1. Abinit Workshop
Sornthep Vannarat

2. Lesson 1
Hydrogen Molecule

3. Lesson 1 cd ~abinit/Tutorial mkdir work copy ../t1x.files .
edit t1x.files
copy ../t11.in .
../../abinis < t1x.files > log
../t11.in
t1x.out
t1xi
t1xo
t1x
../../Psps_for_tests/01h.pspgth
t11.in
t11.out
t1xi
t1xo
t1x
../../Psps_for_tests/01h.pspgth

4. Lesson 1: Starting abinit
Program name: abinis.exe
Input files: t11.in and t1xi*
Output files: t11.out and t1xo*
Temporary files: t1x*
Pseudo potential files ../../Psps_for_tests/01h.pspgth

5. Lesson 1: Input parameters
Input file: t11.in
acell # Cell size is 10**3
ntypat # One type of atom
znucl # Atomic number is one
natom # There are two atoms
typat # They both are of type 1
xcart # Location of the atoms
# atom 1, in Bohr
# atom 2, in Bohr
ecut # Cut-off energy, in Hartree
nkpt # One k point
nstep # Maximal number of SCF cycles
toldfe 1.0d # Threshold
diemac # Preconditioner
diemix # Using standard preconditioner
# for molecules in a big box

6. Lesson 1: Output Abinit version Input/output files
Values of input parameters
Data Set and Pseudo potential file
Number of plan waves
Iterations
Stress tensor
Eigen values
Max/Min Electronic density
Total energy
Values of input parameters (after calculation)
Log file: interactive input, more details of iterations

7. Lesson 1: Inter-atomic distance (1)
3 approaches:
compute total energy E(d) or force F(d)
Use relaxation
Multiple datasets
t12.in: ndtset, xcart, xcart+, getwfk, nband
Edit t1x.files and run
Look at t12.out
Data sets: symmetry and number of plane waves
Data sets: coordinates xangst, xcart, xred
Data sets: Number of iterations
etotal and fcart
Plot data

8. Lesson 1: Inter-atomic distance (2)
Use relaxation: ionmove, ntime, tolmxf, toldff
Multiple datasets
t13.in
Edit t1x.files and run
Look at t13.out
BROYDEN STEP
value of coordinates after relaxation xangst, xcart, xred

9. Lesson 1: Charge density
prtden = 1, t14.in
move atoms to middle of box
cut3d convert to OpenDX

10. Lesson 1: Atomization energy
Eatomization = (2EHatom – EH2molecule)  per molecule
Caution:
Calculations with the same setting
Spin: nsppol, spinat
Degeneracy: HOMO and LUMO (see lesson_4)
Ground-state charge density NON-spherical, automatic determination of symmetries should be disabled (nsym)
For Hydrogen,
ground state is spherical (1s orbital)
HOMO and LUMO have a different spin
t15.in: define occupation of each spin, occopt and occ
Output file: Eigen values, Max/Min spin
Atomization energy =?

11. Lesson 1: Summary System Method Results
H2 molecule in a big box 10x10x10 Bohr^3
Method
Using cut-off energy 10 Ha
LDA (LSDA for atom) with ixc=1 (default)
Pseudopotential from Goedecker-Hutter-Teter table
Results
Bond length Bohr (1.401 Bohr)
Atomisation energy Ha = eV (4.747 eV)

12. Lesson 2
Convergence Study

13. Lesson 2: Combined calculation
t21.in
ndtset 2
acell
ecut 10
#First dataset
natom1 2
ionmov1 3 # BD algorithm
ntime1 10
tolmxf1 5.0d-4
xcart
toldff1 5.0d-5
nband1 1
#Second dataset
natom2 1
nsppol2 2 # LSDA
occopt2 2
nband # Spin up, down
occ
toldfe2 1.0d-6
xcart
spinat2
# Init spin

14. Lesson 2: Convergence Calculation parameters: ecut acell
number of k-points
convergence of SCF cycle: toldfe, toldff
convergence of geometry optimization: tolmxf

15. Lesson 2: ecut t22.in ndtset 12 udtset 6 2 acell 10 10 10
ecut:? ecut+? 5
#First dataset: bond length
natom?1 2
ionmov?1 3
ntime?1 10
tolmxf?1 5.0d-4
xcart?
toldff?1 5.0d-5
nband?1 1
#Second dataset: H-atom
natom?2 1
nsppol?2 2
occopt?2 2
nband?2 1 1
occ?
toldfe?2 1.0d-6
xcart?
spinat?

