The code phcg.x contained in the Gamma/ subdirectory is a specialized 
phonon code, calculating phonon modes only at Gamma (q=0), and using 
only Gamma (k=0) for the sum over the Brillouin Zone. It performs direct
minimization of the energy functional expanded at second order in the
atomic displacements. The code was written having molecular applications 
in mind : Raman and IR spectra calculations in C60 (JCP100, p.8537, 1994) 
and later in models of the GFP chromophore (Chem.Phys. 287/1-2, p.33, 2003).

The (non resonant) Raman cross sections are calculated by finite differences 
of the dielectric tensor with respect to small atomic displacements. This 
method is simple but slow. The Raman calculation using such as second-order
response, as implemented in code ph.x, should be much faster. The calculation
of Raman cross sections in phcg.x was retained for testing purposes, or for
some special cases (high-symmetry molecules for instance). Note that this
feature has not been tested since a long time, so it may not actually work.

Note that:
- the code reads a file produced by pw.x with Gamma point only and
  Gamma-point special tricks (half of the plane waves and so on)
- Ultrasoft PP's are not implemented
- the symmetry is used in a different way wrt all other PWscf codes:
  only inequivalent atoms are displaced. This has an historical reason: 
  C60 has just 3 inequivalent atoms when put into in a cubic cell with 
  standard orientation (the isolated molecule has 1 inequivalent atom)
- the code saves partial and final results in files "restart_e" and 
  "restartph". Specify "recover=.true." in the input data in order to
  restart from saved data.

Input:
  title (a string of characters)
  &inputph [variable1=value1, variable2=value2,...] /
  displacement patterns (optional, see below)

Input variables as in the phonon code:

  outdir
  prefix
  fildyn
  epsil    Note that effective charges are also computed if epsil=.true.,
  trans
  recover
  tr2_ph   Note that Conjugate-Gradient algorithm stops when 
           || A\delta\psi - B || < tr2_ph, where A and B define
           the DFT functional expanded at second order:
           E^{(2)} = (1/2) (\delta\psi A \delta\psi) - B\delta\psi

Variables specific to this code:

  asr      use Acoustic Sum Rule to reduce by 3 the number of phonon
           calculations to be performed (used only if trans=.true.)
  nmodes   use the specified displacement patterns, provided after the
           namelist as nmodes vectors, each with 3*nat components
           (nat=number of atoms); nmodes < 3*nat is allowed (I think). 
           If not set, uses all 3*nat displacement patterns (one atom
           at the time, along x, or y, or z)

Raman-specific variables for this code:

  raman    perform a calculation of Raman cross sections by finite
           differences
  deltatau finite difference (a.u.): typically a small but not too
           small amount, something like 0.01 a.u, or so
  nderiv   type of finite derivative formula: nderiv=2 is a simple
           two-point formula (two calculations per displacement)
            [ f (-deltatau) + f(+deltatau) - 2 f(0) ] / 2/ deltatau^2
           nderiv=4 is a four-point formula (4 calculations/displacement)
  first, last
           calculate raman intensities only for phonon modes from the
           "first" to the "last" (in increasing order of energy, as
           produced by the code after diagonalization of the dynamical
           matrix), using these phonon modes as displacement patterns.
           Requires nderiv*(last-first+1) calculations of the dielectric
           tensor. If not set, first calculate all derivatives of the 
           dielectric tensor wrt atomic displacements (nderiv*3*nat 
           calculations); then, Raman intensities for all phonon modes.

