A brief user`s guide for atompaw code
Contents
1. A summary of the atomic all electrons computation and PAW dataset properties can be found in the Atom name file 4tom name 1s the first parameter of the input file Resulting PAW dataset can be output in several different formats o Atom name atomicdata file keyword PWPAWOUT Specific format for pwpaw and soccoro codes o Atom name XCfunc xml file keyword XMLOUT Normalized xm file according to specifications from http wiki fysik dtu dk stuff pawxml pawxml xhtml can be used with abinit code o Atom name XCfunc paw abinit file keyword ABINITOUT Specific format for abinit code o Atom name XCfunc paw upf file keyword PVSCFOUT Specific format for pwscf code Additional details can be found in Notes for revised form of atompaw code http www wfu edu natalie papers pwpaw notes atompaw atompawEgqns pdf Part I manuscript pdf http dx doi org 10 1016 S0010 4655 00 00244 7 be careful some obsolete chapters inside User s guide for atompaw 3 Input file for atompaw In red mandatory arguments In green optional arguments Keywords are in normal font Numbers are in italics Atom name Z XC functional rel keyword nucleus keyword grid keyword logderivrange max max max max p Ng Ne n n l oco One line for each empty or partially occupied n l state n l OCC 00 T One line for each nl state 1 0 states first then l states Atomic all electrons computation Repeated for2. Y Download LibXC tarball from http www tddft org programs octopus wiki index php Libxc download Y Build LibXC and install it with the standard Linux procedure see LibXC manual configure make make install Let s suppose in the following that LibXC is installed in 1ibxc Y Build atompaw with LibXC support At configure process add the following options enable libxc with libxc incs I libxc include Wwith libxe libs L libxc lib lxce Then build and install atompaw make make install How to use atompaw with a LibXC functional Y Choose an Exchange functional and a Correlation functional or directly one single Exchange Correlation functional in LibXC list http www tddft org programs octopus wiki index php Libxc manual Available functionals Y If your choice is an Exchange Correlation functional put its name as XC functional keyword in atompaw input file If your choice is an Exchange and a Correlation functional put the xc_functional keyword as a merge of the two names separated by a plus Examples if you want to use XC GGA XC B97 put XC GGA XC B97 if you want to use xc LDA xand xc LDA C PW put XC LDA X4XC LDA C PW Example of input file using LibXC GGA PBE functional 5 Q Q X PBE XC GGA C PBE loggrid 2001 00 0 on NI 0 1 0 D WKB WX PRP gg A ONN AW Note for experts you also can address LibXC functionals in input file by their numerical identifi
3. cut off energy Eeu used to optimize the projectors G E 2 Default if missing is 10 Rydberg gfact Optional argument but if present must follow ecut in the input Define the factor y G max used to optimize the projectors Default 1f missing is 2 werror Optional argument but if present must follow g act in the input Define the error JW used to optimize the projectors Default if missing is 0 0001 Default if missing is nooptim Note If you just want to produce a PAW dataset for abinit without any additional data treatment you can use the default keyword 2 Default Or ABINITOUT Default User s guide for atompaw 13 Quantum Expresso ZAttp www pwscf org To obtain a file formatted for PWscf code Unified Pseudopotential Format enter the following lines 3 r upfxmin upfzmesh Enter 3 or PWSCFOUT UPF grid keywords allare optional and may occur in any order to activate output in UPF format For the PAW mode the pwscf code needs a logarithmic grid of the form 1 upfmin id r i e e i upfzmesh upfzmesh Optional argument Define the inverse of the radial step of the grid 1 Default if missing is 1 0 a u upfxmin Optional argument exp up xmin is the minimum radius given by the grid i71 Default if missing is 9 0 upfdx Optional argument Define the logarithmic step of the grid Default 1f missing is 0 005 Note fo
4. each additional 1 0 partial wave shape Fvloc core p f n Repeated for each additional l 1 partial wave One paragraph for each 0 lt l sl Repeated for each additional l l nay partial Ifprojector keyword Bloechl projector keyword ps s hempe PFERP psebemecshapefunction Partial waves basis lioc Eloc Vloc scheme generation As many times One line for each empty or as desired partially occupied n l state Test configurations Output for ABINIT Output for PWscf Output for various codes mamat dee mene ambi le Ao mama n NIXON dE AAA wei A Euer User s guide for atompaw 4 Detailed description of keywords 1 Atomic all electron computation Atom name Z b benc n Atom name Z Symbol of atomic specie Atomic number total number of electrons XC functional rel keyword nucleus_keyword grid_ keyword gridsize Trax E Tmatch logderivrange Emin Emax Npoints m See next page XC functional Name of exchange correlation functional used in DFT atomic configuration resolution Possible values LDA PW for Perdew Wang 92 LDA functional PRB 45 13244 1992 GGA PBE for Perdew Burke Ernzerhof 96 GGA functional PRL 77 3865 1996 LibXC keyword for use of one of the functionals provided by the LibXC external library see appendix rel keyword Relativistic approximation used to solve atomic wave equation Possible values nonrelativistic solve n
