Javier Junquera Alberto Garc ía Optimization of the parameters that define the basis set the Simplex code Set of parameters Isolated atom KohnSham Hamiltonian Pseudopotential ID: 1002988
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1. How to optimize automatically the parameters that determine the quality of the basisJavier JunqueraAlberto García
2. Optimization of the parameters that define the basis set: the Simplex codeSet of parametersIsolated atom Kohn-Sham Hamiltonian+PseudopotentialExtra chargeConfinement potentialFull DFT calculationof the system for whichthe basis is to be optimized(solid, molecule,...)Basis setSIMPLEXMINIMIZATIONALGORITHMETot = ETotJ. Junquera et al. Phys. Rev. B 64, 235111 (2001)
3. Compiling the Simplex code to automatically optimize the basis setAssuming that you have downloaded and unpacked the Siesta distribution in a directory ~/siesta, go to the ~/siesta/Util/Optimizer directory$cd ~/siesta/Util/Optimizer and type $ makeThis will compile the simplex using the same arch.make file as the one you to compile siesta
4. Compiling the Simplex code to automatically optimize the basis setCreate a directory to run the simplex for the desired system (in this particular case, the water molecule), and copy thereThe pseudopotential files The Siesta input file, that in this case will be called TEMPLATEA file with the tunable operational parameters, called PARAMSA file with the list of variables over which to optimize, and their ranges of variability, called VARSThe script file which defines the operations that are to be carried out, called run_script.sh
5. The TEMPLATE fileA soft confinement potential will be used for default for all the atom shellsFor the meaning of these input variables, read the Siesta Manual Default value for the prefactor of the soft confinement (for all atoms and shells)Default value for the inner radius of the soft confinement (for all atoms and shells):a fraction of the outer confinement radius determined by the energy shift Some variables are not defined, but kept as variables (with a leading $). Those are the variables that will be optimized in the Simplex minimization.They might change, depending on your particular problemIn this particular example
6. The TEMPLATE fileThe VARS fileDO NOT leave any blank lines in the VARS (not even at the end). Match the names that you use in the TEMPLATE (without the leading ‘$’) with those in the VARS fileBoth files define the variables that will be optimized in the Simplex minimization
7. The TEMPLATE fileThe VARS fileMinimum value for this variableMaximum value for this variableStarting value (optional)If the starting value is missing, a random starting pointin the appropriate range is chosen.
8. The PARAMS fileTunable operational parameters for the optimization algorithm are defined hereInitial criteria Defines the size of the initial hyper-tetrahedronit uses a two-level approach, with amoeba-like iterations followed by periodic restarts with new simplex hyper-tetrahedra of progressively smaller sizes
9. The PARAMS fileTunable operational parameters for the optimization algorithm are defined hereStopping criteria a fractional energy tolerance (compared to the differences between the highest and lowest energies of the vertices)a minimumfractional size for the hyper-tetrahedron.andit uses a two-level approach, with amoeba-like iterations followed by periodic restarts with new simplex hyper-tetrahedra of progressively smaller sizes
10. To run an optimization$ ~/siesta/Util/Optimizer/simplex > simplex.out & Fourth: if not converged, an amoeba-like iterations is performed, searching for the minimum and producing simplex hyper-tetrahedra of progressively smaller sizesFirst: it dumps the information of the VARS and PARAMS filesSecond: it builds the initial simplex and computes values of the energies at the vertices of the initial simplexThird: it computes the fractional energy tolerance and checks for the convergence criteria$ tail -f simplex.outThe driver program (simplex) call the script run_script.shThe script can perform substitutions on suitable template files.The user has nothing to do at this level.
11. At the end of a successful minimization: the final.sed file $ more final.sedIt contains the optimized values of the parameters $ tail simplex.outThey can be found also at the end of the output file after running simplex