ADF The universal density functional package for chemists!

Power Tools

for Quantum

Chemists

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The ADF density functional package

• Properties and environments for any molecule

• Excels in transition and heavy metal compounds

• Fast, robust, and accurate

• Expert support and active user community

• Uses Slater functions, beats Gaussians!

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I IntroductionIa ADFThe Amsterdam Density Functional package (ADF) is software for first-principles electronic structure calculations (quantum chemistry). ADF is used both by academic and by industrial researchers worldwide, in such diverse fields as pharmacochemistry and materials science. It is particularly popular in the research areas of homogeneous and heterogeneous catalysis, inorganic chemistry, heavy-element chemistry, biochemistry, and various types of spectroscopy.

The package consists of the molecular ADF program, the periodic structure program BAND, and a graphical user interface (GUI) for ADF. Several smaller utility and property programs, as well as free third-party utilities, are available.

ADF is based on Density Functional Theory (DFT), which has dominated quantum chemistry applications since the early 1990’s. DFT gives superior accuracy to Hartree-Fock theory and semi-empirical approaches. In contrast to conventional ab initio methods (MP2, CI, CC), it enables accurate treatment of transition metal compounds with hundreds of atoms (thousands with QM/MM).

Ib Academic ADF development groupsHistorically, ADF has been developed mainly at the well-known theoretical chemistry groups in Amsterdam (Prof. Baerends and coworkers) and Calgary (Prof. Ziegler and coworkers). Nowadays, many academic developers across the US, Canada, and Europe are contributing further developments to ADF and BAND.

1c Scientific Computing & Modelling NV (SCM)Scientific Computing & Modelling NV (SCM) is a spin-off company of the Baerends group, established in 1995. Its primary mission is to assist in further development of ADF, and to support the ADF user community. The SCM staff consists of scientists with Ph.D. degrees in theoretical chemistry and with many years of experience in ADF development and applications.

1d CommunityThe ADF users and developers form an active community. Topics of mutual interest are discussed on the ADF mailing list. A fully searchable archive of the mailing list is accessible from the SCM website. The academic developers are in close contact with each other and with SCM, thus ensuring rapid further development of ADF.

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II Functionality

The ADF package can be applied to isolated molecules, polymers, slabs, solids, molecules in solvents, and molecules in protein environments. It can treat all elements of the periodic table, and contains state-of-the-art relativistic methods (ZORA [1] and spin-orbit coupling) to treat heavy nuclei. ADF is especially suited for transition metal compounds. It is efficient due to a combination of linear scaling and parallelization techniques, and contains many standard methods for studying potential energy surfaces, as well as a wide range of molecular properties. Chemically relevant analysis methods are available (including bond energy decomposition, fragment orbitals, and charge decomposition). The QM/MM implementation enables the treatment of protein environments with many thousands of atoms. ADF includes the very latest meta-GGA and hybrid exchange-correlation functionals, as well as a full range of standard functionals (including B3LYP).

IIa Geometry optimizations, transition states, reaction paths, and infrared frequenciesADF enables geometry optimizations in Cartesian and internal coordinates. An initial Hessian estimate speeds up the optimizations. Various constraints (including initially unsatisfied and combined) can be imposed. Transition state searches, intrinsic reaction coordinates, and linear transit calculations are available to further analyze the energy path from reactants, via the transition state, to the final products. A fast, parallel analytic second derivatives implementation yields IR frequencies and Hessians. These Hessians are helpful in finding and characterizing the transition states.

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Fig. 1 Gas phase optical absorption spectrum

of Ni-octaethylporphyrin. Spectra of

(metal) porphyrins and related compounds

can be understood in detail through ADF

calculations [2].

IIb Molecular propertiesAn important strength of ADF is the variety of accessible molecular properties available and the accuracy with which they can be obtained. The time-dependent DFT implementation yields UV/Vis spectra (singlet and triplet excitation energies, as well as oscillator strengths, fig.