16. Lesson 2: ecut
What determines ecut?
What if H is changed to Cl?

17. Lesson 2: acell t23.in ndtset 12 udtset 6 2 acell:? 8 8 8
ecut 10
#First dataset: bond length
natom?1 2
ionmov?1 3
ntime?1 10
tolmxf?1 5.0d-4
xcart?
toldff?1 5.0d-5
nband?1 1
#Second dataset: H-atom
natom?2 1
nsppol?2 2
occopt?2 2
nband?2 1 1
occ?
toldfe?2 1.0d-6
xcart?
spinat?

18. Lesson 2: acell
What determines acell?
What if H is changed to Cl?

19. Lesson 2: Optimum parameters and GGA calculation
Use the optimum ecut and acell to determine H2 bond length and atomization energy.
Switch to GGA calculation by changing ixc
No need to change pseudo-potential for H (small core)
No need to change ecut
No need to change acell
Compare results

20. Lesson 3
Crystalline Silicon

21. Lesson 3: Introduction Crystalline silicon (Diamond structure, 2 FCC)
the total energy
the lattice parameter
the band structure (actually, the Kohn-Sham band structure)
Parameters:
k-points,
smearing of cut-off

22. Lesson 3: Introduction Parameters: rprim: premitive vectors
xred: reduced coordinates
K-point sampling
kptopt: 0 read from input, 1,2,3 generates, negative for band calculation
ngkpt: numbers of k-points in 3 directions
nshiftk shiftk kptrlatt
alternatively use kptrlen
Larger cell  smaller Brillouin zone

23. Lesson 3: Sample k-points generation
ngkpt = 2,2,2
First mesh has 8 points, (0,0,0), (0,0,½), (0,½,0), (0,½,½), (½,0,0), (½,0,½), (½,½,0), (½,½,½)
nshiftk = 4, shiftk = (½,½,½), (½,0,0), (0,½,0), (0,0,½)
First shift with (½,½,½), 8 k-points become (¼,¼,¼), (¼,¼,¾), (¼,¾,¼), (¼,¾,¾), (¾,¼,¼), (¾,¼,¾), (¾,¾,¼), (¾,¾,¾)
Second shift with (½,0,0), 8 k-points become (¼,0,0), (¼,0,½), (¼,½,0), ...
Third shift with (0,½,0), 8 k-points become (0,¼,0), (0,¼,½), (0,¾,0), ...
Forth shift with (0,0,½), 8 k-points become (0,0,¼), (0,0, ¾), (0,½,¼), ...
Value ki larger than ½ can be translated to ki-1 e.g. ¾  -¼
Totally 32 points obtained by shifting first mesh, but can be reduced by symmetry

24. Lesson 3: Silicon crystal
Look at input file t31.in, meaning of acell, rprim, xred, kptopt, ngkpt, nshiftk, shiftk, diemac
Try running and check the result
Try changing
kptopt to 3
ngkpt to 3,2,2 etc.
nshiftk, shiftk
using kptrlen instead, with prtkpt = 1,0

25. Lesson 3: Silicon k-point convergence
Look at t32.in and try running it
Why problem occurs?
Change t32.in to correct the problem and to perform a series of calculations to test convergence against number of k-points
ndtset 4
ngkpt
ngkpt
ngkpt
ngkpt
Note number of k-points and energy convergence
Convergence of wavefunction and charge density can also be verified

26. Lesson 3: Silicon k-point convergence
Test k-point, when begin the study new material
Test (at least) three efficient k-point sets
CPU time is proportional to number of k-points
Symmetry reduce number of k-points, but need to be weighted (wtk)
Reference: Monkhorst and Pack paper, Phys. Rev. B 13, 5188 (1976)

27. Lesson 3: Silicon Lattice Parameter
Parameters (t34.in)
optcell 1
ionmov 3
ntime 10
dilatmx 1.05
ecutsm 0.5
Experimental value: Angstrom at 25 degree Celsius, see R.W.G. Wyckoff, Crystal structures Ed. Wiley and sons, New-York (1963)
Calculated value =?
Using LDA with the 14si.pspnc pseudopotential
What are 2 data sets?

