Hybrid Functionals, van der Waals Corrections and ASE Interface to CP2K
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1 Hybrid Functionals, van der Waals Corrections and ASE Interface to CP2K Sanliang Ling University College London CP2K Summer School, 23rd - 26th August 2016, King's College London
2 Part I: Hybrid Functionals 2
3 What are hybrid functionals? Hybrid functionals: mixing non-local Hartree-Fock exchange with local/semi-local DFT/GGA exchange 3
4 4 Why do we need hybrid DFT? Improved description of the thermochemistry (e.g. atomisation energy, heats of formation, etc) of molecular systems Improved description of the lattice constants, surface energies, ionisation potentials and band gaps of semiconductors and insulators
5 Why do we need hybrid DFT? /PBE0 Mean absolute errors (Mae) for atomisation energies (kcal/mol) Scuseria et al., J. Chem. Phys., 110, 5029 (1999) 5
6 Why do we need hybrid DFT? Band gap error (ev) statistics for the SC/40 test set Scuseria et al., J. Chem. Phys., 123, (2005) 6
7 Hybrid DFT Calculations with CP2K Total energy as a functional of the electron density Exchange-correlation energy with a hybrid functional Guidon, Hutter and VandeVondele, J. Chem. Theory Comput., 6, 2348 (2010) 7
8 Hybrid DFT Calculations with CP2K Hartree-Fock exchange energy Four-centre two-electron integrals (ERIs): O(N 4 ) scaling Guidon, Hutter and VandeVondele, J. Chem. Theory Comput., 6, 2348 (2010) 8
9 Interaction potential Standard Coulomb potential (used in B3LYP, PBE0, etc) (see POTENTIAL_TYPE keyword in &INTERACTION_POTENTIAL subsection) Guidon et al., J. Chem. Phys., 128, (2008) 9
10 Interaction potential Range-separated Coulomb potential parameter short-range (used in HSE06, etc) long-range (see POTENTIAL_TYPE keyword in &INTERACTION_POTENTIAL subsection) Guidon et al., J. Chem. Phys., 128, (2008) Heyd & Scuseria, J. Chem. Phys., 118, 8207 (2003) 10
11 Interaction potential Truncated Coulomb potential parameter (used in PBE0-TC-LRC, etc) (see POTENTIAL_TYPE keyword in &INTERACTION_POTENTIAL subsection) Guidon et al., J. Chem. Theory Comput., 5, 3010 (2008) Spencer & Alavi, Phys. Rev. B, 77, (2008) 11
12 Auxiliary Density Matrix Methods Introducing auxiliary density matrix approximation original density matrix auxiliary density matrix Guidon, Hutter and VandeVondele, J. Chem. Theory Comput., 6, 2348 (2010) 12
13 ADMM basis sets (see $CP2K/cp2k/data/BASIS_ADMM) Guidon, Hutter and VandeVondele, J. Chem. Theory Comput., 6, 2348 (2010) 13
14 ADMM basis sets Choice of auxiliary basis set for ADMM FIT3: three Gaussian exponents for each valence orbital cfit3: a contraction of FIT3 pfit3: FIT3 + polarization functions cpfit3: cfit3 + polarization functions aug-fit3, aug-cfit3, aug-pfit3, augcpfit3: augmented with a diffuse function (see $CP2K/cp2k/data/BASIS_ADMM) Guidon, Hutter and VandeVondele, J. Chem. Theory Comput., 6, 2348 (2010) 14
15 ADMM basis sets (see $CP2K/cp2k/data/BASIS_ADMM_MOLOPT) 15
16 Uncontracted basis sets FIT10: 4s + 3p + 3d ADMM basis sets FIT11: 4s + 3p + 3d + 1f FIT12: 4s + 3p + 4d + 1f FIT13: 4s + 4p + 4d + 1f Contracted basis sets (double-z quality) cfit10 / cfit11 / cfit12 / cfit13 recommended for solids Names of the ADMM basis sets for main group elements will differ slightly, and usually the first ADMM basis set will not contain polarisation function. (see $CP2K/cp2k/data/BASIS_ADMM_MOLOPT) 16
