ADF The universal density functional package for chemists Prof. Mauro Stener (Trieste University)

16 April 2008 ADF workshop at CINECA ADF overview Outline General intro DFT ADF overview –Application areas –Technical features Recent developments ADF –New functionality

16 April 2008 ADF workshop at CINECA ADF overview 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 E xc 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

16 April 2008 ADF workshop at CINECA ADF overview  Density Functional Theory (DFT) Nobel prize Walter Kohn 1998 in chemistry(!) Electron density  is basic quantity Exchange and correlation effects included through approximate E xc [  ] : (meta-) GGA’s, hybrid functionals Successful applications: equilibrium geometries, binding energies molecular properties accessible: IR, NMR, ESR, UV/Vis, CD, ….   

16 April 2008 ADF workshop at CINECA ADF overview DFT: the Kohn-Sham (KS) equations ADF solves the KS equations for molecules KS Hamiltonian Molecular orbitals Orbital energies

16 April 2008 ADF workshop at CINECA ADF overview DFT: the Kohn-Sham (KS) equations Electron density Exchange-correlation energy functional APPROXIMATED! Must be properly chosen!

16 April 2008 ADF workshop at CINECA ADF overview 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!

16 April 2008 ADF workshop at CINECA ADF overview ADF developers Baerends group, Amsterdam (1973 – now) Ziegler group, Calgary ( now) Many other academic groups SCM: –Spin-off Baerends group –Coordinate developments –User & developer support –GUI development –Implement what users want.. Tom Ziegler Evert-Jan Baerends

16 April 2008 ADF workshop at CINECA ADF overview 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

16 April 2008 ADF workshop at CINECA ADF overview Accurate, tunable numerical integration scheme 1 No pseudopotential or ECP approximations needed Stable SCF convergence for transition metal compounds Modern exchange-correlation functionals Slater Type basis sets … Accuracy of ADF 1: G. te Velde and E. J. Baerends, J. Comput. Phys. 99 (1), 84 (1992)

16 April 2008 ADF workshop at CINECA ADF overview 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 = –frozen core and all-electron –Relativistic and non-relativistic (ZORA) –SZ, DZ, DZP, TZP, TZ2P, QZ4P (basis set limit) –Even-tempered, diffuse

16 April 2008 ADF workshop at CINECA ADF overview 1.LCAO formulation (STO basis set) 2.Numerical integrals 3.Density fitting ADF: numerical techniques

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

16 April 2008 ADF workshop at CINECA ADF overview Modern meta-GGA and hybrid E xc functionals Approx. 50 E xc functionals evaluated in single shot

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.

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

16 April 2008 ADF workshop at CINECA ADF overview 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)

16 April 2008 ADF workshop at CINECA ADF overview Model Hamiltonian options State-of-the-art xc functionals – potential: LDA, GGA, GRAC 1, SAOP 2, 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) : Grüning et al. J.Chem. Phys. 114 (2001)

16 April 2008 ADF workshop at CINECA ADF overview Spectroscopic properties Fast Raman intensities Spin-orbit effects in Time-dependent DFT Vibrational Circular Dichroism

16 April 2008 ADF workshop at CINECA ADF overview 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

16 April 2008 ADF workshop at CINECA ADF overview 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?

16 April 2008 ADF workshop at CINECA ADF overview 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

16 April 2008 ADF workshop at CINECA ADF overview : 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 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)

16 April 2008 ADF workshop at CINECA ADF overview Improved geometry optimizer Strong coordinates, 30 organic molecules Optimizer Average #steps to convergence ADF ADF2007-cart7.3 ADF2007-delocal6.1 Weak coordinates, 18 weakly bound systems –ADF –ADF2007-cart15.5 –ADF2007-delocal9.8 Improvements largest for strict convergence criteria, weakly bound, and floppy systems Swart, Bickelhaupt, Int. J. Quant. Chem. 2006, 106, 2536

16 April 2008 ADF workshop at CINECA ADF overview 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

16 April 2008 ADF workshop at CINECA ADF overview 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

16 April 2008 ADF workshop at CINECA ADF overview Thank you for your attention! Questions now? Free 30-day trial available at Questions outside presentation to:

16 April 2008 ADF workshop at CINECA ADF overview 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, : p F. Wang, and T. Ziegler, the Journal of Chemical Physics, : p

16 April 2008 ADF workshop at CINECA ADF overview 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

16 April 2008 ADF workshop at CINECA ADF overview 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