mirror of https://gitlab.com/QEF/q-e.git
1249 lines
55 KiB
Plaintext
1249 lines
55 KiB
Plaintext
Input data format: { } = optional, [ ] = it depends
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All quantities whose dimensions are not explicitly specified are in
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RYDBERG ATOMIC UNITS
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===============================================================================
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&CONTROL
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...
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/
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&SYSTEM
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...
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/
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&ELECTRONS
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...
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/
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[ &IONS
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...
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/ ]
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[ &CELL
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...
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/ ]
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[ &PHONON
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...
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/ ]
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ATOMIC_SPECIES
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X Mass_X PseudoPot_X
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Y Mass_Y PseudoPot_Y
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Z Mass_Z PseudoPot_Z
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ATOMIC_POSITIONS { alat | bohr | crystal | angstrom }
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in all cases except calculation = 'neb' or 'smd' :
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X 0.0 0.0 0.0 {if_pos(1) if_pos(2) if_pos(3)}
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Y 0.5 0.0 0.0
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Z O.0 0.2 0.2
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if calculation = 'neb' .OR. 'smd' :
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first_image
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X 0.0 0.0 0.0 {if_pos(1) if_pos(2) if_pos(3)}
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Y 0.5 0.0 0.0
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Z O.0 0.2 0.2
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{ intermediate_image 1
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X 0.0 0.0 0.0
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Y 0.9 0.0 0.0
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Z O.0 0.2 0.2
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intermediate_image ...
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X 0.0 0.0 0.0
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Y 0.9 0.0 0.0
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Z O.0 0.2 0.2 }
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last_image
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X 0.0 0.0 0.0
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Y 0.7 0.0 0.0
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Z O.0 0.5 0.2
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K_POINTS { tpiba | automatic | crystal | gamma }
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if (gamma)
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nothing to read
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if (automatic)
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nk1, nk2, nk3, k1, k2, k3
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if (not automatic)
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nks
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xk_x, xk_y, xk_z, wk
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[ CELL_PARAMETERS { cubic | hexagonal }
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a(1,1) a(2,1) a(3,1)
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a(1,2) a(2,2) a(3,2)
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a(1,3) a(2,3) a(3,3) ]
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[ OCCUPATIONS
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f_inp(1,1) f_inp(2,1) f_inp(3,1) ... f_inp(10,1)
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f_inp(11,1) f_inp(12,1) ... f_inp(nbnd,1)
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[ f_inp(1,2) f_inp(2,2) f_inp(3,2) ... f_inp(10,2)
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f_inp(11,2) f_inp(12,2) ... f_inp(nbnd,2) ] ]
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[ CLIMBING_IMAGES
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list of images, separated by a comma ]
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[ CONSTRAINTS
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nconstr constr_tol
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constr_type(.) constr(1,.) constr(2,.) { constr_target(.) } ]
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[ COLLECTIVE_VARS
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nconstr constr_tol
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constr_type(.) constr(1,.) constr(2,.) { constr_target(.) } ]
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===============================================================================
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NAMELIST &CONTROL
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calculation CHARACTER
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a string describing the task to be performed:
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'scf', 'nscf', 'bands', 'phonon', 'relax', 'md',
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'vc-relax', 'vc-md', 'neb', 'smd', 'metadyn'
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(vc = variable-cell). Default: 'scf'
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title CHARACTER
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reprinted on output. Default: ' '
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verbosity CHARACTER
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'high' | 'default' | 'low' | 'minimal'
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restart_mode CHARACTER
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'from_scratch' : from scratch ( default )
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NEB and SMD only: the starting path is obtained
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with a linear interpolation between the images
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specified in the ATOMIC_POSITIONS card.
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Note that in the linear interpolation
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periodic boundary conditions ARE NON USED.
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'restart' : from previous interrupted run
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wf_collect LOGICAL ( default = .FALSE. )
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This flag controls the way wavefunctions are stored to disk :
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.TRUE. collect wavefunctions from all processors and store
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them into the output data directory outdir/prefix.save
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.FALSE. do not collect wavefunctions, leave them in temporary
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local files (one per processor). The resulting format
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will be readable only by jobs running on the same
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number of processors and pools. Useful if you do not
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need the wavefunction or if you want to reduce the I/O
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or the disk occupancy.
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nstep INTEGER
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number of ionic + electronic steps
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default: 1 if calculation = 'scf', 'nscf', 'bands'
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0 if calculation = 'neb', 'smd'
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50 for the other cases
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iprint INTEGER
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band energies are written every iprint iterations
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default: write only at convergence
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tstress LOGICAL
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calculate stress. Set to .TRUE. if calculation='vc-md'
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tprnfor LOGICAL
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print forces. Set to .TRUE. if calculation='relax','md','vc-md'
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dt REAL ( default = 20.D0 )
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time step for molecular dynamics, in Rydberg atomic units
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(1 a.u.=4.8378 * 10^-17 s : beware, CP and FPMD codes use
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Hartree atomic units, half that much!!!)
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outdir CHARACTER ( default = current directory ('./') )
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input, temporary, output files are found in this directory,
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see also 'wfcdir'
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wfcdir CHARACTER ( by default same as outdir )
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this directory specifies where to store files generated by
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each processor (*.wfc{N}, *.igk{N}, etc.). The idea here is
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to be able to separately store the largest files, while
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the files necessary for restarting still go into 'outdir'
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(for now only works for stand alone PW )
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prefix CHARACTER ( default = 'pwscf' )
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prepended to input/output filenames:
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prefix.wfc, prefix.rho, etc.
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max_seconds REAL ( default : 1.D+7, or 150 days, i.e. no time limit )
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jobs stops after max_seconds CPU time
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etot_conv_thr REAL ( default = 1.0D-4 )
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convergence threshold on total energy (a.u) for ionic
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minimization: the convergence criterion is satisfied
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when the total energy changes less than etot_conv_thr
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between two consecutive scf steps.
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See also forc_conv_thr - both criteria must be satisfied
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forc_conv_thr REAL ( default = 1.0D-3 )
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convergence threshold on forces (a.u) for ionic
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minimization: the convergence criterion is satisfied
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when all components of all forces are smaller than
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forc_conv_thr.
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See also etot_conv_thr - both criteria must be satisfied
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disk_io CHARACTER
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'high', 'default', 'low', 'minimal'
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pseudo_dir CHARACTER ( default = '$HOME/pw/pseudo/' )
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directory containing pseudopotential files
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tefield LOGICAL ( default = .FALSE. )
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If .TRUE. a sawlike potential simulating an electric field
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is added to the bare ionic potential. See variables
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edir, eamp, emaxprog, eopreg for the form and size of
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the added potential.