5. equation at 1 and E Ejge ultrasoft use a pseudization scheme without norm conservation constraint A PS wave function is deduce from atomic one and chosen to have the form F PQ fa for r lt ryioc Then V is deduced by inverting the 77 wave equation at 1 and E Ejg bessel V is simply derived from Vg by a simple pseudization scheme using a on POP erm zero order spherical Bessel function Es for rry In that case Zve and Empc are ignored and can be omitted Default 1f missing is troulliermartins IC IfProjector keyword Bloechl rca One line for each partial wave FCbasis size rci atomic units Matching radius used to get pseudo partial waves 9 r from partial wave P r As many radii as partial waves have to be entered one per line Ifprojector_keyword is bloechl or VNCT these radii DO NOT HAVE TO BE GIVEN In that case they all are taken as re r paw User s guide for atompaw 10 3 Options for further exploring testing and outputing datasets After the basis and projector functions have been calculated the program enters a keyword driven mode The keywords can be listed in any order Typically the user would choose to output the dataset in one or more formats ABINITOUT XMLOUT PWSCFOUT PWPAWOUT or to try several different pseudopotential paprameters EXPLORE or test the given data set SCFPAW The looping structure of the program is
6. gramschmidtortho Note that projector keyword vanderbilt is strictly equivalent to custom polynom vanderbiltortho projector keyword bloechl is equivalent to custom bloechlps gramschmidtortho AND all r defined later equal to rj User s guide for atompaw 9 shapefunction tol Option governing the analytic form of shape functions g r used in compensation density definition Can be sinc g r N r k r with k r sin a rs Ier 1 nuu tol parameter is ignored and can be omitted gaussian tol g r N r Kk r with k r exp E r dy d parameter is deduce so that k f snape tol Default of tol parameter if missing is 107 besselshape g r al j qir a j qir Gee PRB 59 1758 1999 tol parameter is ignored and can be omitted Default if missing is sinc lioc E1oc Vloc scheme a Vloc scheme Option governing the scheme used to get V r local pseudopotential from all electron effective potential V r Matching radius for pseudization is ri Can be troulliermartins use a norm conserving Troullier Martins scheme A PS wave lioc Eloci l quantum number and reference energy Rydberg units for use when Vloc scheme troulliermartins or Vloc scheme ultrasoft function is deduce from atomic one and chosen to have the form Won A3 AQ lt GG for r lt yioc Where p is an even 12 order polynomial Then V is deduced by inverting the wave
7. stopped with an END or 0 keyword a Test configurations After the arguments used to generate the PAW dataset the user can give electronic test configurations in order to test the validity of the created PAW dataset For each electronic configuration the PAW Hamiltonian will be solved and resulting states printed Each test configuration has to be given as follow One line for each empty or n OCCpi partially occupied n l state n 1 occen1 Enter 1 or SCFPAW For each electronic shell of the atomic specie enter a to begin a new test line with configuration n l quantum numbers of the shell occ electronic occupation of the shell Actually only shells whose electronic occupation is different from the all electron computation one are needed other shells can be omitted Charged excited configurations are of course accepted A 0 0 0 zero zero zero line ends the configuration To end the list of configurations Enter a line with 0 zero to finish the calculations 0 Tests configurations are not mandatory and one can directly enter another integer value 0 2 3 or 4 or keyword without having given any configuration User s guide for atompaw 11 b Output for various DFT codes In the rest of the input file the user can optionally ask atompaw to write the PAW dataset in a specific format for various DFT codes In addition it is possible to apply a specific treat
8. 0 10 300 4300 Up to 4s 4p and 3d 0 2 0 Electronic configuration 3d 4s 4p 0 2 0 1 6 0 0 2 0 1 6 0 2 9 0 01 0 10 0 00 1s 2s 3s 4s valence 2p 3p 4p valence 3d valence Basis contains s p and d partial waves rpaw 2 3 rshape 2 3 rveff 1 1 rcore 2 2 Additional s partial wave at Eref 4 0 Ry 3 2 3 1 1 2 2 Additional p partial wave at Eref 4 0 Ry Additional d partial wave 5 NK SD AKB AK NHYNNGKGAATKGCANANACHKHBRWWWNHNEFY B 5 at Eref 2 5 Ry custom rrkj gramschmidtortho sinc RRKJ PW sinc shape func Bessel Simple Bessel Vloc 2 3 Matching radius for Phil 1 0 2 3 Matching radius for Phi2 1 0 2 3 Matching radius for Phi3 1 1 2 3 Matching radius for Phi4 1 1 2 3 Matching radius for Phi5 1 2 2 3 Matching radius for Phi6 1 2 1 10 2 0 Test configuration 3d 4s 2 0 2 0 2 1 6 0 3 0 2 0 3 1 6 0 3 2 8 0 40 2 0 000 2 Output for abinit prtcorewf noxcnhat rsoptim 12 2 0 00001 logspline 500 0 03 abinit options 3 Output for PWscf upfdx 0 005 upfxmin 9 0 upfzmesh 1 0 PWscf options 0 END User s guide for atompaw 16 Advice for use In the following we give some keys for non experienced users so that they can build input files for atompaw for new materials Short write up The first advice is to begin with a simple expression of the input file setting most of the keywords to their default values O Concerning the all electrons atomic comput
