PWscf, FPMD and CP (Democritos Package) Tutorial

1
PWscf, FPMD and CP (Democritos Package)Tutorial

• Carlo Cavazzoni(High Performance Computing
  Group) CINECA

2
Outline

• ab-initio simulations introduction
• PWSCF and Democritos package
• Installation
• Functionality
• Simple examples

3
The scope of computersimulation

• Measure theories. Solve equations which could not
  be solved otherwise. Get numbers out of
  theories much in the same way as experiments
  get numbers out of a natural process
• Do virtual experiments where experimental
  conditions can be controlled down to the atomic
  scale in ways which would not be possible in the
  lab

4
Ab initio simulations
The Born-Oppenheimer approximation (Mgtgtm)
5
Density functional theory
Kohn-Sham Hamiltonian
6
Kohn-Sham equations from functional minimization
Helmann Feynman
Kohn Sham
7
The tricks of the trade

• Expanding the Kohn-Sham orbitals into a suitable
  basis set turns DFT into a multi-variate
  minimization problem, and the KS equation into a
  non-linear matrix eigenvalue problem
• The use of pseudo-potentials allows to ignore
  chemically inert core states and to use plane
  waves (the name of the game!)

8
The tricks of the trade (II)

• Plane waves are orthogonal and the matrix
  elements are usually easy to calculate the
  effective completeness of the basis is easy to
  check
• Plane-waves allow to calculate efficiently
  matrix-vector products and to solve the Poisson
  equation using FFTs
• Supercells for treating finite (or semi-infinite)
  systems
• Iterative diagonalization vs. global minimization

9
The tricks of the trade (III)

• Summing over occupied states special-point and
  Gaussian-smearing techniques
• Non-linear extrapolation for SCF acceleration and
  density prediction in MD
• Choice of fictitious masses in CP dynamics

10
Which algorithm shall I use?

• Electronic structure SCF diagonalization vs.
  energy minimization
• Geometry optimization standard DFT
• Lattice vibrations, static response functions
  DF perturbation theory
• Dynamics Car-Parrinello vs. Born-Oppenheimer
• Slow kinetics and rare events path sampling vs.
  Parrinello-Laio metadynamics
• Optical properties, excited states
  Time-dependent DFT many-body perturbation theory

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PWSCF and Democritos (www.democritos.it)
(DEmocritos MOdeling Center for Research in
aTOmistic Simulatios)
Democritos is a National Simulation Center of the
Italian Istituto Nazionale per la Fisica della
Materia (INFM). Hosted by SISSA in Trieste
PWSCF is promoted, maintained and developed by
Democritos
CINECA is a Partner of Democritos.
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Democritos and Scientific Software
GOAL Development of software for next generation
parallel computers (Ngt10000 processors) Productio
n of high-quality software package for atomistic
simulations based on density-functional theory
(DFT), plane wave (PW) and pseudopotentials (PP)
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PWSCF is also part of a merge effortof
pre-existing scientific software
PWscf package electronic structure, structural
optimization, molecular dynamics, vibrational and
dielectric properties. Developed by S. Baroni, S.
de Gironcoli, A. Dal Corso (SISSA, Trieste), P.
Giannozzi (Scuola Normale, Pisa) and others.See
http//www.pwscf.org for more information and
downloads.
CP code Car-Parrinello variable-cell molecular
dynamics. Developed by A. Pasquarello (IRRMA,
Lausanne), K. Laasonen (Oulu), A. Trave
(UCBerkeley), R. Car (Princeton), P. Giannozzi
and others. Based on the original code written by
R. Car and A. Pasquarello. Download CP (initial
public release)
FPMD code Car-Parrinello variable-cell molecular
dynamics. Developed by C. Cavazzoni (CINECA,
Bologna), S. Scandolo (ICTP, Trieste), G.
Chiarotti (SISSA, Trieste), P. Focher, G.
Ballabio and others. Based on the original code
written by R. Car and M. Parrinello. Download
FPMD (initial public release)
GNU License
http//www.democritos.it/scientific.php
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Present Package Status

• The Package is developed in Fortran90
• The codes in the Package share
• installation
• most parts of the basic code
• input format
• PP format
• a graphical GUI is being developed
• output format (CP/FPMD fully compatible/restartab
  le)

