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1. make a self-consistent calculation for Al using a dense grid of k-points.   The dense grid must contain all k and k+q grid points used in the
   subsequent  electron-phonon calculation and must be dense enough to
produce accurate el-phon coefficients (in particular the double-delta  integral at Ef is very critical).

ÎÊÌâ1£ºµÚÒ»²½¾ÍÉæ¼°qµãºÍkµãÉèÖÃÎÊÌ⣬Àý×ÓÖÐÊÇÉèÖóÉ4 £º2 £º1µÄ¹ØÏµ£¬¼´£º16x16x16, 8x8x8, 4x4x4¡£ÇëÎÊqµãµÄÉèÖÃÒÀ¾ÝÊÇʲô£¿Ò»°ãÓ¦ÉèÖóɶàÉÙºÏÊÊ£¿
        Ê²Ã´ÊÇ the double-delta  integral at Ef £¿

2. make aself-consistent calculation for Al using a grid of k-points   that is suitable for good self-consistency and phonon calculation.This example uses a (888) MP grid.



3.  make the phonon and electron-phonon calculation for the grid of q-points.   Specify elph=.true., and the name of a file where the derivative of the   potential is stored "fildvscf".This example uses a (444) MP grid of   q-points (nq1=4, nq2=4, nq3=4).
   The output contains the results for the el-ph coefficient at each q-point  lambda(q), gamma(q), and the double-delta integral at several values of   the gaussian broadening (set in filePH/elphon.f90). These are useful   for convergence testing.
   (input=al.elph.in,output=al.elph.out)
   The results are also written into outputfiles "a2Fq2r.*", one per value   of the gaussian broadening, for further use.
   
ÎÊÌâ2£ºµÚÈý²½ÖУ¨1£©5.0.2аæÔÚph.x²½ÖèÉèÖà electron_phonon='interpolated',   ÒÔǰµÄÀϰ汾ÊÇÉè³É£ºelph=.true.,ÇëÎÊÁí¸ö²ÎÊýµÄÇø±ðÔÚÄÄÀ
     £¨2£©convergence testingÊÇËãÍêÖ®ºó²âÊÔ£¿   gaussian broadening ¶Ô¼ÆËã½á¹ûÓÐʲôӰÏ죿
4. Bring to r-space both force constants and el-phon coefficients using "q2r.x"   Output in files "a2Fmatdyn.*", one per value of the gaussian broadening
ÎÊÌâ3£ºµÚËIJ½q2r.x£¬ÎªÊ²Ã´Òª×ª»»µ½Êµ¿Õ¼ä£¿ Óëgaussian broadening ÓÐʲô¹ØÏµ£¿ÕâÒ»²½ÊDZØÐëµÄÂð£¿

5.  Calculate gamma  on selected lines using "matdyn.x" (dos=.false.)
ÎÊÌâ4£º ÕâÒ»²½ÊÇÔÚ¼ÆËãÉù×ÓɫɢÇúÏߣ¬ËüÊǼÆËãµçÉùñîºÏ³£Êý±ØÐëµÄ²½ÖèÂð£¿

6.  Calculate  lambda coefficient (in file"lambda" and the a^2F(omega)
   function using "matdyn.x" (dos=.true.)
ÎÊÌâ5£º ÕâÒ»²½¸Ð¾õÊÇÔÚ¼ÆËãÉù×Ó̬Ãܶȣ¬ÇëÎʸò½ÄÜͬʱ¸ø³ö lambda coefficientºÍa^2F(omega)
   function Âð£¿
7.  Calculate lambda coefficient (in "lambda.out"and Tc using "lambda.x"
ÎÊÌâ6£º ¼ÆËãÈÔÔÚ½øÐÐÖУ¬ÇëÎÊÓйý¼ÆËã¾­ÀúµÄͬÈÊ£¬Ð°æÍ¨¹ýÕâÒ»²½¿ÉÒÔÖ±½ÓËã³öTcÂð£¿

        ×ÛÉÏ£¬¸Ð¾õµÚ5²½£¬µÚ6²½Ëƺõ²»ÊǼÆËãµçÉùñîºÏ³£Êý±ØÐëµÄ²½Ö裬²»ÖªÀí½âÊÇ·ñÕýÈ·¡£ ÍêÕûµÄÀý×ÓÎļþÈçÏÂËùʾ£º
     

# #########SCF at dense k-mesh, good enough forelectronic DOS ¡¾¶àÃÜËãÃÜ¡¿ #######

#

cat >al.scf.fit.in << EOF

&control

   calculation='scf'

   restart_mode='from_scratch',

   prefix='al',

   pseudo_dir = '$PSEUDO_DIR/',

   outdir='$TMP_DIR/'

/

&system

   ibrav= 2, celldm(1) =7.5, nat= 1, ntyp= 1,

   ecutwfc =15.0,

   occupations='smearing',smearing='methfessel-paxton', degauss=0.05,

   la2F= .true.,

/

&electrons

   conv_thr =  1.0d-8

   mixing_beta = 0.7

/

ATOMIC_SPECIES

Al 26.98 Al.pz-vbc.UPF

ATOMIC_POSITIONS

Al 0.00 0.00 0.00

K_POINTS{automatic}

16 16 16 0 0 0

EOF

$ECHO "  running the scf calculation with densek-point grid...\c"

