OptaDOS: User Guide - University of Cambridge
Contents
1. 55 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Since we had efermi optados OPTADOS sets the internal value of the Fermi level to the one it has derived from the DOS This is important for subsequent calculations Other valid options are file where OPTADOS uses the value calculated by the elec tronic structure code that generated the eigenvalues insulator where OPTADOS uses a value calculated from assuming the system is non metallic or a value set by the user OPTADOS now performs some analysis of the DOS at the Fermi level a ae aaa Saas aa O ae DOS at Fermi Energy Analysis l Fermi energy used 5 4109 eV From Adaptive broadening Spin Component 1 DOS at Fermi Energy 0 0011 eln cell lt DEA l Spin Component 2 DOS at Fermi Energy 0 0011 eln cell lt DEA From this we may assume that there is a band gap Importantly then OPTADOS calculates the band energy from the DOS is has calculated OptaDOS User Guide 31 TS SSS SSS SSS assert Band Energy Analysis Band energy Adaptive broadening 1 3609 eV lt BEA Band energy From CASTEP 1 3622 eV lt BEC ee we we a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a e e a a a a e a a a a a a a a a a a ee i i i ii As the quality of the OPTADOS calculation is increased these two values should converge to the same answer Finally OPTADOS shifts the Fe2. Si 1 L2 3 Si 2 K1 Si 2 L1 Si 2 L2 3 i e all edges from all atoms are produced 2 To include a core hole in the calculation first one atom is chosen to have the excitation To begin we will keep two atoms in the unit cell and distinguish one atom by changing the BLOCK POSITIONS_FRAC BLOCK POSITIONS_FRAC Si exi O 0000000000 O 0000000000 O 0000000000 Si 0 2500000000 0 2500000000 0 2500000000 ENDBLOCK POSITIONS_FRAC in the Si2_CORE ce11 file The atom Si exi is the one to have a core hole To create a core hole we remove a 1s electrons from the electronic configuration used in the gener ation of the pseudopotential We have already generated an on the fly pseudopotential without a core hole in the previous section Information about the pseudopotentials is included at the top of the Si2_CORE castep file Element Si Ionic charge 4 00 Level of theory LDA Reference Electronic Structure Orbital Occupation Energy 3p 2 000 0 153 Pseudopotential Definition 3s 2 000 0 400 l Beta I e Rc scheme norm l OptaDOS User Guide 39 Augmentation charge Rinner 1 298 Partial core correction Rc 1 298 1 O 0 400 1 797 qc 0 l 2 0 0 250 1 797 qc 0 l 3 1 0 153 1 797 qc 0 4 1 0 250 1 797 qc 0 l loc 2 0 000 1 797 pn 0 The line 211 8 1 8 1 3 2 13 4130 31 32LGG qc 4 specifies the parameters used to create the pseudopotential We use this as
3. 42 7 7 I think Pve found a bug what should I do 42 A Interface with other codes 43 AT bands file s ecg ecto amied ee 43 A2 some Bin Hle e Ate ae e en i a EER EOE 44 A3 pdosbin file s se s sagis a dama ae EERO AAA epa 45 AA selnes bin file oso ocea ee ee Pa ee hee a e a 47 We would like to thank Phil Hasnip and Keith Refson for very helpful discussions and Gareth Griffiths and Kane O Donnell for extensive beta testing AJM RJN and CJP acknowledge support from the EPSRC Additionally AJM acknowledges the Winton programme for the physics of sustainability and RJN the ERC Grant ERC 2009 StG 240500 JRY acknowl edges support from the Royal Society through a University Research fellowship AJM RJN CJP and JRY September 2013 Chapter 1 Introduction 1 1 Background OPTADOS is a code for calculating optical core level excitation spectra along with full partial and joint electronic density of states DOS The code was developed by merging the LinDOS code of Andrew Morris and Chris Pickard at University College London with the optical properties code of Rebecca Nicholls and Jonathan Yates at Oxford University OPTADOS is written in Fortran 95 and may be run in parallel using MPI At present OPTADOS interfaces with CASTEP and ONETEP output files although it is extendable to perform calculations on any set of band eigenvalues and their derivatives generated by any electronic structure code The code is freely avail
4. 6 Setting DOS_SPACING 0 001 gives a high quality plot as shown in Fig 6 2 7 Other things to try are PDOS Si1 Si2 s Output the PDOS on Si atom 1 and the PDOS on the s channel of Si atom 2 Resulting in two projectors PDOS sum Si1 2 s Output the sum of the s channels on the two Si atoms Resulting in one projector PDOS Si1 p Output the p channel on Si atom 1 Resulting in one projector 6 3 JDOS See examples Si2_JDOS This is a simple example of using OPTADOS for calculating joint electronic density of states We choose to recalculate the Fermi level using the calculated DOS rather than use the Fermi level suggested by CASTEP and so EFERMI OPTADOS is included in the Si2 odi file 1 Execute OPTADOS using the example files The JDOS is outputted to Si2 jadaptive dat A file suitable for plotting using xmgrace is written to Si2 jadaptive agr 2 Check the effect of changing the sampling by increasing and decreasing the value of JDOS_SPACING in the Si2 odi file 3 If TASK compare_jdos is used instead OPTADOS will calculate the JDOS using all the broadening methods This is good practice to see whether the broadening widths are appropriate before more advanced tasks are carried out 36 OptaDOS User Guide 6 4 OPTICS Two sets of example files are provided for calculations of optical properties For each example the CASTEP files containing all the cell and simulation parameters a
5. Ambrosch Draxl and J O Sofo Comput Phys Commun 175 1 2006 P E Bl chl O Jepsen and O K Andersen Phys Rev B 49 23 16223 1994 M Boon M Methfessel and F Mueller J Phys C 19 5337 1986 M Dressel and G Gr ner Electrodynamics of Solids C U P 2002 R F Egerton Electron Energy Loss Spectoscopy in the Electron Microscope Plenum Press 1996 G Lehmann and M Taut Phys Stat Sol b 54 469 1972 M Methfessel M Boon and F Mueller J Phys C 16 1949 1983 M Methfessel M Boon and F Mueller J Phys C 20 1069 1987 H J Monkhorst and J D Pack Phys Rev B 13 5188 1976 A J Morris C J Pickard and R J Needs Phys Rev B 78 184102 2008 J E M ller and J W Wilkins Phys Rev B 8 4331 1984 C J Pickard and M C Payne Phys Rev B 59 7 4685 1999 C J Pickard and M C Payne Phys Rev B 62 7 4383 2000 G Rajagopal R J Needs S Kenny W M C Foulkes and A James Phys Rev Lett 73 1959 1994 K Refson orbitals2bands program see www castep org M D Segall C J Pickard R Shah and M C Payne Mol Phys 89 2 571 1996 J Van Hove Phys Rev 89 6 1189 1953 J R Yates X Wang D Vanderbilt and Souza I Phys Rev B 75 195121 2007 Oleg V Yazyev Konstantin N Kudin and Gustavo E Scuseria Phys Rev B 65 205117 2002 49
