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.

An approximate Kohn-Sham exchange-correlation potential xc SAOP is developed with the method of statistical averaging of ͑model͒ orbital potentials ͑SAOP͒ and is applied to the calculation of excitation energies as well as of static and frequency-dependent multipole polarizabilities and hyperpolarizabilities within time-dependent density functional theory ͑TDDFT͒. xc SAOP provides high quality results for all calculated response properties and a substantial improvement upon the local density approximation ͑LDA͒ and the van Leeuwen-Baerends ͑LB͒ potentials for the prototype molecules CO, N 2 , CH 2 O, and C 2 H 4 . For the first three molecules and the lower excitations of the C 2 H 4 the average error of the vertical excitation energies calculated with xc SAOP approaches the benchmark accuracy of 0.1 eV for the electronic spectra.

No abstract

We report the implementation of the computation of rotatory strengths, based on time-dependent density functional theory, within the Amsterdam Density Functional program. The code is applied to the simulation of circular dichroism spectra of small and moderately sized organic molecules, such as oxiranes, aziridines, cyclohexanone derivatives, and helicenes. Results agree favorably with experimental data, and with theoretical results for molecules that have been previously investigated by other authors. The efficient algorithms allow for the simulation of CD spectra of rather large molecules at a reasonable accuracy based on first-principles theory. The choice of the Kohn-Sham potential is a critical issue. It is found that standard gradient corrected functionals often yield the correct shape of the spectrum, but the computed excitation energies are systematically underestimated for the samples being studied. The recently developed exchange-correlation potentials ''GRAC'' and ''SAOP'' often yield much better agreement here with experiments for the excitation energies. The rotatory strengths of individual transitions are usually improved by these potentials as well.

Shape corrections to the standard approximate Kohn-Sham exchange-correlation ͑xc͒ potentials are considered with the aim to improve the excitation energies ͑especially for higher excitations͒ calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection ͑GRAC͒ of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends ͑LB͒ are seamlessly connected to the ͑shifted͒ xc potential of Becke and Perdew ͑BP͒ with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N 2 , CO, CH 2 O, C 2 H 4 , C 5 NH 5 , C 6 H 6 , Li 2 , Na 2 , K 2 . The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of ͑model͒ orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine ''local'' density functional with an analytical representation.