ADF2007.01 The universal density functional package for chemists

1. ADF2007.01 The universal density functional package for chemists Prof. Mauro Stener (Trieste University) stener@univ.trieste.it

2. Outline • General intro DFT • ADF overview • Application areas • Technical features • Recent developments ADF • New functionality ADF overviewhttp://www.scm.com

3. Hierarchy of Computational Methods • Ab initio quantum chemistry (MP2, CC, CI) • Max. 10 atoms, systematic improvements, accurate if HF is good starting point! • Density functional theory (DFT) • Typically 100 atoms, accurate if Exc reliable • Handles “difficult” systems without problems • QM/MM • Typically 10,000 atoms • DFT accuracy at active site, environment effects included • MM or MD (force fields) • Fast, but inaccurate, no bond-breaking etc. Walter Kohn ADF overviewhttp://www.scm.com

4.  Density Functional Theory (DFT) • Nobel prize Walter Kohn 1998 in chemistry(!) • Electron density  is basic quantity • Exchange and correlation effects included through approximate Exc [] : (meta-) GGA’s, hybrid functionals • Successful applications: • equilibrium geometries, binding energies • molecular properties accessible: IR, NMR, ESR, UV/Vis, CD, ….    ADF overviewhttp://www.scm.com

5. DFT: the Kohn-Sham (KS) equations • ADF solves the KS equations for molecules Orbital energies KS Hamiltonian Molecular orbitals ADF overviewhttp://www.scm.com

6. DFT: the Kohn-Sham (KS) equations Exchange-correlation energy functional APPROXIMATED! Must be properly chosen! Electron density ADF overviewhttp://www.scm.com

7. DFT: the Kohn-Sham (KS) equations • In ADF molecular orbitals are expanded according to LCAO • A basis set must be chosen Basis functions: must be properly chosen! ADF overviewhttp://www.scm.com

8. ADF developers • Baerends group, Amsterdam (1973 – now) • Ziegler group, Calgary (1978 - now) • Many other academic groups • SCM: • Spin-off Baerends group • Coordinate developments • User & developer support • GUI development • Implement what users want .. Evert-Jan Baerends Tom Ziegler ADF overviewhttp://www.scm.com

9. Application areas for ADF • Whole periodic table • Types of systems: • Molecules in gas phase (ADF) • Solvated molecules (e.g. COSMO) • Active site in proteins (QM/MM) • Polymers, slabs & surfaces, solids (BAND) • Applications in chemistry & materials science • Popular application areas: • heavy element and transition metal compounds • homogeneous and heterogeneous catalysis • spectroscopy, molecular properties • Chemical analysis: energy decomposition, fragment orbitals ADF overviewhttp://www.scm.com

10. Accuracy of ADF • Accurate, tunable numerical integration scheme1 • No pseudopotential or ECP approximations needed • Stable SCF convergence for transition metal compounds • Modern exchange-correlation functionals • Slater Type basis sets … 1: G. te Velde and E. J. Baerends, J. Comput. Phys. 99 (1), 84 (1992) ADF overviewhttp://www.scm.com

11. Basis Sets in ADF: Slater Orbitals • Benefits of Slater type basis sets: • nuclear cusp and correct asymptotic behavior • fewer Slaters than Gaussians needed • BAND: numerical orbitals and Slaters • ADF has basis sets for every situation: • Whole periodic table: Z = 1 - 118 • frozen core and all-electron • Relativistic and non-relativistic (ZORA) • SZ, DZ, DZP, TZP, TZ2P, QZ4P (basis set limit) • Even-tempered, diffuse ADF overviewhttp://www.scm.com

12. ADF: numerical techniques • LCAO formulation (STO basis set) • Numerical integrals • Density fitting ADF overviewhttp://www.scm.com

13. Improved Slater type basis sets E. van Lenthe and E.J. Baerends Journal of Computational Chemistry 24 (2003) 1142

14. Modern meta-GGA and hybrid Exc functionals Approx. 50 Exc functionals evaluated in single shot ADF overviewhttp://www.scm.com

15. Analysis with ADF • Fragment analysis • Bond energy decomposition • Electrostatic interaction • Pauli (exchange) repulsion • Orbital interactions • Advanced charge density analyses: Voronoy, Hirshfeld, Nalewajski bond orders • Use of full molecular symmetry • Third-party analysis software: NBO 1: Bickelhaupt & Baerends, Rev. Comput. Chem. 2000, 15, 1.

16. ADF speed • Linear scaling techniques used • Density fitting (atom-pair based) • Efficient in parallel • Symmetry C. Fonseca Guerra, J.G. Snijders, G. te Velde, E.J. Baerends; Theor. Chem. Acc. 99 (1998) 391

17. Functionality of ADF • Energetics, Potential Energy Surfaces • Single point, geometry optimization, transition state search, analytic frequencies, thermodynamics • Tracing of reaction path (IRC) • Computation of any electronic configuration • Spectroscopic properties • NMR, EFG, EPR, Raman, IR, hyperfine interactions, UV/Vis, CD, ORD, VCD, core properties… • Bond energy analysis • Periodic structures treated with comparable method (BAND) ADF overviewhttp://www.scm.com

