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cluster 1.0 user manual Contents

1. to see whether it is at a minimum or maximum in the PES the program will not even start the optimization cycles but abort the candidate and append its structure to the aborted library An example where this is done to create the library of structures that are built is provided in the exam ples noopt folder The input file also shows the use of in the composition for trying to build an NH3 surrounded by twenty water molecules The structural information for the two fragments were copied from the default fragment library which is stored in the 1ib folder of the cluster program In order to not have the molecules touch an extra radius of 0 3A for each fragment is introduced The value is half of the differ ence of an H bond in water 1 7 A from which the sum of the H and O radii are subtracted 0 37 and 0 73A respectively name noopt composition NH3 1 H20 20 charge 0 multiplicity 1 3D 20 matings 0 max_freq 0 fragments 3 H20 0 3 ORCA PBE VDW06 TZVPP PModel TightSCF Opt UseSym O 0 000000 0 000000 0 066734 H 0 000000 0 763595 0 529847 H 0 000000 0 763595 0 529847 4 NH3 0 3 ORCA PBE VDW06 TZVPP PModel TightSCF Opt UseSym N 0 000166 0 079017 0 000004 H 0 470994 0 317856 0 815661 H 0 470988 0 317858 0 815660 H 0 941816 0 317791 0 000005 The result of running this input is that only a noopt_aborted xyz file will be created that contains each structure built To generate only the mated structures based on an available po
2. 0101 46 7 0 0273 0 0498 0 5469 0 0263 0 0737 0 0733 0 1545 0 0711 0 1189 38 3 0 1771 0 2375 0 6545 0 1718 0 1934 0 0836 0 0885 0 1109 0 1303 32 8 0 0514 0 0973 0 0505 0 0517 0 0882 0 0656 0 268 0 524 0 3122 51 8 0 1213 0 116 0 0834 0 1202 0 17 0 0366 0 0292 0 1557 0 0408 92 3 0 3474 0 4314 0 3077 0 3456 0 4123 0 4505 0 1408 0 0505 0 1607 9 test_3D 0 021712211 154 932 533 20 Build 3D scale 1 H 1 1518252540 2 1202304363 0 4178235809 H 0 1886989782 3 6200137545 0 4001815406 S 0 0961472187 2 3469205038 0 0118190440 H 1 2367631676 1 3648574145 0 1764851672 H 2 8606317737 2 0233658701 0 8145101256 S 2 5485261164 1 0962064923 0 0990490047 H 3 0582649197 1 9205378907 0 6013266369 H 2 4364364714 0 2065601384 0 2210352951 S 2 0181987237 1 4756368884 0 1130812179 HAAARAARARARAAAARRRARARARARAAARARARAR ON E AAA RARA RARA RRA AAA RARA AR ARA Thus we can use the cluster input file but with a larger number of geometry cycles for production runs and with the test 1 removed or commented out 6 2 Multiple runs It may be beneficial to run the same cluster search multiple times and refilter the viable or population can didates found from all runs combined This is most easily done by running each input in its own folder It may be useful to make sure that the name keyword contains something that allows one to retrace which run generated a particular
3. 4 REoptiMizig a libraty aen ee A eae OE ye Me A D 6 5 Seeding the population library 2 ee 6 6 No optimization runs oaa aa ee 6 7 Single fragment runs 2 sa gor 2 csc a a e EEA 68 Usine templates osma 2 5 ao a a a de aoe da pa NRP sj he NOVOA hu W Rh 1 Introduction The cluster program implements a gradient enhanced genetic algorithm to generate a set of structures i e a population of candidates associated with verified minima in a multi dimensional potential energy surface PES Candidates consists of one or more fragments where a fragment can be either a single atom or a set of atoms The implementation is loosely based on ideas presented in papers by Anastassia Alexandrova 3 and Deaven and Ho Generally implementations of a genetic algorithms start with a possibly large initial population and use one or more genetic operators to breed new candidates from that population A subset of those new candidates may then replace candidates in the population thus maintaining a fixed sized population In the implementation presented here this approach is slightly modified Due to the goal of only retaining candidates associated with verified minima in the PES it is computa tionally and time wise costly to seed the population with large number of candidates Thus the approach in the cluster program was changed in that it builds a set of candidates that may result in a quite small initial population The goal is
4. AAA RA AAA RARA VAHARAMAARARRARARRARRRRARAAAR FILTERED POPULATION HHHHHRAAA RRA RA AAA RARA RR ARA H2S_r2 3 Filtered E 0 023558996 R 163 685 v 759 80 H2S_r3_28 Filtered E 0 023558354 R 163 576 v 369 30 H2S_r3_4 Filtered E 0 023558056 R 163 867 v 17 70 H2S_r5_3 Filtered E 0 023557837 R 163 538 v 731 20 H2S_r4 3 Filtered E 0 023557507 R 163 550 v 738 60 H2S_r1l 5 Filtered E 0 023556889 R 163 536 v 96 90 H2S_r1l_ 4 Filtered E 0 023556492 R 163 663 v 28 80 H2S_rl1_3 Filtered E 0 023555334 R 163 507 v 26 70 6 4 Reoptimizing a library A library like the one created in the examples H2S al1 folder may be used as the initial population for a reoptimization using another program e g ADF The files for the ADF cluster run are stored in the ex amples H2S ADF folder First we will copy the filtered library into the ADF folder Since we will use the name H2S_ADF the population file that will be reoptimized is called H2S_ADF_population xyz Be cause the cluster program will overwrite the population library file we will keep a copy calledinitial xyz around in case we need to redo this part rkanters ADF rkanters cp p all all_flt xyz initial xyz rkanters ADF rkanters cp initial xyz H2S_ADF population xyz The input file for the cluster run itself should now specifically state that a reoptimization should be done It is important that the composition string is exactly the same as th
5. Consider editing the template s before run Exiting In this case we need to modify all of the template files Since the Freq and ReOpt calculations can use the checkpoint file for the basis set information only the method s needs to be changed to B3LYP ChkBasis e g for the g09 Freq file 3chk 3 root s chk mem 3 memory dMB Snproc processors d B3LYP ChkBasis FREQ NORAMAN geom check guess read scfcyc max_scf d root s Frequency Calculation charge d multiplicity d The Opt template needs to define the method B3LYP Gen as well as the basis set to be used and becomes quite lengthy 3chk 3 root s chk mem 3 memory dMB Snproc processors d B3LYP GEN opt maxcycle max_opt d sym loose scfcyc max_scf d root s Optimization charge d multiplicity d xyz s Li 0 S 6 1 00 6269 2628010 0 20540968826E 03 940 31612431 0 15916554089E 02 214 22107528 0 82869829707E 02 60 759840184 0 33856374249E 01 19 915152032 0 11103225876 7 3171509797 0 27449383329 If you are concerned about whether this will all work you may rerun the Li4a in file and check the test_3D files generated This was done redirecting the cluster standard output to the Li4a_again out file which showed that things should work fine When running the cluster program don t worry about the fact that in the PROGRAM SETTINGS section the default method for the program is echoed as opposed to template 28 VHAAARAAR
6. as the ADF Si Li one but now for Si Lig using Gaussian s g09 the only modification to use g03 is to change g09 in the program line to g03 Note that since g03 and g09 automatically change a calculation to an unrestricted one when the multiplicity is not 1 we do not have to stipulate UB3LYP but we could For clarity the maximum number of optimization and SCF cycles have been explicitly defined name Si4Li3 program g09 method B3LYP SDD processors 8 memory 6000 max_opt 50 max _scf 50 multiplicity 2 charge 0 composition Si 4 Li 3 1D 2 2D 5 3D 10 matings 40 16 energy resolution 5e 4 repulsion resolution 2 5 3 ORCA Requirements The ORCA environment variable should be defined as the folder containing the ORCA executable which should also be in the path because the cluster program calls SORCA orca directly Defaults The default method in the template for ORCA is RKS B3LYP G SV Specifics The energy value is taken from the regular expression match of every line in the output file with r FINAL SINGLE POINT ENERGY 0 9 ORCA Example A Li cluster using ORCA name Li4 program ORCA method RHF SV processors 1 memory 200 multiplicity 1 composition Li 4 charge 0 1D 1 2D 1 3D 1 restart 0 force to start from scratch matings 5 5 4 MOPAC Requirements The MOPAC environment variable should be set to the full path of the MOPAC executable exe file since the cluster program execute
7. candidate 6 5 Seeding the population library Due to the randomness in the build and mating procedures one is not guaranteed to get the same populations every time a cluster job is run If you executed the previous steps in finding a library of H2S 3 molecules it is likely that you would indeed get the same lowest energy structure s but when I executed the same set of runs before I did not encounter the trimer in which all three dangling H s are on the same side of the ring of S atoms To make sure that the program will consider this candidate we will seed the initial population with a duplicate of the lowest energy structure encountered but with the one H on the first H2S moved to the other side We will also remove the other candidates from the file This edited population library will be used in another ADF calculation this time stored in the examples H2S ADF2 folder We also need to flag that the second one needs optimization The initial population file to be used now looks like note the inf in the second structure as well as the change in the z coordinate of the first hydrogen is changed to 1 15 9 H2S ADF 3 1 280270003 183 440 124 91 Population H2S r2_ 1 H 1 8611392375 1 1350155879 1 3998146899 H 0 3947405456 1 3078773930 0 1021772479 S 1 7780389666 1 1034449824 0 0433127875 H 1 8784401317 1 0099340188 1 1544075407 H 1 3354105540 0 3046479439 0 2052837443 S 1 8510702418 0 9959604779 0 2046679226 H 0 9318295376 0 99154318
