User's Guide fast: Fast Absorption Simulation by TDDFT
Contents
1. A negative value of freq_eps causes FAST to deduce this parameter from the number of frequencies according to 3 omega_max omega_min nf f 1 freq_eps Default 0 01 Rydberg nff integer A positive value of nff defines the initial number of frequency points at which to com pute the spectra The initial distribution of points is uniform in the target window Wmin Wma OMEIA_MAL omega min nff 1l A negative value of nff causes the number of points to be controlled by the target regularisation parameter 1 with i 1 nf f wi omega_min 4 nff omega max omega min 1 rra omen gamin 1 Default 257 11 distribution string The type of distribution used to compute the spectra uniform for uniform distribution and adaptive for non uniform distribution In this case the points will be localized near the peaks in the spectrum Default adaptative dist_hierachic_nbiter integer Maximum number of tier one plus tier two iterations when the adaptive algorithm is chosen Default 5 dist_hierachic_nbtransitions integer The number of transitions to atttempt to extract If this number is too large the algorithm returns the number of transitions actually found by the fit algorithm Otherwise the algorithm stops when convergence is reached on the first dist_hierachic_nbtransitions transitions sorted by energy N or oscillator strength fr see also fit_lorentzian_2. Detailed description of program options This section describes all the parameters that define a FAST run with their data types and default values 3 1 General system descriptors SystemLabel string A single word max 20 characters without blanks containing a nickname of the system This name is also the generic name of all SIESTA input files see input files section 3 2 iv integer Controls verbosity for debugging default 0 low set to 1 or 2 for higher verbosity input_directory string The name of the directory where FAST reads all SIESTA files Set to to use the working directory Default input output_filename string Generic name less than 120 characters for all output files For example calculation casel casel N B The directory should be created before runing FAST otherwise the code crashes with error under the Intel compiler forrtl No such file or directory Default output str_SystemLabel where str_SystemLabel is the string set in the System Label keyword Default 1 io_units string Units of frequency for the spectra Input of frequency limits will be inter preted according to this option Output of absorption spectra depends on this option Allowed values Rydberg cm 1 Angstrom Hartree nm eV Default Rydberg 3 2 Input files A FAST TDDFT calculation needs information on the system from the underlying DFT calculation such as the geometry the molecule wavefunctions
3. binaries and CMake source code is available from the CMake homepage The first step is to get the source of TDDFT and uncompress it shell tar zuf FAST 1 0 tar gz shell cd fast shell mkdir build shell cd build 2 2 1 Compilation with Cmake Installation by itself is the fairly common CMake process shell cmake gui shell make shell make test shell make install Options can be activated by setting flags during compilation Several options must be set to use cmake gui interface These options define library paths used in the code and the type of implementation sequential or parallel for example CMAKE INSTALL PREFIX should be set to the path of the installation directory i e prefix FAST_OPENMP Activate set ON default OFF to compile the OpenMP version of FAST FAST_MPI Activate set ON default OFF to compile the MPI version of FAST In this case MPI variables and functions are accessed through module mpi rather than via an include file Moreover the compiler must be mpif90 FAST_DISPLAY_PROD Activate set ON default ON to display all information about orbital products FAST CHECK NBITER_GMRES Activate set ON default ON to verify the number of iterations in the GMRES algorithm FAST_USE MKL Activate set ON default ON to link FAST with the Intel MKL library If disabled linking to third party librairies BLAS LAPACK and FFTW3 has to be set manually namely FAST_BLAS_
4. the pseudo potentials the Hamiltonian and overlap matrices etc When not compiled to be run coupled to SIESTA via MPICPL the FAST program gathers this information from the DIM geometry WFSX packed wavefunctions HSX Hamiltonian and PLD charge density SIESTA output files To generate these files the following two keywords must be present in the input file of SIESTA COOP Write true WriteDenchar true The reader is referred to the SIESTA manual for further details 3 3 Output files input _outputFileName_polarizabilitySpectra txt The polarisability spectra On each line w P w unpolarised i e sum of components the x y and z components Lines starting with a show frequencies where there was a convergence problem or a negative polarisability input_outputFileName_dipol_core txt the dipole core input_outputFileName_numof_iter txt iterations needed to achieve convergence at each fre quency for input_outputFileName_OddFrequency txt frequencies where the GMRES had difficulty In additon if the Lorentzian fit to the numerical spectrum is activated input_outputFileName_transitions txt transition energies and the oscillator strengths input_outputFileName_lorentzians txt spectrum and the fitted spectrum at the frequencies at which the polarisability was calculated input_outputFileName_modelledSpectrum txt fitted spectrum on a set of uniformly spaced points not necessarily those where th
