron_dynamics = 'sd'
             /
             &ions
                ion_dynamics = 'none'
             /
             &cell
                cell_dynamics = 'none',
                press = 0.0d0,
              /
              ATOMIC_SPECIES
              C 12.0d0 c_blyp_gia.pp
              H 1.00d0 h.ps
              ATOMIC_POSITIONS (bohr)
              C     2.6 0.0 0.0
              C     1.3 -1.3 0.0
              C    -1.3 -1.3 0.0
              C    -2.6 0.0 0.0
              C    -1.3 1.3 0.0
              C     1.3 1.3 0.0
              H     4.4 0.0 0.0
              H     2.2 -2.2 0.0
              H    -2.2 -2.2 0.0
              H    -4.4 0.0 0.0
              H    -2.2 2.2 0.0
              H     2.2 2.2 0.0

You can find the description of the input variables in file
`Doc/INPUT_CP.*`.

Reaching the electronic ground state
------------------------------------

The first run, when starting from scratch, is always an electronic
minimization, with fixed ions and cell, to bring the electronic system
on the ground state (GS) relative to the starting atomic configuration.
This step is conceptually very similar to self-consistency in a
`pw.x` run.

Sometimes a single run is not enough to reach the GS. In this case, you
need to re-run the electronic minimization stage. Use the input of the
first run, changing `restart_mode = ’from_scratch’` to
`restart_mode = ’restart’`.

NOTA BENE: Unless you are already experienced with the system you are
studying or with the internals of the code, you will usually need to
tune some input parameters, like `emass`, `dt`, and cut-offs. For this
purpose, a few trial runs could be useful: you can perform short
minimizations (say, 10 steps) changing and adjusting these parameters to
fit your needs. You can specify the degree of convergence with these two
thresholds:

> `etot_conv_thr`: total energy difference between two consecutive
> steps\
> `ekin_conv_thr`: value of the fictitious kinetic energy of the
> electrons.

Usually we consider the system on the GS when `ekin_conv_thr`
$< 10^{-5}$. You could check the value of the fictitious kinetic energy
on the standard output (column EKINC).

Different strategies are available to minimize electrons, but the most
used ones are:

-   steepest descent: `electron_dynamics = ’sd’`

-   damped dynamics: `electron_dynamics = ’damp’`, `electron_damping` =
    a number typically ranging from 0.1 and 0.5

See the input description to compute the optimal damping factor.

Relax the system
----------------

Once your system is in the GS, depending on how you have prepared the
starting atomic configuration:

1.  if you have set the atomic positions \"by hand\" and/or from a
    classical code, check the forces on atoms, and if they are large
    ($\sim 0.1 \div 1.0$ atomic units), you should perform an ionic
    minimization, otherwise the system could break up during the
    dynamics.

2.  if you have taken the positions from a previous run or a previous
    ab-initio simulation, check the forces, and if they are too small
    ($\sim 10^{-4}$ atomic units), this means that atoms are already in
    equilibrium positions and, even if left free, they will not move.
    Then you need to randomize positions a little bit (see below).

Let us consider case 1). There are different strategies to relax the
system, but the most used are again steepest-descent or damped-dynamics
for ions and electrons. You could also mix electronic and ionic
minimization scheme freely, i.e. ions in steepest-descent and electron
in with damped-dynamics or vice versa.

-   suppose we want to perform steepest-descent for ions. Then we should
    specify the following section for ions:

                 &ions
                   ion_dynamics = 'sd'
                 /

    Change also the ionic masses to accelerate the minimization:

                 ATOMIC_SPECIES
                  C 2.0d0 c_blyp_gia.pp
                  H 2.00d0 h.ps

    while leaving other input parameters unchanged. *Note* that if the
    forces are really high ($> 1.0$ atomic units), you should always use
    steepest descent for the first ($\sim 100$ relaxation steps.

-   As the system approaches the equilibrium positions, the steepest
    descent scheme slows down, so is better to switch to damped
    dynamics:

                 &ions
                   ion_dynamics = 'damp',
                   ion_damping = 0.2,
                   ion_velocities = 'zero'
                 /

    A value of `ion_damping` around 0.05 is good for many systems. It is
    also better to specify to restart with zero ionic and electronic
    velocities, since we have changed the masses.