8. candidate while keeping the rest of the input the same In the examples H2S folder this is done in the folders rl r2 r3 r4 and r5 The input file in the r1 folder rl in is as follows name H2S_rl program MOPAC method PM7 PRECISE max_opt 500 charge 0 multiplicity 1 composition H2S 3 1D 2 2D 5 3D 20 matings 30 energy resolution 5e 4 repulsion resolution 2 fragmentlib fragments xyz When the cluster runs are finished one may quickly see which runs generated which candidates in the popu lations by using grep on LINUX UNIX type systems only rkanters H2S rkanters grep _ r pop xyz v1 H2S_rl_population xyz H2S_rl_4 0 023556492 163 663 28 80 Build 2D scale 1 r1 H2S_rl _population xyz H2S_rl_18 0 021987541 144 368 3 40 Build 3D scale 1 r2 H2S_r2 population xyz H2S_r2 1 0 021989498 145 184 3 10 Build 1D scale 1 r2 H2S_r2 population xyz H2S_r2 43 0 015519401 194 769 18 50 H2S_r2 4 x H2S_r2 4 r2 H2S_r2 population xyz H2S_r2 4 0 012641140 180 537 13 10 Build 2D scale 1 r3 H2S_r3 population xyz H2S_r3_4 0 023558056 163 867 17 70 Build 2D scale 1 1r3 H2S_r3_population xyz H2S_r3_13 0 022450474 159 517 22 30 Build 3D scale 1 1r3 H2S_r3_population xyz H2S_r3_1 0 021960593 142 241 4 70 Build 1D scale 1 r4 H2S_r4 population xyz H2S_r4 6 0 022375850 160 280 31 90 Build 2D scale 1 r5 H2S_r5 population xyz H2S r5 4 0 021980137 143 607 5 50 Build 2D scale 1 And it is immediately clear that in most runs the candidate
9. fragmentlib fragments xyz After executing the cluster program with this input file the folder will contain the input and output files for each of the test runs using the name test_3D as the root name for the 3D build candidate that is generated The resulting output from the cluster program itself which was redirected to the test out file shows that the prototype of the trimer indeed uses 3 H2S fragments from the fragment library which have an extra radius of 0 3 A HHH HAHAHAHA A AY LIBRARIES READ WHILE PARSING INPUT HAHAHA AAA AA AAA AA fragmentlib fragments xyz HHMAHMARAARARAAARARARARAA AEA EH YE BUILDING PROTOTYPE HAHAHA ARA AAA THEA AA AEE 3 x H2S extra radius 0 300 Angstrom H 0 2863440033 0 0647336800 0 9761714367 H 0 4595735367 0 6015626800 0 6826481633 S 0 1732295333 0 5368290000 0 2935232733 For an overall composition of H2S 3 Having 9 atoms and 54 electrons HHHMAHMARAARARAAARARARARAAARAARARA PROGRAM SETTINGS HAHAHA ARA ARA THEA EAA EE Below that a one liner result of the optimization and frequency runs are given each followed with the cluster library entry for the candidate after the computational program finished No ReOpt run is performed since the MOPAC interface does not support this Inspection of the Opt and Freq output lines shows that no error codes are returned the None values More importantly the geometry optimization was not able to converge in the default 50 optimization cycles allowed Since the MOP
10. from within in a folder located on a local file system By defining the OUT_DIR environment variable the output can be directed to a more convenient folder e g the one from where the program was submitted to the queue Example scripts for an SGE and PBS queue system are provided in the distribution These are the actual scripts used to run the cluster program at the University of Richmond so they will require some modifications to make them work elsewhere Cluster standard output The text output generated is printed to the standard output stream Using the verbosity level of 0 it consists of the contents of the input file excluding any fragment definitions some information about the settings used in the program and the status of a candidate as the calculations for it progresses This status is a single line containing the name a message about the status the energy of the cluster in hartree or inf if not known yet the nuclear repulsion in hartree the lowest non zero vibrational frequency in cm or None if not known yet and a comment Cluster candidate libraries The cluster program will also generate several library files all ending with xxx xyz where xxx is the name of the library listed below These library files are multi step xyz files see Section 4 4 so they can be easily read by programs like Jmol The contents of these libraries are updated as the program progresses aborted candidates for which no acceptable minimum
11. order to provide more flexibility it is also possible to read a new definitions from a user specified files or by defining elements directly in the input file The file format is a sequence of one liners defining an element or a comment comment_line element line comment_line string element_line string key string element_name int Z float radius The radius is in A If the key string is omitted element_name will be used as the key If the key string is present as in the examples below any text after the radius will be ignored The key is the string that needs to be used in fragment element names and or in the composition string of candidates One can define atomic ions as if it were an element e g F and Hg with the lines F F 91 2 larger than the 0 71 Angstrom in the built in library Hg2 Hg 80 0 7 smaller than the 1 49 Angstrom in the built in library and use it in the composition or in fragment definition s 4 3 Fragment library and fragments format The predefined library of fragments located in in the library folder of the cluster program lib frag ments xyz consists of optimized geometries calculated with ORCA using PBE TZVPP and VDWO6 In order to provide more flexibility it is also possible to read fragments from user specified files The file for mats consists of a concatenation single fragment descriptions each of which is xyz file formatted with the modification that in that the comment line has
12. the modules for the program as well as the predefined elements and fragments this pdf file some example queue submission script generating python scripts as well as an examples folder with input and output files for the the usage examples in Section 6 2 3 Running the cluster program The program needs to be called from the command line Ifone wants the output to be immediately written to the standard output which may be redirected to a file one can invoke the program using the u option for the python interpreter python u clusterl 0 cluster py d h v v inputfilename The cluster1 0 7 part refers to the full path of where the cluster py file resides The items between square brackets are optional and have the following meaning d debug mode generates a lot more output for debugging purposes h provides this help text and exits v v verbosity level v an integer should be gt 0 Default value is 0 for minimum output The structure of the input file is provided in Section 3 All sample output in this manual are from running the cluster program with the default verbosity level 2 4 Cluster program output Output folder Unless changed by setting the OUT_DIR environment variable the cluster program writes output files in the directory where the program was invoked Setting the OUT_DIR environment variable is useful when running the program on a computational cluster where programs are executed on a compute node often
13. used the energy criterion will be ignored The default is about 0 1 kcal mol repulsion resolution float 0 05 The value in hartree within which the nuclear repulsion R of two candidates needs to be the same to be considered duplicates If a negative value is used the nuclear repulsion energy criterion will be ignored energy window float 0 16 The amount of energy in hartree above the lowest E in the population within which new candidates are accepted If a negative value is used the window will be ignored The default value is about 100 kcal mol 3 7 Genetic operations Most genetic algorithms implement several genetic operators usually at least a crossover a k a recombina tion or mating operator as well as a mutation operator Mating procedure To create a child two parents are randomly chosen from the population where the probability of choosing each parent is determined by the mating probability keyword Each parent is cloned and randomly rotated around the center of the fragment centers The child is initially set equal to the clone of the first parent The recombination itself then consists of transferring as many of the same type of fragments based on their names whose centers lie below the xy plane from the second parent s clone to the child This may fail to produce any transfers if no fragments of the same type are below the two planes If that is the case the random rotation and transfer is attempted again up to max_mate
14. 1 Not Converged E 0 533228167 R 263 045 v None Si4Li_6 ReOpt 1 Converged E 0 549502938 R 256 877 v None Si4Li_ 6 Opt 2 Converged E 0 549446191 R 256 875 v None Si4Li_6 Frequencies E 0 549446206 R 256 875 v 79 511 Si4Li_ 6 Aborted E 0 549446206 R 256 875 v 79 511 Si4Li_6n Opt 3 Converged E 0 570403659 R 273 269 v None Si4Li_6n Viable E 0 570428117 R 273 269 v 14 538 Si4Li_ 6p Si4Li 6n E 0 570403472 R 273 284 v None In this example one sees that after the initial 2D build of the candidate the first optimization didn t converge A frequency calculation whose results are not reported since it doesn t have any meaning is executed and using the Hessian a reoptimization is performed which did converge The second cycle results in a converged optimization so the frequencies are calculated Since the lowest non zero frequency is considered a negative frequency this candidate aborted but with bifurcation default turned on two new candidates with their atoms displaced in opposite directions along this vibrational mode are generated for use in the next and last cycle 3 The first of the two converged and since the frequency calculation shows that is a minimum it is flagged as a viable candidate The other one after the optimization is considered to be a duplicate of the one just found The following keywords affect the optimization procedure max _ freq int 3 The maximum number o
15. 37 0 1432715487 H 0 0384564056 2 1715810038 1 1502910739 S 0 0607162347 2 0844603286 0 2061706737 9 ignored inf H 1 8611392375 1 1350155879 1 15 24 H 0 3947405456 1 3078773930 0 1021772479 S 1 7780389666 1 1034449824 0 0433127875 H 1 8784401317 1 0099340188 1 1544075407 H 1 3354105540 0 3046479439 0 2052837443 S 1 8510702418 0 9959604779 0 2046679226 H 0 9318295376 0 9915431837 0 1432715487 H 0 0384564056 2 1715810038 1 1502910739 S 0 0607162347 2 0844603286 0 2061706737 The input file should not request a reoptimization since H2S_ADF 3 is still OK A regular restart will detect the inf for the energy of the second candidate which we called ignored and reoptimize only this candidate The input file looks the same as the earlier reoptimization one just without the reoptimization line itself name H2S_ADF program ADF method XC nLDA SCF VWN nEND n nBASIS ntype TZP ncore Large nEND processors 8 memory 6000 multiplicity 1 charge 0 composition H2S 3 matings 0 energy resolution 1 repulsion resolution 1 energy window 1 fragmentlib home rkanters work cluster H2S fragments xyz Since we ran the input in a new folder where only a population library existed and not the all library and converged library the newly optimized structure numbers start with 1 above the largest one in the population library 1 e 4 The default duplicate checking will start with an empty list of converged structures to check agai