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Basic Data Type
Real space
Charge density
3D arrays

Wave functions
1D arrays
Reciprocal space
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Reciprocal Space Representation
Wave Functions
To truncate the infinite sum
Charge Density
To retain the same accurancy as the wave function
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DFT Functional
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FFTs
Ecut
4Ecut
Reciprocal Space
G2/2lt Ecut
G2/2lt 4Ecut
FFT
Real Space
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ParallelizationReciprocal Space distribution
PWSCF parallelize also over K-points
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ParallelizationFFT algorithm
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SP4, optimization issues

• use essl
• use non-blocking communications
• use mass
• modify strides to reduce TLB misses
• use block-algorithm whenever possible ATLAS
  strategy

22
Case study matrix transposition
do ib 1, nb ioff (ib-1) bsiz do jb 1,
mb joff (jb-1) bsiz do j 1, bsiz
do i 1, bsiz buf(i,j) x(iioff,
jjoff) enddo enddo do j 1, bsiz
do i 1, j-1 bswp buf(i,j)
buf(i,j) buf(j,i) buf(j,i) bswp
enddo enddo do i1,bsiz do
j1,bsiz y(jjoff, iioff) buf(j,i)
enddo enddo enddo enddo
do i1,n do j1,m y(j,i) x(i,j)
enddo enddo
block-algorithm bsiz block size nb n /
bsiz mb n / bsiz more code for reminder
MOD(n / bsiz) / 0 OR MOD(m / bsiz) / 0
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Block algorithm for matrix transposition
80
70
60
50
Mips
40
30
20
10
0
0
20
40
60
80
100
120
block dimension
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CP code
Developed by A. Pasquarello (IRRMA, Lausanne), K.
Laasonen (Oulu), A. Trave (UCBerkeley), R. Car
(Princeton), P. Giannozzi and others. Based on
the original code written by R. Car and A.
Pasquarello.
Verlet dynamics with mass preconditioning Temperat
ure control Nose thermostat, velocity
rescaling Metallic systems Nose thermostat for
both electrons and ions electronic and ionic
minimization via damped dynamics Modified kinetic
functional for costant-pressure
calculations grid box for fast treatment of
augmentation terms in Ultrasoft PPs Nudget
Elastic Band (NEB) scheme for transition paths
and energy barriers
Limitations no k-points no fancier minimization
chemes no constraints
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FPMD code
Developed by C. Cavazzoni (CINECA, Bologna), S.
Scandolo (ICTP, Trieste), G. Chiarotti (SISSA,
Trieste), P. Focher, G. Ballabio and others.
Based on the original code written by R. Car and
M. Parrinello.
Verlet dynamics with mass preconditioning Temperat
ure control Nose thermostat, velocity
rescaling Metallic systems Nose thermostat for
both electrons and ions Various electronic and
ionic minimization schemes Modified kinetic
functional for costant-pressure
calculations Macroscopic polarization via Berry
Phase Nudget Elastic Band (NEB) scheme for
transition paths and energy barriers Constrained
dynamics
Limitations no Ultrasoft PPs
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PWSCF code
Developed by S. Baroni, S. de Gironcoli, A. Dal
Corso (SISSA, Trieste), P. Giannozzi (Scuola
Normale, Pisa) and others.
Self-consistent ground-state energy and Kohn-Sham
orbitals Structural optimization Molecular
dynamics on the ground-state Born-Oppenheimer
surface Variable-cell molecular dynamics Phonon
frequencies and eigenvectors at a generic wave
vector Effective charges and dielectric
tensors Electron-phonon interaction coefficients
for metals Third-order anharmonic phonon
lifetimes Macroscopic polarization via Berry
Phase Nudget Elastic Band (NEB) scheme for
transition paths and energy barriers
Limitations no Car-Parrinello dynamics very
limited constrained minimization and dynamics
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Access the anonymous CVS of theDemocritos
PW-PP-DFT Package
anonymous CVS contains the whole package, with
all the codes
(tcsh/csh) setenv CVS_RSH ssh setenv