6. 46 0 00 0 00 0 00 5 46 ENDBLOCK LATTICE_CART BLOCK POSITIONS_FRAC Si exi 0 0000000000 0 0000000000 0 0000000000 Si 0 5000000000 0 5000000000 0 0000000000 Si 0 5000000000 0 0000000000 0 5000000000 Si 0 0000000000 0 5000000000 0 5000000000 Si 0 2500000000 0 2500000000 0 2500000000 Si 0 7500000000 0 2500000000 0 7500000000 Si 0 2500000000 0 7500000000 0 7500000000 Si 0 7500000000 0 7500000000 0 2500000000 ENDBLOCK POSITIONS_FRAC Run OPTADOS and compare the spectrum from the face centred unit cell with that from the primitive unit cell Continue constructing larger unit cells until the core hole spectrum stops changing with increasing separation between the periodic images 4 Other things to try include Changing the geometry from polycrystalline to polarised Including life time and instrumentation broadening Chapter 7 Frequently Asked Questions 7 1 OptaDOS crashes complaining that it can t read the seed bands or seed cst_ome file Which version of CASTEP are you using See Sect 5 2 5 7 2 The examples do not work and I m using castep version 6 0 CASTEP version 6 0 was released during the transition of the spectral module and features The easiest way to solve this is to obtain a copy of CASTEP gt 6 0 where OPTADOS will work out of the box However to make the examples work with CASTEP 6 0 the OPTADOS examples require a few tweaks outlined below e Replace SPECTRAL_KPOINTS_MP_GRID in the cell fil
7. Er Fon K AEn P 2 1 and occ unocc meje D E Pon lK Er 2 2 where Epp are the energy eigenvalues of the system They are also extendable to integration over spin polarised channels in a straightforward way 2 2 Brillouin Zone Sampling Schemes Since the crystal momentum k is a continuous quantum number the band structure in an ab initio calculation is approximated using specific k points within the first Brillouin zone These k points may be chosen through symmetry perhaps using a Monkhorst Pack grid or the multi k point generalisation to the Baldereschi scheme Obtaining the energy bands from a set of eigenenergies at discrete k points is non trivial This simplest way of assigning bands by counting eigenvalues at k points implicitly assumes that there are no band crossings in the BZ This is further complicated by band kissing where bands approach but due to small interactions between the bands breaking the degeneracy they remain continuous Considering band coefficients and the overlap matrix it has been shown how to assign bands to individual eigenenergies however these still require a broadening scheme to obtain a DOS Below we detail some approaches to obtaining a DOS from a set of eigenenergies 10 OptaDOS User Guide 2 2 1 Gaussian broadening The reciprocal space is discretised into sub cells each containing a k point which contributes to the integral corresponding to the energy of
8. angular decompose as s p d etc species decompose onto atomic species C H etc sites decompose onto atomic sites C1 H1 H2 etc species_ang decompose onto angular momentum channels and species Cs Cp etc C H decompose onto Carbon and Hydrogen sites C1 C3 C4 C8 decompose onto atoms C1 C2 and C4 C5 C6 C7 C8 i1 s d decompose onto s and d channels for atom Sil sum C1 C3 C4 C8 decompose onto atoms Cl C2 and C4 C5 C6 C7 C8 and combine into the single projection 5 6 Optics Parameters 5 6 1 character len 20 optics_geom Specifies the geometry for the optics calculation Possible options polycrystalline Isotropic average polarized unpolarized tensor Full dielectric tensor The default is polycrystalline 5 6 2 real kind dp optics_qdir 3 Direction of polarisation Must be specified if optics_geom polarized or optics_geom unpolarized There is no default value 26 OptaDOS User Guide 5 6 3 logical optics_intraband If true the intraband contribution to the dielectric function will be calculated Important for metals The default is FALSE 5 6 4 real kind dp optics_drude_broadening Value of broadening included in the Drude term expressed in s The default value is 1E 14 5 6 5 real kind dp optics_lossfn_broadening FWHM of Gaussian used to broaden the loss function The default value is 0 i e no broad
9. but this time it lists sequentially the interband contribution intraband contribu tion and total dielectric function for each component 4 This time if additional broadening for the loss function is included by using the key word optics_lossfn_broadening AL_OPTICS_loss_fn dat will contains four sequen tial data sets These are the interband contribution the intraband contribution the total loss function without the additional broadening and the broadened total loss func tion 6 5 CORE See examples Si2_CORE This is a simple example of using OPTADOS for calculating core level absorption spectra for crystalline silicon We assume that the reader is familiar with the previous section on calculating DOS 38 OptaDOS User Guide 1 We begin by running a CASTEP calculation using the files provided in examples Si2_CORE Note that we do not specify pseudopotentials in the Si2_CORE cell file hence require CASTEP to generate on the fly pseudopotentials This is important as most pseudopo tential formats do not contain enough information for the PAW reconstruction needed for a CORE calculation For any atom a CORE spectra is to be calculated an On the fly pseudopotential must be used Execute OPTADOS using the OPTADOS input file provided and the file Si2_CORE_core_edge dat will be created The file contains two columns the first is the energy and the second is the spectrum This file contains the following edges Si 1 K1 Si 1 Li
10. first column The header of the file shows the results of the two sum rules associated with the loss function f I m z5 w dw Ness w and Je Im 33 l div 7 Si2_0PTICS_reflection dat This file contains the reflection coefficient second column as a function of energy first column i2_OPTICS_refractive_index dat This file contains the refractive index The columns are the energy and real and imaginary parts of the refractive index re spectively Corresponding agr files are also generated which can be plotted easily using xmgrace 2 Change parameters JDOS_SPACING and JDOS_MAX and check the effect on the optical properties Note all of the other optical properties are derived from the dielectric function OptaDOS User Guide 37 3 The OPTADOS input file has been set up to calculate the optical properties in the polycrystalline geometry optics_geom polycrystalline It is possible to calcu late either polarised or unpolarised geometries or to calculate the full dielectric tensor To calculate the full dielectric tensor set optics_geom tensor This time only the file Si2_OPTICS_epsilon dat is generated The format of this file is the same as before the columns are the energy and the real and imaginary parts of the dielectric func tion respectively but this time the six different components of the tensor are listed sequentially in the order xz Eyy Ezz Ezy Ezz aNd Eyz 4 Additional broadening ca
11. logical keyword can be set to true using any of the following strings T true true 19 20 OptaDOS User Guide 5 2 General Parameters 5 2 1 character len 20 task Tells the code what to compute The valid options for this parameter are dos default compare_dos compare_jdos jdos pdos optics core all Several tasks can be specified e g to compute dos and jdos use task dos jdos However the compare_dos and compare_jdos tasks can only be combined with each other and no additional tasks compare_dos and compare_jdos calculate the DOS and JDOS respectively using all broadening schemes It is good practice to check the quality of the underlying DOS before other tasks are requested 5 2 2 character len 50 broadening Specified the scheme used to broaden a discrete sampling of the Brillouin Zone to a continuous spectral function The valid options for this parameter are adaptive default fixed linear quad not currently implemented 5 2 3 integer iprint This indicates the level of verbosity of the output from 1 the bare minimum 2 with progress reports to 3 which corresponds to full debugging output The default value is 1 OptaDOS User Guide 21 5 2 4 character len 20 energy_unit The energy unit to be used for writing quantities in the output files The valid options for this parameter are eV default Ha 5 2