16. AC interface only supports running several direct optimizations in a row without a frequency analysis and reoptimization in between we should increase the max_opt The frequency calculation does indeed give us frequencies which suggests that that calculation works as it should Note that even though it has converged True in the information about the Freq calculation one does not have to worry about this because the cluster program will retain the information about the geometry convergence from the earlier geometry re optimization s HHHHHHHHHHH HHH HHH HHHHE TEST INPUT FILES FOR A 3D CANDIDATE 4 H HHHHHHHHEET Opt None code None E 2 169030E 02 converged False failed False Freq 9 test_3D 0 021690302 154 932 inf Build 3D scale 1 H 1 1518252540 2 1202304363 0 4178235809 19 H 0 1886989782 3 6200137545 0 4001815406 S 0 0961472187 2 3469205038 0 0118190440 H 1 2367631676 1 3648574145 0 1764851672 H 2 8606317737 2 0233658701 0 8145101256 S 2 5485261164 1 0962064923 0 0990490047 H 3 0582649197 1 9205378907 0 6013266369 H 2 4364364714 0 2065601384 0 2210352951 S 2 0181987237 1 4756368884 0 1130812179 Freq None code None E 2 171221E 02 converged True failed False Freq 533 2 0 0076 0 0021 0 0222 0 0066 0 0142 0 0031 0 0084 0 0502 0 0221 89 8 0 0059 0 0083 0 0471 0 0056 0 0 0 0153 0 0119 0 0222 0 0304 81 5 0 1259 0 0057 0 1394 0 1259 0 0188 0 0139 0 6485 0 0363 0
17. ARARAA RARA AA RAARAARA RARA PROGRAM SETTINGS HHHHHHRAAARA AAA AAA RARA RARA RARA System command g09 lt in s inp gt gt out s out 2 gt amp 1 processors 8 memory in MB 6000 method B3LYP 3 21G max_opt 50 max_scf 50 The input file did contain method template the default method is echoed here but the 3 method s string echoed in the PROGRAM SETTINGS is not in the templates anymore so its value will not be used the run References 1 Anastassia N Alexandrova and Alexander I Boldyrev Search for the ee aa aes n 5 7 lowest energy structures using the ab initio gradient embedded algorithm GEGA Elucidation of the chemical bonding in the lithium clusters J Chem Theory Comput 1 566 580 2005 Anastassia N Alexandrova Alexander I Boldyrev You Jun Fu Xin Yang Xue Bin Wang and Lai Sheng Wang Structure of the Na Cl x 1 4 clusters via ab initio genetic algorithm and photoelectron spectroscopy J Chem Phys 121 12 5709 5719 2004 Anastassia N Alexandrova H H20 clusters Microsolvation of the hydrogen atom via molecular ab initio gradient embedded genetic algorithm GEGA J Phys Chem A 114 12591 12599 2010 D M Deaven and K M Ho Molecular geometry optimization with a genetic algorithm Phys Rev Let 75 2 288 291 1995 XYZ file format URL http en wikipedia org wiki XYZ file format Jmol an open source java viewer for chemical structures in 3d URL http jmo
18. _try times Thus a mating may fail to produce offspring If that happens the mating_rebuild keyword determines whether or not a 3D build will be used as the child as opposed to aborting the mating If it was possible to transfer fragments the set of fragments transferred as a whole is positioned along the translation vector of the center of the atoms transferred such that atoms will at most touch similar to the method used in the build procedure see Section 3 4 but without using a scale factor for the translation vector A status text line will be printed that conveys how many fragments were transferred between which parents e g the following line shows that candidate number 7 was created from a candidate 1 into which two fragments were transferred from candidate 5 Si4Li_7 1 lt 2 5 E inf R 220 656 v None Two examples of successful matings are shown in Figure 1 Only four keywords affect the mating algorithm mating probability int 1 The probability method used in the selection process of the parents from the population The probability p for each parent 7 which has energy E is proportional to the following expressions where Emin is the lowest energy in the population and Emax the highest Ei Emin 5 E 1 Boltzmann p e Em with Em determined by the mating_energy keyword Ei Emin 2 Linear ranges p 1 0 EEA IE TE with n number of candidates in the population 3 Equal ranges p 1 0 10 paren
19. and exit if the number of electrons in the candidate is incompatible with the provided multiplicity 3 4 Population initialization In order for a genetic algorithm to work an initial population of acceptable candidates needs to be available The population may be initialized by reading the population from a previous run and or by building and optimizing a set of new candidates Building candidates Based on the composition a prototype is created after the whole input file is parsed in which every fragment is centered at the origin i e all fragments are on top of each other The new candidate is a clone of this prototype in which the fragments are in a random sequence randomly rotated around their center and depending on the dimensionality of the build nD with n 1 2 3 translated along a random n dimensional vector The translation along that vector is such that the newly placed fragment atoms will at most touch one or more atoms in the already placed fragments so as to avoid inter atomic distances that are too small which could cause computational problems The atom size is the sum of the element radius and a possibly non zero extra radius associated with the definition of the fragment to whom the atom belongs see also Section 4 3 Finally the translation vectors are multiplied by the value of scale a scale factor that allows for a more closed or open topology of the candidate After the build is performed a status line for the candida
20. andidates reflecting the geometry at minima in the PES any can didate that is generated either by a build or mating procedure needs to have its geometry optimized In order to optimize the candidates calculations are executed by a computational program defined with the program keyword The type of calculation performed may be a geometry optimization frequency calculation and if the program allows for it a restart of a geometry optimization using the Hessian from the previous frequency calculation The final geometry is always read from the computational program output and if the reorient flag is not zero the structure is reoriented in an attempt to make visual comparison with programs like Jmol easier If any calculation performed by the computational program encounters problems e g SCF convergence issues causing the generated output file not to contain the information needed to decide what to do with the result a status line with Failed x where x is the return code from the call to the computational program is printed before the candidate is added to the aborted library and the optimization is aborted For example in the output below the frequency calculation that followed the unconverged geometry optimzation caused the computational program to return the error code 256 Si4Li_7 2D Build E inf R 202 734 v None Si4Li_7 Opt 1 Not Converged E 1165 189208430 R 202 734 v None Si4Li_7 Failed 256 E 1165 189208430 R 202 734 v N
21. ary will be performed before the program exits This is useful if the initially used acceptance criteria were too small and duplicate candidates still ended up in the population library The program appends the filter argument to the name keyword for the names of the new xyz and csv files generated so the user has to be careful not to use a string value that would overwrite the regular libraries created by the cluster run i e do not use aborted all converged duplicate population or viable Since the filtering is purely based on inter preting the comment line in the viable library structures see Section 4 4 a run in which filter is used does not require the definition of the candidate composition or anything else except for non default values for du plicate and acceptance settings see Section 3 6 i e energy resolution repulsion resolution energy window as well asnfreq_cutoff and possibly reorient inputs int 0 If 0 creates an input file based on each template associated with the program for a 3D cluster The user can use these to determine whether or not the input files created by the cluster program may work The names of the input files will be test_3D JOB inp where JOB is the name of the template used to create the file If the test keyword 0 as well the test jobs will be executed before the program exits test int 0 If 4 0 runs a single set of jobs on a 3D cluster and exits 3 3 Candidate definition The candidates to
22. ased on how the composition was defined This approach allows one to force the program to consider a candidate that it may not otherwise consider Any optimization done at this stage will also be checked for duplicates thus if one edits a candidate in the population so that it is taken out of the existing population as opposed to adding new ones that need to be optimized it may not be added again depending on how the duplicate check is performed see the duplicate keyword in Section 3 6 If 0 all library files as well as output files associated with the candidates from possible earlier runs are deleted and an empty population library will be the starting point thus triggering the build procedures reoptimize int 0 If 0 the population library is read and all of the candidates are reoptimized This is useful if the calculation program or method is changed and one wants to use the population from an earlier run All library files and candidate output files from the earlier run are deleted as if restart 0 since their contents are not valid due to possible program or method changes build int 0 If 0 will force the cluster program to build and optimize candidates to be added to a possibly already existing population This is useful for a restart run where one hopes to be able to increase the population by executing more builds before starting the sequence of matings 3 5 Cluster optimization Since the goal is to build a population of c
