ABSTRACT:We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn-Sham molecular orbital (MO) theory, and illustrate the power of the Kohn-Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the "Activation-strain TS interaction" (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena.

mIt is shown how the regularized two-component while many basis functions are required. If one wants to use a variational technique, one has to make sure that no spurious solutions appear. This can be done using so-called kinetically balanced basis sets, but, then, one needs an even larger basis for the small component than for the large component of the Dirac spinor. An attractive alternative is to transform the Dirac Hamiltonian into two-component form. We refer to the discussion by Kutzelnigg 111 for a detailed exposition of the various approaches and the difficulties that they give rise to in the form of divergent terms and singularities at the nuclei.The source of the difficulties is that the expansions that are being used implicitly or explicitly rely on an expansion in ( E -V )/2mc2, which is invalid for particles in a Coulomb potential, where there will always be a region of space (close to the

In this paper we will discuss relativistic total energies using the zeroth order regular approximation (ZORA). A simple scaling of the ZORA one-electron Hamiltonian is shown to yield energies for the hydrogenlike atom that are exactly equal to the Dirac energies. The regular approximation is not gauge invariant in each order, but the scaled ZORA energy can be shown to be exactly gauge invariant for hydrogenic ions. It is practically gauge invariant for many-electron systems and proves superior to the (unscaled) first order regular approximation for atomic ionization energies. The regular approximation, if scaled, can therefore be applied already in zeroth order to molecular bond energies. Scalar relativistic density functional all-electron and frozen core calculations on diatomics, consisting of copper, silver, and gold and their hydrides are presented. We used exchange-correlation energy functionals commonly used in nonrelativistic calculations; both in the local-density approximation (LDA) and including density-gradient (‘‘nonlocal’’) corrections (NLDA). At the NLDA level the calculated dissociation energies are all within 0.2 eV from experiment, with an average of 0.1 eV. All-electron calculations for Au2 and AuH gave results within 0.05 eV of the frozen core calculations.

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In this paper we will calculate the effect of spin-orbit coupling on properties of closed shell molecules, using the zero-order regular approximation to the Dirac equation. Results are obtained using density functionals including density gradient corrections. Close agreement with experiment is obtained for the calculated molecular properties of a number of heavy element diatomic molecules.

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One of the most important steps in a Kohn-Sham (KS) type density functional theory calculation is the construction of the matrix of the KS operator (thè`F ock'' matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchangecorrelation and Coulomb potentials within a particular implementation (the Amsterdam density functional, ADF, code) of the KS method. In the ADF scheme the matrix elements are completely determined by 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development is desirable for the treatment of the Coulomb potential.

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