12. the bands file 5 3 5 real kind dp dos_max_energy Upper energy range for DOS and related properties Default value is 5eV above the highest eigenvalue in the bands file 5 3 6 real kind dp dos_nbins Instead of setting a Default value dos_spacing the total number of DOS bins may be given Useful for comparison with LinDOS 24 OptaDOS User Guide 5 3 7 real kind dp dos_spacing Resolution at which to compute the DOS and related properties Default value is 0 1eV 5 3 8 logical set_efermi_zero Shift energy scales so that the Fermi energy is at 0 Default value FALSE 5 4 JDOS Parameters 5 4 1 real kind dp jdos_max_energy Upper energy range for JDOS and related properties Default value is the difference between the valence band maximum or Fermi level and the highest eigenvalue in the bands file 5 4 2 real kind dp jdos_spacing Resolution at which to compute the DOS and related properties Default value is 0 01eV 5 4 3 real kind dp scissor_op Value of the scissor operator Default value is 0eV i e not used 5 4 4 real kind dp exclude_bands This allows a list of bands which are NOT to be included in the JDOS or OPTICS cal culation to be specified The bands 1 2 4 5 6 for example can be specified using exclude_bands 1 2 4 6 OptaDOS User Guide 25 5 5 PDOS Parameters 5 5 1 character pdos Defines which components to include in the pdos analysis
13. the k point at their centre Band dispersion may be crudely approximated by smearing each sub cell s contribution by a fixed width Gaussian function of some width w 5 En E gt exp Ens E Ju 2 3 wy 2T 2 This approach requires a large number of k points to converge the DOS since when choosing w there is a trade off between representing the sharp features such as van Hove singularities and not introducing spurious oscillations due to the limited k point sampling The band crossing problem is not present since the bands are modelled as dispersionless Fixed width Gaussian broadening may be chosen for OPTADOS calculations with broadening fixed 2 2 2 Interpolative schemes In the linear tetrahedron interpolative scheme the BZ is divided into roughly equal size tetra hedra with the band energy calculated at each vertex The DOS contribution of each tetrahedron is then calculated analytically by linear interpolation Linear interpolation suffers from the band crossing problem since the interpolation always joins the lowest energy bands together which has the effect of avoiding all band crossing and kissing The method also does not describe van Hove singularities well since the interpolation is linear Higher order interpolation schemes such as the quadratic tetrahedron scheme have been proposed which converge the singularities more rapidly than the linear scheme but these still require a high densi
14. 5 logical legacy_file_format TRUE Read CASTEP input compatible with versions lt 6 0 FALSE Default Read CASTEP input compatible for use with CASTEP versions 6 0 and generated with the castep spectral task 5 2 6 real kind dp adaptive_smearing Set the relative smearing in the adaptive scheme Default value is 0 4 5 2 7 real kind dp fixed_smearing Smearing width for fixed broadening If spectral_scheme fixed default value is 0 3eV 5 2 8 real kind dp linear_smearing Smear the linear broadening with a Gaussian of this width Default value is 0 0 5 2 9 character len 20 efermi Choose which Fermi energy to use The valid options for this parameter are optados default OPTADOS recalculates the Fermi energy by performing a DOS cal culation file Take the value from the output of the ab initio calculation 22 OptaDOS User Guide insulator Assume that the material is an insulator and counts filled bands to find the Fermi energy lt real number gt User supplied value The default value is optados 5 2 10 character len 20 output_format Format in which to output data The valid options for this parameter are gnuplot grace default 5 2 11 logical finite_bin_correction Force each Gaussian to be larger than a single energy bin Useful for adaptive smearing and semi core states when numerical_intdos TRUE Default value TRUE 5 2 12 logical
15. CASTEP website www castep org 2 Perform an OPTADOS calculation Add LEGACY_FILE_FORMAT true inthe Si2_DOS odi input file if the CASTEP version you are using is before 6 0 Then execute optados lt SYSTEM gt lt BUILD gt lt COMMS_ARCH gt x86_64 Si2 This generates 3 files 29 OptaDOS User Guide e Si2 odo OPTADOS general output file e Si2 adaptive dat The adaptive broadened DOS raw output data e Si2 adaptive agr The adaptive broadened DOS in a file suitable to be plotted by xmgrace 3 Open the Si2 odo file in a text editor e g vi or emacs OPTADOS has performed a Density of States calculation HRS SS Fermi Energy Analysis 22 92 2 22223222222H21225 From Adaptive broadening l Spin Component 1 occupation between 3 99961 and 4 00003 lt Dc Spin Component 2 occupation between 3 99961 and 4 00003 lt Oc Fermi energy Adaptive broadening 5 4109 eV lt EfA It has used the integrated DOS to work out the Fermi level and has suggested the error in the integration by indicating the number of electrons at the Fermi level Since we had 4 up electrons and 4 down in the input file this analysis seems satisfactory a Electronic Data 5 Number of Bands 23 l Grid size 10 x 10 x 10 Number of K points 110 Spin Polarised Calculation True l Number of up spin electrons 4 00 Number of down spin electrons 4 00 4
16. CH x86_64 Si2 but your MPI implementation may be different 6 In Si2 odo we now have a new section analysing the band gap in various ways PES SPSS Bandgap Anal y 818 2 2 5 2 5 27 5 5 gt 95 Number of kpoints at VBM CBM Spin 1 3 1 1 Spin 2 1 1 32 OptaDOS User Guide Electronic Density of States Generated by OptaDOS A _ up spin channel down spin channel 10 20 30 Energy eV 0 5 eDOS o 0 5 Figure 6 1 Density of States of Silicon generated by adaptive broadening and a very coarse energy sampling of 0 1 eV Thermal Bandgap 0 6676272107 eV Between VBM kpoint 0 05000 0 05000 0 05000 and CBM kpoint 0 45000 0 05000 0 45000 gt Indirect Gap Optical Bandgap Spin 1 2 5542517447 eV Spin 2 2 5542463024 eV Number of kpoints with this gap Spin E 3 1 Spin 2 1 Average Bandgap Spin l E 3 8121372691 eV Spin 2 3 8121342659 eV Weighted Average 3 8121357675 eV OPTADOS is very careful in its band gap analysis It uses the bare eigenvalues un broadened and works out the nature and size of the thermal gap optical gap and the average gap over all of the Brillouin zone In cases of multi valleyed semiconductors OPTADOS will report the number of conduction band minima or valence band maxima with identical energies but will not report the nature of the gap Increasing the number of integration points has improved the band energy of the ada