9. 0rg eese eene 14 EXAMPLES ct 15 ADVICE FOR USE T nE ENESE 17 Short Write UDPsssssssssirsscesssissserssssscous M 17 edibus 18 P dulci o b dp 22 Appendix A use of LibXC library 4 eeeeeee esee ee esee seen entente natns tna toss ens ets stesse es stesse eas sense 23 Appendix B comparison between DFT codes eee eee eee eee eite teen seen stessa sten sene sneen eee 24 User s guide for atompaw 1 Method for PAW dataset generation PAW calculations require for each atomic species a set of basis partial waves and projectors functions plus some additional atomic data stored in a PAW dataset A PAW dataset has to be generated in order to reproduce atomic behavior as accurately as possible while requiring minimal CPU and memory resources in executing the DFT code for the crystal simulations These two constraints are conflicting The PAW dataset generation is done according the following procedure 1 2 A 1 CA 1 nN 1 AQ 1 All parameters that should be given in an atompaw input file are in bold Choose and define the concerned chemical species name and atomic number Solve the atomic all electrons problem in a given atomic configuration The atomic problem is solved within the DFT formalism using an exchange c
10. A user s guide for atompaw code Marc Torrent Commissariat l Energie Atomique et aux Energies Alternatives DAM DIF F 91297 Arpajon France Natalie A W Holzwarth Wake Forest University Winston Salem NC 27109 USA Contact emails marc torrent a cea fr natalie wfu edu Source code URL http pwpaw wfu edu Revised August 2 2013 Compatible with atompaw v4 0 and later METHOD FOR PAW DATASET GENERATION ccce eene 2 HOW IO USE ATOMPAJVW itexunkcc iu tikasu nen ncaa ELLE ELLE ELLE ELLE rere ane rere a ER een nee 3 INPUT FILE FOR ATOMPAW iucscusustuscasi edu acu suapuusdcu eU neu ue ings EDU MEE uEMaM ES E EUM KH REDUM FREE DE MEE DUE dS 4 DETAILED DESCRIPTION OF KEYWORDS scssiscssessiicsines irene enun eu cnenaM Su n cuC nsu ncn cn ERES aun euinaMudS 5 1 Atomic all electron computation Lee eeee esee eese eene e eren eene een eee enes sees ases sto ns se tno sena 5 2 Partial wave basis generation eee eee eene eene eene eene en atenta setas ease tasa tasa tasa toss seven een eee sno 8 3 Test configurations corno onerat eon essere eeu S EUR ssepe e E pO REESH Y REPE CE sveeassessdeastesuossvscss ensesee 11 4 Output for various DFT codes eee ee cessere eere eese ette eee seven seta soto nest ense esse to se setas sena 12 ABINIT Attp www abinit org eese ee ee eese eene enn ener innen 12 Quantum Expresso Attp www pwscf
11. al grid Try to select 700 points in the logarithmic grid and check if any noticeable difference in the results appears If yes adjust the size of the grid else keep 700 points If the results are difficult to get converged try a regular grid For use with the pwpaw code linear or logarithmic grids can be used For use with the abinit code the logarithmic grid is preferred o The relativistic approximation of the wave equation scalarrelativistic option should give better results than non relativistic one but it sometimes produces difficulties for the convergence of the atomic problem either at the all electrons resolution step or at the PAW Hamiltonian solution step If convergence cannot be reached try a nonrelativistic calculation not recommended for high Z materials o A summary of the atomic all electrons computation and the PAW dataset properties can be found in the Atom name file 4tom name is the first parameter of the input file A look at the different values of evale valence energy is important All electron value has to be as close to others as possible evale has to be insensitive to grids parameters 2 Havea look at the partial waves PS partial waves and projectors Plot the wfn i files in a graphical tool of your choice You should get 3 curves per file 9 r 9 r and Pi r o The 9 r should meet the 9 r near or after the last maximum or minimum If not it is preferable to change the value
12. ation prefer a logarithmic grid test the influence of the number of grid points and in case of difficulties choose a regular grid Begin with a scalar relativistic solution of the wave equation If the system shows convergence problems try non relativistic choice not recommended when Z becomes high Concerning the partial waves basis generation simply begin with an unique radius rj 2 partial waves per angular momentum if r is small enough 1 wave per may suffice bloechl choice for projector keyword a norm conserving Troullier Martins pseudopotential at jj 1 and E 0 This choice should give a stable PAW dataset with correct physical results but Bl chl s scheme for projectors can produce inefficient datasets in the sense that they may need a large number of plane waves to converge the DFT calculation To increase performance choose the vanderbilt option for projector keyword The gain can be noticeable But generally the best choice for performance would be custom rrkj projectors O Concerning the pseudopotential V r norm conserving Troullier Martins is generally the best choice but it can produce ghost states for d and f materials If this happens a simple Bessel pseudopotential can solve the problem But in the later case one has to noticeably decrease the matching radius 7 4 try 0 677 44 first The other keywords in the input file can be adjusted by