23. ation using the PM3 method with the PRECISE keyword Note that the maximum number of optimization cycles allowed is increased by quite a bit from the standard 50 This example also forces the calculation to start from scratch 1 e any previously calculated results found in the work folder will be deleted name w5 program MOPAC method PM3 PRECISE max_opt 500 composition H20 5 charge 0 multiplicity 1 restart 0 2D 3D 20 40 matings 50 repulsion_resolution 1 6 Cluster usage examples This section shows some examples on approaches of using the cluster program The input and output files are stored in the examples folder provided 6 1 Testing input To test an input file that will be used later with the computational method planned a test run calculation may be performed The input file shown below and available in the examples H2S test folder has already the planned build mating and acceptance keywords but since it contains the line test 1 only a single test 18 of the program templates available will be executed Note that in this case the definition of H2S is stored externally in the H2S folder s fragments xyz file since it is not a fragment in the standard library and we will be using it a few times in these examples name H2S test 1 program MOPAC method PM7 PRECISE charge 0 multiplicity 1 composition H2S 3 1D 2 2D 5 3D 20 matings 30 energy resolution 5e 4 repulsion_resolution 2
24. be considered are built by positioning fragments A fragment may consist of a single atom or a group of atoms The cluster program has a set of pre defined built in element and fragment libraries that are already ini tialized before the input file is parsed The element radii are taken from the WebElements web site The frag ments are ORCA optimized fragments using PBE TZVPP and VDW06 The somewhat arbitrary fragments H2 H2 N2 N2 OH CO H20 H20 NH3 NH3 CO MeOH CH30H EtOH CH3CH20H BeF BeF2 and BeCl2 BeCl are provided but the user can re define fragments and elements at will Whenever the parser encounters definitions for elements elements fragments fragments or the request to use a user defined element or fragment library eLementlib and fragmentlib respectively the directives are immediately processed so that the internal list of elements or fragments is immediately changed Thus these four keywords may occur multiple times in the input file Whenever a fragment is defined its atoms will have the properties of the elements as they are defined in the element library at that time of execution This way a redefinition of an element does not affect the existing fragments but will only affect fragments that are defined after the element was redefined Only after the full input file is parsed will the prototype of a cluster be built so that it always uses the last defined fragments and elements The current defaults are for a H H20 2 clu
25. cluster 1 0 user manual Ren P F Kanters July 2014 Contents 1 Introduction 2 Getting started 2 1 Prerequisites cinc a ee a da da a we 22 Mnstallatiom sd a ek AER cs a ty Ca 2 3 Running the cluster program ee 2 4 Cluster program output o 3 Methodology and keywords 3 1 Computational program settings o oaoa eee 3 2 Utility TUNS 3 ef ale e Base Sia deed Seale a ewe We eA ces 3 31 Candidate definitions se s ra a e BS Bw es ee ee SS or RE Rk Bae OS 3 4 Population initialization 2 ee 3 5 Clusteroptimization s 2 as aye Sinden ae Ae BE a Valin pale 3 6 Duplicate and acceptance determination 0 00 eee eee 3 7 Genetic operations aaa eie noni a a ee 3 8 Termination a ree ES TT Gk A A ae Pa ae ee Bae 4 File Formats 4 1 Computational program templates o ee 4 2 Element library and elements format o e e 4 3 Fragment library and fragments format o 4 4 Candidate library format s copii a a dr dd Wea ls 5 Computational program interfaces and examples Del ADB sie ii in A ae AAA eee Ek DR A ee en 5 2 BOMBOS RA A eae pos Bee AL Ek Be Dee Bee es D3 ORCA a e hee anal ne a atypia Sie ee foe ene a Re ag 4 MOPAG ence eee sink ee HE Ge ik ae OS Se A ae ES 6 Cluster usage examples 651 Testa Input no see ie AO LA ee ek as ba Oe LIZ AS is i ed 6 2 Multiple UDS x ci bs a id a eG SES 6 3 Sorting and refiltering libraries ee 6
26. e one used to generate the libraries since it affects the sequence in which atoms are expected to be found in the xyz file formats The input file listed below is to be run on a computational cluster where the programs are executed in a temporary folder and not within the current working directory This means that one has to use the full path for ragment1ib or element lib which should be on a file system that all compute nodes have access to Thus H2S_ADF in looks like name H2S_ADF program ADF method XC nLDA SCF VWN nEND n nBASIS ntype TZP ncore Large nEND processors 8 memory 6000 multiplicity 1 charge 0 composition H2S 3 reoptimize 1 matings 0 energy resolution 1 repulsion resolution 1 energy window 1 fragmentlib home rkanters work cluster H2S fragments xyz Just for illustrative reasons the cluster program is to not filter out any optimized geometries based on the energies by turning off all energy related acceptance criteria Normally one would have a reasonable idea 23 about the criteria to use and avoid unnecessary frequency calculations Also no matings are requested since we only want to reoptimize the population library At the end of the cluster output we see that four of the six candidates are reoptimized to basically the same structure From the inspection of the H2S_ADF_population csv file it is clear just how close the first four structures are in energy 1 e within 0 011 kcal mol and a range of the repuls
27. eason is to keep complexity down Secondly the computational program optimizes all atomic positions which effectively are already muta tions of atomic positions but admittedly not random ones Thirdly a form of mutation is inherent in the mating methodology by virtue of the random rotation of the parents in the procedure Even when mating the same parents multiple times different children will result thus a set of children from the two same parents will be different just as if a mutation was applied Finally it also bears pointing out that in a system with molecular fragments due to the geometry optimiza tion of the candidates not only the relative positions of the fragment centers themselves changes but also the relative atomic positions within the fragment This can be considered a mutation of the fragments themselves which may be used in future mating procedures 11 3 8 Termination As described above the cluster program will build or rebuild an initial population that will be used as a source of parents for the creation of a single child which will be optimized in each mating cycle Two keywords are available that can be used to terminate the main cycle of matings Whenever one of them is met the program will exit matings int 1 The maximum number of matings attempted unchanged int 0 The maximum number of consecutive times that the population is allowed not to be changed by the mating cycles If set to a value lt 0 thi
28. ed into the population library The method used to decide the promotion into the population library is explained in section 3 6 Independent of whether or not the candidate ends up in the population library the optimization is finished at this stage e If the stationary point was a maximum a status line with Frequencies is printed followed by one with Aborted before the candidate is added to the aborted library If no more frequency calculations are allowed the optimization is terminated otherwise the whole cycle is recursively re entered with a candidate whose geometry moves away from the local maximum along the lowest non zero vibrational mode The size of that step is determined by nfreq_displacement and may be done in one or two directions If nfreq_bifurcate 0 both directions are followed otherwise only one direction is followed Thus a single candidate may generate multiple candidates The names of these candidates have an n or p appended to them When re entering the cycle the number of frequency calculations performed is not reset to zero so that each candidate will have in its history a maximum ofmax_freq frequency calculations and the recursion will never go into an infinite loop A little excerpt of status lines printed may help to understand the sequence in which the optimization ofa candidate progresses Here the default values for the optimization keywords were used Si4Li_6 2D Build E inf R 250 604 v None Si4Li_6 Opt
29. ese decisions The energy E of the candidate is a good metric since that is the property of the candidate that is minimized and provided by the computational programs But different structures may accidentally have very similar energies so the nuclear repulsion energy R i e the sum of all pair wise Coulomb repulsion energies of the nuclei may be used as a metric as well The nuclear repulsion is calculated by the cluster program itself so it is known at any time R is quite sensitive to differences in relative nuclear positions Using both criteria allows the cluster program to consider two geometrically different structures that happen to have very similar E values to still be unique and keep them both in the population library Note that these comparisons are not able to distinguish between non super imposable mirror images of candidates Duplicate determination method Candidate 1 having an energy E Ej and nuclear repulsion energy R R is considered a duplicate of candidate 2 which has E Ex and R Rg if e its energy is less than the value ofenergy resolution dE above that of candidate 2 i e Ej gt Ez and E E2 lt OE as well as when e the repulsions differ by less than repulsion_resolution OR i e Ri Ra lt R Ifa candidate is checked against a candidate in the converged library that has negative frequencies the absolute difference of the energies of the two is compared against the energy resolution Only
30. f times that a frequency calculation may be performed in the optimization procedure If max_freq 0 no optimization for any built candidate will be performed since the optimization cycle will be immediately aborted and the candidate is immediately added to the aborted library nfreq_cutoff float 0 0 If the smallest non zero frequency reported by the frequency analysis is larger than this cut off value the candidate is assumed to represent a minimum in the PES and thus may be considered a viable candidate nfreq_bifurcate int 1 If 0 only a positive step along the lowest non zero vibrational mode will be followed off a stationary point If 0 both directions will be followed nfreq_displacement float 0 5 The multiplication factor for displacement along the lowest non zero vibrational mode Internally the dis placement vector for the vibration is scaled to a 1A sized vector so the multiplication vector may be con sidered the step size in A along that vector Depending on the types of structures and the type of vibrational mode involved the 0 5 value may be too small duplicate int 2 A flag for determining which duplication check procedure should be used 0 donot check for duplicates This may result in lots of unnecessary frequency calculations and geometry reoptimizations 1 use the population library 2 use the converged library i e all unique mimima and maxima encountered For a previously encoun tered maximum only the absolu