17. FINITE_BIN_CORRECTION true Linear broadening may also be improved by using HYBRID_LINEAR true Van Hove singularities and other sharp features are now described at the adaptive broadening level if the bands are flatter than HYBRID_LINEAR_GRAD_TOL Hybrid linear may also take advantage of the finite bin correction if required 8 Compare the fixed and adaptive DOS and see the advantage of adaptive broadening over standard Gaussian smearing 6 2 Projected Density of States We assume the reader is familiar with the previous section on Density of States calculations and is now familiar with choosing broadening widths and running OPTADOS e Outline This is a simple example of using OPTADOS for calculating electronic density of states of 2 atoms of crystalline silicon projected onto LCAO basis states e Input Files examples Si2_PD0S Si2_dos cell The CASTEP cell file containing information about the simulation cell examples Si2_PD0S Si2_dos param The CASTEP param file containing infor mation about the parameters for the SCF and spectral calculations examples Si2_PDOS Si2_dos odi The OPTADOS input file containing the pa rameters necessary to run OPTADOS OptaDOS User Guide Choose a broadening scheme for the projected DOS calculation and test using TASK compare_dos as explained in the previous example Checking that the DOS_SPACING is sufficiently fine for the band energies to match Once the DOS
18. OptaDOS User Guide Version 1 2 380 Andrew J Morris Rebecca J Nicholls Chris J Pickard Jonathan R Yates Department of Physics University of Cambridge 19 J J Thomson Ave Cambridge CB3 OFF UK Department of Materials University of Oxford Parks Road Oxford OX1 3PH UK and Department of Physics and Astronomy University College London Gower Street London WC1E 6BT UK February 2015 University of Cambridge University of Oxford and University College London 2013 2015 A J Morris R J Nicholls C J Pickard and J R Yates First published 2010 This edition 2015 10987654321 Part of this work published in OptaDOS A Tool for Obtaining Density of States Core loss and Optical Spectra from Electronic Structure Codes Andrew J Morris Rebecca J Nicholls Chris J Pickard and Jonathan R Yates Comp Phys Comm 185 5 1477 2014 Further information about OPTADOS may be obtained from www optados org Nota bene OPTADOS optados or OptaDOS but never OPTADOS Font Computer Modern 11pt Typeset by the authors using ATEX Contents 1 Introduction 7 1 1 Background 2 024422 4 42446 4 bdo OG a PR EEE Re REE OS 7 1 2 Features 4 5 ce ee eg E bas qe Bie eek Bl ek oh Gs ed g 7 2 Theoretical Background 9 2 1 Integrals over the Brillouin Zone 0 0000000050 9 2 2 Brillouin Zone Sampling Schemes 0 0 0 00000200005 9 2 3 Density of Electronic States 2 0 ee 11 2 4 Diel
19. able through the GPL licence with the request that the following citation quoted in full is required in any publication resulting from the use of OPTADOS Andrew J Morris R J Nicholls C J Pickard and Jonathan R Yates OPTADOS A Tool for Obtaining Density of States Core level and Optical Spectra from Electronic Structure Codes Comp Phys Comm 185 5 1477 2014 Further information and examples can be found at www optados org 1 2 Features OPTADOS generates optical core level excitation spectra along with full partial and joint electronic DOS The DOS PDOS and JDOS take advantage of the linear and adaptive broad ening schemes which are more accurate than standard Gaussian broadening since they exploit knowledge of the gradients of the bands at each k point in the Brillouin zone These DOS are the basis of the more advanced functionality of OPTADOS the core and optical spectra Along with data text files OPTADOS also generates agr files of results to be read by grace Chapter 2 Theoretical Background 2 1 Integrals over the Brillouin Zone Many energy resolved spectral properties of a material take the form of an integration of some function Fam k in reciprocal space over the BZ where Fm k are the elements of a periodic operator which commutes with the crystal translational symmetry Perhaps the two simplest examples of integrals hereinafter referred to as type a and type b take the form at T 0K of LODHA
20. e with BS_KPOINTS_MP_GRID and OPTICS_KPOINTS_MP_GRID e Remove SPECTRAL_TASK DOS from the param file e Add DEVEL_FLAG o1d_filename to the odi file e Add WRITE_CELL_STRUCTURE true to your CASTEP cell file to generate the symme tries of the cell if you are doing pdos core or optics calculations e Read Section 7 3 if you are planning to do a partial density of states calculation 7 3 Pm getting odd results for my PDOS calculation when using castep version 6 0 The spectral module in CASTEP 6 0 generates the pdos weights commensurate with the optics grid you have chosen However this gets overwritten by the main routines Hence to get the 41 42 OptaDOS User Guide right PDOS weights you must set PDOS_CALCULATE_WEIGHTS FALSE in the param file 7 4 OptaDOS is reporting the wrong number of kpoints This is a rare bug that can happen if you have picked the magic k point offset for your grid that is a 3 4n offset where n is the number of MP grid points in that direction It is a very difficult edge case to catch Until a permanent workaround is found you can tell OPTADOS the right number using the KPOINT_MP_GRID nx ny nz in the odi file 7 5 Pd like OptaDOS to do X as well Contact the developers we re always interested in discussing new functionality 7 6 Pd like to help what can I do Contact the developers there s always more functionality that we d like to add to the code 7 7 Ithink I ve found a bug what shou
21. ebug information 3 1 3 COMMS_ARCH Whether to compile for serial or parallel execution The valid values are serial default mpi 3 1 4 PREFIX Choose where to place the OPTADOS binary The default is the OPTADOS directory 3 2 Usage optados x86_64 seedname e seedname If a seedname string is given the code will read its input from a file seedname odi The default value is CASTEP Chapter 4 Structure of the Program The schematic structure of the program is outlined in Fig 4 1 Each rounded cornered box represents a Fortran95 module and the lines represent module dependencies Modules only use data and subroutines from lower modules in the diagram The modules are grouped into functional structural utility and low level Low level modules set up the environment for communication in serial or parallel between nodes and to disk The utility modules are not context dependent on the problem and contain general algorithms and an interface to write xmgrace input files Structural modules define data structures hold data and perform low level operations on them The functional modules perform the higher level data operations and generate output A description of the purpose of each module is given below algorithms subroutines not specific to electronic structure cell real and reciprocal space data manipulation and storage e g cell vectors and k points comms interfaces to parallel libraries constants d