CVSROOT pservercvsanon_at_democritos.sissa.it/home
/cvs (sh/bash) export CVS_RSHssh export
CVSROOTpservercvsanon_at_democritos.sissa.it/home
/cvs Then cvs login (password cvsanon).
For the first code download cvs co O-sesame
Open-Sesame Open-Source Scalable Electronic
Structure and Atomistic Modeling Environment
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Installation
./configure make target
where target is one of the following pw
basic code for scf, structure optimization,
MD fpmd FPMD code for Car-Parrinello
MD cp CP code CP MD with ultrasoft
pseudopotentials ph phonon code pp
postprocessing programs gamma
Gamma-only version of phonon code nc
non collinear magnetic version of pw code
pwcond ballistic conductance d3
third-order derivatives tools misc tools
for data analysis upf utilities for
pseudopotential conversion pwall same as
"make pw ph pp gamma nc pwcond d3 tools" all
same as "make pwall fpmd cp upf" links
creates links to executables in bin/ clean
remove executables and objects veryclean
revert distribution to the original status
tar create a tarball of the source tree
tar-gui create a tarball of the GUI sources
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Installation (DEMO)
how to configure configure?
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Directories tree I/II
include
includes files
Modules
clib
flib
upftools
common modules, subroutine and tools
CPV
FPMD
PW
main codes directories
D3
PP
PH
pw post-processing codes
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Directories tree II/II
cpdocs
pwdocs
documentation
pseudo
pseudopotential library
install
preconfigured installation parameter files
cp_examples
pw_examples
run examples
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Input files
PWscf, CP and FPMD share the same input files
format
All codes read input parameters from standard
input
Codes read from files PP data, all codes read the
same PP files
In directory upftools there are conversion tools
for PP formats (there is one also for CPMD)
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Standard Input Layout
The standard input is divided in two main section
the first contains fortran namelists
the seconds contains optional input CARDS
all input parameter are described in cpdocs
and pwdocs file.
all input parameter for all codes are
contained in file Modules/input_parameters.f90
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layout
CONTROL control_parameter_1,
control_parameter_2, ....... / SYSTEM
sistem_parameter_1, sistem_parameter_2,
....... / ELECTRONS electrons_parameter_
1, electrons_parameter_2,
....... / IONS ions_parameter_1,
ions_parameter_2, ....... / CELL
cell_parameter_1, cell_parameter_2,
....... / ATOMIC_SPECIES label_1 mass_1
pseudo_file_1 label_2 mass_2 pseudo_file_2 .....
ATOMIC_POSITIONS label_1 px_1 py_1 pz_1 label_2
px_2 py_2 pz_2 .....
the namelist order is fixed, but within a
namelist the parameter sequence is irrelevant
namelists
card order is irrelevant, but within a card the
parameter layout is fixed
cards
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Input Namelists
CONTROL input variables that control the flux
of teh calculation and the amount of I/O on disk
and on the screen
SYSTEM input variables that specify the system
under study
ELECTRONS input variables that control the
algorithms used to reach the self-consistent
solution of KS equations for the electrons, and
the electrons dynamics (for CP and FPMD)
IONS input variables that control ionic motion
in molecular dynamics run or structural relaxation
CELL input variables that control cell-shape
evolution in a variable-cell MD run or structural
relaxation
36
Input Cards
ATOMIC_SPECIES name, mass and pseudopotential
used for each atomic species present in the system
ATOMIC_POSITIONS type and coordinate of each
atom in the unit cell
K_POINTS coordinate and weights of the k-points
used for BZ integration
CELL_PARAMETERS
OCCUPATIONS
CLINBING_IMAGES
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Silicon Band Structure(www.cineca.it/acv0/Public
/PWSCF_Tutorial.tgz)