31. if all criteria that are to be checked suggest that the candidates are duplicates will the candidate be considered a duplicate Acceptance determination method In order to determine whether a viable candidate can be accepted in the population it is added to a list of the candidates in the population which is then sorted and filtered sequentially for duplicates starting with the lowest energy candidate A duplicate is removed from the list before the next higher energy candidate is considered If the energy of the candidate is more than energy window higher than the lowest energy candidate it is also removed Since the progression through the population is from low to high E more candidates may remain than if the list was traversed the other way An example illustrates this Let the energies for three candidates be 0 0 0 9 and 1 8 With an energy resolution of 1 0 the duplicates filtered population will retain the candidates with E of 0 0 and 1 8 If one were to traverse the from high to low energy only the candidate with the E of 0 0 energy would remain The more accepting methodology was chosen so as to reduce the chance that the population may be filtered too heavily The energy units used for E and R are in hartree Eh 1 Eh 627 509469 kcal mol 27 21138386 eV energy_resolution float 1 6e 4 The value in hartree that a new candidate has to differ from an existing one in order to be considered a different candidate Ifa negative value is
32. inear structures so the displacement in the opposite direction will result in the same solution and the nfreq_bifurcate was set to 0 The output created does indeed show that a viable candidate was created from this HEATH TE AAA AA ee CREATING 1D CANDIDATES 1 47 AAA Si4Li_1 1D Build E inf R 221 950 v None Si4Li_1 Opt 1 Converged E 0 575560063 R 228 936 v None Si4Li_1 Frequencies E 0 575560062 R 228 936 v 98 08557 Si4Li_1 Aborted E 0 575560062 R 228 936 v 98 08557 Si4Li_lp Opt 2 Not Converged E 0 640778775 R 268 970 v None Si4Li_lp Opt 3 Converged E 0 692719694 R 276 828 v None Si4Li_lp Viable E 0 692719704 R 276 828 v 24 27 HHMMAMARAAARAAARARARARAAAARAARASR INITIAL POPULATION HHHHAHHAAAR ARA ARA RAR AAA RAR AA RA Si4Li_ lp population E 0 692719704 R 276 828 v 24 27 HHMAMAHAARARAAARARARARAAARAAARARA START ALGORITHM HAHAHAHA AR ARA RAR AR AAA AR AR AEE HAHAHAHA HHARHARHAAA ALGORITHM END CONSIDERED 0 MATINGS HHHHHHHHHHHAHH AHHH The run generated 1 candidate HHMAMARAARARAAARARARARAAARAARARA FINAL POPULATION HAHAHAHA AR ARA AR ARA AR AA AA RA Si4Li_ lp population E 0 692719704 R 276 828 v 24 27 HHMAHMARAAARAAAAARARARAAARARAAARAARA TIMINGS HHHHAHRARARAA AEA AEA 6 8 Using templates The use of templates can be a bit tricky so one may want to make use of utility runs to verify that the input files are created as you think the templates should as well as that the co
33. ion resolutions of about 0 6 hartree name E Eh dE Eh dE eV dE kcal mol R Eh Freq cm 1 comment H2S_ADF_3 1 280270003 0 000000000 0 000000000 0 000000 183 440 124 91 Population H2S_r2_1 H2S_ADF_1 1 280264632 0 000005371 0 000146155 0 003370 183 708 127 36 Population H2S_r3_4 H2S_ADF_2 1 280255768 0 000014235 0 000387342 0 008932 183 184 125 34 Population H2S_ r3_13 H2S_ADF_4 1 280252325 0 000017677 0 000481028 0 011093 183 530 125 93 Population H2S r5 2 H2S_ADF_5p 1 280045216 0 000224787 0 006116765 0 141056 183 402 119 34 Population H2S_r2_ 43 H2S_ADF 5n 1 274771463 0 005498540 0 149622877 3 450386 183 227 72 85 Population H2S_r2_ 43 H2S_ADF_6 1 267672306 0 012597697 0 342800768 7 905174 160 478 12 37 Population H2S r2_ 4 Thus we really wasted some time calculating the frequencies for candidates 2 and 4 1 would always be calculated and since 3 ends up with a slightly lower energy it would be calculated as well Inspection of the population library shows that within the four lowest energy structures contain non superimposable mirror images which even a slight filtering would have considered duplicates It is interesting to note that here we see a case where the bifurcation results in two different candidates in the population i e H2S_ADF_5p and H2S_ADF_5n both are the result from the optimization of the H2S_r2_43 candidate from the initial population as can be gleaned from the comment for each
34. l sourceforge net Covalent radius URL http www webelements com periodicity covalent_radius Accessed May 5 2012 Hartree URL http en wikipedia org wiki Hartree 29 Index 1D 5 template 3 12 14 2D 5 test 3 4 3D 5 unchanged 12 build 6 charge 5 composition 5 13 23 duplicate 6 8 elementlib 3 4 23 elements 3 4 13 energy_resolution 4 8 10 energy window 4 9 10 filter 4 15 fragmentlib 3 5 23 fragments 3 5 13 inputs 3 4 keep fail 7 9 mating energy 10 11 mating max 11 mating probability 10 11 mating rebuild 10 11 matings 12 max_freq 7 8 18 26 max_mate try 10 max_opt 3 18 19 max_scf 3 memory 3 14 18 method 3 12 14 29 multiplicity 5 name 3 4 20 23 nfreq_bifurcate 7 8 27 nfreq_cutoff 4 7 8 15 nfreq_displacement 7 8 OUT_DIR 2 processors 3 18 program 3 4 6 reoptimize 6 reorient 4 7 9 repulsion_resolution 4 9 10 restart 6 22 scale 5 6 10 30
35. mputational program does not have problems with it If the latter were to happen during a regular run of the cluster program it may quickly generate a lot of Failed candidates The easiest way to get started using templates is to use the cluster program to generate the template files that it needs based on the defaults for the program Here we will choose a Gaussian input and work with a system for which we have to define the basis set i e the Li system using the def2 TZVPP basis set and B3LYP calculations Since initially the folder examples tempate does not contain g09 template files the program will create them for us and exit We will use two input files Li4a in and Li4b in where the only difference is that the Li4b in does not have the test 1 line in it since that is the one that will actually do the cluster search The Li4a in will be used twice first to create the template files needed and second to run the tests on the template files after they have been modified The Li4a in looks as follows name Li4 test 1 program g09 method template processors 8 memory 6000 27 composition Li 4 multiplicity 1 charge 0 2D 2 3D 5 matings 10 The output generated tells us that indeed the three template files were written HHMAMARAAAAAAAARARARARAAARARAAAARRAR TEMPLATES HHHHHAAARARAA AAA ARA AR AAAAAAAA RARA Written template for Freq to g09 Freq Written template for Opt to g09 Opt Written template for ReOpt to g09 ReOpt WARNING
36. n boldface text and is followed by the type of the argument s followed by a colon and the default value of the keyword which are in a monospaced font If the parser encounters a keyword that does not exist it will report the error and exit the program Note the keywords are case sensitive The order in which the keywords are encountered in the input file is not important except for the el ementlib fragmentlib elements and fragments More details on this are provided in the Sec tion 3 3 3 1 Computational program settings This set of keywords may affect the contents of the input files for the computational program which are created from text templates that are either built in or read from the user defined template files see also Section 4 1 Note that not all programs allow one to set all corresponding parameters listed here In that case the parameter is not used in the template so it does not end up in the input file for the program If in doubt either run with method template to see what the actual template is that is created or perform a inputs or test utility run to have the program generate input files and optionally execute each type of calculation that the computational program is expected to be able to perform see also Section 3 2 program string ORCA The string is the key for the program to be used At the moment the cluster program has interfaces for ORCA g03 g09 ADF and MOPAC Associated with each program is a defaul
37. nst In the output we see that the final population has the new structure optimized and indeed named H2S ADF 4 CHMAHAAMHAHRARHARRAA ALGORITHM END CONSIDERED 0 MATINGS 4 HHHHHHHHEHHAE The run generated 1 candidate HHHHHHHHHHHH HEHEHE HEHEHE AHHH HEH FINAL POPULATION HHHHHAAAAARAA RARA ARAHAR AEE H2S ADF 3 population E 1 280270003 R 183 440 v 124 91 H2S_ADF_ 4 population E 1 280059430 R 183 484 v 121 957 HHAMMAARAHAAARARRARHMAARAARARRARRAHAA TIMINGS HHHHAMRARRAR RAR RAR HEHEHE AEH From the csv file it is easy to see that the energy difference is only 0 135 kcal mol and the repulsion resolutions are only 0 044 hartree different while the comment for it suggests that 1t came from a reoptimization of the initial population name E Eh dE Eh dE eV dE kcal mol R Eh Freg cm 1 comment H2S_ADF 3 1 280270003 0 000000000 0 000000000 0 000000 183 440 124 91 Population H2S_r2_1 H2S_ADF_4 1 280059430 0 000210573 0 005729991 0 132137 183 484 121 96 Initial 6 6 No optimization runs A somewhat peculiar use of the cluster program but considered a feature is to use it to only generate a library of structures that the cluster program would generate without automatically optimizing them This is achieved 25 by setting the max_ freq to 0 since that flags the program that no frequency calculations are allowed Since there is no point in running a geometry optimization because any converged geometry can not be checked
38. nvironment variables g09root or g03root are defined as well as that their respective login files have been sourced i e the normal gaussian setup has been performed because the cluster programs executes either g03 or g09 directly Defaults The default method for gaussian calculations is B3LYP 3 21G Specifics The g09 and g03 program interfaces are the same with respect to input file create and output file parsing The only differences are in how the program is called and that the g03 program limits the number of processors to 8 e Because the text used to report the energy is not the same for the different methods that Gaussian supports several regular expression patterns are used when matching the lines from the output file The last match encountered will be the energy that the cluster program reports and uses for comparison The list of patterns and the type of calculation it matches are as follows EpatSearch re compile r SCF Done 0 9 eED SE g09 HF DFT re compile r E CORR 0 9 eED CCx and QCI re compile r E UR MP 0 9 eED MP2 3 and CIS re compile r UR MP4 0 9 eED MP4 re compile r E CI 0 9 eED CISD re compile r E 2PLYP 0 9 eED 2PLYP re compile r CBS X 0 K 0 9 eED CBS re compile r s Energy 0 9 eED NIter SE from g03 g09 Example A similar example