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dipfield LOGICAL ( default = .FALSE. )
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If .TRUE. and tefield=.TRUE. a dipole correction is also
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added to the bare ionic potential - implements the recipe
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of L. Bengtsson, PRB 59, 12303 (1999). See variables edir,
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emaxprog, eopreg for the form of the correction, that must
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be used only in a slab geometry, for surface calculations,
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with the discontinuity in the empty space
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lelfield LOGICAL ( default = .FALSE. )
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If .TRUE. a homogeneous finite electric field described
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through the modern theory of the polarization is applied.
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This is different from "tefield=.true." !
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lberry LOGICAL (default = .FALSE.)
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If .TRUE. perform a Berry phase calculation
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See the header of PW/bp_c_phase.f90 for documentation
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gdir INTEGER
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For Berry phase calculation: direction of the k-point
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strings in reciprocal space. Allowed values: 1, 2, 3
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1=first, 2=second, 3=third reciprocal lattice vector
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For calculations with finite electric fields
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(lelfield==.true.), gdir is the direction of the field
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nppstr INTEGER
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For Berry phase calculation: number of k-points to be
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calculated along each symmetry-reduced string
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The same for calculation with finite electric fields
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(lelfield==.true.)
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nberrycyc INTEGER ( default = 1 )
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In the case of a finite electric field ( lelfield == .TRUE. )
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it defines the number of iterations for converging the
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wavefunctions in the electric field Hamiltonian, for each
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external iteration on the charge density
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===============================================================================
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NAMELIST &SYSTEM
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ibrav INTEGER
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bravais-lattice index (must be specified)
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see at the end of this file
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celldm(i) REAL, DIMENSION(6)
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crystallographic constants - see at the end of this file
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alat = celldm(1) is the lattice parameter "a" (in BOHR)
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only needed celldm (depending on ibrav) must be specified
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a, b, c, cosab, cosac, cosbc:
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REAL
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traditional crystallographic constants (a,b,c in ANGSTROM,
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cosab = cosine of the angle between axis a and b
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specify either these OR celldm but NOT both
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nat INTEGER
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number of atoms in the unit cell - must be specified
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ntyp INTEGER
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number of types of atoms in the unit cell - must be specified
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nbnd INTEGER
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number of electronic states (bands) to be calculated.
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Default: for an insulator, nbnd = (number of valence bands)
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(nbnd=nelec/2, see below for nelec)
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for a metal, 20% more (minimum 4 more)
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Note that in spin-polarized calculations the number of
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k-point, not the number of bands per k-point, is doubled
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nelec REAL
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number of electron in the unit cell
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(may be noninteger if you wish)
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Default: the same as ionic charge (neutral cell)
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A compensating jellium background is inserted
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to remove divergences if the cell is not neutral
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tot_charge INTEGER ( default = 0 )
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total system charge. Used only if nelec is unspecified,
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otherwise it is ignored.
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ecutwfc REAL
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kinetic energy cutoff (Ry) for wavefunctions
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(must be specified)
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ecutrho REAL ( default = 4 * ecutwfc )
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kinetic energy cutoff (Ry) for charge density and potential
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May be larger ( for ultrasoft PP ) or somewhat smaller
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( but not much smaller ) than the default value. Note that
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if you have norm-conserving PP only, setting it to a larger
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value than the default is a waste of time.
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nr1,nr2,nr3 INTEGER
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three-dimensional FFT mesh (hard grid) for charge
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density (and scf potential). If not specified
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the grid is calculated based on the cutoff for
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charge density (see also "ecutrho")
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nr1s,nr2s,nr3s INTEGER
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three-dimensional mesh for wavefunction FFT and for the smooth
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part of charge density ( smooth grid ).
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Coincides with nr1, nr2, nr3 if ecutrho = 4 * ecutwfc ( default )
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nosym LOGICAL ( default = .FALSE. )
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if (.TRUE.) symmetry is not used. Note that a k-point grid
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provided in input is used "as is"; an automatically generated
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k-point grid will contain only points in the irreducible BZ
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of the lattice. Use with care in low-symmetry large cells
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if you cannot afford a k-point grid with the correct symmetry.
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occupations CHARACTER
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'smearing': gaussian smearing for metals
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requires a value for degauss
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'tetrahedra' : for metals and DOS calculation
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(see PRB49, 16223 (1994))
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Requires uniform grid of k-points,
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automatically generated (see below)
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'fixed' : for insulators with a gap
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'from_input' : The occupation are read from input file.
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Presently works only with one k-point
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(LSDA allowed).
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degauss REAL ( default = 0.D0 Ry )
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value of the gaussian spreading (Ry) for brillouin-zone
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integration in metals.
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smearing CHARACTER
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'gaussian', 'gauss':
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ordinary Gaussian spreading (Default)
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'methfessel-paxton', 'm-p', 'mp':
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Methfessel-Paxton first-order spreading
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(see PRB 40, 3616 (1989)).
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'marzari-vanderbilt', 'cold', 'm-v', 'mv':
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Marzari-Vanderbilt cold smearing
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(see PRL 82, 3296 (1999))
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'fermi-dirac', 'f-d', 'fd':
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smearing with Fermi-Dirac function
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nspin INTEGER
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nspin = 1 : non-polarized calculation (default)
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nspin = 2 : spin-polarized calculation, LSDA
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(magnetization along z axis)
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nspin = 4 : spin-polarized calculation, noncollinear
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(magnetization in generic direction)
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DO NOT specify nspin in this case;
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specify "noncolin=.TRUE." instead
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noncolin LOGICAL
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if .true. the program will perform a noncollinear calculation.
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DEFAULT: .false.
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starting_magnetization(i)
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REAL
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starting spin polarization (values between -1 and 1)
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on atomic type 'i' in a spin-polarized calculation.
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Breaks the symmetry and provides a starting point for
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self-consistency. The default value is zero, BUT a value
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MUST be specified for AT LEAST one atomic type in spin
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polarized calculations. Note that if start from zero
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initial magnetization, you will get zero final magnetization
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in any case. If you desire to start from an antiferromagnetic
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state, you may need to define two different atomic species
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corresponding to sublattices of the same atomic type.
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If you fix the magnetization with "nelup/neldw" or with
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"multiplicity" or with "tot_magnetization", you should
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not specify starting_magnetization.
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If you are restarting from a previous run, or from an
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interrupted run, starting_magnetization is ignored.
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nelup, neldw REAL
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number of spin-up and spin-down electrons, respectively
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Note that this fixes the final value of the magnetization.