28. Lesson 3: Silicon Band Structure
Two steps
SCF calculation of charge density
Non-SCF calculation of eigen values (bands)
Use L-Gamma-X-Gamma circuit
In eight-atom cell coordinates: (1/2 1/2 1/2)-(0 0 0)-(1 0 0)-(1 1 1)
In two-atom cell coordinates: (1/2 0 0)- (0 0 0)- (0 1/2 1/2)-(1 1 1)
Parameters (t35.in)
prtden, iscf, getden, nband, kptopt, ndivk, enunit, tolwfr
kptbounds to
# L point
# Gamma point
# X point
# Gamma point in another cell.
Results: kpt#

29. Crystalline Aluminum and Surface Energy
Lesson 4
Crystalline Aluminum
and Surface Energy

30. Lesson 4: Introduction Aluminum, the bulk and the surface.
the total energy
the lattice parameter
the relaxation of surface atoms
the surface energy
Smearing of the Brillouin zone integration
Preconditioning the SCF cycle

31. Lesson 4: Smearing occopt = 4,5,6,7 tsmear
Use Fermi-Dirac when trying to mimic physical electronic temperature. It is less convenient to use due to "long-tailed“, need more bands.
In general Gaussian-like smearings are preferable.
If you are interested only in the total energies, you can just use a Gaussian smearing - but need to extract corrected energy by taking the semisum of the energy and the free energy.
Methfessel-Paxton and Marzari-Vanderbilt do this automatically for you, and also provide forces, stresses, and whatever else corrected for the leading term in the temperature.
tsmear

32. Lesson 4: Smearing delta functions

33. Lesson 4: Bulk Al Look at t41.in ecut 6 Ha, compare to previous cases
H needed 30 Ha
Si needed 8 Ha
Run
Look at output and note 2 points
Components of energy
Occupation of each band
Test ecut convergence

34. Lesson 4: k-point convergence
How to check k-point convergence?
Look at t42.in
Run
Look at the result
Total energy
acell
Try with a different tsmear

35. Lesson 4: tsmear and k-point covergence
Aluminum:
Total energy (E) and Lattice parameters (A) calculated
using tsmear = 0.05, 0.10 as functions of k-point grid
Larger tsmear converges faster, but ...
Try t43.in

36. Lesson 4: Al (001) surface energy
Slab calculation: Al layer + vacuum layer
Thicknesses of Al and Vacuum layers
Reference energy: Bulk calculation with equivalent parameters, i.e. cell shape, k-point grid, ecut
Esurface = (Eslab/nslab – Ebulk/nbulk)/(2 Asurface)
Look at t44.in and t45.in, what do they represent?
Difficulties: surface reconstruction and different top-buttom surfaces

37. Lesson 4: Al surface energy
Vacuum layer thickness
Defining atomic positions in Cartesian coordinates is more convenient
Preconditioner (dielng) for metal+vacuum case
How many layers of vacuum are needed?
t46.in

38. Lesson 4: Al surface energy
Al layer thickness
Preconditioner (dielng) for metal+vacuum case
Use an effective dielectric constant of about 3 or 5
With a rather small mixing coefficient ~0.2
Alternatively, Use an estimation of the dielectric matrix governed by iprcel=45
Repeat the 3 aluminum layer case for comparison
t47.in
See t47_STATUS to check status of long calculation
How many Al layers are needed?