5. 411848 DOI 10 1002 PSSB 200983811 http hal inria fr inria 00457652 en 2 P Koval D Foerster O Coulaud A Parallel Iterative Method for Computing Molecular Absorption Spectra in Journal of Chemical Theory and Computation 2010 vol 6 no 9 p 26542668 DOI 10 1021 CT100280X http hal inria fr inria 00488048 en 4 3 Olivier Coulaud Patrice Bordat Pierre Fayon Vincent LeBris Isabelle Baraille Ross Brown Extensions of the Siesta DFT code for simulation of molecules Inria research report 8221 http hal inria fr hal 00787088 2 Installation This section discusses configuration installation and running the code on a Unix like operating system such as Linux or Mac OS X 2 1 Prerequisites Before installing FAST obtain and install the following e Fortran and C compilers Intel version 12 x or higher Gnu 4 2 1 or higher e CMake version 2 8 2 or higher and a working compiler On Unix like operating systems FAST also requires Make e The SIESTA XC Exchange correlation library e The BLAS LAPACK and FFTW libraries e MPI version 1 4 4 or higher if parallel execution is required e The GNU scientific library version 1 15 or higher is required N B Although FAST is a parallel code all the above routines are used in sequential mode in the tddft code 2 2 Compilation The project is packaged under CMake http www cmake org General information about CMake as well as installation of
6. PATH path to the BLAS library FAST_BLAS_FLAGS flags needed to link with BLAS FAST_LAPACK_PATH path to the LAPACK library FAST_LAPACK_FLAGS flags needed to link with LAPACK FAST_FFTW3_PATH path to the FFTW3 library FAST_FFTW3_FLAGS flags needed to link with FFTW3 FAST_FFTW3_INCLUDE_PATH path to the include file for FFTW3 FAST SIESTA COUPLING Activate set ON default OFF to enable coupling with SIESTA through mpicpl Requires FAST_MPI options enabled FAST_PRINT_SPECTRUM_ITER Activate set ON default OFF to active print out of spectrum and integral during each iteration 2 2 2 Cmake work around If Cmake is unavailable on your system a work around with the Intel compilers the mkl library and openmp is shell mkdir build shell cd build shell CC icc FC ifort CXX icpc cmake D FAST_OPENMP BOOL ON D FAST_USE_MKL BOOL ON D CMAKE_INSTALL_PREFIX PATH usr local fast D CMAKE_BUILD_TYPE STRING RELEASE D SIESTA_XC_DIR PATH 5HOME Dev src nossi siesta bzr Obj SiestaXC D GSL_CONFIG_EXECUTABLE FILEPATH opt intel softs bin gsl config followed by shell make shell make install 2 3 Running FAST Basic running of the code requires an input file of parameters and files pre computed with SIESTA see the input section 3 2 Run the code with the comand line bin tddft input_file_name where input_file_name is the name of the file of input parameters see the next section 3
7. USERS GUIDE fast Fast Absorption Simulation by TDDFT Version 1 0 January 2013 Ross Brown Cedric Castagne Olivier Coulaud Dietrich Foerster Peter Koval Copyright c 2013 FAST is Open Source software you can redistribute it and or modify it under the terms of the CeCILL free software license agreement version 2 See the CeCILL FREE SOFTWARE LICENSE AGREEMENT URL http www cecill info licences Licence_CeCILL_V2 en html Acknowledgements It is a pleasure to thank Professor James Talman University of Western Ontario who kindly donated important routines for 3j 6j 9j symbols and a fast Hankel transform The ongoing encouragement and advice of the SIESTA development team particularly Alberto Garcia In stitut de Ci ncia de Materials de Barcelona and Daniel Sanchez Portal Centro de Fisica de Materiales Donostia San Sebastian and of Luc Giraud Inria Bordeaux Sud Ouest is gratefully acknowledged This work was supported by A N R grant CIS 2007 NOSSI Contents 1 About fast 2 Installation 2 1 Prerequisites 2444 2 was nun Sen a nennen 2 2 Compilation 4 26 6 ebb ap Ree ee nen 2 2 1 Compilation with Cmake o e e e 222 Cmake work around lt e s ss riesa ea eoe ea i e a a a 2 3 Running FAST e soe 2a i e u seo a di ehe ee S 3 Detailed description of program options 4 5 A a She ds eee E ees a ee ne a ey a ee ee ee eae ee eae ee ee ee a te eee pe La
8. e spectrum was computed 3 4 Base compression parameters At the heart of the FAST program is the suppression or reduction of linear dependence in the space of atomic orbital products used to describe the linear response see papers 1 amp 2 above Dominant products are defined by diagonalisation of the Couloomb metric in the space of prod ucts of atomic orbitals and retention of a sub set of eigenvectors with the largest eigenvalues Several parameters control this process Default values below have produced good results on test systems but users are encouraged to experiment eigmin local real Defines the threshold for eigenvalues of the metric of orbital products on the same atom Eigenvectors with smaller eigenvalues will be dropped in the computation of the sigma matrices and spectrum Default 1 0 E 3 eigmin_bilocal real Defines the threshold for eigenvalues of the metric of orbital products on different atoms Eigenvectors with smaller eigenvalues will be dropped in the computation of the sigma matrix and spectrum Default 1 0 E 4 use_eigmin_local_H boolean If true use a special threshold for hydrogen local products Default false eigmin_local_H real Threshold for hydrogen local products Default eigmin_local 10 use_rcut boolean If true drop orbital products for pairs of atoms with small geometrical orbital overlap using criterion Teut set with the reut keyword Default false rcut real Allows