17 Some general suggestions Always check the convergence of CUTOFF (see Always check the convergence of properties (e.g. lattice parameters, band gaps) with respect to supercell sizes Always start from pre-converged GGA (e.g. PBE) wavefunction and geometry Always check the convergence of primary and ADMM basis sets (start from a small basis and gradually increase the size) ADMM has only been implemented for use with GPW 17
18 Work Flow 1. Convergence test (primary basis, CUTOFF, supercell, etc) 2. GGA optimisation with selected primary basis 3. Name GGA wave function file for use with ADMM 4. Construct ADMM input with auxiliary basis (e.g. FIT3) 5. Run calculations and check convergence of ADMM basis 18
19 Input Structure: ADMM &DFT BASIS_SET_FILE_NAME./BASIS_MOLOPT (files can be found in $CP2K/cp2k/data) BASIS_SET_FILE_NAME./BASIS_ADMM WFN_RESTART_FILE_NAME ${project}-restart.wfn &SCF SCF_GUESS RESTART &END SCF &AUXILIARY_DENSITY_MATRIX_METHOD METHOD BASIS_PROJECTION ADMM_PURIFICATION_METHOD MO_DIAG &END AUXILIARY_DENSITY_MATRIX_METHOD &XC &END XC &END DFT &SUBSYS &KIND Si BASIS_SET DZVP-MOLOPT-SR-GTH AUX_FIT_BASIS_SET FIT3 POTENTIAL GTH-PBE-q4 &END KIND &END SUBSYS (see examples in $CP2K/cp2k/tests/QS/regtest-admm-1/2/3/4) 19
20 Which functional to use? PBE0-TC-LRC HSE06 Guidon et al., J. Chem. Theory Comput., 5, 3010 (2008) Spencer & Alavi, Phys. Rev. B, 77, (2008) Scuceria et al., J. Chem. Phys., 125, (2006) Empirical parameters: a, R c, and w 20
21 Input Structure: PBE0 vs. HSE06 &XC &XC_FUNCTIONAL &PBE SCALE_X 0.75 SCALE_C 1.0 &END PBE &PBE_HOLE_T_C_LR CUTOFF_RADIUS 2.0 SCALE_X 0.25 &END PBE_HOLE_T_C_LR &END XC_FUNCTIONAL &HF &SCREENING EPS_SCHWARZ 1.0E-6 SCREEN_ON_INITIAL_P FALSE &END SCREENING &INTERACTION_POTENTIAL POTENTIAL_TYPE TRUNCATED CUTOFF_RADIUS 2.0 T_C_G_DATA./t_c_g.dat &END INTERACTION_POTENTIAL &MEMORY MAX_MEMORY 2400 EPS_STORAGE_SCALING 0.1 &END MEMORY FRACTION 0.25 &END HF &END XC PBE0-TC-LRC (t_c_g.dat can be found in $CP2K/cp2k/data) &XC &XC_FUNCTIONAL &PBE SCALE_X 0.0 SCALE_C 1.0 &END PBE &XWPBE SCALE_X SCALE_X0 1.0 OMEGA 0.11 &END XWPBE &END XC_FUNCTIONAL &HF &SCREENING EPS_SCHWARZ 1.0E-6 SCREEN_ON_INITIAL_P FALSE &END SCREENING &INTERACTION_POTENTIAL POTENTIAL_TYPE SHORTRANGE OMEGA 0.11 &END INTERACTION_POTENTIAL &MEMORY MAX_MEMORY 2400 EPS_STORAGE_SCALING 0.1 &END MEMORY FRACTION 0.25 &END HF &END XC HSE06 (see examples in $CP2K/cp2k/tests/QS/regtest-admm-1/2/3/4) 21
22 A few more remarks Libint library is used to calculate ERIs and their analytic derivatives, see $CP2K/cp2k/INSTALL for more details on installation and linking with CP2K Hybrid DFT calculations of large systems are memory demanding, try to increase MAX_MEMORY or run the job with more MPI processes For extremely large hybrid DFT calculations, try hybrid MPI/OpenMP binary (i.e. cp2k.psmp) 22
23 Example: Diamond Band Gap 3x3x3 supercell Guidon, Hutter and VandeVondele, J. Chem. Theory Comput., 6, 2348 (2010) 23
24 Part II: Van der Waals Corrections 24
25 25 Where does van der Waals force come from? vdw force results from interaction of fluctuating charge distributions in one particle with those in an adjacent particle (particle = atom, molecule, molecular fragment, etc)
26 Why van der Waals force is important? experimental crystal structure after MD simulation without dispersion term Hobza et al. J. Am. Chem. Soc., 130, (2008) helical to ladder structural transition in DNA 26
27 Conventional DFT Fails for vdw Force B3LYP PBE B3LYP PBE Reference: CCSD(T), see Grimme, WIREs Comput. Mol. Sci., 1, 211 (2011) Conventional DFT methods cannot provide correct 1/R 6 dependence of vdw force on R 27
28 Methods to include vdw force in Conventional DFT non-local vdw correlation functional environment dependent C 6 correction simple C 6 correction Michaelides et al., J. Chem. Phys., 137, (2012) vdw corrected pseudopotential stairway to heaven for long range dispersion interactions 28
