Recent developments in ADF

1
ADF2007.01 The universal density functional
package for chemists Prof. Mauro Stener (Trieste
University) stener_at_univ.trieste.it
2
Outline

• General intro DFT
• ADF overview
• Application areas
• Technical features
• Recent developments ADF
• New functionality

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
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-) GGAs, hybrid
  functionals
• Successful applications
• equilibrium geometries, binding energies
• molecular properties accessible IR, NMR, ESR,
  UV/Vis, CD, .

?
?
??
5
DFT the Kohn-Sham (KS) equations

• ADF solves the KS equations for molecules

Orbital energies
KS Hamiltonian
Molecular orbitals
6
DFT the Kohn-Sham (KS) equations
Exchange-correlation energy functional APPROXIMATE
D! Must be properly chosen!
Electron density
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!
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
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

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)
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

12
ADF numerical techniques

1. LCAO formulation (STO basis set)
2. Numerical integrals
3. Density fitting

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
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)

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
19
Spectroscopic properties

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

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

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?

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
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
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
Improved geometry optimizer

• 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
• 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
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

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-GGAs in BAND
• Speed-ups large ADF jobs and NMR calculations

28
Thank you for your attention! Questions now?
Free 30-day trial available at www.scm.com Questio
ns outside presentation to info_at_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
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

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