22. ectric response ee 11 3 Getting Started 15 3 1 Installation 2 2644 6e44 e4 8 066 wae begs eee ee eee Ee a ee 15 32 WSOC goo vk A ehh dk Rw ew ek eek Po Bia ok Eo we eee Boe 16 4 Structure of the Program 17 5 Parameters 19 Dil seednam odt Elle ss simens a Gees ese ew es a N 19 5 2 General Parameters a soa eao e acs E aa e 20 5 9 DOS Parameters s i doaa e eane i a e e A oaa ao aE ai 23 5 4 JDOS Parameters oo scotea ua s ea e ae ee 24 5 5 PDOS Parameters cq ed ca ra pust oe e a AR A a 25 5 6 Optics Parameters gt eec carse bsc arnesi e gka kpe phus au 25 5 Core level Parameters eme s ab toe ee we a A a i 26 4 OptaDOS User Guide 6 Examples 29 6 1 Density of States soa ras Re ee Aa Ww we ee ee ee 29 6 2 Projected Density of States sq a r aoia a k e aa ioe o 33 6 3 JDOS o ceuo e e a a E gE A oe he oo aS 35 64 OPTICS orando e ey a e o pl 36 Gos CORD 2 card oe ne a e O ae de a ee eet eee 37 7 Frequently Asked Questions 41 7 1 OPTADOS crashes complaining that it can t read the seed bands or seed cst_ome fless t e a LA A DR EAE ES AES 41 7 2 The examples do not work and I m using CASTEP version 6 0 41 7 3 Um getting odd results for my PDOS calculation when using CASTEP version 6 0 41 7 4 OPTADOS is reporting the wrong number of kpoints 42 7 5 Ud like OPTADOS to do X as well o 42 7 6 Ud like to help what can I do o o e e
23. ed the total width of the Lorentzian used will be core_lorentzian_width energy above the Fermi level x core_lorentzian_scale The default value if core_LAI_broadening true is 0 1 5 7 8 real kind dp LAI_lorentzian_offset Energy in eV above the Fermi level that the energy dependent broadening starts The default value if core_LAI_broadening true is 0 Chapter 6 Examples Each example in the examples directory contains example CASTEP input files and a sample OPTADOS input file To keep the OPTADOS distribution light CASTEP output files for the examples have not been provided You need to run CASTEP on the CASTEP input files before running OPTADOS on the examples 6 1 Density of States e Outline This is a simple example of using OPTADOS for calculating electronic density of states of crystalline silicon in a 2 atom cell e Input Files examples Si2_D0S Si2_dos cell The CASTEP cell file containing information about the simulation cell examples Si2_D0S Si2_dos param The CASTEP param file containing informa tion about the parameters for the SCF and spectral calculations examples Si2_D0S Si2_dos odi The OPTADOS input file containing the pa rameters necessary to run OPTADOS 1 Perform a CASTEP calculation on the bulk silicon using the Si2_dos cell and Si2_dos param input files castep Si2 This should take a couple of seconds to run More help can be found in the tutorials on the
24. efinition of constants and conversion factors core perform core level calculation dos perform DOS calculation dos_utils perform type a integral evaluation electronic read electronic eigenvalue data Store electronic data variables io error handling timing and input and output units jdos perform JDOS calculation jdos_utils perform type b integral evaluation optados main program 17 OptaDOS User Guide Sa gt SS Functional optados dos pdos core jdos optics A a jdos_utils Structural E electronic parameters cell 11 Utility algorithms xmgrace_utils constants Figure 4 1 Schematic structure of the program optics calculate dielectric function then generate optical properties parameters read store and check input file parameters pdos perform PDOS calculation xmgrace_utils routines to write out data in xmgr format Chapter 5 Parameters 5 1 seedname odi File The OPTADOS input file seedname odi has a flexible free form structure The ordering of the keywords is not significant Case is ignored so smearing_width is the same as Smearing_Width Characters after or are treated as comments Most keywords have a default value that is used unless the keyword is given in seedname odi Keywords may be set in any of the following ways smearing_width 0 4 smearing width 0 4 smearing width 0 4 A
25. ening is used 5 7 Core level Parameters 5 7 1 character len 20 core_type Determines if we want absorption transition from core to conduction ELNES XANES or emission transition from valence to core XAS It is also possible to plot both absorption default emission all 5 7 2 character len 20 core_geom Specifies the geometry for the core spectra calculation Possible options polycrystalline Isotropic average polarized The default is polycrystalline OptaDOS User Guide 27 5 7 3 real kind dp core_qdir 3 Direction of polarisation Must be specified if core_geom polarized There is no default value 5 7 4 logical core_LAI_broadening Include life time and instrumentation broadening The default is FALSE 5 7 5 real kind dp LAI_gaussian_width FWHM of Gaussian function used to broaden spectrum The default value if core_LAI_broadening true is 0 i e no Gaussian used 5 7 6 real kind dp LAI_lorentzian_width FWHM of fixed Lorentzian function used to broaden spectrum The default value if core_LAI_broadening true is 0 i e no fixed Lorentzian used 5 7 7 real kind dp LAI_lorentzian_scale Variation of Lorentzian function with energy i e the width of the Lorentzian is energy above the Fermi level x core_lorentzian_scale If set to zero no energy dependent broadening is included If core_lorentzian_scale and core_lorentzian_width are both specifi
26. ermi num_spins Fermi level calculated from electronic structure code for each spin real dp cell_lattice 1 3 1 3 Real space lattice vectors real dp kpoint_positions num_kpoints 1 3 K point position vectors in fractions of Brillouin Zone real dp kpoint_weight num_kpoints K point weight real dp band_energy max_eigenv num_spins num_kpoints Energy eigenvalue list write band_unit a i4 Number of k points num_kpoints write band_unit a i1 Number of spin components num_spins if num_spins gt 1 then 43 44 OptaDOS User Guide write band_unit a 2g10 4 Number of electrons num_electrons else write band_unit a g10 4 Number of electrons num_electrons endif if num_spins gt 1 then write band_unit a 2i4 Number of eigenvalues num_eigenvalues else write band_unit a i4 Number of eigenvalues num_eigenvalues endif if num_spins gt 1 then write band_unit a 2f12 6 Fermi energy in atomic units efermi else write band_unit a f12 6 Fermi energies in atomic units efermi endif write band_unit a Unit cell vectors write band_unit 3f 12 6 cell_lattice 1 write band_unit 3f12 6 cell_lattice 2 write band_unit 3 12 6 cell_lattice 3 do ik 1 num_kpoints write band_unit a i4 4f12 8 K poin