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The sum must yield nelec that must also be specified
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explicitly in this case. Not valid for spin-unpolarized
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or noncollinear calculations, only for LSDA. Obsolescent:
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use multiplicity or tot_magnetization instead.
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multiplicity INTEGER ( default = 0 [unspecified] )
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spin multiplicity (2s+1). 1 is singlet, 2 for doublet etc.
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Note that this fixes the final value of the magnetization.
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if unspecified or a non-zero value is specified in nelup/neldw
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then multiplicity variable is ignored.
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Do not specify both multiplicity and tot_magnetization.
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tot_magnetization INTEGER ( default = -1 [unspecified] )
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majority spin - minority spin (nelup - neldw).
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if unspecified or a non-zero value is specified in nelup/neldw
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then tot_magnetization variable is ignored.
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Do not specify both multiplicity and tot_magnetization.
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YES, there is redundancy! nelup/neldw are enough to specify
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the spin state. However these variables are not very convenient
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and will be eliminated from the input in future versions.
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It is recommended to use either 'multiplicity' or equivalently
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'tot_magnetization' to specify the spin state.
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ecfixed REAL ( default = 0.0 )
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qcutz REAL ( default = 0.0 )
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q2sigma REAL ( default = 0.1 )
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parameters for modified functional to be used in
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variable-cell molecular dynamics (or in stress calculation).
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"ecfixed" is the value (in Rydberg) of the constant-cutoff;
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"qcutz" and "q2sigma" are the height and the width (in Rydberg)
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of the energy step for reciprocal vectors whose square modulus
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is greater than "ecfixed". In the kinetic energy, G^2 is
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replaced by G^2 + qcutz * (1 + erf ( (G^2 - ecfixed)/q2sigma) )
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See: M. Bernasconi et al, J. Phys. Chem. Solids 56, 501 (1995)
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xc_type CHARACTER
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Exchange-correlation functional
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Presently unused: XC functional is read from PP files
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lda_plus_u LOGICAL ( default = .FALSE.)
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Hubbard_U(I) REAL ( default = 0.D0 for all species)
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Hubbard_alpha(I) REAL ( default = 0.D0 for all species)
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parameters for LDA+U calculations
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If lda_plus_u = .TRUE. you must specify, for species I,
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the parameters U and (optionally) alpha of the Hubbard
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model (both in eV). See:
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Anisimov, Zaanen, and Andersen, PRB 44, 943 (1991);
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Anisimov et al., PRB 48, 16929 (1993);
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Liechtenstein, Anisimov, and Zaanen, PRB 52, R5467 (1994);
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Cococcioni and de Gironcoli, PRB 71, 035105 (2005).
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IMPORTANT: LDA+U works only for a few selected elements.
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Modify PW/set_hubbard_l.f90 and PW/tabd.f90 if you plan to
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use LDA+U with an element that is not configured there.
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starting_ns_eigenvalue(m,ispin,I) REAL (default = -1.d0 that means NOT SET)
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In the first iteration of an LDA+U run it overwrites
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the m-th eigenvalue of the ns occupation matrix for the
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ispin component of atomic species I. Leave unchanged
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eigenvalues that are not set. This is useful to suggest
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the desired orbital occupations when the default choice
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takes another path.
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U_projection_type CHARACTER (default='atomic')
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Only active when lda_plus_U is .true., specifies the type
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of projector on localized orbital to be used in the LDA+U
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scheme.
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Currently available choices:
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'atomic': use atomic wfc's (as they are) to build the projector
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'ortho-atomic': use Lowdin orthogonalized atomic wfc's
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'file': use the information from file "prefix".atwfc that must
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have been generated previously, for instance by pmw.x
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(see PP/poormanwannier.f90 for details)
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NB: forces and stress currently implemented only for the
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'atomic' choice.
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edir INTEGER
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The direction of the electric field or dipole correction is
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parallel to the bg(:,edir) reciprocal lattice vector, so the
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potential is constant in planes defined by FFT grid points;
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edir = 1, 2 or 3. Used only if tefield is .TRUE.
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emaxpos REAL ( default = 0.5D0 )
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Position of the maximum of the sawlike potential along crystal
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axis "edir", within the unit cell (see below), 0 < emaxpos < 1
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Used only if tefield is .TRUE.
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eopreg REAL( default = 0.1D0 )
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Zone in the unit cell where the sawlike potential decreases.
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( see below, 0 < eopreg < 1 ). Used only if tefield is .TRUE.
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eamp REAL ( default = 0.001 a.u. )
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Amplitude of the electric field (in a.u. = 51.44 10^10 V/m )
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The sawlike potential increases with slope "eamp" in the
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region from (emaxpos+eopreg-1) to (emaxpos), then decreases
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to 0 until (emaxpos+eopreg), in units of the crystal
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vector "edir". Used only if tefield is .TRUE.
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angle1(i) REAL
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The angle expressed in degrees between the initial
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magnetization and the z-axis. For noncollinear calculations
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only. I runs over the atom types.
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angle2(i) REAL
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The angle expressed in degrees between the projection
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of the initial magnetization on x-y plane and the x-axis.
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For noncollinear calculations only.
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constrained_magnetization CHARACTER ( defalt = 'none' )
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Used to perform constrained calculations in magnetic systems
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Currently available choices:
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`none` : no constraint
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`total`: total magnetization is constrained
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If nspin=4 (noncolin=.True.) constraint is imposed by
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adding a penalty functional to the total energy:
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- LAMBDA * SUM_{i} ( magnetization(i) - fixed_magnetization(i) )**2
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where the sum over i runs over the three components of
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the magnetization. Lambda is a real number (see below).
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If nspin=2 constraint is imposed by defining two Fermi
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energies for spin up and down.
|
|
Only fixed_magnetization(3) can be defined in this case.
|
|
`atomic`: atomic magnetization are constrained to the defined
|
|
starting magnetization adding a penalty
|
|
- LAMBDA * SUM_{i,itype} ( magnetic_moment(i,itype) - mcons(i,itype) )**2
|
|
where i runs over the components (1-3) and itype over
|
|
the types (1-ntype).
|
|
mcons(:,:) array is defined from starting_magnetization,
|
|
angle1 and angle2 variables. lambda is a real number
|
|
`atomic direction`: not all the components of the atomic
|
|
magnetic moment are constrained but only the cosine
|
|
of angle1, and the penalty functional is:
|
|
- LAMBDA * SUM_{itype} ( mag_mom(3,itype)/mag_mom_tot - cos(angle1(ityp) )**2
|
|
|
|
fixed_magnetization(3) REAL (default 0.d0)
|
|
value of the total magnetization to be maintained fixed when
|
|
constrained_magnetization='total'
|
|
|
|
B_field(3) REAL (default = 0.d0)
|
|
A fixed magnetic field defined by the vector B_field is added
|
|
to the exchange and correlation magnetic field.