1), frequency-dependent (hyper-)polarizabilities (nonlinear optics), Raman intensities, and van der Waals dispersion coefficients. Rotatory strengths and optical rotatory dispersion (optical properties of chiral molecules) as well as frequency-dependent dielectric functions for periodic structures are available. NMR chemical shifts and spin-spin couplings, ESR (EPR) g-tensors, magnetic and electric hyperfine tensors, and nuclear quadrupole coupling constants can all be calculated, as well as more standard properties like IR frequencies and intensities, and multipole moments. Relativistic effects (ZORA and spin-orbit coupling) can be included for most properties. The implementation of most of these properties, including optical and NMR properties, fully exploits the speed-ups of parallel computers.

IIc Modeling solvents, proteins, and other environmentsThe conductor-like screening model (COSMO) is available for molecules in a solvent. The QM/MM implementation enables treatment of active sites in protein environments with many thousands of atoms. Homogeneous electric fields and point charges can be specified.

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IId Graphical User InterfaceA full Graphical User Interface for ADF (ADF-GUI) is being developed and released module by module. The input builder ADFinput enables all users to set up very complicated calculations with a few mouse clicks (fig. 2).

ADFview provides graphical representations of many parts of the output, such as the computed Kohn-Sham orbitals, deformation densities and electrostatic potentials (fig. 3), the Electron Localisation Function (ELF), and many more. ADFspectra (fig. 4) visualizes spectra (such as IR, optical, and DOS), and ADFmovie displays the nuclear displacements during a geometry optimization or molecular vibration. High priority is given to further enhancements of the ADF-GUI.

Fig. 3 The values of the electrostatic potential of a

porphyrin sandwich molecule are shown in

color on an isodensity surface.

Fig. 2 The ADFinput module of the ADF-GUI allows

users to build or import a molecule, and select the

appropriate options rapidly.

Fig. 4 The ADFspectra module

can display various types of

molecular spectra calculated

by ADF.

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IIe Polymers, slabs, and solids with BANDBAND is a periodic structure program for the study of bulk crystals, polymers, and surfaces. It uses numerical and Slater atomic orbitals and avoids pseudo-potential approximations. BAND is often used in heterogeneous catalysis studies. It provides densities-of-states (total, partial, population) analyses, and the Potential Energy Surface (PES) of, for instance, a chemisorption system or a chemical reaction at a metal surface (fig. 5).

Fig. 5 PES for H2 on three-layer platinum slab for study on dissociative adsorption and direct absorption

(work by O.M. Løvvik and R. Olsen).

Fig. 6 Comparison of theoretical and experimental

results for the imaginary part of the

dielectric function of solid InSb [3].

BAND offers a variety of density functionals, and the choice between spin-restricted and spin-unrestricted calculations. It provides an analysis of the ‘bonding’ (cohesive) energy in conceptually useful components, Mulliken-type population analyses, and the charge density Fourier analysis (form factors). A fragment analysis feature is available for decomposition of Density-of-States data in terms of the molecular orbitals of (molecular) fragments. BAND uses the same relativistic methods as ADF and is well suited to treat heavy nuclei. A time-dependent DFT implementation enables the accurate calculation of frequency-dependent dielectric functions (fig. 6). Further work on magnetic and electric properties of extended systems is ongoing.

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III Analysis

ADF contains several unique analysis options, offering the possibility of gaining detailed understanding of the chemical problem at hand. These methods stress the underlying philosophy that the Kohn-Sham orbitals in DFT can be used for a ‘quantitative MO theory’ [4].

IIIa Molecule built from fragmentsADF and BAND analyze their results in terms of user-specified subsystems from which the total system is built. The program tells you how the ‘fragment orbitals’ (FO’s) of the chemically meaningful sub-units mix with FO’s on other fragments to combine to the final molecular orbitals (fig. 7).

Fig. 7 Analysis of the electronic structure of porphyrin rings in terms of 4 pyrrolic fragments, made possible by the

fragments option in ADF.