18. Model Hamiltonian options • State-of-the-art xc functionals • potential: LDA, GGA, GRAC1, SAOP2, hybrids • energy: LDA, GGA, meta-GGA, and hybrid energy functionals • Spin: restricted or unrestricted • Relativistic effects • scalar approximation: ZORA (superior to Pauli) • spin-orbit (double-group symmetry) • Environment • Solvent: COSMO, QM/MM, DRF, Frozen density embedding • Protein: QM/MM 1: Schipper et al., J.Chem. Phys. 112 (2000) 1344-1356 2: Grüning et al. J.Chem. Phys. 114 (2001) 652-660 ADF overviewhttp://www.scm.com

19. Spectroscopic properties • Fast Raman intensities • Spin-orbit effects in Time-dependent DFT • Vibrational Circular Dichroism ADF overviewhttp://www.scm.com

20. Potential Energy Surface - improvements • MO6 class of xc energy functionals implemented (2007) • SCF convergence trouble-shooting (2006 & 2007) • Hybrid functionals during SCF (2006) • Analytic frequencies at GGA level (2006) • Improved Optimizer (2007) • Transition state search improvements (2007) • Frequency scan also after analytical frequencies (2007): to remove doubt on imaginary frequencies • Spin-orbit gradients (2007): geometry optimization, TS, numerical frequencies ADF overviewhttp://www.scm.com

21. SCF convergence trouble-shooting • Typical problematic systems for SCF convergence • Many close-lying energy levels around HOMO and LUMO • Certain lanthanides with open-shell f-electrons • Molecules with multiple transition metals, metal clusters • New methods (ADF2006): • Electron smearing with stepwise reduction of smearing parameter • Averill-Painter method with gradual change in (fractional) occupations • ADF2007: NEWDIIS – improved DIIS implementation? ADF overviewhttp://www.scm.com

22. ADF2006: Hybrid functionals during SCF • Uses “energetic fit” (Prof. Handy et al.) with additional efficiency refinements • Provides: • orbitals • orbital energies • (some) molecular properties [ESR] with hybrids • Gradients with hybrids not yet available E. van Lenthe, unpublished ADF overviewhttp://www.scm.com

23. 2006: Analytic frequencies at GGA level • Important for IR spectra and classification stationary point on PES (minima, TS) • Frequency calculations time-consuming • ADF2006 analytical implementation (CPKS) • Four times faster than numerical frequencies • Timing example • 105 atoms, DZ basis, “accint” 3 • 128 Itanium2 1.6 GHz cores • 2.7 hours wall-clock time S. K. Wolff, Int. J. Quantum Chem., 2005, 104: 645 ADF overviewhttp://www.scm.com

24. ADF scaling on SGI hardware Large frequency calculation scales up to 128 cores Best scaling with Itanium2, quad-core and dual-core Xeons also OK Recently scaling improved further (development version)

25. Strong coordinates, 30 organic molecules Optimizer Average #steps to convergence ADF2006 7.4 ADF2007-cart 7.3 ADF2007-delocal 6.1 Weak coordinates, 18 weakly bound systems ADF200641.5 ADF2007-cart15.5 ADF2007-delocal 9.8 Improvements largest for strict convergence criteria, weakly bound, and floppy systems Improved geometry optimizer Swart, Bickelhaupt, Int. J. Quant. Chem. 2006, 106, 2536 ADF overviewhttp://www.scm.com

26. Technical: Parallel Windows & HP-MPI • Parallel Windows version: • Impressive speed on quad-core • Limited speed-up from 2 to 4 due to memory bandwidth • HP-MPI message passing library • Supports many interconnects • no recompilation needed • included in ADF distribution • performance improvement ADF overviewhttp://www.scm.com

27. Some non-confidential future plans .. • 3D-RISM, solvent model (Gusarov, Kovalenko, Ziegler) • DFTB (DF Tight-Binding), fast DFT-based semi-empirical method • Magnetic Circular Dichroism property • Hybrid TDDFT & NBO analysis properties (Autschbach) • Python scripting, combine with other codes / methods • Meta-GGA’s in BAND • Speed-ups large ADF jobs and NMR calculations ADF overviewhttp://www.scm.com

28. Thank you for your attention! Questions now? Free 30-day trial available at www.scm.com Questions outside presentation to: info@scm.com ADF overviewhttp://www.scm.com

29. ADF2006: Spin-orbit splitting in excitations Double-group symmetry used Shows split up in UV/Vis spectra due to spin-orbit coupling Important for optical spectra of heavy elements F. Wang, T. Ziegler, E. van Lenthe, S.J.A. van Gisbergen, and E.J. Baerends, Journal of Chemical Physics, 2005 122: p. 204103183. F. Wang, and T. Ziegler, the Journal of Chemical Physics, 2005 123: p. 194102 ADF overviewhttp://www.scm.com

30. Transition State search improvements • Nudged Elastic Band • HCN example in ADF now converges in 9 steps (was 38) • End points optimized at same time (minimizations) • Partial Hessian • Improves (semi-empirical) Hessian guess, e.g. molecule on metal surface • Difference between convergence and non-convergence • Still considerable speed-up for less critical cases ADF overviewhttp://www.scm.com

31. Environment effects (2)Frozen-density embedding, subsystem DFT • “DFT in DFT”, QM/QM • One active site, multiple frozen sites • Efficient for large systems • Solvent effects on spectroscopic properties studied • Original implementation by Wesolowski • More recent work in ADF by Jacob, Neugebauer, Visscher ADF overviewhttp://www.scm.com