39. olution 5e 4 repulsion resolution 2 ADF Example 2 This example shows how the definition of a fragment can be done by using the fragments keyword With only three fragments in the cluster 1t is not really necessary to generate 3D candidates since the centers of three fragments are always in a 2D plane thus the default of not creating 3D candidates is kept in place In this particular case the nfreq_cutoff is set to a negative value because earlier runs showed that it was hard to get structures without slightly negative frequencies after the initial build A filter run see ADF Example 3 can be performed later to get rid of these name 3xCal2 program ADF method XC nGGA BLYP nEND n nBASIS ntype TZP ncore Large nEND processors 8 multiplicity 1 charge 0 composition Cal2 3 1D 2 2D 10 matings 40 nfreq_cutoff 5 0 energy resolution 5e 4 repulsion_resolution 4 fragments 0 0 2 8316 2 8316 ADF Example 3 An example of a filter utility run where now the candidates with negative frequencies are removed from the viable population keeping the original file intact but generating the newly filtered population in the file 3xCaI2_flt xyz as well as the associated csv file The repulsion resolution has been set to a bit more lenient value as well name 3xCal2 filter flt energy resolution 5e 4 repulsion resolution 10 15 5 2 209 203 Requirements The gaussian interfaces for g09 and g03 require that the gaussian root e
40. olution of 2 will filter several duplicates out as shown in the 1t out which is the result of using the 1t in input file HERAT AAA ee ee DUPLICATES IN VIABLES HR HEE AAA H2S rl 4 H2S r3 4 E 0 023556492 R 163 663 v 28 80 H2S rl 3 H2S r3 4 E 0 023555334 R 163 507 v 26 70 H2S_r4_6 H2S_r3_13 E 0 022375850 R 160 280 v 31 90 H2S_r1_18 H2S_r2 1 E 0 021987541 R 144 368 v 3 40 H2S_r5_4 H2S r2 1 E 0 021980137 R 143 607 v 5 50 H2S_ rl 1 H2S r5 2 E 0 021974507 R 142 948 v 6 20 H2S r3_1 H2S r5 2 E 0 021960593 R 142 241 v 4 70 AAMARARAAAAAAAAAAARAAAAARARA FILTERED POPULATION HAHA EEE ARAN AR AMAR AAA H2S_r3 4 Filtered E 0 023558056 R 163 867 v 17 70 H2S_r3 13 Filtered E 0 022450474 R 159 517 v 22 30 H2S r2_1 Filtered E 0 021989498 R 145 184 v 3 10 H2S r5 2 Filtered E 0 021979759 R 143 056 v 3 70 H2S r2 43 Filtered E 0 015519401 R 194 769 v 18 50 H2S_r2 4 Filtered E 0 012641140 R 180 537 v 13 10 Note that H2S_r2_1 and H2S_r5_2 have very similar energies but their nuclear repulsion resolutions are quite different suggesting that they may be different structures Keep in mind that since no new optimizations are performed none ofthis will find any candidates that were considered duplicates during the initial runs but not according to the new criteria i e setting the duplicate detection criterion settings tighter than what wa
41. one If the keep_fail flag 4 0 the computational program s output file is retained so that the user can inspect more closely why the computational program had issues otherwise all files associated with the candidate are deleted The optimization of a candidate is performed by executing up to max_ freq times cycles that consist of a geometry optimization followed by a frequency calculation and a reoptimization of the geometry At the beginning of each cycle the candidate is added to the all library The implemented methodology tries to avoid time consuming calculations as much as possible One way in which that is done is by using libraries of converged structures 1 e the population library and converged library and comparing any newly converged structure against the candidates in one of those libraries Whether this comparison is done and which library may be used is determined by the duplicate keyword The method used to determine whether a candidate is considered a duplicate is explained in section 3 6 If the new candidate is a duplicate the status line with name where name is the name of the previously encountered candidate is printed before it is added to the duplicate library and the optimization aborted This way one may avoid unnecessary frequency calculations During the optimization frequency calculation and reoptimization cycle the following decisions are made e If the geometry optimization did not converge a status line wi
42. pulation library from a run which therefor should be present in the folder one would only have to change the matings to the number of children to be created and rely on the default restart settings for the program Note that since the mated structures would be appended to the aborted library one may want to delete that file first 6 7 Single fragment runs Since the cluster program is able to follow the PES off a stationary point that is not a minimum the program may also be useful to do just optimizations of a structure that consist of a single fragment An example of the optimization of an SisLi uncharged doublet system stored in examples Si4Li uses the Si4Li in input file name Si4Li program ADF method XC nLDA SCF VWN nEND nBASIS ntype TZP ncore Large nEND nUNRESTRICTED processors 8 fragmentlib Si4Li xyz composition Si4Li 1 charge 0 26 multiplicity 2 restart 0 1D 1 nfreg bifurcate 0 matings 0 to only request a single 1D build of the fragment which really is the whole structure to be optimized The input structure stored as an external fragment is a linear structure known to have imaginary frequencies If the symmetry of a converged maximum is low it may be possible that the opposite directions of following the lowest frequency can give rise to different structures in which case one may benefit from the default nfreg _bifurcate value as was seen in Section 6 4 In this case the input structure and the maximum are l
43. s MOPAC directly Defaults The default method is PM7 17 Specifics Since MOPAC does not write output to the standard output stream it can not be redirected to be ap pended to an earlier output in the program call itself Thus the final output file for a viable candidate only consists of the latest i e frequency calculation Since it wasn t clear how to restart an optimization using the Hessian from an earlier frequency calcula tions the reoptimization part is not implemented in the candidate optimization cycle so only multiple starts of optimizations will be performed up to max_ freq times The default max _opt may be too small Since MOPAC is quite fast it doesn t hurt to make max_opt a lot larger Consider using PRECISE after the method as well e g PM7 PRECISE This will tighten convergence criteria for the optimizations MOPAC reports the heat of formation energy in kcal mol which the cluster program converts to hartree units the memory and processors are not used in the templates Because the optimization and the frequency calculation report energies slightly differently two regular expression patterns are used when matching the lines from the output file The last match encountered will be the energy that the cluster program reports and uses for comparison The two patterns are r HEAT OF FORMATION 0 9 eE r HEAT 0 9 eE MOPAC Example A water pentamer cluster H20 5 calcul
44. s parameter will not affect termination 4 File Formats In order to provide flexibility in the workings of the program several types of files will be created or inter preted The notation for the file formats description uses for optional contents and for a repetition of 0 or more items between the If the is followed by a symbol that symbol refers to the number of times this item is expected The symbol separates different options of which one should be present 4 1 Computational program templates The cluster program uses hard coded python strings with placeholders to generate input files for the com putational programs it interfaces with To provide more flexibility in the complexity of the input files it is possible to have the cluster program read template strings from files in the working directory Ifmethod is set to template the template files with Opt for a geometry optimization Restart for a restart of a geometry optimization using force constants Freq for a frequency analysis Hessian calculation concatenated to the program may be needed The restart and frequency calculation runs can expect the cluster program to have kept the restart information needed If the required template files are not found in the current working directory the program will create them and exit If one needs the extra flexibility that the use of templates provides it is advised to first have the cluster program generate the template file
45. s that the implemented interface in the cluster program requires This can be done by not having any template files in the folder as the cluster program is executed with the method keyword set to template The template files created may then be modified as needed and will be used in future runs of the cluster program in that folder see also Section 6 8 A template file should be a properly formatted input file and may have the following placeholders for the parameters see also Sections 3 1 and 3 3 xyz s the cartesian coordinate block for optimization charge d the charge of the candidate multiplicity d the multiplicity of the candidate 2S 1 spin polarization d the number of unpaired electrons 25 method s the computational method and basis set etc to be used processors d the number of processors memory d the amount of memory in MB max_scf d the maximum number of SCF cycles max_opt d the maximum number of geometry optimization steps root s will be the name of the candidate rootpath s will be the OUT_DIR path with the name of the candidate appended If one keeps the 3 method s placeholder in the template file the default method for the particular program will be used 12 4 2 Element library and elements format The element radii in the library of predefined elements are taken from the WebElements web site They are read from a file in the cluster program s library folder lib elements dat In