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IIIb Bond energy analysisADF calculates various chemically meaningful terms that add up to the bond energy, with an adaptation [5, 4] of Morokuma’s bond energy decomposition to the Kohn-Sham MO method. The individual terms are chemically intuitive quantities such as electrostatic energy, steric repulsion, Pauli repulsion, and orbital interactions. The latter are symmetry decomposed according to the Ziegler transition state method.

IIIc Advanced charge density analysisIn addition to Mulliken charge analysis, ADF calculates several atomic charges that do not share the flaws of Mulliken (strong basis set dependence). The multipole-derived charge analysis exactly reproduces dipole and higher multipole moments of the molecule. Other charge analysis methods (‘Voronoy deformation density’ and ‘Hirshfeld’) provide atomic charges that agree well with chemical intuition.

IIId Molecular symmetryADF uses the full molecular symmetry, including non-Abelian groups. The proper symmetry labels to orbitals, excitations, and vibrational modes are provided on output.

IIIe Third party analysis softwareThe SCM web site contains several pointers to third party software that can be used in combination with ADF. These include interfaces to the popular free graphical interfaces Molden and Molekel, an interface to Prof. Bader’s Atoms-in-Molecules (AIM) program, and an interface to a program that calculates the Electron Localization Function (ELF). The GENNBO executable from Prof. Weinhold’s Natural Bond Orbital package, NBO 5.0, is available in the ADF distribution.

Fig. 8 The energy decomposition

method in ADF allows for a

detailed understanding of

chemical bonding.

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IV Accuracy

ADF combines a set of unique technical features that ensure reliable and accurate calculations.

IVa Slater-type basis setsADF uses Slater-Type Orbitals (STO’s) as basis functions. These resemble the true atomic orbitals more closely than the more common Gaussian-Type Orbitals (GTO’s). Therefore, fewer STO’s than GTO’s are needed for a given level of accuracy. ADF has a database with thoroughly tested basis set files, ranging in quality from single-zeta to quadruple-zeta basis sets with various diffuse and polarization functions. They are available for all elements, including lanthanides and actinides. In the BAND program, numerical atomic orbitals are used in addition to Slater-type orbitals. Fig. 9 displays the systematic decrease in basis set error for bond energies when the basis set size is increased.

Fig. 9 The basis set error quickly falls off to a

negligible number if the basis set quality

is increased.

IVb Integration schemeADF and BAND use the unique Te Velde - Baerends [6] numerical integration scheme, in which the grid is automatically adapted to the available basis functions and to the number of significant digits demanded by the user through a single input parameter. It is straightforward to do very accurate integrations with far fewer points than in less highly developed schemes.

Improved Slater type basis sets

Decreased basis set errors(test on 200 diatomics)

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IVc Transition metal compounds and heavy elementsUsers recommend ADF for its ability to provide the same stability for complex transition metal compounds as for simpler systems containing only light atoms. The relativistic methods and basis sets in ADF enable treatment of molecules with very heavy elements (fig. 10).

The ADF approach removes the need for pseudopotential and effective core potential (ECP) approximations, even for lanthanides and actinides.

Fig. 10 A 100-atom Pt-complex can currently be handled easily on

a modern PC.

IVd Modern xc energy functionals and potentialsA variety of the most accurate modern (meta-)GGA and hybrid exchange-correlation (xc) energy functionals are all evaluated simultaneously in ADF (fig. 11). For reliable property calculations, improved xc potentials with correct asymptotic behavior, such as SAOP and GRAC, are available in ADF.

Fig. 11 The Voorhis-Scuseria energy functional yields an average error of only 3 kcal/mol

over the G2 test set. It clearly improves upon regular GGA functionals

(Meta) GGAs

Exc performance G2 test set

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V Efficiency, treatment of large molecules

One of the main complications that can arise in chemically relevant applications of DFT software is the treatment of large molecules. ADF has several qualities to enable treatment of such systems.