27. l spectra are calculated in OPTADOS using the task core command Several different experimental geometries are possible for core level experiments and OPTA DOS allows the calculation of spectra with q in a particular direction or an isotropic average In core level absorption spectra there are several sources of broadening coming from the ex perimental set up and lifetime effects These can be included in OPTADOS by broadening the theoretical spectrum using a combination of Gaussian and Lorentzian functions To include instrumentation and lifetime effects core_LAI_broadening should be set to true 2 4 2 Optical properties In the low loss EELS regime the approximations used for core level spectroscopy do not hold and the full form of the loss function needs to be calculated This is done by calculating 2 using equations 2 7 and 2 8 and then using the Kramers Kronig relations to find 1 Once the dielectric function has been calculated the loss function is simulated without local field effects using equation 2 9 As the dielectric function has been calculated several other optical properties which are listed below can also be computed OptaDOS User Guide 18 Conductivity in units of Sm is computed using O1 E0EQW 2 10 07 0 1 e1 w 2 11 The refractive index is calculated using N n ik 2 12 where n and k are obtained from pe 5 led rey wid pea e el er 2 13 The absorption coefficient in units
28. ld I do e Check and re check that it is a bug e Check the output of the electronic structure code e Check that you re using the latest version of OPTADOS e Email the developers the input and output files with iprint 3 and as much infor mation about the problem as possible Appendix A Interface with other codes Currently OPTADOS is interfaced with CASTEP and ONETEP This appendix consists of Fortran95 code which defines the input files for OPTADOS so as to aid its interfacing with other electronic structure codes Presented below are the type declaration statements and write statements that may be used in other electronic structure codes or converters to generate the bands ome_bin pos_bin and elnes_bin files used as inputs to OPTADOS These code snippets are also available in the tools directory of the OPTADOS distribution A l bands file The bands file is necessary for any calculation using OPTADOS it contains the energy eigenvalues at each k point and data about the electronic properties of the system The bands file is a formatted file integer parameter dp selected_real_kind 15 300 Define double precision integer num_kpoints Number of kpoints integer num_spins Number of spins integer max_eigenv Number of bands included in matrix elements integer num_electrons num_spins Number of electrons of each spin integer num_eigenvalues num_spins Number of eigenvalues of each spin real dp ef
29. lectron ey is the permittivity of free space Q is the volume of the unit cell and q is the momentum transfer Using the dipole approximation expressing q as qt and taking the limit that q gt 0 2 can be written as an integral of type b 2 ea w IO hw 2 7 0 where Famlk Wea hop 2 8 Once e2 is known it is possible to use the Kramers Kronig relations to obtain e and hence obtain an expression for the full dielectric function The dielectric function is a tensor and in OPTADOS it is either possible to output the full dielectric tensor or calculate dielectric function for the isotropic average of q a particular direction of q or the average of q over a plane perpendicular to a given direction Once the dielectric function has been calculated core level spectra and optical properties can be calculated Core level and low loss EELS spectra are all related to the loss function which is defined as 7 a 2 9 2 4 1 Core level spectra For core level spectroscopy core loss EELS and x ray absorption near edge spectroscopy XANES the incident perturbation is far from resonance and since 1 and e2 gt 1 equation 2 9 reduces to A ez The type b integral in equation 2 7 becomes a type a integral as the energy of the core state is fixed Emission spectra transitions from valence to core XAS can also be calculated by considering a sum over the occupied rather than unoccupied states Core leve
30. looks suitable switch to TASK pdos We choose to decompose the DOS into angular momentum channels PDOS angular and as in the previous example we choose to recalculate the Fermi level using the calculated DOS rather than use the Fermi level suggested by CASTEP Execute OPTADOS The output can be found in Si2 pdos dat FERORERORO ORO RERO HORROR ROH RERO RRHH RRHH RRHH REHARERO RRHH ROH R ROH RRORORERIORO ROHE ROHOREREHO RRE HORERORORERORORERRRAARAA OptaDOs output file Generated on 13 Feb 2012 at 10 15 10 HEHHHHHHHHHHHHHHHHHHHHHHHHHHEHHHHHHHHHHEHHPHHHHHHHEHHEHEHHHHH HEHEHE HHH HEHEHE Partial Density of States Projectors Hp q qA q qq q A A A A A A A O Projector 1 contains Atom AngM Channel Si 1 s si 2 s HA S r EE Projector 2 contains Atom AngM Channel Si 1 p Si 2 p HA A O Projector 3 contains Atom AngM Channel Si 1 d si 2 d Ht A a Projector 4 contains Atom AngM Channel Si 1 f si 2 f P A The header shows that there are four projectors described below The first containing the s channels of both silicon atoms the second the p channels etc The output is easily plotted using xmgrace xmgrace nxy Si2 pdos dat OptaDOS User Guide 35 s channel p channel Projected eDOS 0 Energy eV Figure 6 2 Density of States of Silicon generated by adaptive broadening projected onto LCAO momentum states
31. may be chosen for OPTADOS calculations with broadening adaptive 2 3 Density of Electronic States When Fram Kk 1 the type a integral represents the electronic density of states DOS at E and the total ground state energy Egs is obtained by integrating over the occupied energies E Ez f TD E Fam k DOE 2 4 0 where Ep is the Fermi energy The DOS is plotted with OPTADOS using the task dos command The partial or projected DOS PDOS J is obtained by projecting the DOS onto local orbitals u at each atomic site In this case Fan RATIO T 19 S 197 2 5 where Tim k Y k k are the overlap matrices between LCAO linear combination of atomic orbitals basis f and planewave states Yn and Sim k n k 0 k the overlap matrices of the LCAO basis The PDOS is plotted with OPTADOS using the task pdos command The projection is defined using the pdos keyword as described in the user manual In the case of the type b integral when F k 1 we obtain the joint DOS JDOS for frequency w The JDOS is plotted with OPTADOS using the task jdos command 2 4 Dielectric response Core level spectra and optical properties are related to the complex dielectric function 1 189 Within the random phase approximation the imaginary part of the dielectric function is 2 ii 69 w 5 kegle Wh 2 2 6 E09 q 12 OptaDOS User Guide where e is the charge on an e
32. mber of k points integer num_spins Number of spins integer num_popn_orb Number of LCAO projectors integer max_eigenv Number of bands included in matrix elements real dp file_version 1 0_dp File version integer species 1 num_popn_orb Atomic species associated with each projector integer ion 1 num_popn_orb Ion associated with each projector integer am_channel 1 num_popn_orb Angular momentum channel integer num_eigenvalues 1 num_spins Number of eigenvalues per spin channel real dp kpoint_positions 1 num_kpoints 1 3 k_x k_y k_z in fractions of BZ real dp pdos_weights 1 num_popn_orb max_eigenv num_kpoints num_spins Matrix elements character len 80 file_header File header comment write pdos_file file_header write pdos_file file_version write pdos_file num_kpoints write pdos_file num_spins write pdos_file num_popn_orb write pdos_file max_eigenv write pdos_file species 1_ num_popn_orb write pdos_file ion 1 num_popn_orb write pdos_file am_channel 1 num_popn_orb do nk 1 num_kpoints write pdos_file nk kpoint_positions nk do ns 1 num_spins write pdos_file ns write pdos_file num_eigenvalues ns do nb 1 num_eigenvalues ns 46 OptaDOS User Guide write pdos_file real pdos_weights num_popn_orb nb nk ns end do end do end do A 4 elnes_bin file The elnes_bin file is required for ELNES calculations The elnes_bin file is an unformatted file in