39. Dynamical Matrix, Dielectric Tensor and Effective Charge
Lesson 5
Dynamical Matrix, Dielectric
Tensor and Effective Charge

40. Lesson 5: Response functions
Response functions are the second derivatives of total energy (2DTE) with respect to different perturbations, e.g.
phonons (Dynamical metrix)
static homogeneous electric field (Dielectric tensor, Born effective charges)
strain (Elastic constants, internal strain, piezoelectricity)
ABINIT computes FIRST-order derivatives of the wavefunctions (1WF)
2DTE is calculated from 1WF
References:
X. Gonze, Phys. Rev. B55, (1997)
X. Gonze and C. Lee, Phys. Rev. B55, (1997).

41. Lesson 5: Response functions
ABINIT gives
phonon frequencies
electronic dielectric tensor
effective charges
Derivative DataBase (DDB)
Contains all 2DTEs and 3DTEs
MRGDDB
Anaddb

42. Lesson 5: Perturbations
Phonon
displacement of one atom (ipert) along one of the axis (idir) of the unit cell, by a unit of length (in reduced coordinates
characterized by two integer numbers and one wavevector
rfatpol defines the set of atoms to be moved
rfdir defines the set of directions to be considered
nqpt, qpt, and qptnrm define the wavevectors to be considered
Electric field
DDK: dH/dk, auxiliary for RF-EF (ipert=natom+1)
Homogeneous electric field (q=0), only (ipert=natom+2), idir = direction
Homogeneous Strain
Uniaxial strain: ipert = natom+3, idir = 1,2,3 for xx,yy,zz
Shear strain ipert = natom+4, idir = 1,2,3 for yz, zx, xy
No internal coordinate relaxation

43. Lesson 5: Ground State of AlAs
trf1_1.in, trf1_x.files (2 potentials)
Note: tolvrs 1.0d-18
Run
Is tolvrs reached? (18)
What is the total energy? (15 digits)

44. Lesson 5: Frozen-phonon E’’
tr1_2.in
Read in previous wavefunction file (irdwfk = 1)
Al is moved (xred)
Need to rename tr1_xo_WFK to tr1_xi_WFK
Edit tr1_x.files to run tr1_2.in
Run
Compare tr1_1.out and tr1_2.out
Symmetry, K-points
Cartesian forces
RMS dE/dt
Estimate E’’ from E(x) = E0+xdE + x2d2E /
x = change in Al position from its equilibrium

45. Lesson 5: Response-Function E’’
d2E/dx2; x = change in Al position from its equilibrium
tr1_3.in
Read in previous wavefunction file (irdwfk = 1)
kptopt = 2
Atomic positions not changed (xred)
Phonon perturbation (rfphon)
Perturbation on Al atom (rfatpol)
Direction (rfdir) and wave-vector (nqpt, qpt)
Run
Output files: *.out (2DEtotal), 1WF, DDB,

46. Lesson 5: RF Full Dynamical Matrix
At Gamma [q=(0,0,0)]
Perturbation J(m,n):
m = Atom number (rfatpol 1 natom)
n = Direction (Reduced) (rfdir 1 1 1)
Dynamical matrix M[j1,j2]
Run
Output files: *.out, 1WF, 1WF4, DDB,
Perturbation of each atom is applied in each direction in turns
idir 2,3 is symmetric with previous calculation
ipert 1,2,4 (electric field)
Note the symmetry M[i,j] = M[j,i]?
Rerun with tolvrs = 10-18
Phonon Energies

47. Lesson 5: Recipe: K-Points
Input k-point set for RF should NOT have been decreased by using spatial symmetries, prior to the loop over perturbations
ABINIT will automatically reduce k-points
kptopt=1 for the ground state
kptopt=2 for response functions at q=0
kptopt=3 for response functions at non-zero q

48. Lesson 5: Recipe: Steps Atomic displacement with q=0,
SC GS IBZ (with kptopt=1)
SC RF Phonon Half Set (with kptopt=2)
Atomic displacement with q=k1-k2 (k1,k2 are special k-points),
SC RF Phonon Full Set (with kptopt=3)
Atomic displacement for a general q point,
NSC GS k+q (might be reduced due to symmetries, with kptopt=1)
Electric Field (with q=0),
NSC RF DDK Half Set (with kptopt=2, and iscf=-3)
SC RF EF Half Set (with kptopt=2)