$PW_COMMAND  < al.scf.fit.in > al.scf.fit.out





# ########## SCFat k-mesh good enough for phonons¡¾¶àºÃËãºÃ£¡¡¿######

#

cat > al.scf.in<< EOF

&control

   calculation='scf'

   restart_mode='from_scratch',

   prefix='al',

   pseudo_dir = '$PSEUDO_DIR/',

   outdir='$TMP_DIR/'

/

&system

   ibrav= 2, celldm(1) =7.5, nat= 1, ntyp= 1,

   ecutwfc =15.0,

   occupations='smearing',smearing='methfessel-paxton', degauss=0.05

/

&electrons

   conv_thr = 1.0d-8

   mixing_beta = 0.7

/

ATOMIC_SPECIES

Al 26.98 Al.pz-vbc.UPF   ####  Pseudopotential type: NORMCONS



ATOMIC_POSITIONS

Al 0.00 0.00 0.00

K_POINTS{automatic}

8 8 8  00 0

EOF

$ECHO "  running the scf calculation...\c"

$PW_COMMAND <al.scf.in > al.scf.out



#############################

cat >al.elph.in << EOF

Electron-phonon coefficients for Al

&inputph

tr2_ph=1.0d-10,

prefix='al',

fildvscf='aldv',

amass(1)=26.98,

outdir='$TMP_DIR/',

fildyn='al.dyn',

  electron_phonon='interpolated',   #Óëelph=.true.,µÄÇø±ðºÎÔÚ£¿

trans=.true.,

ldisp=.true.

nq1=4, nq2=4, nq3=4

/

EOF

$ECHO "  running the el-ph calculation...\c"

$PH_COMMAND <al.elph.in > al.elph.out





#

#   q2r and matdyn

#

cat > q2r.in<< EOF

&input

zasr='simple',  fildyn='al.dyn', flfrc='Al444.fc', la2F=.true.

/

EOF

$ECHO "  running q2r...\c"

$Q2R_COMMAND < q2r.in > q2r.out

#

###########Éù×ӯףºÉù×ÓɫɢÇúÏß####

cat >matdyn.in.freq << EOF

&input

   asr='simple',  amass(1)=26.98,

   flfrc='Al444.fc', flfrq='Al444.freq', la2F=.true., dos=.false.

/

19

0.000 0.0 0.0     0.0

0.125 0.0 0.0     0.0

0.250 0.0 0.0     0.0

0.375 0.0 0.0     0.0

0.500 0.0 0.0     0.0

0.750 0.0 0.0     0.0

1.000 0.0 0.0     0.0

0.825 0.125 0.125 0.0

0.750 0.250 0.250 0.0

0.625 0.375 0.375 0.0

0.500 0.500 0.500 0.0

0.325 0.325 0.325 0.0

0.250 0.250 0.250 0.0

0.125 0.125 0.125 0.0

0.000 0.000 0.000 0.0

0.125 0.125 0.000 0.0

0.250 0.250 0.000 0.0

0.325 0.325 0.000 0.0

0.500 0.500 0.000 0.0

EOF

$ECHO "  running matdyn for frequencycalculation...\c"

$MATDYN_COMMAND< matdyn.in.freq > matdyn.out.freq

check_failure $?



###########Éù×Ó̬ÃܶȼÆËã####

cat >matdyn.in.dos << EOF

&input

   asr='simple',  amass(1)=26.98,

   flfrc='Al444.fc', flfrq='Al444.freq', la2F=.true., dos=.true.

   fldos='phonon.dos', nk1=10, nk2=10, nk3=10,ndos=50

/

EOF

$ECHO "  running matdyn for a2F(omega) calculation...\c"

$MATDYN_COMMAND< matdyn.in.dos > matdyn.out.dos

check_failure $?

$ECHO "  done"

#

#

############Eliashbergº¯Êýalpha^2 FºÍµçÉùñîºÏ³£Êýlamda¼ÆËã########

cat > lambda.in<< EOF

10  0.12 1    ! emax (something more thanhighest phonon mode in THz), degauss, smearing method

   8         ! Number of q-points for which EPC is calculated,

   0.0000000 0.0000000  0.0000000   1.00 ! the first q-point, use kpoints.x program to calculate

   -0.2500000 -0.2500000  0.2500000  8.00  ! q-points and their weight

   -0.5000000 -0.5000000  0.5000000  4.00  !

    0.0000000 0.0000000  0.5000000   6.00 ! 4th q-point, qx,qy,qz

   -0.2500000 -0.2500000  0.7500000 24.00  !

   -0.5000000 -0.5000000  1.0000000 12.00  !

    0.0000000 0.0000000  1.0000000   3.00 !

   -0.5000000 0.0000000  1.0000000   6.00 ! the last q-point

elph. 0.000000.0.000000. 0.000000 ! elph output file names,

elph.-0.250000.0.250000.-0.250000 ! in the same order as the q-points before  

elph.0.500000.-0.500000. 0.500000

elph. 0.000000.0.500000. 0.000000

elph.0.750000.-0.250000. 0.750000

elph. 0.500000.0.000000. 0.500000

elph.0.000000.-1.000000. 0.000000

elph.-0.500000.-1.000000.0.000000

0.10                     ! \mu the Coloumbcoefficient in the modified

                        ! Allen-Dynes formulafor T_c (via \omega_log)

EOF

$ECHO "  running lambda.x for lambdacalculation...\c"

$LAMBDA_COMMAND< lambda.in > lambda.out
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