    Change further the ionic masses to accelerate the minimization:

                   ATOMIC_SPECIES
                   C 0.1d0 c_blyp_gia.pp
                   H 0.1d0 h.ps

-   when the system is really close to the equilibrium, the damped
    dynamics slow down too, especially because, since we are moving
    electron and ions together, the ionic forces are not properly
    correct, then it is often better to perform a ionic step every N
    electronic steps, or to move ions only when electron are in their GS
    (within the chosen threshold).

    This can be specified by adding, in the ionic section, the
    `ion_nstepe` parameter, then the &IONS namelist become as follows:

                 &ions
                   ion_dynamics = 'damp',
                   ion_damping = 0.2,
                   ion_velocities = 'zero',
                   ion_nstepe = 10
                 /

    Then we specify in the &CONTROL namelist:

                   etot_conv_thr = 1.d-6,
                   ekin_conv_thr = 1.d-5,
                   forc_conv_thr = 1.d-3

    As a result, the code checks every 10 electronic steps whether the
    electronic system satisfies the two thresholds `etot_conv_thr`,
    `ekin_conv_thr`: if it does, the ions are advanced by one step. The
    process thus continues until the forces become smaller than
    `forc_conv_thr`.

    *Note* that to fully relax the system you need many runs, and
    different strategies, that you should mix and change in order to
    speed-up the convergence. The process is not automatic, but is
    strongly based on experience, and trial and error.

    Remember also that the convergence to the equilibrium positions
    depends on the energy threshold for the electronic GS, in fact
    correct forces (required to move ions toward the minimum) are
    obtained only when electrons are in their GS. Then a small threshold
    on forces could not be satisfied, if you do not require an even
    smaller threshold on total energy.

Let us now move to case 2: randomization of positions.

If you have relaxed the system or if the starting system is already in
the equilibrium positions, then you need to displace ions from the
equilibrium positions, otherwise they will not move in a dynamics
simulation. After the randomization you should bring electrons on the GS
again, in order to start a dynamic with the correct forces and with
electrons in the GS. Then you should switch off the ionic dynamics and
activate the randomization for each species, specifying the amplitude of
the randomization itself. This could be done with the following &IONS
namelist:

              &ions
                ion_dynamics = 'none',
                tranp(1) = .TRUE.,
                tranp(2) = .TRUE.,
                amprp(1) = 0.01
                amprp(2) = 0.01
              /

In this way a random displacement (of max 0.01 a.u.) is added to atoms
of species 1 and 2. All other input parameters could remain the same.
Note that the difference in the total energy (etot) between relaxed and
randomized positions can be used to estimate the temperature that will
be reached by the system. In fact, starting with zero ionic velocities,
all the difference is potential energy, but in a dynamics simulation,
the energy will be equipartitioned between kinetic and potential, then
to estimate the temperature take the difference in energy (de), convert
it in Kelvin, divide for the number of atoms and multiply by 2/3.
Randomization could be useful also while we are relaxing the system,
especially when we suspect that the ions are in a local minimum or in an
energy plateau.

CP dynamics
-----------

At this point after having minimized the electrons, and with ions
displaced from their equilibrium positions, we are ready to start a CP
dynamics. We need to specify `’verlet’` both in ionic and electronic
dynamics. The threshold in control input section will be ignored, like
any parameter related to minimization strategy. The first time we
perform a CP run after a minimization, it is always better to put
velocities equal to zero, unless we have velocities, from a previous
simulation, to specify in the input file. Restore the proper masses for
the ions. In this way we will sample the microcanonical ensemble. The
input section changes as follow:

               &electrons
                  emass = 400.d0,
                  emass_cutoff = 2.5d0,
                  electron_dynamics = 'verlet',
                  electron_velocities = 'zero'
               /
               &ions
                  ion_dynamics = 'verlet',
                  ion_velocities = 'zero'
               /
               ATOMIC_SPECIES
               C 12.0d0 c_blyp_gia.pp
               H 1.00d0 h.ps

If you want to specify the initial velocities for ions, you have to set
`ion_velocities =’from_input’`, and add the ATOMIC\_VELOCITIES card,
after the ATOMIC\_POSITION card, with the list of velocities in atomic
units.