|
|
The three components of the magnetic field are given in Ry.
|
|
Only B_field(3) can be used if nspin=2.
|
|
|
|
In all calculations with a finite magnetic field,
|
|
we print the total energy WITHOUT the B dot M term.
|
|
In the calculations with the penalty functional we write
|
|
only the total energy, NOT the penalty functional.
|
|
|
|
lambda REAL
|
|
parameter used for constrained_magnetization calculations
|
|
NB: LAMBDA is reduced in the first iterations and is increased
|
|
slowly up to the input value.
|
|
|
|
report INTEGER
|
|
It's the number of iterations after which the program
|
|
write all the atomic magnetic moments.
|
|
|
|
lspinorb LOGICAL
|
|
if .TRUE. the noncollinear code can use a pseudopotential with
|
|
spin-orbit.
|
|
|
|
===============================================================================
|
|
NAMELIST &ELECTRONS
|
|
|
|
electron_maxstep
|
|
INTEGER ( default = 100 )
|
|
maximum number of iterations in a scf step
|
|
|
|
conv_thr REAL ( default = 1.D-6 )
|
|
Convergence threshold for selfconsistency:
|
|
estimated energy error < conv_thr
|
|
|
|
mixing_mode CHARACTER
|
|
'plain' : charge density Broyden mixing ( default )
|
|
'TF' : as above, with simple Thomas-Fermi screening
|
|
(for highly homogeneous systems)
|
|
'local-TF': as above, with local-density-dependent TF screening
|
|
(for highly inhomogeneous systems)
|
|
|
|
mixing_beta REAL ( default = 0.7D0 )
|
|
mixing factor for self-consistency
|
|
|
|
mixing_ndim INTEGER ( default = 8)
|
|
number of iterations used in mixing scheme
|
|
|
|
mixing_fixed_ns
|
|
INTEGER ( default = 0 )
|
|
For LDA+U : number of iterations with fixed ns ( ns is the
|
|
atomic density appearing in the Hubbard term )
|
|
|
|
diagonalization
|
|
CHARACTER
|
|
'david': Davidson iterative diagonalization with overlap matrix
|
|
(default)
|
|
'cg' : conjugate-gradient-like band-by-band diagonalization
|
|
'diis' : DIIS-like diagonalization - PRESENTLY DISABLED
|
|
|
|
diago_thr_init
|
|
REAL
|
|
Convergence threshold for the first iterative diagonalization
|
|
(the check is on eigenvalue convergence).
|
|
For scf calculations, the default is 1.D-2 if starting from a
|
|
superposition of atomic orbitals; 1.D-5 if starting from a
|
|
charge density. During self consistency the threshold (ethr)
|
|
is automatically reduced when approaching convergence.
|
|
For non-scf calculations, this is the threshold used in the
|
|
iterative diagonalization. The default is conv_thr / nelec.
|
|
For 'phonon' calculations, diago_thr_init is ignored:
|
|
the threshold is always set to conv_thr / nelec .
|
|
|
|
diago_cg_maxiter
|
|
INTEGER
|
|
For conjugate gradient diagonalization:
|
|
max number of iterations
|
|
|
|
diago_david_ndim
|
|
INTEGER ( default = 4 )
|
|
For Davidson diagonalization: dimension of workspace
|
|
(number of wavefunction packets, at least 2 needed).
|
|
A larger value may yield a faster algorithm but uses
|
|
more memory
|
|
|
|
diago_diis_ndim
|
|
INTEGER ( default = 3 )
|
|
For DIIS: dimension of the reduced space.
|
|
|
|
diago_full_acc
|
|
LOGICAL ( default = .FALSE. )
|
|
If .TRUE. all the empty states are diagonalized at the same level
|
|
of accuracy of the occupied ones. Otherwise the empty states are
|
|
diagonalized using a larger threshold (this should not affect
|
|
total energy, forces, and other ground-state properties).
|
|
|
|
efield REAL ( default = 0.D0 )
|
|
For finite electric field calculations (lelfield == .TRUE.),
|
|
it defines the intensity of the field in a.u.
|
|
|
|
startingpot CHARACTER
|
|
'atomic': starting potential from atomic charge superposition
|
|
( default for scf, *relax, *md, neb, smd )
|
|
'file' : start from existing "prefix".pot file
|
|
( default, only possibility for nscf, bands, phonon )
|
|
|
|
startingwfc CHARACTER
|
|
'atomic': start from superposition of atomic orbitals ( default )
|
|
If not enough atomic orbitals are available,
|
|
fill with random numbers the remaining wfcs
|
|
'random': start from random wfcs
|
|
'file': start from a wavefunction file
|
|
|
|
|
|
===============================================================================
|
|
NAMELIST &IONS ( only if calculation = 'relax', 'md',
|
|
'vc-relax', 'vc-md', 'neb', 'smd' )
|
|
|
|
ion_dynamics CHARACTER
|
|
specify the type of ionic dynamics.
|
|
For constrained dynamics or constrained optimisations add the
|
|
CONSTRAINTS card (when the card is present the SHAKE algorithm is
|
|
automatically used).
|
|
For different type of calculation different possibilities are
|
|
allowed and different default values apply:
|
|
|
|
CASE ( calculation = 'relax' )
|
|
'bfgs' : (default) a new BFGS quasi-newton algorithm, based
|
|
on the trust radius procedure, is used
|
|
for structural relaxation (experimental)
|
|
'damp' : use damped (quick-min Verlet)
|
|
dynamics for structural relaxation
|
|
CASE ( calculation = 'md' )
|
|
'verlet' : (default) use Verlet algorithm to integrate
|
|
Newton's equation
|
|
CASE ( calculation = 'vc-relax' )
|
|
'damp' : (default) use damped (Beeman) dynamics for
|
|
structural relaxation
|
|
CASE ( calculation = 'vc-md' )
|
|
'beeman' : (default) use Beeman algorithm to integrate
|
|
Newton's equation
|
|
|
|
phase_space CHARACTER ( defauld = 'full' )
|
|
'full' : the full phase-space is used for the ionic
|
|
dynamics.