33. n be included in the calculation of the loss function This is done by including the keyword optics_lossfn_broadening in the OPTADOS input file If you include this keyword and re run OPTADOS you will find that the file i2_OPTICS_loss_fn dat now has three columns These are the energy unbroadened spectrum and broadened spectrum respectively 6 4 2 Aluminium 1 As for the silicon example a broadening scheme for the JDOS should first be determined 2 Aluminium is a metal so we need to include both the interband and intraband contribu tions to the dielectric function To include the intraband contribution optics_intraband true must be included in the OPTADOS input file When you run OPTADOS the same files are generated as when only the interband term is included The A1_0PTICS_epsilon dat file has the same format as before but it now contains sequentially the interband contribution the intraband contribution and the total dielec tric function The file A1_OPTICS_epsilon agr only contains the interband term In the same way Al_OPTICS_loss_fn dat contains the interband contribution intraband contribution and total loss function All other optical properties are calculated from the total dielectric function and the format of the output files remains the same 3 In the case where the dielectric tensor is calculated and the intraband term is included only the Al_OPTICS_epsilon dat file is generated As before it contains each compo nent
34. numerical_intdos Calculate the integrated dos by numerical integration instead of semi analytically Useful for comparison with LinDOS Default value FALSE 5 2 13 logical hybrid_linear Switch from linear broadening scheme to adaptive broadening when band gradient less than hybrid_linear_grad_tol This allows for a good description of very flat bands such as defect and semi core states May also be used in conjunction with finite_bin_correction further improving the DOS and band energy Default value FALSE 5 2 14 real kind dp hybrid_linear_grad_tol Tolerance for switching from linear to adaptive broadening when using hybrid_linear option The default value is 0 01eV A OptaDOS User Guide 23 5 2 15 character len 50 devel_flag Not a regular keyword Its purpose is to allow a developer to pass a string into the code to be used inside a new routine as it is developed No default 5 3 DOS Parameters 5 3 1 logical compute_band_energy Compute the band energy by summing bands both using CASTEP s eigenvalue and OPTA DOS s density of states Default value TRUE 5 3 2 logical compute_band_gap Compute the optical thermal and average band gap Default value FALSE 5 3 3 logical dos_per_volume Present DOS per simulation cell volume Default value FALSE 5 3 4 real kind dp dos_min_energy Lower energy range for DOS and related properties Default value is 5eV below the lowest eigenvalue in
35. of m is computed using a 2 14 E and reflection coefficient R from n 1 k R n D2 k2 2 15 All optical properties are calculated in OPTADOS using the task optics command 2 4 3 Intraband term For metals it is necessary to consider an intraband contribution to the optical response i e a term when n m in equation 2 2 The contribution to e can be written as a type a integral with hw set to Ep e 1 intra e a api a En 2 16 e T Ez w 1 Ep 2 17 9Q w w 12 where I denotes the relaxation rate Chapter 3 Getting Started 3 1 Installation OPTADOS is usually obtained in a gzipped tarball optados X X tar gz Extract this tar xzf optados X X tar gz in the desired directory Inside the optados directory are a number of sub directories documents examples and tools The code may be compiled using the Makefile in the optados directory The SYSTEM BUILD COMMS_ARCH and PREFIX flags must be set either in the makefile system or from the command line for example make BUILD fast 3 1 1 SYSTEM Choose which compiler to use to make OPTADOS The valid values are g95 default gfortran ifort nag pathscale pgf90 sun 3 1 2 BUILD Choose the level of optimisations required when making OPTADOS The valid values are fast default All optimisations 15 16 OptaDOS User Guide debug No optimisations full d
36. p tive smearing Band energy Adaptive broadening 1 3623 eV lt TBg lt OBg lt OBg lt ABg lt ABg lt wAB lt BEA OptaDOS User Guide 33 7 Now set TASK compare_dos and re run OPTADOS OPTADOS will calculate DOS using all the broadening methods this is good practice to see whether the broadening widths are appropriate before more advanced tasks are carried out such as Joint DOS core and optical calculations Plotting the linear broadened DOS over the adaptive we see that the default adaptive broadening is appropriate xmgrace Si2 adaptive agr nxy Si2 linear dat Linear broadening although a massive improvement over fixed broadening sometimes appears noisy if used with very low numbers of k points Linear and adaptive DOS should be compared and ADAPTIVE_SMEARING may be tuned by eye until the adaptive DOS contains the features of the linear DOS but with less noise Adding a random shift to a k point mesh can greatly increase the quality of the DOS especially if the k point set contained the I point It generally pays off in computational time to have a coarse mesh at low symmetry points than a fine mesh centred on high symmetry points Both fixed and adaptive broadening can fail to plot the sharpest features such as semi core states if the bin widths are too broad These sharp features may be forced to be present using the narrowest Gaussian still reproducible by the chosen bin widths by setting
37. re included along with an OPTADOS input file We assume that the reader is familiar with the previous sections on DOS and JDOS examples Si2_OPTICS This is a simple example of using OPTADOS to calculate the optical properties of crystalline silicon which is an insulator examples Al_OPTICS This is a simple example of using OPTADOS to calculate the optical properties of a metal aluminium 6 4 1 Silicon 1 Choose a broadening scheme for the JDOS as explained in the JDOS example Once the JDOS looks suitable switch the task from JDOS to OPTICS and execute OPTADOS to calculate the optical properties Several dat files are produced i2_OPTICS_absorption dat This file contains the absorption coefficient sec ond column as function of energy first column Si2_OPTICS_conductivity dat This file contains the conductivity outputted in SI units Siemens per metre The columns are the energy real part and imaginary part of the conductivity respectively i2_OPTICS_epsilon dat This file contains the dielectric function The columns are the energy and real and imaginary parts of the dielectric function respectively The file header also includes the result of the sum rule fY Ime w dw Ne pp lw Neff is the effective number of electrons contributing to the absorption process and is a function of energy i2_OPTICS_loss_fn dat This file contains the loss function second column as a function of energy