49. Lesson 5: Recipe: Combinations
Full dynamical matrix, Dielectric tensor and Born effective charges
SC GS IBZ (with kptopt=1)
Three NSC RF DDK (one for each direction) Half Set (with kptopt=2, and iscf=-3)
SC RF Phonon+EF Half Set (with kptopt=2)
Phonon at q=0 and general q points
Perturbations at different q wavevectors cannot be mixed.
NSC GS k+q points (might be reduced due to symmetries, with kptopt=1)
SC RF Phonon q0 Full Set (with kptopt=3)

50. Lesson 5: Full RF calculation of AlAs
Three Data Sets
SC GS IBZ
NSC RF DDK Half k-point set
SC RF Phonon+EF Half k-point set
New parameters
rfelfd, getwfk, getddk
trf1_5.in
Run
Output
Dynamical matrix
Dielectric tensor
Effective charge
Phonon energies

51. Lesson 5: Multiple q Phonon
When qk1-k2,
NSC GS with nqpt=1, qpt, getwfk, getden, kptopt=3, tolwfr, iscf4=-2
SC RF Phonon with rfphon=1, rfatpol, rfdir, nqpt=1, qpt, getwfk=1, getwfq=4, kptopt=3, tolvrs, iscf
Notice: splitting between TO and LO

52. Interatomic Force Constants, Phonon and Thermodynamic Properties
Lesson 6
Interatomic Force Constants,
Phonon and Thermodynamic Properties

53. Lesson 6: DDB File
DDB contains dE with respect to 3 perturbations : phonons, electric field and stresses
Header: DDB version number, natom, nkpt, nsppol, nsym, ntypat, occopt, and nband or array nband (nkpt* nsppol) if occopt=2, acell, amu, ecut, iscf,...
Data:
Number of data blocks
For each block: Type of the block, Number of Elements, List of Elements
In most cases, each element consists of 4 integer and 2 real numbers [idir1, ipert1, idir2, ipert2, Re(2DTE), Im(2DTE)]
Symmetries may reduce number of elements
DDB files can be merged by Mrgddb

54. Lesson 6: Build DDB trf2_1.in has 10 Data Sets
1st SC GS IBZ
2nd NSC RF DDK Half Set
3rd SC RF Phonon+EF Half Set (q=0)
4th-10th SC RF Phonon Full Set (q=Δk)
Note: need to overwrite default parameters in some Data Sets
Data Sets 4-10 use selected K-Points which may be generated by trf2_2.in
Run
See trf2_1o_DS*_DDB

55. Lesson 6: Merging DDB Files
Steps to use Mrgddb
name output
description
number of DDB files
file name list
trf2_3.in
Run
Look at trf2_3.ddb.out
How many datasets?

56. Lesson 6: ANADDB
ANADDB analyses DDB for properties e.g. phonon spectrum, frequency-dependent dielectric tensor, thermal properties
Files: input, output, DDB, other files
To run anaddb < anaddb.files > log &
Common parameters: dieflag, elaflag, elphflag, ifcflag, instrflag, nlflag, piezoflag, polflag, thmflag

57. Lesson 6: Interatomic Force Constants
Dynamical Matrix and Interatomic Force Constants are Fourier Transforms of each other
Calculated Dynamical Matrix on a grid of wavevectors  IFC; IFC vanishes rapidly with interatomic distance
ifcflag=1; (ifcflag=0 is for checking, or when there is not enough information in DDB)
Q-point grid: brav, nqgpt, nqshft, q1shft
Energy conservation and charge neutrality: asr, chneut
Others: dipdip, ifcana, ifcout, natifc, atifc
Run ..\..\anaddb < trf2_4.files > trf2_4.log

58. Lesson 6: IFC Results On site term of Al trace = 0.28080
First NN = 4 As atoms at 4.6 trace =
Second NN = 12 Al atoms at 7.5 trace =
Third NN = 12 As atoms at 8.8 trace =
Fourth NN = 6 Al atoms at 10.6 trace =
Fifth NN = 12 As atoms at 11.6 trace =
Sixth NN Al atoms at 13.0 trace =
Applications:
Phonon dispersion curve
Elastic constants
MD (Harmonic approximation)