|
|
'coarse-grained' : a coarse-grained phase-space, defined by a set
|
|
of constraints, is used for the ionic dynamics
|
|
(used for calculation of free-energy barriers)
|
|
|
|
pot_extrapolation
|
|
CHARACTER ( default = "atomic" )
|
|
used to extrapolate the potential from preceding ionic steps
|
|
'none' : no extrapolation
|
|
'atomic' : extrapolate the potential as if it was a sum of
|
|
atomic-like orbitals
|
|
'first_order' : extrapolate the potential with first-order
|
|
formula
|
|
'second_order': as above, with second order formula
|
|
|
|
wfc_extrapolation
|
|
CHARACTER ( default = "none" )
|
|
used to extrapolate the wavefunctions from preceding ionic steps
|
|
'none' : no extrapolation
|
|
'first_order' : extrapolate the wave-functions with first-order
|
|
formula
|
|
'second_order': as above, with second order formula
|
|
|
|
remove_rigid_rot
|
|
LOGICAL ( default = .FALSE. )
|
|
this keyword is useful when simulating the dynamics and/or the
|
|
thermodynamics of an isolated system. If set to true the total
|
|
torque of the internal forces is set to zero by adding new forces
|
|
that compensate the spurious interaction with the periodic
|
|
images. This allowes for the use of smaller supercells.
|
|
BEWARE: since the potential energy is no longer consistent with
|
|
the forces (it still contains the spurious interaction with the
|
|
repeated images), the total energy is not conserved anymore.
|
|
However the dynamical and thermodynamical properties should be
|
|
in closer agreement with those of an isolated system.
|
|
Also the final energy of a structural relaxation will be higher,
|
|
but the relaxation itself should be faster.
|
|
|
|
!
|
|
! ... keywords used for moleculer dynamics
|
|
!
|
|
|
|
ion_temperature
|
|
CHARACTER
|
|
'rescaling' : velocity rescaling
|
|
'langevin' : ion dynamics is over-damped Langevin
|
|
'not_controlled': default
|
|
|
|
tempw REAL ( default = 300.D0 )
|
|
starting temperature (Kelvin) in MD runs
|
|
|
|
tolp REAL ( default = 1.D-3 )
|
|
tolerance for velocity rescaling. Velocities are not rescaled
|
|
if the ratio of the run-averaged and target temperature differs
|
|
from unit less than tolp.
|
|
This keyword is used only in the case of variable cell
|
|
calculations.
|
|
|
|
delta_t REAL ( default = 1.D0 )
|
|
delta_t = 1 : every 'nraise' step the actual
|
|
temperature is rescaled to tempw
|
|
delta_t /= 1 && delta_T > 0 : at each step the temperature is
|
|
multiplied by delta_t; this is
|
|
done rescaling all the velocities.
|
|
delta_t < 0 : every 'nraise' steps temperature
|
|
is reduced by -delta_T
|
|
This keyword is NOT used in the case of variable cell
|
|
calculations.
|
|
|
|
nraise INTEGER ( default = 100 )
|
|
the temperature is reduced of -delta_T every 'nraise' steps.
|
|
This keyword is NOT used in the case of variable cell
|
|
calculations.
|
|
|
|
refold_pos LOGICAL ( default = .FALSE. )
|
|
this keyword applies only in the case of molecular dynamics or
|
|
damped dynamics. If true the ions are refolded at each step into
|
|
the supercell.
|
|
|
|
!
|
|
! ... keywords used only in BFGS calculations
|
|
!
|
|
|
|
upscale REAL ( default = 10.D0 )
|
|
max reduction factor for conv_thr during structural optimization
|
|
conv_thr is automatically reduced when the relaxation
|
|
approaches convergence so that forces are still accurate,
|
|
but conv_thr will not be reduced to less that
|
|
conv_thr / upscale
|
|
|
|
bfgs_ndim INTEGER ( default = 1 )
|
|
number of old forces and displacements vectors used in the
|
|
PULAY mixing of the residual vectors obtained on the basis
|
|
of the inverse hessian matrix given by the BFGS algorithm.
|
|
When bfgs_ndim = 1, the standard quasi-Newton BFGS method is
|
|
used.
|
|
(bfgs only)
|
|
|
|
trust_radius_max
|
|
REAL ( default = 0.8D0 )
|
|
maximum ionic displacement in the structural relaxation
|
|
(bfgs only)
|
|
|
|
trust_radius_min
|
|
REAL ( default = 1.D-3 )
|
|
minimum ionic displacement in the structural relaxation
|
|
BFGS is reset when trust_radius < trust_radius_min
|
|
(bfgs only)
|
|
|
|
trust_radius_ini
|
|
REAL ( default = 0.5D0 )
|
|
initial ionic displacement in the structural relaxation
|
|
(bfgs only)
|
|
|
|
w_1, w_2
|
|
REAL ( w_1 = 0.01D0, w_2 = 0.5D0 )
|
|
parameters used in line search based on the Wolfe conditions
|
|
(bfgs only)
|
|
|
|
!
|
|
! ... keywords used only in NEB and SMD calculations
|
|
!
|
|
|
|
num_of_images INTEGER ( default = 0 )
|
|
number of points used to discretize the path
|
|
(it must be larger than 3)
|
|
|
|
opt_scheme
|
|
CHARACTER ( default = "quick-min" )
|
|
specify the type of optimization scheme
|
|
"sd" : steepest descent
|
|
"broyden" : quasi-Newton Broyden's second method (suggested)
|
|
"quick-min" : an optimisation algorithm based on the
|
|
projected velovity Verlet scheme
|
|
"langevin" : finite temperature langevin dynamics of the
|
|
string (smd only). It is used to compute the
|
|
average path and the free-energy profile.
|
|
|
|
CI_scheme CHARACTER. ( default = "no-CI" )
|
|
specify the type of Climbing Image scheme
|
|
"no-CI" : climbing image is not used
|
|
"auto" : original CI scheme. The image highest in energy
|
|
does not feel the effect of springs and is
|
|
allowed to climb along the path
|
|
"manual" : images that have to climb are manually selected.
|
|
See also CLIMBING_IMAGES card
|
|
|
|
first_last_opt LOGICAL ( default = .FALSE. )
|
|
also the first and the last configurations are optimised
|
|
"on the fly" (these images do not feel the effect of the springs)
|
|
|
|
temp_req REAL ( default = 0.D0 Kelvin )
|
|
temperature used for the langevin dynamics of the string.
|
|
|
|
ds REAL ( default = 1.D0 )
|
|
optimisation step length ( Hartree atomic units ).
|
|
If opt_scheme="broyden", ds is used as a guess for the diagonal
|
|
part of the Jacobian matrix.
|
|
|
|
k_max, k_min REAL ( default = 0.1D0 Hartree atomic units )
|
|
set them to use a Variable Elastic Constants scheme
|
|
elastic constants are in the range [ k_min, k_max ]
|
|
this is useful to rise the resolution around the saddle point
|
|
|
|
path_thr REAL ( default = 0.05D0 eV / Angstrom )
|
|
the simulation stops when the error ( the norm of the force
|
|
orthogonal to the path in eV/A ) is less than path_thr.