38. rmi level to 0eV for the output files 4 The DOS is outputted to Si2 adaptive dat This contains 5 columns as described in the header of the file PETE A TEE A TE E E T PLETED TIE TE E A EE TE E TE E HE E E TE HE TE E BEE EE TE E E E E AE AE E HEROE OptaDOs output file Density of States using adaptive broadening Generated on 12 Feb 2012 at 16 50 37 Column Data 1 Energy eV ff 2 Up spin DOS electrons per eV 3 Down spin DOS electrons per eV 4 Up spin Integrated DOS electrons 5 Down spin Integrated DOS electrons EAE TEA TE T E TE E E TE A E TE E T TE A TE E E EE E E DE AE TE E TE TE HE ETE TE HEHE EE TE E PEPE AE EEE HERO HEE HE This file can be plotted by your favourite graph plotting software However OPTADOS has made things easy and generated a Si2 adaptive agr file which is directly plottable using xmgrace as shown in Fig 6 1 xmgrace Si2 adaptive agr 5 We now try again with a better sampling of the DOS by setting DOS_SPACING 0 001 and also analyse the band gap by setting COMPUTE_BAND_GAP true You can remove all of the OPTADOS output files by using tools optados_clean in your working directory If you have a parallel version of OPTADOS compiled now might be the time to try it out if not the serial version will be fine but just take a bit longer You can set IPRINT 2 to see a progress report in Si2 odo In parallel mpirun np lt nprocs gt optados SYSTEM BUILD COMMS_AR
39. t ik amp kpoint_positions num_kpoints 1 3 kpoint_weight num_kpoints do is 1 num_spins write band_unit a i1 Spin component is do ib 1 num_eigenvalues is write band_unit band_energy ib is ik end do end do end do A 2 ome_bin file The ome_bin file is required for adaptive and linear broadening and for optics calculations Note that a dome file is just the diagonal elements of the ome The ome_bin file is an unformatted file integer parameter dp selected_real_kind 15 300 Define double precision real dp file_version 1 0_dp File version character len 80 file_header File header comment integer num_kpoints Number of k points integer num_spins Number of spins integer max_eigenv Number of bands included in matrix elements integer num_eigenvalues 1 num_spins Number of eigenvalues per spin channel complex dp optical_mat max_eigenv max_eigenv 1 3 1 num_kpoints num_spins OMEs OptaDOS User Guide 45 write ome_unit file_version write ome_unit file_header do ik 1 num_kpoints do is 1 num_spins write ome_unit optical_mat ib jb i ik is ib 1 num_eigenvalues is amp amp jb 1 num_eigenvalues is i 1 3 end do end do A 3 pdos_bin file The pdos_bin file is required for PDOS calculations The pdos_bin file is an unformatted file integer parameter dp selected_real_kind 15 300 Define double precision integer num_kpoints Nu
40. teger parameter dp selected_real_kind 15 300 Define double precision integer tot_core_projectors Total number of core states included in matrix elements integer max_eigenvalues Number of bands included in matrix elements integer num_kpoints Number of k points integer num_spins Number of spins integer num_eigenvalues 1 num_spins Number of eigenvalues integer species 1 tot_core_projectors Atomic species associated with each projector integer ion 1 tot_core_projectors Ion associated with each projector integer n 1 tot_core_projectors Principal quantum number associated with each projector integer lm 1 tot_core_projectors Angular momentum quantum number associated with each projector real dp elnes_mat tot_core_projectors max_eigenvalues 3 num_kpoints num_spins matrix elements write elnes_file tot_core_projectors write elnes_file max_eigenvalues write elnes_file num_kpoints write elnes_file num_spins write elnes_file write elnes_file write elnes_file n 1 tot_core_projectors write elnes_file do nk 1 num_kpoints do ns 1 num_spins write elnes_file elnes_mat orb nb indx nk ns orb 1 amp amp tot_core_projectors nb 1 num_eigenvalues ns indx 1 3 end do end do lm 1 tot_core_projectors species 1 tot_core_projectors ion 1 tot_core_projectors aping was sodesdo Li Bibliography 10 11 12 13 14 15 16 17 18 19 C
41. the starting point and then remove one of the core 1s electrons to create a core hole pseudopotential This is done by including 1s1 00 in the pseudopotential string as shown 211 811 811 31213 14130 31 32LGG11s1 00 qc 4 If instead of removing a 1s electron we wanted to remove a 2s electron from the core we would have included 2s1 00 instead of 181 00 in the pseudopotential string We are only interested in the spectra from the atom with the core hole and so copy the pseudopotential file generated by the previous calculation Si_OFT usp to Si_LDA usp Then include BLOCK SPECIES_POT Si exi 211 811 811 31213 14130 31 32LGG11s1 00 qc 4 Si Si_LDA usp ENDBLOCK SPECIES_POT in the CASTEP Si2_CORE cell file To maintain the neutrality of the cell we include CHARGE 1 in the Si2_CORE param file Run the calculation This time the Si2_CORE_core_edge dat file will contain only the edges from the core hole atom Compare the K edge from the core hole calculation with the previous non core hole calculation 3 The periodic images of the core hole will interact with one another As this is unphysical we need to increase the distance between the core holes This is done by creating a supercell To start with we use a face centred unit cell rather than the primitive unit cell This is done by changing the lattice parameters and fractional co ordinates to 40 OptaDOS User Guide BLOCK LATTICE_CART 5 46 0 00 0 00 0 00 5
42. ty k point grid to mitigate the band crossing problem 2 2 3 Extrapolative schemes Extrapolating from each k point rather than interpolating between adjacent points eliminates the band crossing problem Miiller and Wilkins show that for free electron bands the DOS is a smooth parabola when using the extrapolative method and a rough unconverged spectrum with the interpolative approach when using the same k point mesh The linear extrapolative scheme still does not represent van Hove singularities as well as a second order approach Band curvatures may be combined with Lowdin perturbation theory to extrapolate to higher order Linear extrapolative broadening may be chosen for OPTADOS calculations with broadening linear OptaDOS User Guide 11 2 2 4 Adaptive broadening schemes An approximation to linear extrapolation method was proposed by Yates et al Each sub cell s contribution to the DOS is broadened by a Gaussian function whose width w is proportional to the energy band gradient as its k point This simple approach removes the spurious oscillations of the fixed broadening whilst maintaining the sharper features The adaptive broadening scheme was introduced in Ref in the context of Wannier interpolation of BZ quantities However the scheme is more general that this and with OPTADOS we apply adaptive broadening directly to the quantities obtained from the electronic structure calculation Adaptive broadening
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