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.

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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.

Two three-dimensional numerical integration schemes are presented for molecular integrands such as matrix elements of one-electron operators occurring in the Fock operator and expectation values of oneelectron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product-Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8-10 digits) may be obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.