|
|
|
|
use_masses LOGICAL ( default = .FALSE. )
|
|
If. TRUE. the optimisation of the path is performed using
|
|
mass-weighted coordinates.
|
|
|
|
use_freezing LOGICAL ( default = .FALSE. )
|
|
If. TRUE. the images are optimised according to their error:
|
|
only those images with an error larger than half of the largest
|
|
are optimised. The other images are kept frozen.
|
|
|
|
write_save LOGICAL ( default = .FALSE. )
|
|
used to write the prefix.save file for each image ( needed for
|
|
post-processing )
|
|
|
|
!
|
|
! ... keywords used only in meta-dynamics calculations ( see also the card
|
|
! ... COLLECTIVE_VARS )
|
|
!
|
|
|
|
fe_step(i) REAL ( default = 0.04 )
|
|
meta-dynamics step length (in principle different for each
|
|
collective variable), defined using the same units used
|
|
to define the collective variables themselves.
|
|
The step also defines the spread of the Gaussian-like bias
|
|
potential.
|
|
|
|
g_amplitude REAL ( default = 0.005 Hartree )
|
|
Amplitude of the gaussians used in meta-dynamics.
|
|
|
|
fe_nstep INTEGER ( default = 100 )
|
|
Maximum number of steps used to evaluate the potential of
|
|
mean force.
|
|
|
|
shake_nstep INTEGER ( default = 10 )
|
|
Number of steps used to switch to the new values of the
|
|
collective variables.
|
|
|
|
===============================================================================
|
|
NAMELIST &CELL ( only if calculation = 'vc-relax', 'vc-md' )
|
|
|
|
cell_dynamics
|
|
CHARACTER
|
|
specify the type of dynamics for the cell.
|
|
For different type of calculation different possibilities
|
|
are allowed and different default values apply:
|
|
|
|
CASE ( calculation = 'vc-relax' )
|
|
'none': default
|
|
'sd': steepest descent ( not implemented )
|
|
'damp-pr': damped (Beeman) dynamics of the Parrinello-Rahman
|
|
extended lagrangian
|
|
'damp-w': damped (Beeman) dynamics of the new Wentzcovitch
|
|
extended lagrangian
|
|
CASE ( calculation = 'vc-md' )
|
|
'none': default
|
|
'pr': (Beeman) molecular dynamics of the Parrinello-Rahman
|
|
extended lagrangian
|
|
'w': (Beeman) molecular dynamics of the new Wentzcovitch
|
|
extended lagrangian
|
|
|
|
press REAL ( default = 0.D0 )
|
|
target pressure [KBar] in a variable-cell md or relaxation run.
|
|
|
|
wmass REAL ( default = sum of atomic masses in the cell )
|
|
fictitious cell mass [amu] for variable-cell simulations
|
|
(both 'vc-md' and 'vc-relax')
|
|
|
|
cell_factor REAL ( default = 1.2D0 )
|
|
used in the construction of the pseudopotential tables.
|
|
It should exceed the maximum linear contraction of the
|
|
cell during a simulation.
|
|
|
|
press_cov_thr REAL ( default = 0.5D0 Kbar )
|
|
convergence threshold on the pressure for variable cell
|
|
relaxation ('vc-relax' : note that the other convergence
|
|
thresholds for ionic relaxation apply as well).
|
|
|
|
===============================================================================
|
|
&PHONON ( only in calculation = 'phonon' )
|
|
|
|
modenum INTEGER ( default = 0 )
|
|
for single-mode phonon calculation
|
|
|
|
xqq(3) REAL
|
|
q-point (units 2pi/a) for phonon calculation
|
|
|
|
|
|
===============================================================================
|
|
CARDS: { } = optional
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
ATOMIC_SPECIES
|
|
|
|
Syntax:
|
|
|
|
ATOMIC_SPECIES
|
|
X(1) Mass_X(1) PseudoPot_X(ntyp)
|
|
X(2) Mass_X(2) PseudoPot_X(ntyp)
|
|
...
|
|
X(ntyp) Mass_X(ntyp) PseudoPot_X(ntyp)
|
|
|
|
Description:
|
|
X CHARACTER : label of the atom
|
|
Mass_X REAL : mass of the atomic species [amu: mass of C = 12]
|
|
not used if calculation='scf','nscf', 'bands', 'phonon'
|
|
PseudoPot_X CHARACTER: file containing PP for this species
|
|
|
|
The pseudopotential file is assumed to be in the new UPF format.
|
|
If it doesn't work, the pseudopotential format is determined by
|
|
the file name:
|
|
*.vdb or *.van Vanderbilt US pseudopotential code
|
|
*.RRKJ3 Andrea Dal Corso's code (old format)
|
|
none of the above old PWscf norm-conserving format
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
ATOMIC_POSITIONS { alat | bohr | crystal | angstrom }
|
|
|
|
alat : atomic positions are in units of alat (default)
|
|
bohr : atomic positions are in a.u.
|
|
crystal : atomic positions are in crystal coordinates (see below)
|
|
angstrom: atomic positions are in A
|
|
|
|
- in all cases EXCEPT calculation = 'neb' or 'smd' :
|
|
|
|
There are "nat" cards like the following
|
|
X x y z {if_pos(1) if_pos(2) if_pos(3)}
|
|
where :
|
|
X Character: label of the atom as specified in ATOMIC_SPECIES
|
|
x, y, z Real: atomic positions
|
|
if_pos: Integer, optional ( default = 1 ): component i of the force for
|
|
this atom is multiplied by if_pos(i), which must be either 0 or 1.
|
|
Used to keep selected atoms and/or selected components fixed in
|
|
meta-dynamics, neb, smd, MD dynamics or structural optimization
|
|
run.
|
|
|
|
- if calculation = 'neb' .OR. 'smd'
|
|
|
|
There are at least two groups of cards, each group composed by an identifier
|
|
followed by "nat" cards as specified above:
|
|
identifier
|
|
X x y z {if_pos(1) if_pos(2) if_pos(3)}
|
|
The first group ( identifier="first_image" ) contains the first image,
|
|
the last group ( identifier="last_image" ) contains the last image.
|
|
There is also the possibility of specifying intermediate images; in this case
|
|
their coordinates must be set between the first_image and the last_image.
|
|
( identifier="intermediate_image", followed by "nat" position cards ).
