Efficient use of CP2K

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1 Efficient use of CP2K Fawzi Mohamed 1 1 Department of Chemisty Humboldt University of Berlin June 10, 2009

2 cp2k Fortran 95 opensource (GPL) general framework for different methods DFT no official release

3 Atomistic simulation program Classical MD (FIST) DFT QS Semi empirical (SE) MC montecarlo Polarizable force fields (KG)

4 No release check the regtest cp2k is quite taxing for compilers

5 No release check the regtest cp2k is quite taxing for compilers check the regtest... of your executable

6 No release check the regtest cp2k is quite taxing for compilers check the regtest... of your executable look at regtests to understand input files, but understand the method: regtests are written to be fast never use blindly the parameters of a regtest

7 Documentation of cp2k can be found on the website can be generated by the cp2k executable itself cp2k.sopt [-c check] [-e echo] [-h help] [ html-manual] [ xml] [-r -run] [-o ouput file] [ permissive-echo] [[-i] input file] the documentation generated by the executable is always consistent with its version, website refers to the latest version.

8 Input Syntax sections that start with & and end with &END each section can contain other sections and keywords followed by values section names and the keyword names are case insensitive the special characters # and! denote the beginning of a comment that goes until the end of the line if the value of the keyword is expressed in units, preceding the value by the units in square bracket changes them. The units should have no space. [m] switches to meters. A long line of input can be split using the \ character at the end of the line keywords with a logical value (flags), often have a value that is false when the keyword is missing; the value true when one writes just the keyword, or they can be given an explicit value after the keyword as normal (for example KEYWORD FALSE).

9 Sections can have a default parameter that comes right after the section value. For example the OT section has a logical default parameter that controls the activation of the OT method. So, &OT... &END OT activates the OT method and &OT FALSE... &END OT (or the absence of the OT section) deactivates it.

10 Preprocessor limited preprocessing capabilities that can be filename.inc # includes the VAR value # sets variable ${VAR} or $VAR # expands # conditional statement, no else, no nesting, single condition check

11 Gaussian Plane Waves Density Functional Theory E = n(r)n(r ) 2 r r drdr + n(r)v I (r)+e XC [n]+e II (1) represent density with a localized basis set n(r) = P µν φ µ (r)φ ν (r) (2) use an uniform grid as auxiliary density ñ(r i,j,k ) = P µν φ µ (r i,j,k )φ ν (r i,j,k ) (3) used for the electrostatic part, and E XC

12 Pseudopotentials needed in this approach GTH pseudo are used analytic few parameters accurate harder than other pseudos no non-linear core correction

13 Multigrids Use a constant number of grid points for each gaussian pair combine different grids together memory cost of multi grids 1.5 O(N) collocation force eval/dft/qs/map consistent commensurate grids (QMMM)

14 Gaussian Basis Set Local atom centred ψ jlm (r) = i c j i r l Y lm e α i r 2 (4) basisset file: ATOM BASIS NAME N sets Nl min l max n exp n baslmin...n baslmax α 1 c 0 1 c c α 2 c 0 2 c c... P nbas 1 P nbas α nexp c 0 n exp c 2 n exp...c P n bas n exp 2

15 force eval/dft/mgrid rel cutoff: cutoff for α = 1, 30 reasonably accurate, 50 is very accurate. gaussian collocated on grid with at least α relative cutoff cutoff: cutoff of the finest grid often sharpest gaussians contribute little, if s orbital the cutoff can be a little lower than 2relCutoff (max i α i )

16 Basis Sets Core part is pseudopotential dependent, but rather xc functional independent (i.e. CP2K specific) DFT: e-e cusp description not so important Pseudopotentials less electrons, less BSSE Condensed phase: BSSE mostly a shift wrt. Gas Phase GTH BASISET: atom optimized core part and Dunnings inspired polarization/augmentation BASIS MOLOPT: molecularly optimized basis set, much higher quality for same size. SR (short range) basis set well suited for condensed phase. Normal very good for reference or gasphase (polarization,...) calculation BASIS ZIJLSTRA: fast calculations Diffuse basis (exponent<0.1) are important to describe the decay in gas phase, polarization, but give rise to very bad condition numbers of S in condensed phase

17 GAPW put only part of the density on the uniform grid residual density in the core region use projectors to extract the core region integrate the core density on local atomic grids compensating charge Cutoff can be chosen almost freely can cope with all electron Exact only if projectors are complete atomic grids (radial and lebedev grid) integrate the core density on local atomic grids less tested/robust than GPW

18 Accuracy GPW accuracy cutoff and basis force eval/dft/qs/eps default: convergence of integral calculation, overlap cutoff, neighboring lists... and sets a slew of other eps * keywords so that the KS matrix is calculated with the requested precision. eps scf which controls the convergence of the scf procedure. In general one should have an error ef on the forces one should have eps scf < ef and eps default < eps scf, and in general around 1.e 3 is the error that you need to have reasonable MD.