59. Lesson 6: Phonon Band Structure
ifcflag=1
Q-point grid: brav, nqgpt, nqshft, q1shft
Energy conservation and charge neutrality: asr, chneut
Others: dipdip
Band: eivec, nph1l, qph1l, nph2l, qph2l
Run ..\..\anaddb < trf2_5.files > trf2_5.log
trf2_5_band2eps.freq .dspl are obtained
Run ..\..\band2eps < trf2_6.files > trf2_6.log
trf2_6.out.eps is obtained
view with ghostview; note discontinuity of Optical Phonon at Gamma point
Edit trf2_5_band2eps.freq, lines 1 and 31, correct LO freq. (trf2_5.out)
Run band2eps again

60. Lesson 6: Thermodynamic Properties
Normalized phonon DOS
Phonon internal energy, free energy, entropy, constant volume heat capacity as a function of the temperature
Debye-Waller factors (tensors) for each atom, as a function of the temperature (DISABLED, SORRY)
Parameters: thmflag, ng2qpt, ngrids, q2shft, nchan, nwchan, thmtol, ntemper, temperinc, tempermin
..\..\anaddb < trf2_7.files > trf2_7.log
At T F(J/mol-c) E(J/mol-c) S(J/(mol-c.K)) C(J/(mol-c.K))
(A mol-c is the abbreviation of a mole-cell, that is, the
number of Avogadro times the atoms in a unit cell)
E E E E+00
E E E E+00
E E E E+01
E E E E+01
E E E E+01
E E E E+01
E E E E+01
E E E E+01
E E E E+01
E E E E+01

61. Other Response-Function Tutorials
Optic: Frequency-dependent linear and second order nonlinear optical response
Frequency dependent linear dielectric tensor
Frequency dependent second order nonlinear susceptibility tensor
Electron-Phonon interaction and superconducting properties of Al.
Phonon linewidths (lifetimes) due to the electron-phonon interaction
Eliashberg spectral function
Coupling strength
McMillan critical temperature
Elastic and piezoelectric properties.
Rigid-atom elastic tensor
Rigid-atom piezoelectric tensor (insulators only)
Internal strain tensor
Atomic relaxation corrections to the elastic and piezoelectric tensor
Static non-linear properties
Born effective charges
Dielectric constant
Proper piezoelectric tensor (clamped and relaxed ions)
Non-linear optical susceptibilities
Raman tensor of TO and LO modes
Electro-optic coefficients

62. Quasi Particle Band Structure
Lesson 7
Quasi Particle Band Structure

63. Lesson 7: Introduction System Approach
Nucleus + Electrons
Approach
Electron wave function
Electron density  DFT
Quasiparticles
Quasiparticle = Bare particle + Decorations
Modify
Equation of motion
Energy, Mass
Life time

64. Lesson 7: GW Approximation
In the quasiparticle (QP) formalism, the energies and wavefunctions are obtained by the Dyson equation:
QP equation
S self-energy (a non-local and energy dependent operator) is the difference
between the energies of bare particle and quasiparticle.
Within the GW approximation,S is given by:
GW Self-Energy
Green
Function
Dynamical
Screened
Interaction

65. Lesson 7: Green function
Green function G corresponding to QP equation is
Green function G may be approximated by the independent particle G(0):
The basic ingredient of G(0) is the Kohn-Sham electronic structure:

66. Lesson 7: Dynamical Screened Interaction
W is approximated by RPA:
Dynamical Screened Interaction
Dielectric Matrix
Coulomb
Interaction
RPA approximation
Independent Particle Polarizability
Adler-Wiser expression
ingredients: KS wavefunctions and KS energies

67. Lesson 7: GWA correction to LDA
QP equation
KS equation
Difference = Vxc is replaced by S.
Thus GWA correction to the DFT KS eigenvalues by 1st order PT:
0-order wavefunctions
0-order
Non Self-Consistent G0WRPA, Plasmon Pole model

68. Lesson 7: GWA Performance
LDA, GWA, and experimental energy gaps for semiconductors and
insulators.
GWA corrects most of the
LDA band gap underestimation.
The discrepancy for LiO2 results from the neglect of excitonic effects.
The experimental value for BAS is tentative.