• Select the appropriate unit cell
• Input the atomic coordinate
• Choose the pseudopotentials
• Determine k-point sampling
• Select the size of the basis set (Ecut)

38
Select the appropriate unit cell
ibrav bravais lattice celldm(.) cell
parameters celldm(1) a, celldm(2)
b/a, celldm(3) c/a celldm(4)
cos(bc) celldm(5) cos(ac) celldm(6) cos(ab)

• 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(aalpha)
• 6 Tetragonal P (st)
  celldm(3)c/a
• 7 Tetragonal I (bct)
  celldm(3)c/a
• Orthorhombic P
  celldm(2)b/a,
• 
  celldm(3)c/a
• Orthorhombic base-centered(bco)
  celldm(2)b/a,
• 
  celldm(3)c/a
• Orthorhombic face-centered
  celldm(2)b/a,
• 
  celldm(3)c/a
• Orthorhombic body-centered
  celldm(2)b/a,
• 
  celldm(3)c/a

39
Unit cell
ibrav 2, cubic fcc
ibrav 1, simple cubic
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Unit cell (supercells)
ibrav 1, simple cubic (crystal with defects)
ibrav 6, tetragonal (surfaces)
41
Silicon Crystal unit cell
control prefix'silicon', pseudo_dir
'PSEUDO_DIR/', outdir'TMP_DIR/' /
system ibrav 2, celldm(1) 10.20, nat
2, ntyp 1, ecutwfc 12.0, / electrons /
empty namelist, keep default values for
Self-Consistent Field iterations
42
Atomic Positions
ATOMIC_POSITION (units) units if units is not
specified, unit of celldm(1) is assumed units
bohr position in Bohr radius units angstrom
position in Angstrom units crystal position
in crystal coord.
ATOMIC_SPECIES Si 28.086 Si.vbc.UPF ATOMIC_POSI
TIONS Si 0.00 0.00 0.00 Si 0.25 0.25 0.25
43
K-points set
Automatic
K_POINTS (automatic) 2 2 2 1 1 1
k-points grid
grid off-set
K_POINTS 2 0.25 0.25 0.75 3.0 0.25 0.25
0.25 1.0
User specified
number of k-points
k-points weight
k-points coordinate (crystal coord.)
start with coarse grid, then try finer ones to
check convergence
44
Input for Silicon Crystal SCF calculation
control prefix'silicon', pseudo_dir
'PSEUDO_DIR/', outdir'TMP_DIR/' /
system ibrav 2, celldm(1) 10.20, nat
2, ntyp 1, ecutwfc 12.0, / electrons
/ ATOMIC_SPECIES Si 28.086 Si.vbc.UPF ATOMIC_PO
SITIONS Si 0.00 0.00 0.00 Si 0.25 0.25 0.25
K_POINTS 2 0.25 0.25 0.75 3.0 0.25 0.25
0.25 1.0
pw.x lt inputfile
45
Non SCF calculation
To compute band structure, we need the value
of eigenvectors on all k-point of the bands.
If the computation is converged with respect
to the k-points grid, we do not need to repeat
the SCF calculation on all k-points of the
bands, but we can diagonalize the Hamiltonian
using the SCF Kohn-Sham potential.
46
Input for Non SCF calculation
control calculation'nscf' pseudo_dir
'PSEUDO_DIR/', outdir'TMP_DIR/',
prefix'silicon' / system ibrav 2,
celldm(1) 10.20, nat 2, ntyp 1, ecutwfc
12.0, nbnd 8, / electrons
/ ATOMIC_SPECIES Si 28.086 Si.vbc.UPF ATOMIC_PO