46. s used in the initial runs will not increase the number of candidates in the resulting population library Thus if one thinks that the initial input file that created the viable library contained too generous duplicate determination criteria one should inspect the duplicate library for the runs to see whether a restart could be in order Ofcourse one may want to consider sorting without any filtering i e also allowing negative frequencies in the candidates but doing that with the converged library as opposed to the viable library This allows one to see whether there are low energy maxima that had problems optimizing to a lower energy structure suggesting that an actual minimum that should be present was not found For instance in the examples H2S converged folder one may execute cat r conv xyz gt conv_viable xyz And use the following input file to only sort the candidates leaving candidates with negative frequencies in the mix by using inf for the frequency cutoff as shown in conv_sorted in name conv filter sorted energy resolution 1 repulsion resolution 1 energy window 1 nfreq cutoff inf 22 The start of the filtered population that this gives shows that the frequency calculation may be problematic for the lowest energy candidates listed here even though they really are practically the same structures based on inspection of the generated population library VAAARAMRARAARARARRARARAR AE DUPLICATES IN VIABLES HH RARA
47. s were found during the build stage and not the mating cycles Since the population library is a subset of the viable library we will combine the viable libraries of all runs into aanal1l_viable xyz library file in the examples H2S al1 folder wherein is executed with the idea that any filter utility run using name al1 will be working with the library cat r via xyz gt all_viable xyz The all_viable xyz viable library can now be used for sorting and or refiltering as described next 6 3 Sorting and refiltering libraries Since the viable library does not store the candidates sorted by energy it may be useful to perform a filter utility run that will only sort not actually filter it to create a new population library that contains all the viable candidates sorted by energy Inspecting the resulting library or inspecting the text output may help in determining the repulsion and energy resolution values one should use to filter out only the unique structures in a subsequent run To sort the viable library all one needs is a simple filter input file which is in the examples H2S all folder called sort_via in By turning all energy acceptance criteria off every structure inthe all_viable xyz will be considered unique Since the original viable libraries contained candidates with positive frequencies we can keep the frequency based filter to its default settings name all filter sorted energy resolution 1 repulsion resolution 1 energ
48. specific information encoded i e the fragment library format is as follows int natoms string name float radius string string elementkey float x float y float z natoms The name is the string needed in the composition string of candidates while radius is an additional radius in A used in building candidates and genetic operations see Sections 3 4 and 3 7 The elementkey in an xyz file is the element name The cluster program allows a bit more flexibility because the key is the key for the element in the element library which may differ from the actual element name thus it is possible to use the following fragment definition as long as the Hg2 and F elements are defined see Section 4 2 3 HgF2 1 0 just a silly example Hg2 0 0 0 F 2 0 0 F 200 4 4 Candidate library format The file format for a library of candidates is also a slightly modified version of the standard multistep xyz file format in that the comment line has specific information encoded for the name energy nuclear repulsion energy R and lowest vibrational frequency freq followed by an optional comment If the energy and or frequency are not computed the float strings inf and inf are used respectively The file format for a cluster library is as follows int natoms string name float E float R float freq string string elementname float x float y float z natoms 13 5 Computational program interfaces and examples This sec
49. stently Restart and reoptimization using the population library Since it is hard to predict how many candidates should be built and how many matings may be required to get a good sampling of the PES it is useful to be able to restart the cluster program in such a way as to use results from earlier runs and or build new candidates If after the initialization stage based on the restart and reoptimization options the size of the population is still zero or if build 4 0 the build methodology is used for the requested nD canidates The default settings are such that a restart will be performed restart int 1 If 4 0 the population library is used as the starting population The converged library is also read so duplicates can be checked against results from the previous run The all library file is read to determine the candidate number needed to avoid overwriting old candidate output files By using inf for the energy in the comment line for a candidate in the population library see Section 4 4 or only have the name in the comment line without anything else the program will ignore the given name and optimize the candidate before adding any resulting acceptable candidates to the population It is up to the user to maintain consistency in the computational method used in the separate runs When seeding the population with user built candidates in this fashion care has to be taken that the atoms are in the sequence that the program expects which is b
50. ster elementlib string The path to an element library file see Section 4 2 The elements in the file are interpreted immediately and may define new elements or redefine existing ones They are only used for fragments that are defined after the element library was read Thus existing fragments will not be affected elements element_line This keyword forces the parser to interpret the following lines until an empty line is encountered as single line definitions of elements see Section 4 2 The internally defined elements are immediately updated but any fragments that were already defined are not affected similarly to reading an element library fragmentlib string The path to a fragment library file see Section 4 3 The fragments in the file are immediately interpreted and may define new fragments or redefine existing ones fragments fragment A sequence of fragment definitions see Section 4 3 The sequence of fragments needs to be terminated by an empty line composition name amount H 1 H20 2 A sequence of one or more fragment or element names followed by the amount of those in the candidate each separated by a space The symbol can be used to signify the start of a new layer in the build sequence i e the fragments before the are always positioned before the ones following the charge int 1 The charge of the candidate multiplicity int 1 The multiplicity of the candidate The cluster program will check
51. t 1 parent 2 parent 1 parent 2 O rotated O rotated rotated rotated te A om o A e eS oad transfer O transfer Figure 1 Two examples of matings On the left for SiaLi where two Si atomic fragments from parent 2 are transferred to parent 1 and positioned in the final child so as to avoid interatomic distances that are too small On the right hand side three water molecules are transferred in a H20 s cluster All images are viewed along y with the z axis pointing up mating energy float 1 0 A parameter used in the Boltzmann distribution based mate selection i e mating probability 1 If lt 0 the Em used will be Em Emaz Emin otherwise it will be used as is mating max int 3 The amount of times that mating is attempted before it is considered to have failed mating rebuild int 1 If 4 0 performs a 3D build if a mating fails Mutation procedure Mutation of a single candidate is not implemented for several reasons In our type of candidates i e unique geometries representing minima on a multidimensional potential energy surface a mutation is a geometry modification of fragments and or atoms in such a way that the mutation is still a candidate that a computational program can work with This means that care needs to be taken to not create inter atomic distances that are too small which is not a trivial requirement for three dimensional structures with possibly a large amount of atoms Thus the first r
52. t method the specifics of which are provided for each program in Section 5 method strings RKS B3LYP G SV The remainder of the line after the keyword itself will be used in the input templates If the method definition needs more than one line in the computational input file one should use n in the one liner If a more complicated form of input files for the system is needed use the word template see Section 4 1 In that case if the program does not encounter the template files needed in the current working directory it will create them and exit This allows the user to adjust the template file s as needed and rerun the cluster application processors int 1 The number of processors to use in the run The value may be used to create the input file and or to call the program memory int 2000 The amount of memory to be used in MB max_scf int 50 The maximum number of SCF cycles allowed max_opt int 50 The maximum number of geometry optimization cycles allowed name string c The root name of the files and candidate names to be created Only the first word in the string will be used 3 2 Utility runs A few keywords exist that will not start the population optimization process itself These are useful to either do a post processing of the results of an earlier run or help in testing the input files that the program generates filter string If the argument is not the default empty string a filtering procedure on the viable libr
53. te energy difference between the two candidates is compared against the energy resolution value The assumption is that if the candidate encountered before didn t yield a new candidate in the population earlier it will not do so again This may not necessarily be the case for option 2 since the number of times the optimization cycle has been executed may be less than before and the additional allowed optimizations may yield an acceptable candidate See also Section 3 6 keep_fail int 0 If 0 the computational output files will not be deleted when a calculation failed This allows inspection of the computational program s output file if candidates keep failing to get optimized reorient int 1 If 0 the candidates in the libraries will be centered on the center of the fragments If 0 the coordinates will be such that the structure is centered on the atoms and rotated so that the largest eigenvalue of the charge weighted not mass weighted inertia matrix is along x and the smallest one along z This may aid in comparing similar structures since they will be oriented in a similar fashion For either case the coordinates in the cluster libraries are very likely to be different from the ones shown in the computational program s output file 3 6 Duplicate and acceptance determination Since it is important to determine whether two candidates may be identical and thus not unique it is important to find good metrics that allow us to make th