NOTA BENE: in restarting the dynamics after the first CP run, remember
to remove or comment the velocities parameters:

               &electrons
                  emass = 400.d0,
                  emass_cutoff = 2.5d0,
                  electron_dynamics = 'verlet'
                  ! electron_velocities = 'zero'
               /
               &ions
                  ion_dynamics = 'verlet'
                  ! ion_velocities = 'zero'
               /

otherwise you will quench the system interrupting the sampling of the
microcanonical ensemble.

####  Varying the temperature 

It is possible to change the temperature of the system or to sample the
canonical ensemble fixing the average temperature, this is done using
the Nosé thermostat. To activate this thermostat for ions you have to
specify in namelist &IONS:

               &ions
                  ion_dynamics = 'verlet',
                  ion_temperature = 'nose',
                  fnosep = 60.0,
                  tempw = 300.0
               /  

where `fnosep` is the frequency of the thermostat in THz, that should be
chosen to be comparable with the center of the vibrational spectrum of
the system, in order to excite as many vibrational modes as possible.
`tempw` is the desired average temperature in Kelvin.

*Note:* to avoid a strong coupling between the Nosé thermostat and the
system, proceed step by step. Don't switch on the thermostat from a
completely relaxed configuration: adding a random displacement is
strongly recommended. Check which is the average temperature via a few
steps of a microcanonical simulation. Don't increase the temperature too
much. Finally switch on the thermostat. In the case of molecular system,
different modes have to be thermalized: it is better to use a chain of
thermostat or equivalently running different simulations with different
frequencies.

####  Nośe thermostat for electrons 

It is possible to specify also the thermostat for the electrons. This is
usually activated in metals or in systems where we have a transfer of
energy between ionic and electronic degrees of freedom. Beware: the
usage of electronic thermostats is quite delicate. The following
information comes from K. Kudin:

"The main issue is that there is usually some \"natural\" fictitious
kinetic energy that electrons gain from the ionic motion (\"drag\"). One
could easily quantify how much of the fictitious energy comes from this
drag by doing a CP run, then a couple of CG (same as BO) steps, and then
going back to CP. The fictitious electronic energy at the last CP
restart will be purely due to the drag effect."

"The thermostat on electrons will either try to overexcite the otherwise
\"cold\" electrons, or it will try to take them down to an unnaturally
cold state where their fictitious kinetic energy is even below what
would be just due pure drag. Neither of this is good."

"I think the only workable regime with an electronic thermostat is a
mild overexcitation of the electrons, however, to do this one will need
to know rather precisely what is the fictitious kinetic energy due to
the drag."

Advanced usage
--------------

###  Self-interaction Correction 

The self-interaction correction (SIC) included in the `CP` package is
based on the Constrained Local-Spin-Density approach proposed my F.
Mauri and coworkers (M. D'Avezac et al. PRB 71, 205210 (2005)). It was
used for the first time in Quantum ESPRESSO by F. Baletto, C. Cavazzoni
and S.Scandolo (PRL 95, 176801 (2005)).

This approach is a simple and nice way to treat ONE, and only one,
excess charge. It is moreover necessary to check a priori that the
spin-up and spin-down eigenvalues are not too different, for the
corresponding neutral system, working in the Local-Spin-Density
Approximation (setting `nspin = 2`). If these two conditions are
satisfied and you are interest in charged systems, you can apply the
SIC. This approach is a on-the-fly method to correct the
self-interaction with the excess charge with itself.

Briefly, both the Hartree and the XC part have been corrected to avoid
the interaction of the excess charge with itself.