Va QM/MMFor truly large system sizes (more than a few hundred atoms), a mix of quantum mechanics and molecular mechanics (QM/MM) is often suitable if the major quantum effects are restricted to a certain part of the molecule (‘active site’). QM/MM calculations can be performed on much larger systems (fig. 12) than pure QM calculations, because the approximate MM calculations are very fast. Various standard force fields (SYBYL, Amber, UFF) are available.

Fig. 12 Reliable geometries can be

obtained for the active site in

copper azurin with the QM/MM

implementation in ADF [7].

Fig. 13 Good parallel speed-up up to 90 CPUs is

obtained on a simple pentium cluster in this

example [8].

Vb ParallelizationMost parts of ADF have been efficiently parallelized for both shared-memory and distributed memory systems, such as simple Linux clusters. For most standard types of calculation, including NMR, analytical Hessian, and TDDFT calculations, ADF approaches perfect parallel scaling fairly well, even for a significant number of CPU’s, as shown in (fig. 13).

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Vc Linear scaling / distance cut-offsBecause of the exponential spatial decay of the STO basis functions, ADF can easily exploit the fact that atoms that are far apart do not interact. This reduces the computational complexity from O(Natom

3) to O(Natom) for the most time-consuming parts of the calculation, leading to dramatic savings. This is shown in fig. 14 for the Fock matrix build.

Fig. 14 The new implementation displays linear scaling

with system size (lower curve) [9].

Vd Density fit and frozen core approximationA density fit procedure reduces the cost of the Coulomb potential evaluation. A frozen core approximation can be used to considerably reduce the computation time for systems with heavy nuclei, in a controlled manner.

Ve SymmetryFor symmetric molecules, ADF uses only a fraction of the computation time needed for asymmetric molecules of the same size. Symmetry is exploited by limiting the size of the numerical integration grid, the size of the matrices, as well as the number of matrix elements to be calculated.

Vf Single-CPU performance on various computer platformsSCM cooperates with most major hardware vendors to optimize performance of the ADF software for all popular computer platforms. This includes fine-tuning of the code for different compilers and hardware configurations. These efforts include various types of Linux clusters.

Scaling behavior forFock-matrix set-up

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with cut-offs scales as n1.0

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VI Technical information

VIa Supported platformsWe currently support a wide variety of modern Windows, Macintosh, Unix, and Linux platforms. These include Windows 98, 2000, NT, and XP (all with the free Cygwin Unix emulator), Mac OS X, Pentium/Itanium 2/Opteron/Athlon/Alpha with Linux, SGI, HP (including former Compaq), IBM, NEC, Fujitsu PrimePower, and SUN. The ADF-GUI is also supported on all these platforms. If your favorite platform is currently not supported, contact us about the possibility of porting ADF to this platform. As we provide precompiled executables, installation is straightforward. ADF uses either MPI or PVM for communication in parallel calculations.

VIb Source code availabilityThe ADF and BAND programs are written in Fortran90, with small parts in C. Although limited parts of the package are only distributed in binary form, the majority of the code for ADF and BAND is available. This makes it possible to implement your own extensions, and to check in detail what the program does. SCM actively encourages and facilitates cooperations with scientists who wish to expand the possibilities of the ADF package.

VIc Hardware requirementsThe amount of memory and disk space required depends strongly on the size of the molecule and the type of application. To give an indication, ADF may need a few hundred megabytes of disk capacity for bigger calculations. For BAND the disk storage requirements tend to be considerably higher. The programs may run in as little as 32Mb memory for moderately sized systems. Preferably, one has 128Mb or more available, or more than 512Mb in case of very large calculations (per CPU).

VId Documentation and supportA large set of well-documented test calculations is provided for ADF, BAND, and the separate property programs. User’s Guides, frequently-asked questions (FAQs), and installation manuals are available on our fully searchable web site. An ADF mailing list is available for communication between users. Further help is available from SCM: support@scm.com.