SITIONS Si 0.00 0.00 0.00 Si 0.25 0.25 0.25
K_POINTS
47
K-points set along high symmetry lines
band structure calculation along delta, sigma
and lambda lines
K_POINTS 36 0.5 0.5 0.5 1 0.4 0.4 0.4 2
0.3 0.3 0.3 3 0.2 0.2 0.2 4 0.1 0.1 0.1
5 0.0 0.0 0.0 6 0.0 0.0 0.1 7 0.0 0.0
0.2 8 0.0 0.0 0.3 9 0.0 0.0 0.4 10 0.0
0.0 0.5 11 0.0 0.0 0.6 12
0.0 0.0 0.7 13 0.0 0.0 0.8 14 0.0 0.0
0.9 15 0.0 0.0 1.0 16 0.0 0.1 1.0 17 0.0
0.2 1.0 18 0.0 0.3 1.0 19 0.0 0.4 1.0 20
0.0 0.5 1.0 21 0.0 0.6 1.0 22 0.0 0.7 1.0
23 0.0 0.8 1.0 24
0.0 0.9 1.0 25 0.0 1.0 1.0 26 0.0 0.9
0.9 27 0.0 0.8 0.8 28 0.0 0.7 0.7 29 0.0
0.6 0.6 30 0.0 0.5 0.5 31 0.0 0.4 0.4 32
0.0 0.3 0.3 33 0.0 0.2 0.2 34 0.0 0.1 0.1
35 0.0 0.0 0.0 36
48
Post Processing
inputpp prefix 'silicon' outdir
'TMP_DIR/' filband 'sibands.dat' /
bands.x lt inputfile
prints the bands to graphical files
sibands.dat -6.0 10 sibands.xmgr sibands.ps 6.3369
1.0 6.3369
plotband.x lt inputfile
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the silicon bands!
50
How to find equilibrium lattice parameters
different scf computation, changing cut-off and
lattice parameter
51
Plot Charge Density
chdens cat gt si.chdens.in ltlt EOF input
nfile 1 filepp(1) 'sicharge' weight(1)
1.0 iflag 2 plot_out 1
output_format 2 fileout 'si.rho.dat'
e1(1) 1.0, e1(2)1.0, e1(3) 0.0, e2(1)
0.0, e2(2)0.0, e2(3) 1.0, nx56, ny40
/ EOF ./chdens.x lt si.chdens.in gt si.chdens.out
post-processing for charge density cat gt
si.pp_rho.in ltlt EOF inputpp prefix
'silicon' outdir 'TMP_DIR/' filplot
'sicharge' plot_num 0 / EOF ./pp.x lt
si.pp_rho.in gt si.pp_rho.out
2)
1)
cat gt si.plotrho.in ltlt EOF si.rho.dat si.rho.ps n
0 0.09 6 EOF ./plotrho.x lt si.plotrho.in gt
si.plotrho.out
3)
52
Charge Density
53
MD - Molecular Dynamics
54
DFT - Solution of the KS equation.
55
AIMD ab-Initio Molecular Dynamics
Born-Oppenheimer MD
56
CPMD Car-Parrinello Molecular Dynamics
57
Car-Parrinello Lagrangian (deformable cell
extension)
Density Functionl Energy
Diagonal in Fourier space
Diagonal in Real space
Computationally it is convenient to calculate
quantities in the space where they are diagonal
58
Equations of motion
Electrons treated as classical scalar fields,
follow adiabatically the ions remaining close to
the ground state.
Ions in scaled coordinates, move along the Born
Oppenheimer surface
Cell shape is driven by the imbalance of internal
stress ? and external pressure p.
59
CINECA/Democritos CP Code
FORM
NLRH
Pseudopotential Form factors
RHOOFR
?(r) ? ?(r)2
PRESS
VOFRHO
V(R, ?) VrDFT(R, ?(r)) VGDFT(R, ?(G))
FORCE
Forces on the electrons F?
ORTHO
Orthogonalize wave functions ?
60
A CP simulation require usually many RUNs and JOBs