For example, for the Boron atoms, where we have an even number of
electrons (valence electrons = 3), the parameters for working with the
SIC are:

               &system
               nbnd= 2,
               tot_magnetization=1,
               sic_alpha = 1.d0,
               sic_epsilon = 1.0d0,
               sic = 'sic_mac',
               force_pairing = .true.,

The two main parameters are:

> `force_pairing = .true.`, which forces the paired electrons to be the
> same;\
> `sic=’sic_mac’`, which instructs the code to use Mauri's correction.

**Warning**: This approach has known problems for dissociation mechanism
driven by excess electrons.

Comment 1: Two parameters, `sic_alpha` and `sic_epsilon’`, have been
introduced following the suggestion of M. Sprik (ICR(05)) to treat the
radical (OH)-H$_2$O. In any case, a complete ab-initio approach is
followed using `sic_alpha=1`, `sic_epsilon=1`.

Comment 2: When you apply this SIC scheme to a molecule or to an atom,
which are neutral, remember to add the correction to the energy level as
proposed by Landau: in a neutral system, subtracting the
self-interaction, the unpaired electron feels a charged system, even if
using a compensating positive background. For a cubic box, the
correction term due to the Madelung energy is approx. given by
$1.4186/L_{box} - 1.047/(L_{box})^3$, where $L_{box}$ is the linear
dimension of your box (=celldm(1)). The Madelung coefficient is taken
from I. Dabo et al. PRB 77, 115139 (2007). (info by F. Baletto,
francesca.baletto\@kcl.ac.uk)

###  ensemble-DFT 

The ensemble-DFT (eDFT) is a robust method to simulate the metals in the
framework of "ab-initio" molecular dynamics. It was introduced in 1997
by Marzari et al.

The specific subroutines for the eDFT are in `CPV/src/ensemble_dft.f90`
where you define all the quantities of interest. The subroutine
`CPV/src/inner_loop_cold.f90` called by `cg_sub.f90`, control the inner
loop, and so the minimization of the free energy $A$ with respect to the
occupation matrix.

To select a eDFT calculations, the user has to set:

                calculation = 'cp'
                occupations= 'ensemble' 
                tcg = .true.
                passop= 0.3
                maxiter = 250

to use the CG procedure. In the eDFT it is also the outer loop, where
the energy is minimized with respect to the wavefunction keeping fixed
the occupation matrix. While the specific parameters for the inner loop.
Since eDFT was born to treat metals, keep in mind that we want to
describe the broadening of the occupations around the Fermi energy.
Below the new parameters in the electrons list, are listed.

-   `smearing`: used to select the occupation distribution; there are
    two options: Fermi-Dirac smearing='fd', cold-smearing smearing='cs'
    (recommended)

-   `degauss`: is the electronic temperature; it controls the broadening
    of the occupation numbers around the Fermi energy.

-   `ninner`: is the number of iterative cycles in the inner loop, done
    to minimize the free energy $A$ with respect the occupation numbers.
    The typical range is 2-8.

-   `conv_thr`: is the threshold value to stop the search of the
    'minimum' free energy.

-   `niter_cold_restart`: controls the frequency at which a full
    iterative inner cycle is done. It is in the range $1\div$`ninner`.
    It is a trick to speed up the calculation.

-   `lambda_cold`: is the length step along the search line for the best
    value for $A$, when the iterative cycle is not performed. The value
    is close to 0.03, smaller for large and complicated metallic
    systems.

*NOTE:* `degauss` is in Hartree, while in `PWscf`is in Ry (!!!). The
typical range is 0.01-0.02 Ha.

The input for an Al surface is:

                &CONTROL
                 calculation = 'cp',
                 restart_mode = 'from_scratch',
                 nstep  = 10,
                 iprint = 5,
                 isave  = 5,
                 dt    = 125.0d0,
                 prefix = 'Aluminum_surface',
                 pseudo_dir = '~/UPF/',
                 outdir = '/scratch/'
                 ndr=50
                 ndw=51
                /
                &SYSTEM
                 ibrav=  14,
                 celldm(1)= 21.694d0, celldm(2)= 1.00D0, celldm(3)= 2.121D0,
                 celldm(4)= 0.0d0,   celldm(5)= 0.0d0, celldm(6)= 0.0d0,
                 nat= 96,
                 ntyp= 1,
                 nspin=1,
                 ecutwfc= 15,
                 nbnd=160,
                 input_dft = 'pbe'
                 occupations= 'ensemble',
                 smearing='cs',
                 degauss=0.018,
                /
                &ELECTRONS
                 orthogonalization = 'Gram-Schmidt',
                 startingwfc = 'random',
                 ampre = 0.02,
                 tcg = .true.,
                 passop= 0.3,
                 maxiter = 250,
                 emass_cutoff = 3.00,
                 conv_thr=1.d-6
                 n_inner = 2,
                 lambda_cold = 0.03,
                 niter_cold_restart = 2,
                /
                &IONS
                 ion_dynamics  = 'verlet',
                 ion_temperature = 'nose'
                 fnosep = 4.0d0,
                 tempw = 500.d0
                /
                ATOMIC_SPECIES
                 Al 26.89 Al.pbe.UPF

*NOTA1* remember that the time step is to integrate the ionic dynamics,
so you can choose something in the range of 1-5 fs.\
*NOTA2* with eDFT you are simulating metals or systems for which the
occupation number is also fractional, so the number of band, `nbnd`, has
to be chosen such as to have some empty states. As a rule of thumb,
start with an initial occupation number of about 1.6-1.8 (the more bands
you consider, the more the calculation is accurate, but it also takes
longer. The CPU time scales almost linearly with the number of bands.)\
*NOTA3* the parameter `emass_cutoff` is used in the preconditioning and
it has a completely different meaning with respect to plain CP. It
ranges between 4 and 7.

All the other parameters have the same meaning in the usual `CP` input,
and they are discussed above.

### Free-energy surface calculations

Once `CP` is patched with `PLUMED` plug-in, it becomes possible to
turn-on most of the PLUMED functionalities running `CP` as:
`./cp.x -plumed` plus the other usual `CP` arguments. The PLUMED input
file has to be located in the specified `outdir` with the fixed name
`plumed.dat`.

### Treatment of USPPs

The cutoff `ecutrho` defines the resolution on the real space FFT mesh
(as expressed by `nr1`, `nr2` and `nr3`, that the code left on its own
sets automatically). In the USPP case we refer to this mesh as the
\"hard\" mesh, since it is denser than the smooth mesh that is needed to
represent the square of the non-norm-conserving wavefunctions.

On this \"hard\", fine-spaced mesh, you need to determine the size of
the cube that will encompass the largest of the augmentation charges -
this is what `nr1b`, `nr2b`, `nr3b` are. hey are independent of the
system size, but dependent on the size of the augmentation charge (an
atomic property that doesn't vary that much for different systems) and
on the real-space resolution needed by augmentation charges (rule of
thumb: `ecutrho` is between 6 and 12 times `ecutwfc`).

The small boxes should be set as small as possible, but large enough to
contain the core of the largest element in your system. The formula for
estimating the box size is quite simple:

> `nr1b` = $2 R_c / L_x \times$ `nr1`

and the like, where $R_{cut}$ is largest cut-off radius among the
various atom types present in the system, $L_x$ is the physical length
of your box along the $x$ axis. You have to round your result to the
nearest larger integer. In practice, `nr1b` etc. are often in the region
of 20-24-28; testing seems again a necessity.

The core charge is in principle finite only at the core region (as
defined by some $R_{rcut}$ ) and vanishes out side the core. Numerically
the charge is represented in a Fourier series which may give rise to
small charge oscillations outside the core and even to negative charge
density, but only if the cut-off is too low. Having these small boxes
removes the charge oscillations problem (at least outside the box) and
also offers some numerical advantages in going to higher cut-offs.\"
(info by Nicola Marzari)

### Hybrid functional calculations using maximally localized Wannier functions

In this section, we illustrate some guidelines to perform exact exchange
(EXX) calculations using Wannier functions efficiently.

The references for this algorithm are:

-   Theory: X. Wu , A. Selloni, and R. Car, Phys. Rev. B 79, 085102
    (2009).