13. d to generate smooth PS partial waves when projector keyword custom Possible values bloechlps use P Bloechl PS wave functions and projectors generation scheme PRB 50 17953 1994 a cutoff function k r sin nr r r r is used in a Schr dinger like equation to deduce PS partial waves In that case ortho scheme keyword has to be gramschmidtortho polynom use a eighth degree polynomial function to pseudize partial waves Aa p Below matching radius PS wave function has the form Go CEZU polynom2 p qcur use a polynomial of degree 2p to pseudize partial waves Z Below matching radius PS wave function has the form Gos eZ 77 For m24 C coefficients are computed so that to minimize Fourier coefficients of PS partial wave for q7q Fourier filtering Defaults values of p and qent if missing are p 4 qew 10 0 rrkj use RRKJ scheme to get PS wave functions PRB 41 1227 1990 Below matching radius PS wave function is a sum of 2 Bessel functions Default if missing is bloechlps See next page ortho scheme Option governing the scheme used to generate and orthogonalize projectors when projector keyword custom Possible values gramschmidtortho use a Gram Schmidt like procedure to orthogonalize projectors and PS partial waves vanderbiltortho use D Vanderbilt procedure to orthogonalize projectors and PS partial waves see PRB 41 7892 1990 Default if missing is
14. e input Define the maximum radius of the grid Default if missing is 50 a u when grid is linear 80 a u when grid is logarithmic loggrid 100 a u when grid is logarithmic loggridv4 Lmatcn atomic units Optional argument but if present must follow Ymax in the input This changes the usage of gridsize so that the value of Fmatcn defines an explicit grid point by adjusting the step size h so that there are gridsize grid points between 0 and 77240 A typical value for March is the PAW radius 7 44 in order to keep it constant when the grid size changes The grid is then continued to the first point rer Fmax Default if missing is Fmax logderivrange Emin Emax Npoints Options governing the plotting of logarithmic derivative logderivrange is an optional argument Additional optional arguments Emin Rydberg Optional argument but if present must follow Logderivrange in the input Define the minimum energy of the range used to plot logarithmic derivatives Default if missing is 5 0 Rydberg Eaxn Rydberg Optional argument but if present must follow Emin in the input Define the maximum energy of the range used to plot logarithmic derivatives Default if missing is 4 95 Rydberg Npoints Optional argument but if present must follow Emax in the input Define the number of points energies used to plot logarithmic derivatives Default if missing is 200 User s guide for atompa
15. e use of semi core states are needed to avoid the appearance of the dreaded ghost states Note that all wave functions designated as valence electrons will be used in the partial wave basis o In the partial waves basis generation part Begin with a simple scheme Select most of the keywords at their default values Enter only one matching radius 7 4 Select it to be slightly less than half the inter atomic distance in the solid as a first choice Add additional partial waves if needed choose to have 2 partial waves per angular momentum in the basis this choice is not necessarily optimal but this is the most common one if Fpaw is small enough 1 partial wave per may suffice As a first guess put all reference energies for additional partial waves to 0 Rydberg Select a bloechl projector scheme and a norm conserving Troullier Martins pseudopotential at jj Imax 1 and E 0 bloech1 will probably be changed later to make the PAW dataset more efficient o In the test configuration part Add one test configuration a good idea is to test at least the electronic configuration used in the all electrons atomic computation part At this stage run atompaw The generated PAW dataset is a first draft Several parameters have to be adjusted in order to get accurate results and efficient DFT calculations User s guide for atompaw 18 1 The sensitivity of results to some parameters has to be checked o The radi
16. er XC functional LIBXC 101 LIBXC 130 User s guide for atompaw 23 Appendix B comparison between DFT codes Li 3 GGA PBE loggrid 2001 220000 D O H Cx get Oo anderbilt besselshape 0 4 6 6 2 2 0 v v v 1 T n n v 2 1 1 1 2 d 3 The results of the illustrated atompaw input file result in nearly identical results among the 3 PAW codes pwpaw abinit and PWscf and with the all electron code WIEN2k which uses the LAPW method as shown in the following binding energy curve Binding energy Ry 15 10 5 LiF GGA Bessel x10 O LAPW O PAW 6 12 O PAW 8 16 O QE 8 16 15 8 8 5 Cubic lattice constant bohr User s guide for atompaw 24
