acell 10 10 10 Cell size is 103 ntypat 1 One type of atom znucl 1 Atomic number is one natom 2 There are two atoms typat 1 1 They both are of type 1 xcart Location of the atoms -0.7 0.0 0.0 atom 1 in Bohr 0.7 0.0 0.0 atom 2 in Bohr ecut 10.0 Cut-off energy in Hartree nkpt 1 One k point nstep 10 Maximal number of SCF cycles toldfe 1.0d-6 Threshold diemac 1.0 Preconditioner diemix 0.5 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
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.
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 metalvacuum case
How many layers of vacuum are needed
t46.in
38 Lesson 4 Al surface energy
Al layer thickness
Preconditioner (dielng) for metalvacuum 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 iprcel45
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 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)
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) 20.0 8.1384756E03 8.1463588E03 3.9416450E-01 1.4169102E00 40.0 8.1061319E03 8.2368069E03 3.2668767E00 7.8985027E00 60.0 7.9980215E03 8.4575659E03 7.6590737E00 1.3992227E01 80.0 7.7974376E03 8.7915524E03 1.2426435E01 1.9325165E01 100.0 7.5004823E03 9.2274431E03 1.7269608E01 2.4175005E01 120.0 7.1069991E03 9.7544363E03 2.2061977E01 2.8411187E01 140.0 6.6189292E03 1.0359248E04 2.6716563E01 3.1955266E01 160.0 6.0396228E03 1.1028289E04 3.1179165E01 3.4847422E01 180.0 5.3732225E03 1.1749439E04 3.5423425E01 3.7183863E01 200.0 4.6241912E03 1.2512641E04 3.9442249E01 3.9069447E01 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
62 Lesson 7
Quasi Particle Band Structure
63 Lesson 7 Introduction
System
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 areobtained 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 approximationS is given by GW Self-Energy Dynamical Screened Interaction Green Function 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 Coulomb Interaction Dielectric Matrix 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 ei are Lagrange multipliers to ensure the orthogonality of KS orbitals
So both KS eigenvalues and orbitals are not physical
ei are not energy levels eN (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
Compute
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
nband1 9 Number of bands to be computed
istwfk1 101 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
optdriver2 3 Screening calculation
getkss2 -1 Obtain KSS file from previous dataset
nband2 17 Bands to be used in the screening calculation
ecutwfn2 2.1 Cut-off energy of the planewave set to represent the wavefunctions
ecuteps2 3.6 Cut-off energy of the planewave set to represent the dielectric matrix
ppmfrq2 16.7 eV Imaginary frequency where to calculate the screening
73 Lesson 7 Calculation of Sigma
Third
optdriver3 4 Self-Energy calculation
getkss3 -2 Obtain KSS file from dataset 1
getscr3 -1 Obtain SCR file from previous dataset
nband3 30 Bands for Self-Energy calculation
ecutwfn3 5.0 Planewaves to represents wavefunctions
ecutsigx3 6.0 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
nkptgw3 1 num of k-point for GW correction
kptgw3 k-points which must present in KSS file
bdgw3 4 5 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 ltvxcldagt
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 ltvxclda)
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 ltvxclda)
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 ltvxclda)
What is the appropriate nband and the associated error in band energy
79 Lesson 7 1/e ecutwfn convergence
tgw_6.in ndtset 10 udtset 5 2
Two steps
Data Set 1 calculate screening (1/e)
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 ltvxclda)
If ecutwfn 4.0 is used what is the error in band energy
80 Lesson 7 1/e nband convergence
tgw_7.in ndtset 10 udtset 5 2
Two steps
Data Set 1 calculate screening (1/e)
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 ltvxclda)
To achieve band energy error lt 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/e)
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 ltvxclda)
To achieve band energy error lt 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
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