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VII Further information

Visit our web site http://www.scm.com for pricing and other information or send E-mail to info@scm.com, summarizing your research interests. We will then provide you with relevant information. Our web site contains scientific background information such as review papers, Ph.D. theses and links to the publication lists of some of the main academic development groups of ADF.

Further information on some of the main ADF development groups is available from their web sites: • Baerends group, Amsterdam http://www.chem.vu.nl/tc/index-en.html

• Ziegler group, Calgary http://www.cobalt.chem.ucalgary.ca/group/master.html

• Theoretical Chemistry group, Groningen http://theochem.chem.rug.nl

The review paper [10] entitled ‘Chemistry with ADF’ is available on the SCM web site.

VIII References

[1] E. van Lenthe, E.J. Baerends, and J.G. Snijders, J. Chem. Phys. 99, 4597 (1993)[2] A. Rosa, G. Ricciardi, E.J. Baerends, and S.J.A. van Gisbergen, J. Phys. Chem. A105, 3311 (2001)[3] F. Kootstra, P.L. de Boeij, H. Aissa, and J.G. Snijders, J. Chem. Phys. 114, 1860 (2001)[4] F.M. Bickelhaupt and E.J. Baerends, In: Rev. Comput. Chem.; K.B. Lipkowitz and D.B. Boyd, Eds.; Wiley, New York, 2000, Vol. 15, p.1-86[5] T. Ziegler and A. Rauk, Inorg. Chem. 18, 1558 (1979)[6] G. te Velde and E.J. Baerends, J. Comput. Phys. 99 (1), 84 (1992)[7] Ph.D. thesis M. Swart, available from the SCM web site, picture made with MolScript[8] S.J.A. van Gisbergen, C. Fonseca Guerra, and E.J. Baerends, J. Comput. Chem. 21, 1511 (2000)[9] C. Fonseca Guerra, J.G. Snijders, G. te Velde, and E.J. Baerends, Theor. Chem. Acc. 99, 391 (1998)[10] G. te Velde, F.M. Bickelhaupt, S.J.A. van Gisbergen, C. Fonseca Guerra, E.J. Baerends, J.G. Snijders, T. Ziegler, ‘Chemistry with ADF’, J. Comput. Chem. 22, 931-967 (2001)

The ADF authors currently include: E.J. Baerends, J. Autschbach, A. Bérces, C. Bo, P.L. de Boeij, P.M. Boerrigter,

L. Cavallo, D.P. Chong, L. Deng, R.M. Dickson, D.E. Ellis, L. Fan, T.H. Fischer, C. Fonseca Guerra, S.J.A. van

Gisbergen, J.A. Groeneveld, O.V. Gritsenko, M. Grüning, F.E. Harris, P. van den Hoek, H. Jacobsen, G. van Kessel,

F. Kootstra, E. van Lenthe, V.P. Osinga, S. Patchkovskii, P.H.T. Philipsen, D. Post, C.C. Pye, W. Ravenek, P. Ros,

P.R.T. Schipper, G. Schreckenbach, J.G. Snijders, M. Solà, M. Swart, D. Swerhone, G. te Velde, P. Vernooijs,

L. Versluis, O. Visser, E. van Wezenbeek, G. Wiesenekker, S.K. Wolff, T.K. Woo and T. Ziegler.

Scientific Computing & Modelling NVVrije Universiteit, Theoretical ChemistryDe Boelelaan 10831081 HV AmsterdamThe Netherlands

http://www.scm.cominfo@scm.comT +31 (0)20 444 76 26F +31 (0)20 444 76 29

Our reseller in Japan is Ryoka Systems Inc.(http://www.rsi.co.jp/science.html or E-mail: adf@cubs.bio.rsi.co.jp).

Contact SCM for information on local resellers in China, India, Germany/Switzerland/Austria, and California.

Our US-based partner company Parallel Quantum Solutions (http://www.pqs-chem.com) offers Linux cluster hardware with ADF pre-installed.

© 2004 SCM

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