19 XC force eval/dft/xc important issue, unfortunately results can depend on it I will not discuss it, normally it is a good idea compare with the literature exact exchange or an hybrid functional normally improve the description of barriers and radicals, but are much more costly start with a GGA and meta GGA and switch to hybrid functionals if needed or to check the results

20 Exact exchange force eval/dft/xc/hf truncation needed in periodic systems There are short range exchange functionals all screening methods should be used (computational cost grows very quickly) multiple time step algorithms motion/md/respa should be used

21 Dispersion DFT with GGA or hybrid functionals misses the dispersion contribution Dispersion is important for many systems, especially organic ones Empirical solution use a damped 1 term. Grimme has r 6 parametrized parameters that seem to work quite well. One has to be careful with ions if the parameters were for neutral atoms

22 k-points important for metals CP2K does not (yet) support them, just gamma point supercell approach

23 Smearing fermions, Pauli repulsion, energy levels normally filled up to high level (wrt. kt) OK good approximation for electrons. small or 0 gap can have some smearing at finite temperature useful to simulate it to reduce computational cost force eval/dft/scf/added mos force eval/dft/scf/smear

24 Diagonalization Usual method needs full ao x ao matrixes (memory) Mixing, Broyden, DIIS, multisecant (careful: history increases memory footprint) works well with smearing

25 Orbital Transform minimize directly the occupied subspace, using a smart parameterization (orthogonality constraint becomes a linear), is a simpler problem with correct linesearch guaranteed to converge convergence speed depends preconditioner ao x nel matrices (more memory friendly) without rotations does not optimize the single eigenvectors restricted open shell, smearing

26 force eval/dft/scf/ot in general the usage of OT if possible is a good idea. if the gap is small the convergence slows down full all preconditioner is the best for non huge systems and difficult systems, but does not converge if gap of the H matrix < energy gap is normally a good choice kinetic preconditioner can cope with huge systems for difficult systems linesearch 3pnt and CG optimizing method should be used the force eval/dft/scf/outer scf section, with eps scf equal to the one of the scf loop, and chooing a outer max scf big enough (the total number of iteration is the product of internal and external max scf) as the preconditioner construction can be costly inner scf should be 20-30

27 Restarts, extrapolation force eval/dft/scf/scf guess restart controls how the initial density is built, normally one uses either ATOMIC or RESTART. During an MD this setting normally influences only the initial startup. force eval/dft/qs/extrapolation ASPC is a good extrapolation method extrapolation order controls the extrapolation order MD or continuos processes are advantaged by order like 3, more discontinuous processes work better with smaller values also this history vector uses memory

28 Geometry optimization when usable BFGS is normally the best choice if you are very far the trust radius can slow down convergence LBFGS uses less memory, CG even less, but normally this is relevant for classical systems as wave functions use much more memory (but geo opt memory is replicated) One can fix atoms, not all constraints are kept with all optimizers can be used also to find saddle points

29 Cell Optimization condensed phase, small change in the cell can give huge energy changes important to optimize the bulk cell for surfaces (unless they are fully frozen) pressure convergence is expensive, expect large oscillations variation of the cell introduces Basiset dependent forces in both planewaves and local basis sets energy changes discontinuously with respect to both

30 MD Molecular dynamics a good method to perform themodynamical averages, and to look at dynamical properties. It also a good starting point for many other more advanced techniques. Born Oppenheimer MD: no fictitious mass (now also Erenfest dynamics is available) extrapolation improves much the timings (with ASPC there is also a method that does not converge the wavefunctions fully motion/print/trajectory controls the output of the trajectory the name of the file is by default projectname-pos-1.xyz and projectname is whatever you have written in global/project. the format can be changed from xyz to something else.

31 NVE least Energy conservation has normally two features, short time oscillations (that are larger when the system is not yet equilibrated) and a long range drift. expressed in K/atom and compared to the temperature it is a sensitive test if the system is correctly set up for very heterogeneous system with a small interesting part, checking that part of the system (oscillations, kinetic energy,...) is advisable. starting point should be equilibrated (apart when doing shooting or transition path sampling) build your system in some meaningful way, or from classical simulations temperature is not constant, but does oscillates oscillations connected with specific heat and inversely proportional with system size

32 NVT Needed to equilibrate motion/md/temp tol rescale if velocity is too far away from target CSVR Thermostat, correct oscillations of energy (from Langevin dynamics), a little expensive Nose Hoover chain thermostat, physical, has an extended conserved quantity, not good if far from equilibrium for very long trajectory a weakly coupled thermostat can be useful to compensate the drift

33 NPT equilibrate also the volume pressure is difficult to equilibrate in timescales accessible ab initio same thermostats as before also for the volume/pressure

34 Langevin Langevin introduces a viscous dissipative force and a random forces that are in equilibrium at the given temperature. to simulate removed degrees of freedom, like a solvent can be used also to equilibrate a system gamma of [1/fs] (or larger if you want to equilibrate faster) the smaller gamma the longer it takes to equilibrate, and the closer the trajectory is to an NVE trajectory, the larger gamma the more the environment influences the system similar to a massive CSVR thermostat reduces inhomogeneous energy distribution faster if your system is in a very bad initial configuration it is a good idea to set a temp tol, or first anneal a little the system.

35 Multiple timesteps motion/md/respa allows one to define several force eval advantageous when one has an approximate method that is fast to compute difference between the forges should be long range (low frequncy) evaluate costly method only each few steps can allow for large speedups

36 Conclusions Cp2k has a broad range of methods available that can be combined The DFT part (and GPW in particular) is highly efficient hybrid functionals can be used and their calculation scales well Several sampling methods are available (and we focused on MD based ones) much more is possible...

37 Thanks to the other cp2k developers M. Parinello Prof. J. Sauer and his group for support the Humboldt foundation for financial support the organizers for inviting me... you for your attention

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