69. Lesson 7: Discrepancy of LDA
In Kohn-Sham theory, eigenvalues εi are Lagrange multipliers to ensure the orthogonality of KS orbitals
So both KS eigenvalues and orbitals are not physical
εi are not energy levels; εN (highest level) is chemical potential for metal or negative ionization energy for semiconductor and insulator
In absence of quasiparticle calculations. LDA energy are routinely used to interpreted experimental spectra
LDA energy dispersions are often in fair agreement with experiment; LDA band gaps are sometimes empirically adjusted to fit experimental values
LDA VXC approximate self-energy (neglecting non-local, energy dependent and life-time effects)
LDA generally provides a qualitative understanding.

70. Lesson 7: GWA Calculation Steps
SC GS (fixed lattice parameters and atomic positions)
self-consistent density, potential and Kohn-Sham eigenvalues and eigenfunctions at relevant k-points and on a regular grid of k-points
Compute
susceptibility matrix chi0 and chi, on a regular grid of q-points, for at least two frequencies (zero and a pure imaginary frequency ~ a dozen of eV)
Dielectric matrix epsilon and 1/epsilon
Self-energy sigma at the given k-point, and derive the GW eigenvalues for the target states at this k-point

71. Lesson 7: Generation of KSS File
tgw_1.in, 3 Data Sets
First
nbandkss1 -1 # Number of bands in KSS file
-1 is full diagonalization, see out file for number of plane waves and number of bands
nband # Number of bands to be computed
istwfk *1 #Do not use time reversal symmetry for storing wavefunction
npwkss 0: for same as ecut
kssform 1: for full diag; 3: for conjugated gradient
symmorphi 0: symmorphic symmetry operations, only

72. Lesson 7: Generation of SCR File
Second
optdriver # Screening calculation
getkss # Obtain KSS file from previous dataset
nband # Bands to be used in the screening calculation
ecutwfn # Cut-off energy of the planewave set to represent the wavefunctions
ecuteps # Cut-off energy of the planewave set to represent the dielectric matrix
ppmfrq eV # Imaginary frequency where to calculate the screening

73. Lesson 7: Calculation of Sigma
Third
optdriver # Self-Energy calculation
getkss # Obtain KSS file from dataset 1
getscr # Obtain SCR file from previous dataset
nband # Bands for Self-Energy calculation
ecutwfn # Planewaves to represents wavefunctions
ecutsigx # Dimension of the G sum in Sigma_x
Dimension of Sigma_c = size of screening matrix (SCR file) or size of Sigma_x, whichever is smaller
nkptgw # num of k-point for GW correction
kptgw # k-points, which must present in KSS file
bdgw # calculate GW corrections for bands
zcut for avoiding divergence in integration

74. Lesson 7: GWA Output File
Data Set 1
Kohn-Sham electronic Structure file
Note number of plane waves, number of bands
Check: Test on the normalization of the wavefunctions
Data Set 2
Check: test on the normalization of the wavefunctions
Is it the same as Data Set 1? Effect of ecutwfk
total number of electrons per unit cell
Electron density and plasma frequency
calculating at frequencies omega [eV]:
dielectric constant
Data Set 3
Band energy “E0 <vxclda>”

75. Lesson 7: Convergence Study
Simplify: Gamma Point, only
tgw_2.in: Generate KSS and SCR files
Check Data Sets, KSS is separated from GS
Note values of ecut*
Run, Check normalization, number of electrons, dielectric constant

76. Lesson 7: Sigma ecutwfn convergence
tgw_3.in: ndtset 5, ecutwfn: 3.0, ecutwfn+ 1.0
Note input KSS and SCR file names
Rename
tgw_2o_DS2_KSS to tgw_3o_DS1_KSS
tgw_2o_DS3_SCR to tgw_3o_DS1_SCR
Run
Output
Num. plane-waves for wave function in Sigma and Epsilon calculations
Number of electrons per unit cell
Normalization (grep sum_g)
Band energies (grep –A 2 –i “E0 <vxclda”)
If ecutwfn 5.0 is used, what is the error in band energy?

