CP2K: Selected Developments
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1 CP2K: Selected Developments Jürg Hutter Department of Chemistry University of Zurich
2 Outline Introduction History and Performance Current and Future Developments Post-Hartree-Fock Methods GW Methods RPA and MP2 Future Developments Wavefunction Analysis in CP2K Hirshfeld Charges RESP Charges MAO Analysis
3 25. June 2001 CP2K source repository goes online on berlios.de Now on sourceforge.net 15 years of open development
4 Origins Quickstep DFT Code, Max-Planck-Institute, Stuttgart Gerald Lippert, Matthias Krack, JH Fist MD Code, UPenn, Philadelphia Chris Mundy, S. Balasubramanian, Ken Bagchi
5 Released Versions Date Version Source lines Commit
6 CP2K: Impact on Science
7 CP2K: Application Fields 1 Chemistry Materials Science Physics CP2K > 70% 40% 40% Quantum-Espresso 35% 57% 69% VASP 36% 50% 65% 1 scopus.com
8 Quickstep DFT Code Performance 64 Water, Time/MD step
9 k-points Status of Implementation Energy (Forces, Stress) for GPW, GAPW, DFTB Band structure along special k-point lines also available as post-gamma point calculation Not working Symmetry reduction of k-points Hybrid Functionals (HFX) Interface to wannier90 code ( Parallelization issues Use "PARALLEL_GROUP_SIZE -1" if possible Minimize communication of matrices at k-point Delta Test in preparation (Tiziano Müller
10 vdw Functionals/Potentials Grimme D3 C9 terms: full vs. reference coordination numbers C6 only C9(R) C9 Energy Force nl-vdw DFT Use reduced CUTOFF feature of CP2K Cutoff Time Energy
11 Continuum Solvation Models SCCS (M. Krack) Andreussi, O; Dabo, I; Marzari, N. J. Chem. Phys., 136 (6), (2012). Revised self-consistent continuum solvation in electronic-structure calculations DFT/SCCS Generalized Possion Solver (J. VandeVondele) Bani-Hashemian, M.H.; Brück S.; Luisier, M.; VandeVondele, J J. Chem. Phys., 144, (2016). A generalized Poisson solver for first-principles device simulations DFT/POISSON/IMPLICIT psolver Library (BigDFT) Fisicaro, G.; Genovese, L.; Andreussi, O.; Marzari, N.; Goedecker, S J. Chem. Phys., 144, (2016). A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
12 Post-Hartree-Fock Methods Based on Gaussian and plane waves (GPW) method Resolution of Identity (RI) approach to integrals Periodic, but Γ-Point only RPA and MP2 (Laplace-SOS-MP2) M. DelBen et al. JCTC 9, (2013) G0W0 J. Wilhelm et al. JCTC (2016) Cubic scaling RPA J. Wilhelm et al. JCTC (2016)
13 Resolution of Identity Approach Gaussian Auxiliary Basis Coulomb Metric (Ewald Summation) (ia jb) = PQ (ia P) (P Q) 1 (Q jb) = S (ia S) (S jb) = S B S ia BS jb B S ia = P (ia P) (P S) 1/2 = µ C µi ν C νa (µν S) }{{} GPW Integral J.L. Whitten, JCP 58, 4496 (1973), O. Vahtras, J. Almlöf, M. Feyereisen, CPL (1993)
14 Performance: RPA and MP2 System Atoms Basis MP2 OS-MP2 RPA Urea (6784) 144(12.9) Benzene (10176) 624(12.7) Water (8704) 450(17.3) Timings in seconds on 3200 cores Cray-XK6, Quadrature points: RPA 40, OS-MP2 10.
15 Performance: G0W0 Execution time and speedup for G0W0 calculations of water systems (cc-tzvp basis). Calculation of 20 quasi-particle energies. Numerical integration using 60 points.