9. eters These parameters control the calculation of the interaction kernel in the linear response equa tions use_hartree integer Include exclude 1 0 the Hartree potential in the interaction kernel Default 1 use_exchange integer Include exclude 1 0 the exchange potential in the interaction kernel Default 1 use_correlation integer Include exclude 1 0 the correlation potential in the interaction kernel Default 1 xc_authors string The type of exchange correlation potential cf the SIESTA manual Cur rently LDA only see introduction Default PZ xc_3d_order string Order of Lebedev grid used to evaluate the coefficient of the exchange correlation interaction kernel The order must be in the range 1 to 31 Default 7 xc_3d_nl string Order of Gauss Legendre method used to evaluate the coefficients of the exchange correlation matrix The following order are available 6 12 24 48 96 Default 24 14 4 Coupling FAST to SIESTA via MPICPL It should be clear that connecting two parallel computer codes such as FAST and SIESTA so that they will cooperate is not a trivial undertaking Users of FAST who will be doing one off or infrequent computations e g at a single geometry for different systems are best advised to keep to communication via SIESTA output files However FAST can be coupled directly to SIESTA using the MPICPL MPI Coupling framework MPICPL is dedicated to the coupling of parallel scientific c
10. g Sct ee ee ne ne ae ae A ee a da Coupling FAST to SIESTA via MPICPL 4 1 Compilation evi rc A ad a a A 4 2 Coupling parameters 4 3 Examples s a Dr Ci ae e ada Re a Dee Bae DS Troubleshooting NI N Oo ot ca Qt Oo co N N 13 13 14 15 15 15 16 17 1 About fast FAST is a linear response time dependent density functional program for computing the elec tronic absorption spectrum of molecular systems It uses an O N linear response method based on finite numerical atomic orbitals and deflation of linear dependence in atomic orbital product space This version is designed to work with data produced by the SIESTA DFT code The code produces as principal output a numerical absorption spectrum complex part of the polarisability loosely called the polarisability below and a list of transition energies and oscil lator strengths deduced from fitting Lorentzians to the numerical spectrum Considering the absence of hybrid functionals in SIESTA and that concerning calculation of spectra generalised gradient Hamiltonians are not usually considered to be notably better than the local density approximation the present release of FAST works only with LDA which despite its limitations has provided useful results on the systems to which the present authors have applied it This Reference Manual contains descriptions of all the input output and execution features of FAST but is not intended as a tutorial introduction to the p
11. g to tell if the code is to attempt to connect itself to a running SIESTA computation Default false nossi qm binding name string Name of the link between the FAST code and the SIESTA code The name of this link must be the same as the in the xml file read by the mpicpl wrapper when it launches both codes Default tddft dft 15 nossi_code_name string Name of the FAST code in the xml file See next section Default tddft nossi 4 3 Example In order to use MPICPL the coupling to be set up must be described in an xml file see mpicpl documentation Here is an example for coupling SIESTA and FAST siesta fast xml lt coupling arguments nossi_top gt lt declare all codes gt lt code np 1 cwd nossi_top Examples tddft qm h2o siesta program nossi_top siesta epsn siesta sh name siestaNOSSI args h20_tddft fdf gt lt code np 1 name tddft_nossi cwd nossi_top Examples tddft qm h2o tddft program nossi_top fast tddft_qm args gt lt interconnect codes gt lt binding name tddft dft client tddft_qm server siestaN0SSI gt lt coupling gt The coupled programs are launched by MPICPL_TOP tools mpicplrun d nossi tddft dft xml NOSSI_TOP 16 5 Troubleshooting 1 Unphysical polarisability at some frequency points As explained above linear response TDDFT is caught on the horns of a dilemma between using a small enough regularisation parameter t
