ADF 2007 01 The universal density functional package

ADF 2007. 01 The universal density functional package for chemists Prof. Mauro Stener (Trieste University) stener@univ. trieste. it ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Outline • General intro DFT • ADF overview – Application areas – Technical features • Recent developments ADF – New functionality ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Hierarchy of Computational Methods • Ab initio quantum chemistry (MP 2, 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 Walter Kohn – Typically 10, 000 atoms – DFT accuracy at active site, environment effects included • MM or MD (force fields) – Fast, but inaccurate, no bond-breaking etc. ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

DFT: the Kohn-Sham (KS) equations • ADF solves the KS equations for molecules Orbital energies KS Hamiltonian Molecular orbitals ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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

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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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. . ADF overview http: //www. scm. com Evert-Jan Baerends Tom Ziegler 16 April 2008 ADF workshop at CINECA

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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Accuracy of ADF • • • 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 … 1: G. te Velde and E. J. Baerends, J. Comput. Phys. 99 (1), 84 (1992) ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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, DZP, TZ 2 P, QZ 4 P (basis set limit) Even-tempered, diffuse ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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

Improved Slater type basis sets E. van Lenthe and E. J. Baerends Journal of Computational Chemistry 24 (2003) 1142 ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Modern meta-GGA and hybrid Exc functionals Approx. 50 Exc functionals evaluated in single shot ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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. ADF&overview 16 April 2008 2000, 15, 1. http: //www. scm. com ADF workshop at CINECA

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 ADF overview 16 April 2008 http: //www. scm. com ADF workshop at CINECA

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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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) 1344 -1356 2: Grüning et al. J. Chem. Phys. 114 (2001) 652 -660 ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Spectroscopic properties • Fast Raman intensities • Spin-orbit effects in Time-dependent DFT • Vibrational Circular Dichroism ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Potential Energy Surface - improvements • • MO 6 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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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 (ADF 2006): – Electron smearing with stepwise reduction of smearing parameter – Averill-Painter method with gradual change in (fractional) occupations • ADF 2007: NEWDIIS – improved DIIS implementation? ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

ADF 2006: 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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

2006: Analytic frequencies at GGA level • Important for IR spectra and classification stationary point on PES (minima, TS) • Frequency calculations time-consuming • ADF 2006 analytical implementation (CPKS) – Four times faster than numerical frequencies • Timing example – 105 atoms, DZ basis, “accint” 3 – 128 Itanium 2 1. 6 GHz cores – 2. 7 hours wall-clock time S. K. Wolff, Int. J. Quantum Chem. , 2005, 104: 645 ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

ADF scaling on SGI hardware Large frequency calculation scales up to 128 cores Best scaling with Itanium 2, quad-core and dual-core Xeons also OK Recently scaling improved further (development version) ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Improved geometry optimizer • Strong coordinates, 30 organic molecules Optimizer ADF 2006 ADF 2007 -cart ADF 2007 -delocal Average #steps to convergence 7. 4 7. 3 6. 1 • Weak coordinates, 18 weakly bound systems – ADF 2006 – ADF 2007 -cart 41. 5 15. 5 – ADF 2007 -delocal 9. 8 • Improvements largest for strict convergence criteria, weakly bound, and floppy systems Swart, Bickelhaupt, Int. J. Quant. Chem. 2006, 106, 2536 ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Some non-confidential future plans. . • 3 D-RISM, solvent model (Gusarov, Kovalenko, Ziegler) • DFTB (DF Tight-Binding), fast DFT-based semiempirical 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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Thank you for your attention! Free 30 -day trial available at www. scm. com Questions outside presentation to: info@scm. com Questions now? ADF overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

ADF 2006: 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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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 overview http: //www. scm. com 16 April 2008 ADF workshop at CINECA