54. te is printed showing only a numerical value for the nuclear repulsion in the structure since no other calculations have been performed on it yet e g Si4Li_ 6 2D Build E inf R 250 604 v None A very small number of keywords are needed to direct the program about how and how many initial candidates are built The default settings are such that no candidate will be built 1D int 0 The number of candidates to be built with displaced fragment centers along x only 2D int 0 The number of candidates to be built with displaced fragment centers along x and y only 3D int 0 The number of candidates to be built with displaced fragment centers along x y and z scale float 1 0 The value used as a multiplication factor for the translation vectors of each fragment thus allowing with a value lt 1 0 to create a closed and with values gt 1 0 a more open topology for the candidates Since this keyword is a multiplication factor in the fragment translation fragments farther from the center will be affected more than those close to the center This keyword is only used when building candidates not during matings The mating procedure always treats the clusters as a closed cluster One may want to use the extra radius field in the fragment definitions see Section 4 3 to have better control over the positioning of fragments since this extra radius is respected in both the building and mating procedures of the program and thus is used more consi
55. th Opt x Not Converged with x the optimization cycle number is printed If the computational program can do a geometry reoptimization using the Hessian information from a previous frequency calculation and at least two more frequency calculations may be performed a frequency calculation will be performed followed by a geometry reoptimization calculation If this results in a converged geometry and the candidate is not a duplicate the next cycle in the optimization procedure is started This means that some unnecessary optimization steps may be performed but one would expect that to be a very small number This is preferred since this way any candidate in the viable library and thus population library as well will have been calculated based on the same two last calculations an optimization followed by a frequency calculation If the geometry optimization resulted in a converged geometry that is not a duplicate a status line with Opt x Converged with x the optimization cycle number is printed before a frequency calculation is performed after which the candidate is added to the converged library The stationary point is considered a minimum if the lowest non zero vibrational mode s wavenumber is larger than the cut off value defined by the nfreq_cutoff keyword In that case a status line with Viable is printed before the candidate is added to the viable library Based on the acceptance criteria the candidate may then also be promot
56. then to update the population using genetic operators to create new acceptable candi dates that are different from the ones already present The population growth is implemented as a sequence in which the resulting candidates from only one mating may be added to the population if it is deemed ac ceptable Thus each new generation is the result from just one child This was deemed beneficial because the new acceptable candidate s may immediately be used in the creation of new candidates When using this approach it doesn t make sense to talk about generations anymore but focus on the number of matings performed 2 Getting started 2 1 Prerequisites Since the cluster program is written in python and tested with versions 2 4 3 up to 3 3 2 a python interpreter within that range is required The program has only been tested on Mac OS X and RedHat and makes use of OS calls so it can t be guaranteed to run on other operating systems The cluster program interfaces with a computational program in the background thus the program to be used has to be available and may also require certain environment variables as well as the path to be properly set More specifics of those requirements for each program interface are provided in Section 5 2 2 Installation The compressed tar file cluster1 0 tgz should be decompressed tar zxf clusterl 0 tgz This will result in a cluster1 0 folder with the cluster py main program a lib folder containing
57. tions provides some information regarding the implementation of the interface to specific computa tional packages It is strongly recommended to check out the example inputs for the ADF program even if one doesn t have that available because it shows some more advanced use of some of the available features in the cluster program 5 1 ADF Requirements The ADFBIN environment variable needs to be defined as well as the adfrc sh or adfrc csh should have been sourced because the cluster program calls the ADF program by using SADFBIN adf with the command line option n set to the number of processors requested in the cluster input file Defaults The default method for ADF calculations uses the LDA SCF VWN functional with a TZP basis set and a large core The default geometry optimization criterion for the energy is tightened to 1e 4 from the more permissive le 3 hartree Specifics The ADF program requires the method of calculation and basis set to be provided in blocks containing multiple lines As a result of that n is needed in the method keyword unless one decides to use the template value Note that the former can lead to a very long single line for this keyword ADF expects in the input the number of unpaired electrons as opposed to the spin multiplicity so the cluster program will determine the number of unpaired electrons from the multiplicity setting and uses spin_polarization d in the template file to do so e For the freq
58. uency analysis calculation the default is to use analytical frequencies so a user has to use templates for functionals where analytical frequencies are not available The default frequency calculation template also contains ScanFreq 1000 0 for recalculating the imaginary frequencies The cluster program will replace the initially calculated frequency values as reported in the regular Vibrational and Normal Modes table with the new value from the scan frequencies output section for all vibrations whose old frequency is within 0 01 cm of the initial value so that all frequency values for degenerate modes are replaced The memory placeholder is not used in the templates The energy value is taken from the regular expression match of every line in the output file with r Total Bonding Energy 0 9 ADF Example 1 The example below is for an unrestricted calculation which requires a quite lengthy method line in the input to achieve this Only a small amount of the default values of the keywords may need to be reassigned In this case that has been kept to a minimum name Si4Li Note the method argument should be a single long string the split over two lines should not be in the real input file program ADF method XC nGGA BLYP nEND nBASIS ntype TZP ncore Large nEND nUNRESTRICTED processors 8 multiplicity 2 14 charge 0 composition Si 4 Li 1 1D 2 2D 5 3D 10 matings 40 energy res
59. was found all every candidate for which an cluster optimization cycle was started converged candidates at local extremes on the PES duplicate candidates that are a duplicate of a candidate in the population and or converged libraries population candidates at local minima on the PES that are considered unique viable candidates at local minima on the PES The cluster optimization algorithm see Section 3 5 explains in more detail how the decisions are made as when where and why a candidate is added to which library In addition to these library files a comma separated value csv file is maintained which contains some information about the candidates in the population library in a format that most spreadsheet programs can easily interpret Computational program output If possible the program only retains the last geometry optimization and frequency calculation outputs con catenated for candidates that are in the viable library These files will have the extension out This feature is not possible for MOPAC calculations since the output it creates can not be redirected appended 3 Methodology and keywords This section provides the keywords allowed in the input file It is organized by conceptual groups in associa tion with how they are used in a cluster program s methodology Most sections start with small introduction followed by the list of the keywords that are separated by some vertical space Each keyword in the list is i
60. y window 1 Since the filter procedure only parses the comment lines in the xyz files no composition information is needed The text output it generates shows that indeed no duplicates are taken from the new filtered set of struc tures VAHARAARARAAAARARRARARARARARA DUPLICATES IN VIABLES HH AAA RARA RARA VAHARAMAARARRARARARARARAARRAARA FILTERED POPULATION HHHHHRARAA RARA RARA RARA RARA RARA H2S_r3_4 Filtered E 0 023558056 R 163 867 v 17 70 H2S_r1l_4 Filtered E 0 023556492 R 163 663 v 28 80 H2S_rl1_3 Filtered E 0 023555334 R 163 507 v 26 70 H2S_r3_13 Filtered E 0 022450474 R 159 517 v 22 30 21 H2S_r4 6 Filtered E 0 022375850 R 160 280 v 31 90 H2S r2 1 Filtered E 0 021989498 R 145 184 v 3 10 H2S rl 18 Filtered E 0 021987541 R 144 368 v 3 40 H2S_r5 4 Filtered E 0 021980137 R 143 607 v 5 50 H2S r5 2 Filtered E 0 021979759 R 143 056 v 3 70 H2S rl_1 Filtered E 0 021974507 R 142 948 v 6 20 H2S r3_1 Filtered E 0 021960593 R 142 241 v 4 70 H2S r2_43 Filtered E 0 015519401 R 194 769 v 18 50 H2S r2_4 Filtered E 20 012641140 R 180 537 v 13 10 One may double check by visualizing the structures in the all_sorted xyz file using Jmol or any other visualization program that can deal with multi step xyz files to see which candidates do indeed look similar enough to be considered duplicates An energy resolution of 0 0001 and a very generous repulsion res

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