17. experienced users in order to obtain better results on physical properties by comparison with all electrons calculations User s guide for atompaw 17 Detailed write up Here is a proposal for using atompaw to build new PAW datasets from scratch The procedure detailed here should help the user to generate optimal datasets in most cases In a first stage edit a simple input file for atompaw o In the all electrons atomic computation part Define the material in the first line Choose the exchange correlation functional LDA PW or GGA PBE and select a scalar relativistic wave equation and a 2000 points logarithmic grid second line scalarrelativistic is recommended for high Z materials Then define the electronic configuration an excited configure may be useful if the PAW dataset is intended for use in a context where the material is charged such as oxides Although in our experience the results are not highly dependent on the chosen electronic configuration Select the core and valence electrons in a first approach select only electrons from outer shells But if particular thermo dynamical conditions are to be simulated it is generally needed to include semi core states in the set of valence electrons Semi core states are generally needed with transition metal and rare earth materials There are also some cases such as P where physical conditions do not indicate a need for semi core states but th
18. he procedure from step 2 S Finally have a careful look at physical quantities obtained with the PAW dataset It can be useful to test their sensitivity to some input parameters The analytical form and the cut off radius Fshape of the shape function used in compensation charge density definition By default a sinc function is used but gaussian shapes can have an influence on results Besse1 shapes are efficient and generally need a smaller cut off radius 0 8 r The matching radius rcore used to get pseudo core density from atomic core density The integration of additional semi core states in the set of valence electrons The pseudization scheme used to get V r All these parameters have to be meticulously checked especially if the PAW dataset is used for non standard solid structures or thermo dynamical domains User s guide for atompaw 21 Appendix User s guide for atompaw 22 Appendix A use of LibXC library LibXC is a library available from the web under GNU LGPL written by M Marques that contains a large set of very varied exchange correlations functionals Provided that it is linked to LibXC library atompaw can use these exchange correlation functionals at present only LDA and GGA Note at present only abinit code can use LibXC functionals LibXC is available at nttp www tddft org programs octopus wiki index php Libxc How to build atompaw with LibXC support
19. ial outside a r matching radius Projectors and partial waves are then orthogonalized with a chosen orthogonalization scheme Build a compensation charge density used later in order to retrieve the total charge of the atom This compensation charge density is located inside the PAW spheres and based on an analytical shape function which analytic form and localization radius Tshape Can be chosen Eventually if desired test the resulting PAW dataset on several electronic test configurations User s guide for atompaw 2 How to use atompaw 1 Compile atompaw atompaw uses the standard Linux installation procedure autoconf o In atompaw source tree type mkdir build cd build configure If the configure script complains add additional options FC to select a specific Fortran compiler prefix to specify the destination directory with linalg libs to select your Blas Lapack libraries enable libxc with libxc incs with libxc libs to add LibXC support see appendix configure help for all available options o Then compile and install the code make make install 2 Edit an input file in a text editor content of input is explained in the following 3 Run atompaw atompaw lt inputfile Partial waves PS partial waves and projectors are given in wfn 1 files Logarithmic derivatives from atomic Hamiltonian and PAW Hamiltonian resolutions are given in logderiv l files
20. ing pseudopotential But this is generally not sufficient Changing the pseudopotential scheme is in most cases the only efficient cure Select a simple besse1 pseudopotential can solve the problem But in that case one has to noticeably decrease the matching radius r if one wants to keep reasonable physical results Loosing to much norm for the wave function associated to the pseudopotential can have dramatic effects on the results Selecting a value of ry between 0 677 44 and 0 8 r is a good choice but the best way to adjust r j4 value is to have a look at the two first values of evale in Atom name file They have to be as equal as possible and are sensitive to the choice of ry Change the matching radius rc for one or both partial wave s In some cases changing rc can remove ghost states In most cases changing pseudopotential or matching radius one has to restart the procedure from step 2 only for partial waves 4 Now one has to test the efficiency of the generated PAW dataset Run a DFT computation and determine the size of the plane wave basis needed to get a given accuracy If the cut off energy defining the plane waves basis is too high higher than 20 Hartree if matching radius has a reasonable value some changes have to be made in the input file User s guide for atompaw 20 o First possibility change projector keyword bloechl by projector keyword vanderbilt Vanderbilt projector