12. its are Rydbergs 10 eps_units string Units for the regularisation parameter e Allowed values Rydberg cm 1 Angstrom Hartree nm eV Default Rydberg freq_eps real Regularization parameter e in the response function which defines the apparent width of the resonances cf papers 1 3 A positive value of freq_eps is interpreted as the target value towards which e will be decreased during tier one iterations of the adaptive algorithm Making it small helps to identify resonances and specially to distinguish close resonances But note that the linear response problem solved here describes undamped resonances no relaxation coupling to phonons etc Therefore resonances are in principle infinite whence the presence of the regularisation parameter in the equations to pseudo damp them to finite height Thus if e is too small the linear system to be solved by GMRES tends to singularity when a frequency point happens to lie less than a few e from a transition producing numerical instabilities such as failure of GMRES to converge or unphysical solutions such as negative polarisabilities When choosing freq_eps users should bear in mind that the fit procedure pin points transitions much more accurately than the width of the resonances e in the authors experience typically to a precision of at least e 100 File input_outputFileName_OddFrequency txt provides a list of all frequencies which gave rise to a singular matrix
13. o make individual resonances visible and not choosing it so small that the linear system defining the polarisability is singular If a frequency point happens to lie too close to one of the resonances of the system the matrix is numerically singular and GMRES may fail to converge or return unphysical results such as a negative polarisability Since such singularities point out an underlying resonance it may be useful to increase the regularisation parameter e freq_eps or to shift the bounds of the frequency interval omega_min omega_max or to reduce the number of frequency points The question of numerical instability is in part a question of computer word length Consid ering that the fit procedure with e 107 Ry typically extracts resonances to an accuracy of 107 Ry way beyond the inherent accuracy attainable with any flavour of DFT FAST is written in single precision arithmetic because that saves a factor of about two on the execution time 17
14. oceeds by a two tier iteration In the top level iteration i the number of frequency points used and polarisabilities P w computed beware the cost in CPU time is increased by a constant fraction or ii the reg ularisation parameter e is reduced by a step towards its target value or iii both changes are made In between top level iterations the lower level iteration bears on the distribution of the frequency points It uses the current spectrum to cluster the frequency points around the resonances which improves the estimates of the a sum of Lorentzians to the spectrum Tier two clustering is iterated until the resonance parameters 27 and fr are stable after which tier one update of the number of frequency points and the regularisation parameter or both are updated and the cycle continues until convergence of the resonances between iterations A combination of keywords provided at the end of this section can be used to invoke only tier two iterations The following parameters control the frequencies where FAST computes the optical polarizability P w and how the adaptive algorithm described in paper 3 extracts the transition frequencies and oscillator strengths omega_min real Lower bound of the frequency range Default 0 02 in io_units omega_max real Upper bound of the frequency range Default 0 4 in io_units N B The default values of omega_min and omega_max are suitable for the visible spectral region if io_un
15. odes based on the well known MPI standard It is divided into several independent layers for coupling data redistribution and steering The codes to be coupled are launched and connections between them are set up by mpicpl according to information derived from an xml file The direct coupling option might be attractive to perform a series of TDDFT calculations on the fly for example during a SIESTA molecular dyanmics run This is feasible once the range of frequencies and FAST parameters have been tuned to extract resonances in the desired frequency window e g usually experimental data will be available only for the first one or two excited states Such repetitive calculations are handled on the SIESTA side of the coupling by a set of patches in which a call to FAST communicating via MPICPL is inserted in the move loop of the SIESTA main program MPICPL is downloadable at https gforge inria fr projects mpicpl The SIESTA patches are available at https gforge inria fr frs groupid 1179 4 1 Compilation To activate the coupling with SIESTAthe FAST_MPI option must be set to ON then set FAST_SIESTA_COUPLING option to ON After that the include directory of MPICPLmust be set in MPICPL_INCLUDE_DIR variable To construct the executable tddft qm code just do make clean tddft qm 4 2 Coupling parameters Parameters below are available only if FAST was compiled with NOSSI_COUPLING defined nossi_qm_coupling boolean Fla
