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<H1><A ID="SECTION00030000000000000000">
2 General structure of <TT>ph.x</TT></A>
</H1>
<P>
The behavior of the <TT>ph.x</TT> code is controlled by a set of flags.
In a general run when all control flags are <TT>.true.</TT> the phonon
code computes the following quantities in the given order:
<P>
<PRE>
frequency q perturbations
polarizability iu gamma x,y,z
dielectric constant 0 gamma x,y,z
zeu 0 gamma x,y,z
electro optic coefficient 0 gamma x,y,x
raman tensor 0 gamma 3 x 3
dynamical matrix 0 all q all irreps
zue 0 gamma all irreps
electron phonon interactions 0 all q all irreps
zeu = Born effective charges as derivative of the forces,
zue = Born effective charges as derivative of the polarization
</PRE>
<P>
Two control flags associated to every calculated quantity
allow to set/unset the calculation of that quantity independently from
the others. One of these flags is an input variable:
<P>
<PRE>
fpol, if .TRUE. computes the frequency dependent polarizability
epsil, if .TRUE. computes the dielectric constant
zeu, if .TRUE. computes eff. charges as induced forces
lraman, if .TRUE. computes the raman tensor
elop, if .TRUE. computes the el-optical coefficient
trans, if .TRUE. computes the dynamical matrix
zue, if .TRUE. computes eff. charges as induced polarization
elph if .TRUE. computes the electron phonon coupling
</PRE>
<P>
By default, only the <TT>trans</TT> flag is <TT>.true.</TT>.
The second flag is described in the following Section.
<P>
The phonon code contains three loops.
The outer loop is over <B>q</B> points. The other two loops are inside the
<B>q</B>-point loop, but they are separate and carried out sequentially.
There is a loop over the frequencies that calculates the frequency
dependent polarizabilities and a loop over the irreducible
representations (<TT>irreps</TT>).
In addition to this there is the calculation of the response to the electric
field. The loop over the frequencies and the response to an electric field are
calculated only if <B>q</B> is the <I>Γ</I> point. The size of the loops over
the frequencies and over <B>q</B> points is controlled by input variables.
<P>
<PRE>
nfs ! number of frequencies
fiu(nfs) ! frequencies in Ry
nq1, nq2, nq3 ! the mesh of q points
or
xq ! the coordinates of a q point
start_q ! initial q to calculate
last_q ! last q to calculate
start_irr ! initial representation to calculate
last_irr ! last representation to calculate
</PRE>
<P>
The run can be controlled also in other two ways by the following input
variables:
<P>
<PRE>
nat_todo ! the number of atoms to move
atomo(nat_todo) ! which atoms to move
or
modenum ! the response to a single mode
</PRE>
The first two options limit the calculation to the representations in which
at least one of a set of atoms (specified by <TT>atomo</TT>) moves.
The second option calculates only the motion with respect to one
vibrational mode.
<P>
The flow of the code can be summarized as follows:
<P>
<PRE>
1) Read input and set the flags of the quantities to compute
1.1) Read all the quantities written by pw.x
1.2) Read the pseudopotential data
2) Decide what must be calculated.
2.1) If not already on disk, compute the grid of q points and
all the modes for all q points and save on disk (SD)
2.2) If image parallelization is requested divide the work among images
3) In a recover run check what is already available on the .xml files and
sets the appropriate done flags to .TRUE.
4) Start a main loop over the q points:
4.1) Compute all quantities that do not depend on the response of the system
4.2) Check if a band calculation is needed and do it.
NB: the following points are executed only when q is Gamma.
4.3) Start a loop on the frequencies
4.3.1) Compute the polarizability as a function of iu SD
4.4) Compute the response to an electric field
4.5) Compute epsilon and SD
4.6) Compute zeu and SD
4.7) Compute the electro-optic coefficient and SD
4.8) Compute the second order response to E
4.9) Compute Raman tensor and SD
END NB
5) Start a loop over the irreducible representation
5.1) Compute the response to an irreducible representation
5.1.1) Accumulate the contribution to electron-phonon SD
5.1.2) Accumulate the contribution to the dynamical matrix
5.1.3) Accumulate the contribution to zue
5.1.4) SD this contribution to the dynamical matrix and to zue
continue the loop 5) until all representations of the current q point
have been computed
6) diagonalize the dynamical matrix and SD (only if all representations of
this q have been computed)
7) Sum over k and bands the electron-phonon couplings to calculate gamma_mat
SD (only if all representations of this q have been computed)
8) continue the loop at point 4 until all q points have been computed
</PRE>
<P>
In more detail the quantities calculated by the phonon code and
the routines where these quantities are calculated are:
<P>
<UL>
<LI>4.2.1) The polarization as a function of the complex frequency is a
<TT>3x3</TT> real tensor for each frequency: <TT>polar(3,3,nfs)</TT>
(calculated in <TT>polariz</TT>). These quantities are presently written
on output.