21. l wave The later is obtained by inverting the Schr dinger equation at energy E and angular momentum Go to point 1 to add another partial wave associated with Or Enter n User s guide for atompaw 8 projector keyword ps scheme ortho scheme shapefunction tol projector keyword Option governing the scheme used to generyte smooth PS partial waves and associated projectors Possible values Bloechl or VNCT use P Bl chl PS waNe functions and projectors generation scheme PRB 50 17953 1994 A cutoff function k r sin nNrya AI se Jf is used in a Schr dinger like equation to deduce PS partial waves Projectors are then amp thogonalized with a Gram Schmidt procedure In that case ps scheme and ortho scheme keyWords are ignored Vanderbilt or VNCTV use a polynomial functi amp n to pseudize partial waves and D Vanderbilt projectors generation scheme PRB 41 7892 19903 The polynomial function used to pseudize partial waves is identical as the one used when ps scheNe polynom see below In that case ps scheme and ortho scheme keywords ark ignored custom get PS wave functions according to ps scheme keyword see below and projectors according toortho scheme keyword see below modrrkj use modified RRKJ form for wave function can be used gramschmidtortho or svdortho values for the ortho scheme ith vanderbiltortho ps scheme Option governing the scheme use
22. logderiv l file correspond to I quantum number and contains the logarithmic derivative of the l state ALIA computed for exact atomic problem and with the PAW dataset o The 2 curves should be superimposed as much as possible By construction they are superimposed at the two energies corresponding to the two partial waves If the superimposition is not good enough the reference energy for the second partial wave should be changed o Generally a discontinuity in the logarithmic derivative curve appears at 0 lt Ep lt 4 Rydberg A reasonable choice is to choose the 2 reference energies so that Eo is in between if possible i e if one the 2 partial waves correspond to an unbound state o Too close reference energies produce hard projector functions But moving reference energies away from each other can damage accuracy of logarithmic derivatives o Another possible problem is the presence of a discontinuity in the PAW logarithmic derivative curve at an energy where the exact logarithmic derivative is continuous This generally shows the presence of a ghost state First try to change to value of reference energies this sometimes can make the ghost state disappear If not it can be useful to Change the pseudopotential scheme Norm conserving pseudopotentials are sometimes so deep attractive near r 0 that they produce ghost states A first solution is to change the quantum number used to generate the norm conserv
23. ment to data for these codes ABINIT http www abinit org To obtain a file formatted for abinit code enter the following lines 2 Lo word proj optim keyword comp in XC keyword reduced grid keyword N Enter 2 or ABINITOUT to See next page activate output in abinit comp in XC keyword format Option governing the use of compensation density in eXchange Correlation potential coreWF keyword Possible values Option for the printing of core wave function noxcnhat exchange correlation potential in a file formatted for abinit does not include compensation density Bl chl s formalism This choice is safer as it avoids numerical 2 problems in XC terms calculation prtcorewf print an additional file named Compatible with abinit v6 1 Atom name XCfunc corewf abinit containing core wave functions in abinit usexcnhat exchange correlation potential format includes compensation density Kresse s formalism This choice can produce numerical problems Possible values noprtcorewf no additional printing Default if missing is noprtcorewf in XC calculation For further explanation see Comp Phys Comm 181 1862 2010 Default if missing is noxenhat reduced grid keyword gridsize logstep Option for the use of a reduced grid This option in essentially useful when atompaw uses a linear grid in order to reduce the grid size for the use in abini
