How to optimize automatically the parameters that determine the quality of the basis

1. How to optimize automatically the parameters that determine the quality of the basis Alberto García Javier Junquera

2. Optimizationof the parametersthatdefine the basis set: the Simplex code ETot = ETot Set of parameters SIMPLEX MINIMIZATION ALGORITHM Isolated atom Kohn-Sham Hamiltonian + Pseudopotential Extra charge Confinement potential Full DFT calculation of the system for which the basis is to be optimized (solid, molecule,...) Basis set J. Junquera et al. Phys. Rev. B 64, 235111 (2001)

3. Compiling the Simplex code to automatically optimize the basis set Assumingthatyouhavedownloaded and unpackedthe Siesta distribution in a directory ~/siesta, gotothe ~/siesta/Util/Optimizerdirectory $cd ~/siesta/Util/Optimizer and type $ make Thiswill compile the simplex usingthesamearch.make file as theoneyouto compile siesta

4. Compiling the Simplex code to automatically optimize the basis set Create a directorytorunthe simplex forthedesiredsystem (in this particular case, thewatermolecule), and copythere Thepseudopotential files The Siesta input file, that in this case will be calledTEMPLATE A file withthelist of variables overwhichtooptimize, and theirranges of variability, calledVARS A file withthetunableoperationalparameters, calledPARAMS The script file which defines theoperationsthat are to be carriedout, calledrun_script.sh

5. The TEMPLATE file Forthemeaning of these input variables, readthe Siesta Manual In this particular example A softconfinementpotentialwill be usedfor default foralltheatomshells Default valuefortheprefactor of thesoftconfinement (forallatoms and shells) Some variables are notdefined, butkept as variables (with a leading $). Those are the variables thatwill be optimized in the Simplex minimization. Theymightchange, dependingonyour particular problem Default valuefortheinnerradius of thesoftconfinement (forallatoms and shells): a fraction of theouterconfinementradiusdeterminedbytheenergyshift

6. The VARS file The TEMPLATE file Both files define the variables thatwill be optimized in the Simplex minimization Match thenamesthatyou use in the TEMPLATE (withouttheleading ‘$’) withthose in the VARS file DO NOT leaveanyblanklines in the VARS (noteven at theend).

7. The VARS file The TEMPLATE file Minimumvalueforthis variable Maximumvalueforthis variable Startingvalue (optional) Ifthestartingvalueismissing, a randomstartingpoint in theappropriaterangeischosen.

8. The PARAMS file Tunableoperationalparametersfortheoptimizationalgorithm are definedhere it uses a two-levelapproach, withamoeba-likeiterationsfollowedbyperiodicrestartswithnew simplex hyper-tetrahedra of progressivelysmallersizes Initialcriteria Defines thesize of theinitialhyper-tetrahedron

9. The PARAMS file Tunableoperationalparametersfortheoptimizationalgorithm are definedhere it uses a two-levelapproach, withamoeba-likeiterationsfollowedbyperiodicrestartswithnew simplex hyper-tetrahedra of progressivelysmallersizes Stoppingcriteria a minimum fractionalsizeforthehyper-tetrahedron. and a fractionalenergytolerance (comparedtothedifferencesbetweenthehighest and lowestenergies of thevertices)

10. To run an optimization $ ~/siesta/Util/Optimizer/simplex > simplex.out & The driver program (simplex) callthe script run_script.sh The script can performsubstitutionsonsuitabletemplate files. Theuser has nothingto do at thislevel. $ tail -f simplex.out First:itdumpstheinformation of the VARS and PARAMS files Second:itbuildstheinitial simplex and computes values of theenergies at thevertices of theinitial simplex Third:it computes thefractionalenergytolerance and checksfortheconvergencecriteria Fourth:ifnot converged, anamoeba-likeiterationsisperformed, searchingfortheminimum and producing simplex hyper-tetrahedra of progressivelysmallersizes

11. At the end of a successful minimization: the final.sed file Itcontainstheoptimizedvalues of theparameters $ more final.sed They can be foundalso at theend of the output file afterrunning simplex $ tailsimplex.out