ADF2007.01

The universal density functional package for chemists

Prof. Mauro Stener (Trieste University)

[email protected]

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 (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 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 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 http://www.scm.com

DFT: the Kohn-Sham (KS) equations

• ADF solves the KS equations for molecules Orbital energies

H KS



i

 

i



i

KS Hamiltonian Molecular orbitals ADF overview http://www.scm.com

16 April 2008 ADF workshop at CINECA

DFT: the Kohn-Sham (KS) equations

H KS

  1 2  2

H KS



i

 

i



i

 

Nucl

r

Z Nucl



R

Nucl

 

r

 

r

'

d

r

'  

E XC

    Electron density  

occupied



i



i

2 ADF overview http://www.scm.com

Exchange-correlation energy functional APPROXIMATED!

Must be properly chosen!

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 

i

 

k



k

 

c k

,

i

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 ..

Evert-Jan Baerends Tom Ziegler ADF overview http://www.scm.com

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, DZ, DZP, TZP, TZ2P, QZ4P (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) 

i

 

k



k

 

C ki

2. Numerical integrals 3. Density fitting 

i O



a

 

k w k



i

 

occ



i a n n i



i



i

* : min       

a n

2

n d

r



f n

ADF overview http://www.scm.com

16 April 2008 ADF workshop at CINECA

Improved Slater type basis sets

0,4 0,2 0 1,6 1,4 1,2 1 0,8 0,6

Decreased basis set errors (test on 200 diatomics)

DZ DZP TZP TZ2P

Old vs new Slater type basis sets

QZ4P E. van Lenthe and E.J. Baerends Journal of Computational Chemistry 24 (2003) 1142

Modern meta-GGA and hybrid E

xc

functionals

Exc performance G2 test set

Av. err.

Max. err.

50 45 40 15 10 5 0 35 30 25 20 VS98 Max. err.

Av. err.

PKZB BmTau1 KCIS

(Meta) GGAs

revPBE PW91 Approx. 50 E xc 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. 2000, 15, 1.

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

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

• 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 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 (ADF2006): – Electron smearing with stepwise reduction of smearing parameter – Averill-Painter method with gradual change in (fractional) occupations • ADF2007: NEWDIIS – improved DIIS implementation? ADF overview http://www.scm.com

16 April 2008 ADF workshop at CINECA

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 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 • 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 overview http://www.scm.com

16 April 2008 ADF workshop at CINECA

ADF scaling on SGI hardware

PtSD

10 9 8 7 6 5 4 3 2 1 0 32 Altix XE 210 (X5160 3.00GHz) 64

Number of Cores

Altix XE 310 (X5355 2.66) 96 Altix 4700 (Itanium 2 1.6 GHz) 128 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)

Improved geometry optimizer

• Strong coordinates, 30 organic molecules Optimizer Average #steps to convergence ADF2006 ADF2007-cart ADF2007-delocal 7.4

7.3

6.1

•

Weak coordinates, 18 weakly bound systems

– ADF2006 – ADF2007-cart 41.5

15.5

–

ADF2007-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 ..

• 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 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: [email protected]

Questions now?

ADF overview http://www.scm.com

16 April 2008 ADF workshop at CINECA

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 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