77. Lesson 7: ecutsigmax convergence
tgw_4.in: ndtset 7, ecutsigmax: 3.0, ecutwfn+ 1.0
Note input KSS and SCR file names
Rename
tgw_3o_DS1_KSS to tgw_4o_DS1_KSS
tgw_3o_DS1_SCR to tgw_4o_DS1_SCR
Run
Output
Num. plane-waves for Sigma_x calculations
Number of electrons per unit cell
Normalization (grep sum_g)
Band energies (grep –A 2 –i “E0 <vxclda”)
What is the appropriate ecutsigmax and the associated error in band energy?

78. Lesson 7: Sigma nband convergence
tgw_5.in: ndtset 5, nband: 50, nband+ 50
Note input KSS and SCR file names
Rename
tgw_4o_DS1_KSS to tgw_5o_DS1_KSS
tgw_4o_DS1_SCR to tgw_5o_DS1_SCR
Run
Output
Num. plane-waves are fixed now
Numbers of bands for KSS, Sigma and Epsilon
Number of electrons per unit cell
Normalization (grep sum_g)
Band energies (grep –A 2 –i “E0 <vxclda”)
What is the appropriate nband and the associated error in band energy?

79. Lesson 7: 1/ε ecutwfn convergence
tgw_6.in: ndtset 10, udtset 5 2
Two steps
Data Set ?1: calculate screening (1/ε)
Data Set *2: calculate GW correction (Sigma)
How to prepare KSS and SCR files?
Run
Output
Num. plane-waves for wave function in Sigma and Epsilon calculations
Dielectric constant
Normalization (grep sum_g)
Band energies (grep –A 2 –i “E0 <vxclda”)
If ecutwfn 4.0 is used, what is the error in band energy?

80. Lesson 7: 1/ε nband convergence
tgw_7.in: ndtset 10, udtset 5 2
Two steps
Data Set ?1: calculate screening (1/ε)
Data Set *2: calculate GW correction (Sigma)
How to prepare KSS and SCR files?
Run
Output
Num. plane-waves for wave function in Sigma and Epsilon calculations
Dielectric constant
Normalization (grep sum_g)
Band energies (grep –A 2 –i “E0 <vxclda”)
To achieve band energy error < 0.01 eV, how many bands must be used?

81. Lesson 7: ecuteps convergence
tgw_8.in: ndtset 10, udtset 5 2
Two steps
Data Set ?1: calculate screening (1/ε)
Data Set *2: calculate GW correction (Sigma)
How to prepare KSS and SCR files?
Run
Output
Num. plane-waves for wave function in Sigma and Epsilon calculations
Dimension of epsilon
Dielectric constant
Normalization (grep sum_g)
Band energies (grep –A 2 –i “E0 <vxclda”)
To achieve band energy error < 0.01 eV, how large ecuteps must be used?

82. Lesson 7: (direct) Egap of Silicon
Data Set 1: SC GS
print out the density
10 k-points in IBZ = 4x4x4 FCC grid (Shifted, no Gamma point)
Data Set 2: NSC GS
Kohn-Sham structure, 19 k-points in IBZ but not shifted, Gamma point included
Data Set 3: Calculate Screening
Very time-consuming
ecutwfn = 3.6
nband = 25 [CPU time  nband (Conduction)]
Accuracy of GW energy ~ 0.2 eV
Accuracy of energy difference ~ 0.02 eV
There is no zero of energy defined for bulk system
Data Set 4: Self-energy matrix at Gamma

83. Lesson 7: (direct) Egap of Silicon 2
What are direct Egap of Silicon by LDA and GWA?
Choice of pseudopotential can contribute to Egap variation:
Egap GWA accuracy ~ 0.1 eV
Full band calculation is possible, by shifting the k-point
Simplification: GW corrections are quite linear with the energy

84. Thank you