<P>
</LI>
<LI>4.5) The dielectric constant is a real <TT>3x3</TT> tensor:
<TT>epsilon</TT> (calculated in <TT>dielec</TT>).
<P>
</LI>
<LI>4.6) Zeu is a real array: <TT>zstareu(3,3,nat)</TT>. The first index is
the electric field, while the other two indices give the atom that moves and the
direction.
<P>
</LI>
<LI>The electro-optic tensor is a three indices tensor <TT>eloptns(3,3,3)</TT>
that is calculated by the routine <TT>el_opt</TT>. It requires the response
to the electric field perturbation.
<P>
</LI>
<LI>The raman tensor is a real array <TT>ramtns(3,3,3,nat)</TT> that
gives the derivatives of the dielectric constant when the atom nat moves.
The third index give the direction of the displacement.
It requires the first and the second order response of the wavefunctions
with respect to the electric field perturbation. It is calculated
by the routine <TT>raman_mat</TT>.
<P>
</LI>
<LI>The dynamical matrix is a complex matrix of dimensions
<TT>(3 * nat, 3 * nat)</TT>. It is calculated by three routines:
<TT>dynmat0</TT> computes the part that does not require the linear
response of the system. It has an ion-ion term, a term common to NC, US, and
PAW scheme and the nonlinear core correction term.
The US and PAW schemes have additional parts,
one of them calculated inside <TT>dynmat0</TT> with a call to
<TT>addusdynmat</TT>, and another part calculated in <TT>drho</TT>.
There is then a contribution that requires the response of the
wavefunctions calculated in <TT>drhodv</TT> and <TT>drhodvloc</TT>
which is common to the NC, US, and PAW schemes. The latter two schemes
have other contributions calculated in <TT>drhodvus</TT>. This
routine contains also the additional PAW term.
<P>
</LI>
<LI>5.1.3 Zue is a real array: <TT>zstarue(3,nat,3)</TT>. The first two indices
give the atom that moves and the direction, the third gives the electric
field.
<P>
</LI>
<LI>The electron phonon coefficients are explained in the <TT>PHonon</TT> user guide.
<TT>ph.x</TT> saves on <TT>.xml</TT> files <!-- MATH
$g_{{\bf q},\nu} ({\bf k},i,j)$
-->
<I>g</I><SUB><IMG STYLE="height: 1.05ex; vertical-align: -0.40ex; " SRC="img2.png"
ALT="$\scriptstyle \bf q$">, <I>ν</I></SUB>(<IMG STYLE="height: 1.63ex; vertical-align: -0.10ex; " SRC="img3.png"
ALT="$\bf k$">, <I>i</I>, <I>j</I>)
for all the modes of an irreducible representation. The coefficients are
saved for each <B>k</B> and for all the perturbations. Each irreducible
representation is contained in a different file (see below). Note that
these quantities are gauge dependent, so if you calculate them on
different machines with the GRID parallelization, you can use them only
for gauge invariant quantities. Be very careful with it. (still at an
experimental stage).
<P>
</LI>
</UL>
<P>
All the quantities calculated by the phonon code are saved in the
<TT>fildyn</TT> files with the exception of the
polarization as a function of the complex frequency that is written
on output, and of the electron phonon coefficients. The output of the
code in the latter case is given by the files <TT>a2Fq2r.#.#iq</TT>.
<P>
The charge density response to the electric field perturbations and
to the atomic displacements, or the change of the Kohn and Sham
potential can be saved on disk giving appropriate input variables.
These quantities are saved on disk by <TT>solve_e</TT> and
<TT>solve_linter</TT>.
<P>
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