16 Reduced Scaling Methods RI with Overlap Metric (ia jb) = (ia P) (PQ) 1 (Q R) (RS) 1 (S jb) PQRS Can make use of sparsity of 3-center overlap integrals (a) (b) 10 4 O(N 4 ) RPA O(N 3 ) RPA fit 1: O(N 2.00 ) 10 3 O(N 3 ) RPA O(N 1-2 ) steps fit 2: O(N 1.20 ) O(N 3 ) steps fit: O(N 3.09 ) Execution time (node hours) Number of water molecules Number of water molecules
17 Sparse Tensor Linear Algebra (Partick Seewald) General library for sparse tensors of rank n Tensor contractions make use of DBCSR library [ija] = k [ijk][ka] [(ij), A] = MATMUL([(ij), k], [k, A]) Simplified implementation for new algorithms Post-Hartree-Fock methods RI Hartree-Fock exchange RI Hartree-Fock exchange for k-points
18 Wavefunction Analysis Hirshfeld charges F. L. Hirshfeld, Theor. Chim. Acta (1977) P. Bultink et al, J. Chem. Phys (2007) RESP charges C. Campana et al J. Chem. Theory Comput., (2009) D. Golze et al, PCCP (2015) MAO analysis C. Ehrhardt and R. Ahlrichs, Theor. Chim. Acta (1985) Minimal localized basis analysis W. C. Lu et al, JCP (2004)
19 Hirshfeld AIM Charges Definition of AIM charge distribution Atomic charges ρ A (r) = ρ0 A (r) ρ 0 tot q A = Z A ρ tot (r) ρ A (r) dr Charges depend on ρ 0 A (r), often very small charges Hirshfeld-I charges (Reference density depends on final charge) ρ A (r) = ρ0 A [q A] ρ 0 tot ρ tot (r)
20 Hirshfeld-I Charges Example: LiNH3 Hirshfeld Hirshfeld-I CHELPG Li N H Correlation between Hirshfeld-I and CHELPG charges.
21 Implementation in CP2K Atomic reference charges can be scaled Self-consistent scaling of charges Mulliken scaling of charges
22 RESP Charges Restraint Electrostatic Potential Charges V ESP [ρ](r) A q A ga (r ) r r dr Definition of sampling points Definition of restraints (target charges) Definition of constraints (total charge, atom types) Definition of Gaussian function g A (r)
23 RESP Charges at Surfaces D. Golze et al, PCCP (2015)
24 Wetting of h-bn on Metal Surface
25 Modified Atomic Orbital Analysis C. Ehrhardt and R. Ahlrichs, Theor. Chim. Acta (1985) MAOs are linear combination of functions centered on ONE atom Number of MAOs per atom is given in the input MAOs are determined by projection (= diagonalization of atomic density matrix block) or by minimization of total charge deficiency (N Tr(DS)), where D and S are the density and overlap matrices in the MAO basis.
26 Subspace Projections Projection on a atomic subspace [XYZ...] P XY... = ( µ S 1) ν µν µ ν where µ, ν are MAO functions on all atoms X, Y,... Definition of subspace electron counts: N XY... = TrDP XY... This gives us atomic subspace charges N A, N AB, N ABC,...
27 Interpretation of Atomic Occupations
28 Shared Electron Numbers σ AB = N A + N B N AB σ ABC = N A + N B + N C N AB N AC N BC + N ABC Atomic Charge q A = Z A R A R A = N A 1 σ AB B A σ ABC + B>C A
29 MAO: Water ATOM MAO S P D F 1 O H H Shared electron numbers Atom Atom σ AB 35 O 76 H O 133 H O 134 H O 164 H
30 How to you contribute? Do good science using CP2K. 10% of papers citing CP2K are in high-impact journals. Contribute to the CP2K mailing list Google Groups CP2K Contribute to the CP2K Wiki and the manual e.g. additional material from courses or papers Edit button in online manual. Contribute bug fixes or new features to the code
31 Acknowledgment CP2K Community
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