N18
South China University of Technologywww.compphys.cnStructural
RelaxationXiaobao Yang
Department of
Physicshttp://www.compphys.cn/~xbyang/lectures.html
www.compphys.cn1.Schrdinger Equation
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INCAR POTCARKPOINTS POSCARINCAR
ENCUT = 700ISMEAR = 0SIGMA =0.2NSW = 0EDIFF = 0.001
POTCAR
PAW_PBE H 15Jun2001 1.00000000000000000 parameters from PSCTR
are: VRHFIN =H: ultrasoft test LEXCH = PE EATOM = 12.4884 eV, .9179
RyKPOINTS
Automatic mesh0 ! number of k-points = 0 ->automatic
generation scheme Monkhorst-Pack ! select Monkhorst-Pack (first
letter is significant)1 1 1 ! size of mesh (4x4x4 points along b1,
b2, b3)0. 0. 0. ! shift of the k-mesh
POSCAR
H2 1.0 12 0 0 0 12 0 0 0 12 2Cart0 0 00 0 0.75
www.compphys.cn running on 2 nodes distr: one band on 1 nodes, 2
groups vasp.4.6.31 08Feb07 complex POSCAR found : 1 types and 2
ions LDA part: xc-table for Pade appr. of Perdew POSCAR, INCAR and
KPOINTS ok, starting setup WARNING: wrap around errors must be
expected FFT: planning ... 1 reading WAVECAR WARNING: random
wavefunctions but no delay for mixing, default for NELMDL entering
main loop N E dE d eps ncg rms rms(c)DAV: 1 -0.469211785182E+01
-0.46921E+01 -0.23142E+02 12 0.981E+01DAV: 2 -0.738346878115E+01
-0.26914E+01 -0.26914E+01 12 0.252E+01DAV: 3 -0.741841946701E+01
-0.34951E-01 -0.34951E-01 18 0.423E+00DAV: 4 -0.741843794358E+01
-0.18477E-04 -0.18477E-04 12 0.955E-02DAV: 5 -0.741843809963E+01
-0.15606E-06 -0.15606E-06 18 0.878E-03 0.436E+00DAV: 6
-0.698113710837E+01 0.43730E+00 -0.22006E-01 12 0.179E+00
0.237E+00DAV: 7 -0.674222335613E+01 0.23891E+00 -0.52473E-01 24
0.281E+00 0.269E-01DAV: 8 -0.674568380323E+01 -0.34604E-02
-0.54198E-03 12 0.257E-01 0.257E-01DAV: 9 -0.674122836271E+01
0.44554E-02 -0.74399E-03 12 0.325E-01 0.324E-02DAV: 10
-0.674397109933E+01 -0.27427E-02 -0.55758E-04 12 0.997E-02
0.187E-02DAV: 11 -0.674418356913E+01 -0.21247E-03 -0.58782E-05 18
0.303E-02 1 F= -.67441836E+01 E0= -.67441836E+01 d E =-.241108E-10
writing wavefunctions
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Test everything to ensure convergence
cluster, nanowire, thin film
www.compphys.cnfor i in 250 350 450 500 dofor j in 8 10 12 15
20docat >INCAR "$PBS_JOBID".out.$i.$jrm WAVECAR CHG
CHGCARdonedone
for j in 250 300 350 400 450 500 600 700 docat >INCAR
"$PBS_JOBID".out.$j.$irm WAVECAR CHG CHGCARdonedone
www.compphys.cnHow to move atoms?
Energy is minimum.The gradient is zero.
www.compphys.cnOptimization and Curse of Dimensionality
www.compphys.cnQuasi-Newton method
www.compphys.cnQuasi-Newton method in VASP
www.compphys.cnQuasi-Newton method in VASP
www.compphys.cnSteepest descent method
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Searching directionOptimized stepNew start point
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Optimized stepNew start pointNew start pointSearching
directionStop searching
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f(x) = 1/2 (x - x*)TA(x - x*) , Annx*f(x) 1/2 (x - x*)TA(x - x*)
= c x*.