16. rogram Potential users should consult the papers listed below for details of the methods employed The code is written in Fortran 95 with dynamic memory allocation It uses routines from the BLAS LAPACK and FFTW package see http www fftw org for all FFT routines It may be compiled for serial or parallel execution under OpenMP MPI and MPI OpenMP Owing to licence related reasons users should first obtain and install either the SIESTA code or the standalone SIESTA XC exchange correlation library http www icmab es siesta The present code includes two pieces of software under licence e Routines for numerical quadrature on the sphere distributed through CCL http www ccl net V I Lebedev and D N Laikov A quadrature formula for the sphere of the 131st algebraic order of accuracy Doklady Mathematics Vol 59 No 3 1999 pp 477 481 e A GMRES solver available at http www cerfacs algor Softs V Frayss L Giraud S Gratton and J Langou A set of GMRES routines for real and complex arithmetics on high performance computers CERFACS Technical Report TR PA 03 3 2003 Papers on FAST Users of this code should include references 1 3 below in their publications and in the user and programmers manuals describing their codes 1 P Koval D Foerster O Coulaud Fast construction of the Kohn Sham response function for molecules in Physica Status Solidi B February 2010 vol 247 no 8 p 18
17. rylov integer Maximum dimension of the Krylov space This parameter is also called the restart parameter and it controls the amount of memory required by the matrix in the Krylov space Default 20 solver_itermax integer Maximum number of iterations to reach convergence Default 100 solver_verbose integer Controls output of information on convergence of the solver If the value is non zero output is written in file fort solver_verbose Default 0 solver_eps real tolerance for convergence Default 0 001 3 7 Fit parameters These parameters control the fit of the spectrum by a sum of normalised unit area Lorentzian resonances used to extract transition frequencies and oscillator strengths The spectrum is approximated as Ntrans Ax spectrum w B 5 m Tw 3 w e 3 where Ntrans is the number of Lorentzians B a constant to capture the background due to resonances outside the computed interval wo the kt transition energy and fr 2 Ar its oscillator strength see paper 3 fit_lorentzian_sort integer Specifies whether to sort transitions in order of energy 1 or oscillator strength 2 Default 2 fit_lorentzian_nbpoints integer Controls whether a model spectrum eqn is out put fit_lorentzian_nbpoints gt 1 specifies the number of points output to file input _outputFileName_modelledSpectrum txt No output if fit_lorentzian_nbpoints lt 1 Default 1 13 3 8 Potential param
18. sort Default 1 dist_hierachic_threshold real The threshold 7 to stop the adaptive algorithm The crite rion is to stop at tier one iteration k if max max O max fF z lt n Default 0 01 dist_hierachic_epsiter integer Number of equal steps to reach the final value of e freq_eps see dist_hierachic_epsstart Default 1 dist_hierachic_epsstart real Start regularization parameter During tier one iteration i the regularization parameter e is given by the relation caia freq_eps dist_hierachic_epsstart u _ T i 1 dist_hierachic_epsiter 1 Default 0 01 Rydberg dist_hierachic_increaserate real Specifys the ratio by which to increase the number of points between tier one iterations Default 1 0 N B Updating frequency points only Tier two iterations i e optimisation of a fixed number of points with one value of e can be achieved by choosing nff gt 0 and freq_eps dist_hierachic_epsstart gt 0 An appropriate value of nff would be half the value given by eqn 1 12 3 6 Solver parameters The GMRES method is used to solve the following linear system for the polarisability P w P w y lt di Xilw gt i l 2 1 x w d Xi w x w di 1 2 3 where d is the dipole in the direction yo is the susceptibility of the non interacting Kohn Sham system and gt the interaction kernel cf papers 1 3 The parameters of the method are solver_k
19. suppression of further products based on the thickness of the lens shaped region defined by the intersection of the largest orbitals on a pair atoms A and B All orbital products of a pair of atoms are dropped from the metric when Rmaz Rmax b distance a b lt Teut where Rmaz a resp b is the radius of the support of all atomic orbitals on atom A resp B Default 3 0U where U is the unit of length for atomic positions the atoms stored in the siesta DIM output file read by FAST write_all_eigens boolean If true write all eigenvalues for all pairs of atoms in separate files File names are constructed according to the rules For species the file name is construct input_outputFileName _eigen_ species txt For atoms pairs e g atoms nl and n2 the eigenvalues are stored in file input_outputFileName _eigen_ nin2 txt Default false 3 5 Spectrum parameters The basic task accomplished by FAST is to compute the absorption spectrum P w of a molec ular i e finite system at a set of frequencies w in some user defined interval wmin Wmax Such a spectrum is not in itself very useful since it is a set of discrete resonances with width and heights dependent on the regularisation parameter e Paper 3 therefore describes an adapta tive algorithm to extract transition frequencies 27 and oscillator strengths fr from the raw polarisability spectrum calculated by FAST The algorithm pr
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