29 Simple C 6 Correction pairwise additive dispersion coefficients conventional DFT 29
30 Damped C 6 Correction damped Michaelides et al., J. Chem. Phys., 137, (2012) 30
31 DFT+D2 atomic ionization potentials static polarizability Grimme, J. Comput. Chem., 27, 1787 (2006) 31
32 DFT+D2 &XC &XC_FUNCTIONAL PBE &END XC_FUNCTIONAL &vdw_potential DISPERSION_FUNCTIONAL PAIR_POTENTIAL &PAIR_POTENTIAL TYPE DFTD2 REFERENCE_FUNCTIONAL PBE SCALING??? R_CUTOFF??? &END PAIR_POTENTIAL &END vdw_potential &END XC XC-dependent cutoff radius to calculate E disp (see more examples in $CP2K/cp2k/tests/QS/regtest-dft-vdw-corr-1) 32
33 Methods to include vdw force in Conventional DFT non-local vdw correlation functional environment dependent C 6 correction simple C 6 correction Michaelides et al., J. Chem. Phys., 137, (2012) vdw corrected pseudopotential stairway to heaven for long range dispersion interactions 33
34 Environment Dependent C 6 Correction DFT-D3: pre-calculated C 6 coefficients for various pairs of elements in different hybridisation states Grimme et al., J. Chem. Phys, 132, (2010) DFT-TS: Hirshfeld partitioning of the molecular electron density, compare effective atomic volume with a free atom, and then scale the C 6 coefficients of a free-atom reference Tkatchenko & Scheffler, Phys. Rev. Letts., 102, (2009) 34
35 DFT+D3 coordination number Grimme et al., J. Chem. Phys, 132, (2010) 35
36 DFT+D3 three-body term Grimme et al., J. Chem. Phys, 132, (2010) 36
37 DFT+D3 &XC &XC_FUNCTIONAL PBE &END XC_FUNCTIONAL &vdw_potential DISPERSION_FUNCTIONAL PAIR_POTENTIAL &PAIR_POTENTIAL TYPE DFTD3 ### or DFTD3(BJ) type of damping CALCULATE_C9_TERM.TRUE. include three-body term PARAMETER_FILE_NAME dftd3.dat REFERENCE_FUNCTIONAL PBE D3_SCALING??? R_CUTOFF??? &END PAIR_POTENTIAL &END vdw_potential &END XC XC and basis set dependent cutoff radius to calculate E disp (see more examples in $CP2K/cp2k/tests/QS/regtest-dft-vdw-corr-2; for additional scaling parameters optimised for moderate basis set calculations, see Supporting Information of the D3 paper) 37
38 Methods to include vdw force in Conventional DFT non-local vdw correlation functional environment dependent C 6 correction simple C 6 correction Michaelides et al., J. Chem. Phys., 137, (2012) vdw corrected pseudopotential stairway to heaven for long range dispersion interactions 38
39 Non-local vdw Correlation Functional Michaelides et al., J. Chem. Phys., 137, (2012) Hutter et al., J. Chem. Phys., 138, (2013) 39
40 Non-local vdw Correlation Functional Hutter et al., J. Chem. Phys., 138, (2013) 40
41 &XC &XC_FUNCTIONAL &PBE PARAMETRIZATION revpbe revpbe exchange SCALE_C 0.0 &END PBE &VWN LDA correlation &END VWN &END XC_FUNCTIONAL &vdw_potential DISPERSION_FUNCTIONAL NON_LOCAL &NON_LOCAL TYPE DRSLL type of non-local vdw correlation functional KERNEL_FILE_NAME vdw_kernel_table.dat cutoff of FFT grid used to calculate E nl c CUTOFF??? &END NON_LOCAL &END vdw_potential &END XC vdw-df (see more examples in $CP2K/cp2k/tests/QS/regtest-dft-vdw-corr-3) 41
42 rvv10 &XC &XC_FUNCTIONAL &LIBXC FUNCTIONAL XC_GGA_X_RPW86 XC_GGA_C_PBE &END LIBXC &END XC_FUNCTIONAL &vdw_potential DISPERSION_FUNCTIONAL NON_LOCAL &NON_LOCAL TYPE RVV10 type of non-local vdw correlation functional PARAMETERS parameters relevant to rvv10 KERNEL_FILE_NAME rvv10_kernel_table.dat cutoff of FFT grid used to calculate E nl c CUTOFF??? &END NON_LOCAL &END vdw_potential &END XC (see more examples in $CP2K/cp2k/tests/QS/regtest-dft-vdw-corr-3) 42