|
|
|
|
Image configurations must be specified in the following order:
|
|
|
|
first_image <= mandatory
|
|
X 0.0 0.0 0.0 { if_pos(1) if_pos(2) if_pos(3) }
|
|
Y 0.5 0.0 0.0 { if_pos(1) if_pos(2) if_pos(3) }
|
|
Z 0.0 0.2 0.2 { if_pos(1) if_pos(2) if_pos(3) }
|
|
intermediate_image 1 <= optional
|
|
X 0.0 0.0 0.0
|
|
Y 0.9 0.0 0.0
|
|
Z 0.0 0.2 0.2
|
|
intermediate_image ... <= optional
|
|
X 0.0 0.0 0.0
|
|
Y 0.9 0.0 0.0
|
|
Z 0.0 0.2 0.2
|
|
last_image <= mandatory
|
|
X 0.0 0.0 0.0
|
|
Y 0.7 0.0 0.0
|
|
Z 0.0 0.5 0.2
|
|
|
|
IMPORTANT: the total number of configurations specified in the input file
|
|
must be less than num_of_images (as specified in &IONS).
|
|
The initial path is obtained interpolating between the specified
|
|
configurations so that all images are equispaced (only the
|
|
coordinates of the first and last images are not changed).
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
K_POINTS { tpiba | automatic | crystal | gamma }
|
|
|
|
gamma : use k = 0 ( do not read anything after this card )
|
|
Note that a set of subroutines optimized for calculations
|
|
at the gamma point are used so that both memory and cpu
|
|
requirements are reduced
|
|
automatic: automatically generated uniform grid of k-points
|
|
next card:
|
|
nk1, nk2, nk3, k1, k2, k3
|
|
generates ( nk1, nk2, nk3 ) grid with ( k1, k2, k3 ) offset
|
|
nk1, nk2, nk3 as in Monkhorst-Pack grids
|
|
k1, k2, k3 must be 0 ( no offset ) or 1 ( grid displaced
|
|
by half a grid step in the corresponding direction )
|
|
BEWARE: only grids having the full symmetry of the crystal
|
|
work with tetrahedra. Some grids with offset may not work.
|
|
crystal : read k-points in crystal coordinates
|
|
tpiba : read k-points in 2pi/a units ( default )
|
|
next card:
|
|
nks
|
|
number of supplied special points
|
|
xk_x, xk_y, xk_z, wk
|
|
special points in the irreducible Brillouin Zone
|
|
of the lattice (with all symmetries) and weights
|
|
(see the literature for lists of special points and
|
|
the corresponding weights)
|
|
If the symmetry is lower than the full symmetry
|
|
of the lattice, additional points with appropriate
|
|
weights are generated.
|
|
In a non-scf calculation, weights do not affect the results.
|
|
If you just need eigenvalues and eigenvectors (for instance,
|
|
for a band-structure plot), weights can be set to any value
|
|
(for instance all equal to 1)
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
CELL_PARAMETERS
|
|
|
|
optional card, needed only if ibrav = 0 is specified
|
|
|
|
Syntax:
|
|
|
|
CELL_PARAMETERS
|
|
a(1,1) a(2,1) a(3,1)
|
|
a(1,2) a(2,2) a(3,2)
|
|
a(1,3) a(2,3) a(3,3)
|
|
|
|
a(:,1) = crystal axis 1 alat units if celldm(1) was specified
|
|
2 2 a.u. if celldm(1)=0
|
|
3 3
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
CLIMBING_IMAGES
|
|
|
|
optional card, needed only if calculation = 'neb' and CI_scheme = 'manual'
|
|
|
|
Syntax:
|
|
|
|
CLIMBING_IMAGES
|
|
index1, index2, ..., indexN
|
|
|
|
where index1, index2, ..., indexN are the indices of the images to which
|
|
apply the Climbing Image procedure. If more than an image is specified they
|
|
must be separated by a comma
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
CONSTRAINTS
|
|
|
|
Ionic Constraints
|
|
|
|
Syntax:
|
|
|
|
CONSTRAINTS
|
|
nconstr { constr_tol }
|
|
constr_type(.) constr(1,.) constr(2,.) ... { constr_target(.) }
|
|
|
|
Where:
|
|
|
|
nconstr INTEGER, number of constraints
|
|
constr_tol REAL, tolerance for keeping the constraints satisfied
|
|
|
|
constr_type(.) CHARACTER, type of constrain :
|
|
|
|
'type_coord' : constraint on global coordination-number, i.e. the
|
|
average number of atoms of type B surrounding the
|
|
atoms of type A. The coordination is defined by
|
|
using a Fermi-Dirac.
|
|
(four indexes must be specified).
|
|
|
|
'atom_coord' : constraint on local coordination-number, i.e. the
|
|
average number of atoms of type A surrounding a
|
|
specific atom. The coordination is defined by
|
|
using a Fermi-Dirac.
|
|
(four indexes must be specified).
|
|
|
|
'distance' : constraint on interatomic distance (two atom indexes
|
|
must be specified ).
|
|
|
|
'planar_angle' : constraint on planar angle (three atom indexes must
|
|
be specified).
|
|
|
|
'torsional_angle' : constraint on torsional angle (four atom indexes
|
|
must be specified).
|
|
|
|
'bennett_proj' : constraint on the projection onto a given direction
|
|
of the vector defined by the position of one atom
|
|
minus the center of mass of the others.
|
|
( Ch.H. Bennett in Diffusion in Solids, Recent
|
|
Developments, Ed. by A.S. Nowick and J.J. Burton,
|
|
New York 1975 ).
|
|
|
|
constr(1,.) constr(2,.) ... REAL, these variables have different
|
|
meanings for different constraint
|
|
types:
|
|
'type_coord' : constr(1) is the first index of the
|
|
atomic type involved
|
|
constr(2) is the second index of the
|
|
atomic type involved
|
|
constr(3) is the cut-off radius for
|
|
estimating the coordination
|
|
constr(4) is a smoothing parameter
|
|
'atom_coord' : constr(1) is the atom index of the
|
|
atom with constrained coordination
|
|
constr(2) is the index of the atomic
|
|
type involved in the coordination
|
|
constr(3) is the cut-off radius for
|
|
estimating the coordination
|
|
constr(4) is a smoothing parameter
|
|
'distance' : atoms indices object of the
|
|
constraint, as they appear in
|
|
the 'ATOMIC_POSITION' CARD
|
|
'planar_angle', 'torsional_angle' : atoms indices object of the
|
|
constraint, as they appear in the
|
|
'ATOMIC_POSITION' CARD (beware the
|
|
order)
|
|
'bennett_proj' : constr(1) is the index of the atom
|
|
whose position is constrained.
|
|
constr(2:4) are the three coordinates
|
|
of the vector that specifies the
|
|
constraint direction.
|
|
|
|
constr_target REAL, target for the constrain ( angles are
|
|
specified in degrees ).
|
|
This variable is optional.