1. Minimize the Electronic degrees of freedom (
   d.o.f. )
2. Minimize the ionic d.o.f.
3. Randomize ionic d.o.f.
4. Re-minimize Electronic d.o.f
5. Move Electronic and Ionic d.o.f. using Verlet to
   integrate the equations of motion
6. Change temperature using thermostat
7. Accumulate statistics for few picoseconds of
   simulated time ( 20000 40000 time steps )

www.cineca.it/acv0/Public/tutorial_fpmd.tar.gz
61
Electronic Minimization I/II
CONTROL title ' Water Molecule ',
calculation 'cp', restart_mode
'from_scratch', prefix 'h2o_mol nstep
50, dt 5.0d0, etot_conv_thr 1.d-9,
ekin_conv_thr 1.d-4, / SYSTEM ibrav
1, celldm(1) 10.0, nat 3, ntyp 2,
nbnd 4, nelec 8, ecutwfc 70.0, xc_type
'BLYP' /
CP time step (in a.u.)
number of CP step
convergence threshold, effective only for
minimization
Simulation Cell (in a.u.)
number of bands, and electrons
number of atom, and species
Energy cut-off, in Rydberg
Exchange and correlation functional
62
Electronic Minimization II/II
ELECTRONS emass 400.d0, emass_cutoff
2.5d0, orthogonalization 'ortho',
electron_dynamics 'sd', / IONS
ion_dynamics 'none', / ATOMIC_SPECIES O
16.0d0 O.BLYP.UPF 4 H 1.00d0 H.fpmd.UPF
4 ATOMIC_POSITIONS (bohr) O 0.0099
0.0099 0.0000 H 1.8325 -0.2243
-0.0001 H -0.2243 1.8325 0.0002
Fictitious electron mass (a.u.) m parameter in CP
dynamic
orthogonalization algorithm ortho or
'Gram-Schmidt'
PW Energy cut-off (in Rydberg) for Fourier
Acceleration
electron dynamics sd -gt steepest descend cg -gt
conjugate gradient damp -gt damped verlet -gt
Verlet
Label Mass (uma) PP
ion dynamics none -gt kept fixed sd -gt steepest
descend cg -gt conjugate gradient damp -gt
damped verlet -gt Verlet
Label x y z
63
CP Dynamics I/II
CONTROL title ' Water Molecule ',
calculation 'cp', restart_mode restart',
nstep 50, dt 5.0d0, prefix
'h2o_mol' / SYSTEM ibrav 1, celldm(1)
10.0, nat 3, ntyp 2, nbnd 4, nelec
8, ecutwfc 70.0, xc_type
'BLYP' / ELECTRONS emass 400.d0,
emass_cutoff 2.5d0, orthogonalization
'ortho', electron_dynamics verlet',
electron_velocities zero /
verlet should be used for ions and electrons
IONS ion_dynamics verlet', ion_velocities
zero / ATOMIC_SPECIES O 16.0d0 O.BLYP.UPF
4 H 1.00d0 H.fpmd.UPF 4 ATOMIC_POSITIONS
(bohr) O 0.0099 0.0099 0.0000 H
1.8325 -0.2243 -0.0001 H -0.2243
1.8325 0.0002
in the very first run of dynamics
velocities should be set to zero
64
CP Dynamics II/II ( thermostat )
CONTROL title ' Water Molecule ',
calculation 'cp', restart_mode restart',
nstep 50, dt 5.0d0, prefix
'h2o_mol' / SYSTEM ibrav 1, celldm(1)
10.0, nat 3, ntyp 2, nbnd 4, nelec
8, ecutwfc 70.0, xc_type
'BLYP' / ELECTRONS emass 400.d0,
emass_cutoff 2.5d0, orthogonalization
'ortho', electron_dynamics verlet', /
Termostat temperature and frequency tempw (
Kelvin ) fnosep ( THz )
IONS ion_dynamics verlet',
ion_temperature nose tempw 300, fnosep
70.0 / ATOMIC_SPECIES O 16.0d0 O.BLYP.UPF 4
H 1.00d0 H.fpmd.UPF 4 ATOMIC_POSITIONS (bohr)
O 0.0099 0.0099 0.0000 H 1.8325
-0.2243 -0.0001 H -0.2243 1.8325
0.0002
65
Parrinello-Rahman Dynamics
CONTROL title ' Water Molecule ',
calculation vc-cp', restart_mode
restart', nstep 50, dt 5.0d0,
prefix 'h2o_mol' / SYSTEM ibrav 1,
celldm(1) 10.0, nat 3, ntyp 2, nbnd
4, nelec 8, ecutwfc 70.0, xc_type
'BLYP' / ELECTRONS emass 400.d0,
emass_cutoff 2.5d0, orthogonalization
'ortho', electron_dynamics verlet', /
change the calculation type (variable cell cp)
IONS ion_dynamics verlet', / CELL
cell_dynamics pr, press
0.0 / ATOMIC_SPECIES O 16.0d0 O.BLYP.UPF 4 H
1.00d0 H.fpmd.UPF 4 ATOMIC_POSITIONS (bohr) O
0.0099 0.0099 0.0000 H 1.8325
-0.2243 -0.0001 H -0.2243 1.8325
0.0002
Add the CELL namelists, with cell dynamics pr -gt
parrinello rahman sd -gt steepest descent damp -gt
damped
external pressure (Kbar)
66
high pressure high temperaturewater phase
diagram
C.Cavazzoni, G.L. Chiarotti, S.Scandolo,
E.Tosatti, M.Bernasconi, and M. Parrinello
Superprotonic and metallic states of water and
ammonia at giant planet conditions,
Science.283, 44 (1999).
67
ionic trajectory at finite temperature
H trajectories in the superionic phase
68
Run on SP4 - Water128
69
Run on SP4 - Water32