43 meta-gga: M06-L &XC &XC_FUNCTIONAL &LIBXC T FUNCTIONAL XC_MGGA_X_M06_L XC_MGGA_C_M06_L &END LIBXC &END XC_FUNCTIONAL &END XC Truhlar et al., J. Chem. Phys., 125, (2006) maybe combined with D3 correction analytical stress tensor has not been implemented, i.e. cannot be used for CELL_OPT 43
44 A few more remarks use higher planewave cutoff and tighter energy/force convergence criteria for meta-ggas and functionals from Libxc to use functionals from Libxc, you will need to install Libxc and link CP2K with Libxc, see $CP2K/cp2k/INSTALL for more details Basis set superposition error may mimick the missing dispersion interactions by DFT; check convergence on basis sets 44
45 Part III: ASE interface 45
46 How to use CP2K/ASE interface? A sample CP2K/ASE job script (e.g. on ARCHER): #!/bin/bash --login #PBS -N CP2K-ASE #PBS -l select=20 #PBS -l walltime=01:00:00 #PBS -A XXX-XXX #PBS -j oe # modules that need to be loaded module load cp2k module load python-compute module load pc-numpy module load pc-scipy module load pc-ase/ # environment variables that need to be set export ASE_CP2K_COMMAND="aprun -n 480 cp2k_shell.popt" export CP2K_DATA_DIR=/work/y07/y07/cp2k/ /data # go to the job directory cd $PBS_O_WORKDIR # execute the CP2K-ASE job python job.py account number, replace with your own 46
47 How to use CP2K/ASE interface? A sample CP2K/ASE job input file: #!/usr/bin/python from future import division, print_function import os from ase.structure import molecule from ase.optimize import BFGS from ase.calculators.cp2k import CP2K def main(): calc = CP2K(label='test_H2_GOPT') atoms = molecule('h2', calculator=calc) atoms.center(vacuum=2.0) # Run Geo-Opt gopt = BFGS(atoms, logfile=none) gopt.run(fmax=1e-6) Setting up the system: calc = CP2K(label= sys') sys = io.read('sys.xyz') sys.set_cell([(8.0, 0.0, 0.0), (4.3, 7.0, 0.0), (0.0, 0.0, 21.4)], scale_atoms=false) sys.set_pbc((true, True, True)) sys.set_calculator(calc) # check distance dist = atoms.get_distance(0, 1) dist_ref = assert (dist - dist_ref) / dist_ref < 1e-7 # check energy energy_ref = energy = atoms.get_potential_energy() assert (energy - energy_ref) / energy_ref < 1e-10 print('passed test "H2_GEO_OPT"') main() (see more examples in $ASE/ase/test/cp2k) 47
48 More advanced settings: How to use CP2K/ASE interface? inp = """ &FORCE_EVAL METHOD Quickstep &DFT BASIS_SET_FILE_NAME BASIS_MOLOPT &MGRID CUTOFF 400 &END MGRID &XC &XC_FUNCTIONAL LDA &END XC_FUNCTIONAL &END XC &POISSON PERIODIC NONE PSOLVER MT &END POISSON &END DFT &SUBSYS &KIND H BASIS_SET DZVP-MOLOPT-SR-GTH POTENTIAL GTH-LDA &END KIND &END SUBSYS &END FORCE_EVAL """ # Basically, the entire CP2K input is passed in explicitly. # Disable ASE's input generation by setting everything to None. # For default settings, see $ASE/ase/calculators/cp2k.py. # ASE should only add the CELL and the COORD section. calc = CP2K(basis_set=None, basis_set_file=none, max_scf=none, cutoff=none, force_eval_method=none, potential_file=none, poisson_solver=none, pseudo_potential=none, stress_tensor=false, xc=none, label='test_h2_inp', inp=inp) h2 = molecule('h2', calculator=calc) h2.center(vacuum=2.0) energy = h2.get_potential_energy() energy_ref = diff = abs((energy - energy_ref) / energy_ref) assert diff < 1e-10 print('passed test "H2_None"') main() (see more examples in $ASE/ase/test/cp2k) 48
49 Further Reading Hybrid functionals in CP2K (by Sanliang Ling) Van der Waals corrected DFT (by Sanliang Ling) and references therein. For Atomic Simulation Environment, see 49
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