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
COLLECTIVE_VARS
|
|
|
|
Collective variables used for meta-dynamics calculations
|
|
|
|
Syntax:
|
|
|
|
COLLECTIVE_VARS
|
|
ncolvars { tolerance }
|
|
colvar_type(.) colvar(1,.) colvar(2,.) ...
|
|
|
|
Where:
|
|
|
|
ncolvars INTEGER, number of collective variables
|
|
tolerance REAL, tolerance used for SHAKE.
|
|
|
|
colvar_type(.) CHARACTER, type of collective variable :
|
|
|
|
... see the definition of constr_type in the CONSTRAINTS card.
|
|
|
|
colvar(1,.) colvar(2,.) ... REAL, these variables have different
|
|
meanings for different collective
|
|
variable types. See the definition of
|
|
constr in the CONSTRAINTS card.
|
|
|
|
-------------------------------------------------------------------------------
|
|
|
|
ibrav is the structure index:
|
|
|
|
ibrav structure celldm(2)-celldm(6)
|
|
|
|
0 "free", see above not used
|
|
1 cubic P (sc) not used
|
|
2 cubic F (fcc) not used
|
|
3 cubic I (bcc) not used
|
|
4 Hexagonal and Trigonal P celldm(3)=c/a
|
|
5 Trigonal R celldm(4)=cos(alpha)
|
|
6 Tetragonal P (st) celldm(3)=c/a
|
|
7 Tetragonal I (bct) celldm(3)=c/a
|
|
8 Orthorhombic P celldm(2)=b/a,celldm(3)=c/a
|
|
9 Orthorhombic base-centered(bco) celldm(2)=b/a,celldm(3)=c/a
|
|
10 Orthorhombic face-centered celldm(2)=b/a,celldm(3)=c/a
|
|
11 Orthorhombic body-centered celldm(2)=b/a,celldm(3)=c/a
|
|
12 Monoclinic P celldm(2)=b/a,celldm(3)=c/a,
|
|
celldm(4)=cos(ab)
|
|
13 Monoclinic base-centered celldm(2)=b/a,celldm(3)=c/a,
|
|
celldm(4)=cos(ab)
|
|
14 Triclinic celldm(2)= b/a,
|
|
celldm(3)= c/a,
|
|
celldm(4)= cos(bc),
|
|
celldm(5)= cos(ac),
|
|
celldm(6)= cos(ab)
|
|
|
|
For P lattices: the special axis (c) is the z-axis, one basal-plane
|
|
vector (a) is along x, the other basal-plane vector (b) is at angle
|
|
gamma for monoclinic, at 120 degrees for trigonal and hexagonal
|
|
lattices, at 90 degrees for cubic, tetragonal, orthorhombic lattices
|
|
|
|
sc simple cubic
|
|
====================
|
|
a1 = a(1,0,0), a2 = a(0,1,0), a3 = a(0,0,1)
|
|
|
|
fcc face centered cubic
|
|
====================
|
|
a1 = (a/2)(-1,0,1), a2 = (a/2)(0,1,1), a3 = (a/2)(-1,1,0).
|
|
|
|
bcc body entered cubic
|
|
====================
|
|
a1 = (a/2)(1,1,1), a2 = (a/2)(-1,1,1), a3 = (a/2)(-1,-1,1).
|
|
|
|
simple hexagonal and trigonal(p)
|
|
====================
|
|
a1 = a(1,0,0), a2 = a(-1/2,sqrt(3)/2,0), a3 = a(0,0,c/a).
|
|
|
|
trigonal(r)
|
|
===================
|
|
for these groups, the z-axis is chosen as the 3-fold axis, but the
|
|
crystallographic vectors form a three-fold star around the z-axis,
|
|
and the primitive cell is a simple rhombohedron. The crystallographic
|
|
vectors are:
|
|
a1 = a(tx,-ty,tz), a2 = a(0,2ty,tz), a3 = a(-tx,-ty,tz).
|
|
where c=cos(alpha) is the cosine of the angle alpha between any pair
|
|
of crystallographic vectors, tc, ty, tz are defined as
|
|
tx=sqrt((1-c)/2), ty=sqrt((1-c)/6), tz=sqrt((1+2c)/3)
|
|
|
|
simple tetragonal (p)
|
|
====================
|
|
a1 = a(1,0,0), a2 = a(0,1,0), a3 = a(0,0,c/a)
|
|
|
|
body centered tetragonal (i)
|
|
================================
|
|
a1 = (a/2)(1,-1,c/a), a2 = (a/2)(1,1,c/a), a3 = (a/2)(-1,-1,c/a).
|
|
|
|
simple orthorhombic (p)
|
|
=============================
|
|
a1 = (a,0,0), a2 = (0,b,0), a3 = (0,0,c)
|
|
|
|
bco base centered orthorhombic
|
|
=============================
|
|
a1 = (a/2,b/2,0), a2 = (-a/2,b/2,0), a3 = (0,0,c)
|
|
|
|
face centered orthorhombic
|
|
=============================
|
|
a1 = (a/2,0,c/2), a2 = (a/2,b/2,0), a3 = (0,b/2,c/2)
|
|
|
|
body centered orthorhombic
|
|
=============================
|
|
a1 = (a/2,b/2,c/2), a2 = (-a/2,b/2,c/2), a3 = (-a/2,-b/2,c/2)
|
|
|
|
monoclinic (p)
|
|
=============================
|
|
a1 = (a,0,0), a2= (b*sin(gamma), b*cos(gamma), 0), a3 = (0, 0, c)
|
|
where gamma is the angle between axis a and b
|
|
|
|
base centered monoclinic
|
|
=============================
|
|
a1 = (a/2*sin(gamma), a/2*cos(gamma)-b/2, 0),
|
|
a2 = (a/2*sin(gamma), a/2*cos(gamma)+b/2, 0),
|
|
a3 = (0, 0, c)
|
|
where gamma is the angle between axis a and b
|
|
|
|
triclinic
|
|
=============================
|
|
a1 = (a, 0, 0),
|
|
a2 = (b*cos(gamma), b*sin(gamma), 0)
|
|
a3 = (c*cos(beta), c*(cos(alpha)-cos(beta)cos(gamma))/sin(gamma),
|
|
c*sqrt( 1 + 2*cos(alpha)cos(beta)cos(gamma)
|
|
- cos(alpha)^2-cos(beta)^2-cos(gamma)^2 )/sin(gamma) )
|
|
where alpha is the angle between axis b and c
|
|
beta is the angle between axis a and c
|
|
gamm is the angle between axis a and b
|
|
----------------------------------------------------------------------
|