Power for Quantum Tools Chemists ADF The universal density functional package for chemists! 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!

1 I Introduction

Ia ADF The 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 groups Historically, 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 Community The 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.

1 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 frequencies ADF 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.

2 3 IIb Molecular properties An 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.

B Q

M

Fig. 1 Gas phase optical absorption spectrum "L" N

of Ni-octaethylporphyrin. Spectra of Optical density (metal) porphyrins and related compounds 200 300 400 500 600 700 800 can be understood in detail through ADF Wavelength (nm) calculations [2].

IIc Modeling solvents, proteins, and other environments The 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.

2 3 IId Graphical User Interface A 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).

Fig. 2 The ADFinput module of the ADF-GUI allows users to build or import a molecule, and select the appropriate options rapidly.

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. 4 The ADFspectra module can display various types of molecular spectra calculated by ADF.

4 5 IIe Polymers, slabs, and solids with BAND BAND 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).

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 32 (fig. 6). Further work on magnetic and 24 electric properties of extended systems 16 is ongoing. 8

0 1.5 3 4.5 6

Fig. 6 Comparison of theoretical and experimental Non relativistic (NR) Scalar Relativistic (SR) results for the imaginary part of the Experiment dielectric function of solid InSb [3].

4 5 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 fragments ADF 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.

6 7 IIIb Bond energy analysis ADF 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.

Fig. 8 The energy decomposition method in ADF allows for a detailed understanding of chemical bonding.

IIIc Advanced charge density analysis In 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 symmetry ADF 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 software The 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.

6 7 IV Accuracy

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

IVa Slater-type basis sets ADF 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.

Decreased basis set errors (test on 200 diatomics)

1.4

1.2

1

0.8

0.6

0.4

Av. error in bond energy (eV) 0.2

0 Fig. 9 The basis set error quickly falls off to a DZ DZP TZP TZ2P QZ3P Improved Slater type basis sets negligible number if the basis set quality is increased.

IVb Integration scheme ADF 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.

8 9 IVc Transition metal compounds and heavy elements Users 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 potentials A 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.

Exc performance G2 test set

50 45 40 35 30 25 20 15 10 Error (Kcal/mol) Max. err. 5 Av. err. 0 VS98 VT97 PKZB HCTH/402 BmTau1 BLYP KCIS BOP revPBE BP PW91

(Meta) GGAs

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

8 9 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/MM For truly large system sizes (more than a few hundred Fig. 12 Reliable geometries can be atoms), a mix of quantum mechanics and molecular obtained for the active site in mechanics (QM/MM) is often suitable if the major copper azurin with the QM/MM quantum effects are restricted to a certain part of the implementation in ADF [7]. 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.

Vb Parallelization Parallel scaling TDDFT Most parts of ADF have been efficiently calculation on (H2O)30 parallelized for both shared-memory and

80 distributed memory systems, such as simple Linux clusters. For most standard 60 types of calculation, including NMR, analytical Hessian, and TDDFT calculations, Speed-up 40 ADF approaches perfect parallel scaling fairly well, even for a significant number of 20 CPU’s, as shown in (fig. 13).

20 40 60 80 Number of nodes

Ideal, linear speed-up Matrix elements TDDFT code Set-up Fock elements in SCF Fig. 13 Good parallel speed-up up to 90 CPUs is SCF cycle obtained on a simple pentium cluster in this Total TDDFT code example [8].

10 11 Vc Linear scaling / distance Scaling behavior for cut-offs Fock-matrix set-up Because of the exponential spatial decay 35x103 standard of the STO basis functions, ADF can 30 easily exploit the fact that atoms that are 25 far apart do not interact. This reduces the 20 3 computational complexity from O(Natom ) 15 to O(N ) for the most time-consuming atom 10 parts of the calculation, leading to dramatic 5 savings. This is shown in fig. 14 for the Fock improved 0 matrix build. 200 400 600 800 number of atoms

without cut-offs scales as n3.2 Fig. 14 The new implementation displays linear scaling with cut-offs scales as n1.0 with system size (lower curve) [9].

Vd Density fit and frozen core approximation A 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 Symmetry For 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 platforms SCM 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.

10 11 VI Technical information

VIa Supported platforms We 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 availability The 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 requirements The 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 support A 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: [email protected].

12 13 VII Further information

Visit our web site http://www.scm.com for pricing and other information or send E-mail to [email protected], 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.

12 13 Scientific Computing & Modelling NV Vrije Universiteit, Theoretical Chemistry De Boelelaan 1083 1081 HV Amsterdam The Netherlands http://www.scm.com [email protected] T +31 (0)20 444 76 26 F +31 (0)20 444 76 29

Our reseller in Japan is Ryoka Systems Inc. (http://www.rsi.co.jp/science.html or E-mail: [email protected]).

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 B-ADF-04-03 Bernards/Visser communicatie bv - Leiden - The Netherlands Netherlands The - Leiden - bv communicatie Bernards/Visser