24. of the matching radius rc o The 9 r and P r should have the same order of magnitude If not you can try to get this in three ways Change the matching radius rc for this partial wave but this is not always possible spheres cannot have a large overlap in the solid Change the pseudopotential scheme see later If there are two or more partial waves for the considered angular momentum including additional partial waves unbound states Decreasing the magnitude of projector is possible by displacing the references energies Moving the energies away from each other generally reduce the magnitude of projectors but a too big difference between energies can lead to wrong logarithmic derivatives see following chapter o The two first values of evale valence energy in the Atom name file have to be close If not choices for projectors and or partial waves certainly are not judicious o Example of difficulty with P r when the amplitude of projectors becomes too large atompaw can produce an error with the following message No convergence in boundsep Followed by Best guess of eig dele xxxxx yyyyy This happens during the PAW Hamiltonian resolution which cannot be achieved One can bypass the difficulty by generating softer projectors as explained just above User s guide for atompaw 19 3 Have a look at the logarithmic derivatives They are printed in the logderiv files Each
25. on relativistic Schr dinger equation scalarrelativistic solve scalar relativistic wave equation Koelling Harmon like equation J Phys C 10 3107 1977 Default 1f missing is nonrelativistic nucleus keyword Option governing the form of the potential near r 90 during atomic wave equation resolution Possible values point nucleus solve atomic wave equation assuming point potential for r 0 V r 2Z r finite nuclueus solve atomic wave equation assuming finite nucleus potential for r0 V r 2Z erf r RR r where RR is a nuclear size parameter Default 1f missing is point nucleus User s guide for atompaw 5 These keywords should be on the same line as previous ones grid keyword gridsize Fmax Tmatch Options governing the analytic form of the radial grid used in atompaw Analytical form of the grid is determined by grid keyword ts step and size can be defined by gridsize r and Catch Possible values for grid keyword lineargrid use a linear grid r h i 1 loggrid use a logarithmic grid r h Z exp h i 1 1 loggridv4 use a logarithmic grid r 7 ro Z exp h i 1 1 with rg7107 Default 1f missing is lineargrid Additional optional arguments gridsize Define the number of points in the grid Default if missing is 20001 when grid is linear 2001 when grid is logarithmic Ymax atomic units Optional argument but if present must follow gridsize in th
26. orrelation functional and either a Schr dinger default or scalar relativistic approximation It is a spherical problem and it is solved on a radial grid Other approximations can be given as for example the behavior of the nuclear potential The atomic problem is solved for a given electronic configuration that can be an ionized excited one Choose a set of electrons that will be considered as frozen around the nucleus core electrons The others electrons are valence ones and will be used in the PAW basis The core density is then deduced from the core electrons wave functions A smooth core density equal to the core density outside a given r matching radius is computed Choose the size of the PAW basis number of partial waves and projectors Then choose the partial waves included in the basis The later can be atomic eigen functions related to valence electrons bound states in fact this is mandatory with atompaw and or additional atomic functions solution of the wave equation for a given quantum number at arbitrary reference energies unbound states Generate pseudo partial waves smooth partial waves build with a pseudization scheme and equal to partial waves outside a given re matching radius and associated projector functions Pseudo partial waves are solutions of the PAW Hamiltonian deduced from the atomic Hamiltonian by pseudizing the effective potential a local pseudopotential is built and equal to effective potent
27. r the generation of PAW datasets in UPF format The PWscf code uses the Kresse treatment PRB 59 1758 1999 of the exchange correlation functional which can lead to inaccuracies as explained in Comp Phys Comm 181 1862 2010 To prevent these inaccuracies we recommend using the BESSELSHAPE option for the compensation charge and choosing shape l paw 1 2 For example an input for Li including all electrons in the valence suitable for use with PWscf is as follows Li 3 GGA PBE loggrid 2001 220000 oon oro anderbilt besselshape 2 2 0 v v v T 1 6 n n v 2 1 1 1 n 0 4 6 6 Other output formats 4 or PWPAWOUT output dataset for use in pwpaw or Socorro codes 5 or XMLOUT output dataset in xml format c explore mode of the program The EXPLORE or 10 keyword puts allows the user to run the pseudofunction portion of the program multiple times to search for optimal parameter values See the ATOMPAW Explore Userguide pdf for more details User s guide for atompaw 14 Examples A minimal input file Boron 15 257 2p 4 partial waves in basis iw ORPND UW OorOoYN z oo o 5 wK BSB WK PHEW dQ ONNE W SJ vanderbilt PRPPEN ie 0o User s guide for atompaw 15 A complete input file Nickel 15 2s 2s 357 3p 3d 4s 4p 6 partial waves in basis Nickel 28 GGA PBE scalarrelativistic point nucleus loggrid 1500 80 2 3 loggderivrange 1