-   Implementation: H.-Y. Ko, B. Santra, R. A. DiStasio, L. Kong, Z.
    Li, X. Wu, and R. Car, arxiv.

The parallelization scheme in this algorithm is based upon the number of
electronic states. In the current implementation, there are certain
restrictions on the choice of the number of MPI tasks. Also slightly
different algorithms are employed depending on whether the number of MPI
tasks used in the calculation are greater or less than the number of
electronic states. We highly recommend users to follow the notes below.
This algorithm can be used most efficiently if the numbers of electronic
states are uniformly distributed over the number of MPI tasks. For a
system having N electronic states the optimum numbers of MPI tasks
(nproc) are the following:

-   In case of nproc $\leq$ N, the optimum choices are N/m, where m is
    any positive integer.

    -   Robustness: Can be used for odd and even number of electronic
        states.

    -   OpenMP threads: Can be used.

    -   Taskgroup: Only the default value of the task group (-ntg 1) is
        allowed.

-   In case of nproc $>$ N, the optimum choices are N\*m, where m is any
    positive integer.

    -   Robustness: Can be used for even number of electronic states.

    -   Largest value of m: As long as nj\_max (see output) is greater
        than 1, however beyond m=8 the scaling may become poor. The
        scaling should be tested by users.

    -   OpenMP threads: Can be used and highly recommended. We have
        tested number of threads starting from 2 up to 64. More threads
        are also allowed. For very large calculations (nproc $>$ 1000 )
        efficiency can largely depend on the computer architecture and
        the balance between the MPI tasks and the OpenMP threads. User
        should test for an optimal balance. Reasonably good scaling can
        be achieved by using m=6-8 and OpenMP threads=2-16.

    -   Taskgroup: Can be greater than 1 and users should choose the
        largest possible value for ntg. To estimate ntg, find the value
        of nr3x in the output and compute nproc/nr3x and take the
        integer value. We have tested the value of ntg as $2^m$, where m
        is any positive integer. Other values of ntg should be used with
        caution.

    -   Ndiag: Use -ndiag X option in the execution of cp.x. Without
        this option jobs may crash on certain architectures. Set X to
        any perfect square number which is equal to or less than N.

-   DEBUG: The EXX calculations always work when number of MPI tasks =
    number of electronic states. In case of any uncertainty, the EXX
    energy computed using different numbers of MPI tasks can be checked
    by performing test calculations using number of MPI tasks = number
    of electronic states.

An example input is listed as following:

    &CONTROL
      calculation       = 'cp-wf',
      title             = "(H2O)32 Molecule: electron minimization PBE0",
      restart_mode      = "from_scratch",
      pseudo_dir        = './',
      outdir            = './',
      prefix            = "water",
      nstep             = 220,
      iprint            = 100,
      isave             = 100,
      dt                = 4.D0,
      ekin_conv_thr     = 1.D-5,
      etot_conv_thr     = 1.D-5,
    /
    &SYSTEM
      ibrav             = 1,
      celldm(1)         = 18.6655, 
      nat               = 96,
      ntyp              = 2,
      ecutwfc           = 85.D0,
      input_dft         = 'pbe0',
    /
    &ELECTRONS
      emass             = 400.D0,
      emass_cutoff      = 3.D0,
      ortho_eps         = 1.D-8,
      ortho_max         = 300,
      electron_dynamics = "damp",
      electron_damping  = 0.1D0,
    /
    &IONS
      ion_dynamics      = "none", 
    /
    &WANNIER
      nit               = 60,
      calwf             = 3,
      tolw              = 1.D-6,
      nsteps            = 20,
      adapt             = .FALSE.
      wfdt              = 4.D0,
      wf_q              = 500,
      wf_friction       = 0.3D0,
      exx_neigh         = 60,     ! exx related optional
      exx_dis_cutoff    = 8.0D0,  ! exx related optional
      exx_ps_rcut_self  = 6.0D0,  ! exx related optional
      exx_ps_rcut_pair  = 5.0D0,  ! exx related optional
      exx_me_rcut_self  = 9.3D0,  ! exx related optional
      exx_me_rcut_pair  = 7.0D0,  ! exx related optional
      exx_poisson_eps   = 1.D-6,  ! exx related optional
    /
    ATOMIC_SPECIES
    O 16.0D0 O_HSCV_PBE-1.0.UPF
    H  2.0D0 H_HSCV_PBE-1.0.UPF 