f(x*) = A(x - x*) = 0Ax*f(x)x(1)x(1)f(x(1)) = A(x(1) - x*)
d(1)x(1), d(1)f(x(1))d(1)Tf(x(1)) = 0; , d(2) = x* - x(1),
d(1)TAd(2) = 0
A
www.compphys.cnConjugate Gradient method
Steepest descent method
Conjugate Gradient
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www.compphys.cnStructural relaxationTo obtain the ground state
relaxed geometry of the system.
the equilibrium lattice constants
a given ionic configuration the forces obtained
these forces are greater than some minimum tolerance
the ions are moved in the direction of the forces
www.compphys.cnIBRION-tag in VASP0 Standard ab-initio molecular
dynamics A Verlet algorithm is used to integrate Newton's equations
of motion. POTIM supplies the timestep in femto seconds. 1 A
quasi-Newton algorithm is used to relax the ions into their
instantaneous ground state.2 A conjugate-gradient algorithmi)In the
first step ions :the direction of the steepest descent. The energy
and the forces are recalculated. ii) Interpolation of the change of
the total energy and of the forces, then a corrector step. iii)
After the corrector step the forces and energy are recalculated and
it is checked whether the forces contain a significant component
parallel to the previous search direction.1 initial position 2
trial step 3 corrector step, i.e. positions corresponding to
anticipated minimum 4 trial step 5 corrector step
www.compphys.cnISIF-tag in VASP
www.compphys.cnRelaxation with VASP
www.compphys.cnEnergies vs. Forces
H2 molecularC-2.629 3.681 0.018 C-1.415 2.939 0.026 C-1.493
1.580 0.024 C-2.618 0.818 -0.011 C-3.851 1.541 0.016 C-3.904 2.981
-0.033 H-2.682 4.664 0.020 H-0.585 3.486 -0.047 H-0.544 1.065
-0.022 H-2.613 -0.192 -0.045 H-4.764 1.084 -0.040 H-4.683 3.483
0.032
C6H6 molecular
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www.compphys.cnAWK and VASP aa=`awk '$2 == "TOTAL-FORCE" {print
NR}' OUTCAR` a=`expr $aa + 1` bb=`expr $aa + $num + 2` awk 'NR >
a && NR < bb {print $4,$5,$6}' a=$a bb=$bb OUTCAR
>force.1 paste site.1 velocity.1 force.1 >all.1 awk '{print
$1+$4*h+$7*h*h/2/m*0.0096,$2+$5*h+$8*h*h/2/m*0.0096,$3+$6*h+$9*h*h/2/m*0.0096}'
h=$dt m=$mass all.1>site.2
paste velocity.1 force.1 force.2 >all.2 awk '{print
$1+$4*h/2/m*0.0096+$7*h/2/m*0.0096,$2+$5*h/2/m*0.0096+$8*h/2/m*0.0096,$3+$6*h/2/m*0.0096+$9*h/2/m*0.0096}'
h=$dt m=$mass all.2>velocity.2
www.compphys.cnReview of QN,SD and CG
Steepest descent methodConjugate Gradient
www.compphys.cnPeriodical structures
three lines the three lattice vectors defining the unit cell of
the system are given (first line corresponding to the first lattice
vector, second to the second, and third to the third
Latticeofgraphene & latticeofgrapheneD
www.compphys.cnK-mesh -- Monkhorst-PackSpecial points for
Brillonin-zone integrations, PRB, 13,5188(1976)
q q k-sampling to define the Fermi surface precisely
www.compphys.cnKPOINTS testAutomatic mesh0 ! number of k-points
= 0 ->automatic generation scheme Monkhorst-Pack ! select
Monkhorst-Pack (first letter is significant)Gamma5 5 1 ! size of
mesh (4x4x4 points along b1, b2, b3)4 4 10. 0. 0. ! shift of the
k-mesh
KPOINTS & IBZKPT
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LREAL.FALSE. projection done in reciprocal space .TRUE.
projection done in real space, This expression can be evaluated in
reciprocal or real space:
In reciprocal space the number of operations scales with the
size of the basis set (i.e. number of plane-waves).
In real space, the projection-operators are confined to spheres
around each atom. Therefore the number of operations necessary to
evaluate one does not increase with the system size (usually the
number of grid points within the cut-off-sphere is between 500 and
2000).
The number of atom
