adf2007.01 the universal density functional package for chemists

ADF2007.01The universal density functional

package for chemists

Prof. Mauro Stener (Trieste University)[email protected]

16 April 2008ADF workshop at CINECA

ADF overview http://www.scm.com

Outline

• General intro DFT

• ADF overview– Application areas– Technical features

• Recent developments ADF– New functionality



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



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, ….



DFT: the Kohn-Sham (KS) equations

• ADF solves the KS equations for molecules

iiiKSH

KS HamiltonianMolecular orbitals

Orbital energies




iiiKSH

XC

Nucl Nucl

NuclKS

Ed

ZH '

'

'

2

1 2 rrr

r

Rr

occupied

ii

2Electron densityExchange-correlation energy functional

APPROXIMATED!

Must be properly chosen!




• In ADF molecular orbitals are expanded according to LCAO

• A basis set must be chosen

k

ikki c ,rr

Basis functions: must be properly chosen!



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 ..

Tom Ziegler

Evert-Jan Baerends



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



• 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 …

Accuracy of ADF

1: G. te Velde and E. J. Baerends, J. Comput. Phys. 99 (1), 84 (1992)



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



1. LCAO formulation (STO basis set)

2. Numerical integrals

3. Density fitting

k

kiki Crr

k

kakkikai OwO rrr

n

nn faocc

iiiin '~*

r

rdan2~min:

ADF: numerical techniques

Improved Slater type basis sets

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

Av. erro

r in

bo

nd

en

erg

y (

eV

)

DZ DZP TZP TZ2P QZ4P

Old vs new Slater type basis sets

Decreased basis set errors (test on 200 diatomics)

E. van Lenthe and E.J. BaerendsJournal of Computational Chemistry 24 (2003) 1142



0

5

10

15

20

25

30

35

40

45

50

Err

or

(kca

l/mo

l)

VS98 PKZB BmTau1 KCIS revPBE PW91

Av. err.

Max. err.

(Meta) GGAs

Exc performance G2 test set

Av. err.

Max. err.

Modern meta-GGA and hybrid Exc functionals

Approx. 50 Exc 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



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)



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) 1344-13562: Grüning et al. J.Chem. Phys. 114 (2001) 652-660



Spectroscopic properties

• Fast Raman intensities• Spin-orbit effects in Time-dependent DFT • Vibrational Circular Dichroism



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



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?



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



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 scaling on SGI hardwarePtSD

0

1

2

3

4

5

6

7

8

9

10

32 64 96 128

Number of Cores

Calc

ula

tio

ns p

er

day

Altix XE 210 (X5160 3.00GHz) Altix XE 310 (X5355 2.66) Altix 4700 (Itanium 2 1.6 GHz)

Large frequency calculation scales up to 128 coresBest scaling with Itanium2, quad-core and dual-core Xeons also OKRecently scaling improved further (development version)



Improved geometry optimizer• Strong coordinates, 30 organic molecules

Optimizer Average #steps to convergenceADF2006 7.4ADF2007-cart 7.3ADF2007-delocal 6.1

• Weak coordinates, 18 weakly bound systems– ADF2006 41.5– ADF2007-cart 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



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



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



Thank you for your attention!

Questions now?

Free 30-day trial available at www.scm.comQuestions outside presentation to: [email protected]

http://www.scm.com/

http://www.scm.com/

http://www.scm.com/



ADF2006: Spin-orbit splitting in excitations

Double-group symmetry usedShows split up in UV/Vis spectra due to spin-orbit couplingImportant 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



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



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

adf2007.01 the universal density functional package for chemists

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