Performances
============

`cp.x` can run in principle on any number of processors. The
effectiveness of parallelization is ultimately judged by the "scaling",
i.e. how the time needed to perform a job scales with the number of
processors, and depends upon:

-   the size and type of the system under study;

-   the judicious choice of the various levels of parallelization
    (detailed in
    Sec.[\[SubSec:para\]](#SubSec:para){reference-type="ref"
    reference="SubSec:para"});

-   the availability of fast interprocess communications (or lack of
    it).

Ideally one would like to have linear scaling, i.e. $T \sim T_0/N_p$ for
$N_p$ processors, where $T_0$ is the estimated time for serial
execution. In addition, one would like to have linear scaling of the RAM
per processor: $O_N \sim O_0/N_p$, so that large-memory systems fit into
the RAM of each processor.

As a general rule, image parallelization:

-   may give good scaling, but the slowest image will determine the
    overall performances ("load balancing" may be a problem);

-   requires very little communications (suitable for ethernet
    communications);

-   does not reduce the required memory per processor (unsuitable for
    large-memory jobs).

Parallelization on k-points:

-   guarantees (almost) linear scaling if the number of k-points is a
    multiple of the number of pools;

-   requires little communications (suitable for ethernet
    communications);

-   does not reduce the required memory per processor (unsuitable for
    large-memory jobs).

Parallelization on PWs:

-   yields good to very good scaling, especially if the number of
    processors in a pool is a divisor of $N_3$ and $N_{r3}$ (the
    dimensions along the z-axis of the FFT grids, `nr3` and `nr3s`,
    which coincide for NCPPs);

-   requires heavy communications (suitable for Gigabit ethernet up to
    4, 8 CPUs at most, specialized communication hardware needed for 8
    or more processors );

-   yields almost linear reduction of memory per processor with the
    number of processors in the pool.

A note on scaling: optimal serial performances are achieved when the
data are as much as possible kept into the cache. As a side effect, PW
parallelization may yield superlinear (better than linear) scaling,
thanks to the increase in serial speed coming from the reduction of data
size (making it easier for the machine to keep data in the cache).

VERY IMPORTANT: For each system there is an optimal range of number of
processors on which to run the job. A too large number of processors
will yield performance degradation. If the size of pools is especially
delicate: $N_p$ should not exceed $N_3$ and $N_{r3}$, and should ideally
be no larger than $1/2\div1/4 N_3$ and/or $N_{r3}$. In order to increase
scalability, it is often convenient to further subdivide a pool of
processors into "task groups". When the number of processors exceeds the
number of FFT planes, data can be redistributed to \"task groups\" so
that each group can process several wavefunctions at the same time.

The optimal number of processors for \"linear-algebra\" parallelization,
taking care of multiplication and diagonalization of $M\times M$
matrices, should be determined by observing the performances of
`cdiagh/rdiagh` (`pw.x`) or `ortho` (`cp.x`) for different numbers of
processors in the linear-algebra group (must be a square integer).

Actual parallel performances will also depend on the available software
(MPI libraries) and on the available communication hardware. For PC
clusters, OpenMPI (`http://www.openmpi.org/`) seems to yield better
performances than other implementations (info by Kostantin Kudin). Note
however that you need a decent communication hardware (at least Gigabit
ethernet) in order to have acceptable performances with PW
parallelization. Do not expect good scaling with cheap hardware: PW
calculations are by no means an \"embarrassing parallel\" problem.

Also note that multiprocessor motherboards for Intel Pentium CPUs
typically have just one memory bus for all processors. This dramatically
slows down any code doing massive access to memory (as most codes in the
Quantum ESPRESSO distribution do) that runs on processors of the same
motherboard.