28. s generally are more localized in reciprocal space than Bloechl ones Recheck the plane waves cut off in a DFT calculation it should have decrease but this is not a general rule o Second possibility use RRKJ pseudization for PS partial waves put projector keyword custom and ps keyword rrkj This pseudization is particularly efficient and gives highly localized projectors in reciprocal space This choice has in most cases the best influence on the plane wave basis One has to note that The localization of projectors in reciprocal space can generally be predicted by a look at tprod i files Such a file contains the curve of d FAD AD as a function of q reciprocal space variable q is given in Bohr units it can be connected to the i i 2 Ex plane waves cut off energy in Hartree units by Z 2 These quantities are only calculated for the bound states since the Fourier transform of an extended function is not well defined Generating projectors with Bl chl s scheme often gives the guaranty to have stable calculations atompaw ends without any convergence problem and DFT calculations run without any divergence but they need high plane wave cut off Vanderbilt projectors and even more custom projectors sometimes produce instabilities during the PAW dataset generation process and or the DFT calculations In most cases after having changed the projector generation scheme one has to restart t
29. sgagaa User s guide for atompaw 7 2 Partial wave basis generation Imax Dag Maximum I quantum number for partial waves in PAW basis Ipaw shape Fvloc core Eia fcore atomic units Matching radius used to get pseudo core density e r from atomic core density n r Below rcre pseudo core density has the form FIDA ALL HEJ Default if missing is paw shape atomic units Cut off radius of shape functions gi r used in compensation density definition P Fvloc atomic units Default if missing is rpay Matching radius used to get pseudo potential V r from all electron effective potential Vloc r Default if missing is rpay Y i Repeated for each additional I 0 partial wave Erer n y Repeated for each additional 1 partial wave One paragraph for Erer each 0 Xl sl n y i Repeated for each additional l l nax partial wave Erer n Definition of partial waves basis elements By construction the basis already contains each atomic wave function associated with a valence state each wave function marked as v in the atomic all electron configuration These are bound states To add additional basis elements unbound states proceed as follow For each angular momentum from 0 to Lmax 1 Enter y to add an additional partial wave 2 Enter E real number Rydberg units reference energy used to build the partia
30. t Possible values nospline no additional printing logspline PAW dataset is transferred into a logarithmic grid except non local projectors This gridgrid is defined by r i7 1 a exp b i 2 and r 1 0 The user has to give the size of the grid gridsize and the logarithmic step b in the above formula 1ogstep gridsize Optional argument but if present must follow 1ogspline in the input Define the size of the auxiliary logarithmic grid Default if missing is 350 logstep Optional argument but if present must follow gridsize in the input Define the logarithmic step of the auxiliary logarithmic grid Default if missing is 0 035 Default 1f missing is nospline User s guide for atompaw 12 Output for ABINIT continued proj optim keyword ecut gfact werror Option for the optimization of projectors Possible values nooptim no additional printing rsoptim optimize projectors using Real Space Optimization as in PRB 44 13063 1991 It tries to improve the development of non local projectors by smoothing their development over large G vectors introducing a controlled error The scheme is governed by 3 parameters Gmax Y and W The efficiency of Real Space Optimization strongly depends on the non local projectors it can sometimes be detrimental only experienced users should use it ecut Rydberg Optional argument but if present must follow rsoptim in the input Define the
31. w 6 Maximum n quantum number for electrons Example For Nickel 15 257 2p 3s 3p 3d 4s enter 4A 33n n n l occmsi One line for each empty or partially occupied n l state 000 b For each electronic shell of the atomic species enter a line with n l quantum numbers of the shell occ electronic occupation of the shell n l OCCni Actually only empty or partially occupied shells are needed full shells can be omitted Charged excited configurations are of course accepted A 0 0 0 zero zero zero line ends the configuration Example For excited Nickel 1s 257 2p6 3s 3p 3d 45 simply enter 3 2 8 5 40 1 5 Cory rw One line for each n l state eon y 0 states first DEY then l states c or v E C Or Vv Core or valence characteristic of electronic shell For each electronic shell enter a c or v keyword which can be c the electronic shell is a CORE shell frozen around the nucleus and included in the core density of the PAW data set v the electronic shell is VALENCE shell containing valence electrons included in the PAW data set In addition note that the partial wave associated with such a valence state will be NECESSARILY included in the PAW partial waves basis see below Example For Nickel 15 2s 2p 3s 3p 3d 4s with 3p 3d 4s in the valence enter fel 1s 2s 38 4s valence 2p 3p valence 3d valence q
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