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. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001

Chemistry with ADF

https://zenodo.org/record/1258869/files/article.pdf

NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations

"Chemists familiar with conventional quantum mechanics will applaud and benefit greatly from this particularly instructive, thorough and clearly written exposition of density functional theory: its basis, concepts, terms, implementation, and performance in diverse applications. Users of DFT for structure, energy, and molecular property computations, as well as reaction mechanism studies, are guided to the optimum choices of the most effective methods. Well done!" Paul von RaguE Schleyer "A conspicuous hole in the computational chemist's library is nicely filled by this book, which provides a wide-ranging and pragmatic view of the subject.[...It] should justifiably become the favorite text on the subject for practioneers who aim to use DFT to solve chemical problems." J. F. Stanton, J. Am. Chem. Soc. "The authors' aim is to guide the chemist through basic theoretical and related technical aspects of DFT at an easy-to-understand theoretical level. They succeed admirably." P. C. H. Mitchell, Appl. Organomet. Chem. "The authors have done an excellent service to the chemical community. [...] A Chemist's Guide to Density Functional Theory is exactly what the title suggests. It should be an invaluable source of insight and knowledge for many chemists using DFT approaches to solve chemical problems." M. Kaupp, Angew. Chem.

A Chemist's Guide to Density Functional Theory

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...

Relativistic total energy using regular approximations

https://th.fhi-berlin.mpg.de/site/uploads/Publications/CPC-180-2175-2009.pdf

Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals

We present a new relativistic formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors. The formulation makes use of gauge-including atomic orbitals and is based on density functional theory. The relativistic effects are included by making use of the zeroth-order regular approximation. This formulation has been implemented and the 199Hg NMR shifts of HgMe2, HgMeCN, Hg(CN)2, HgMeCl, HgMeBr, HgMeI, HgCl2, HgBr2, and HgI2 have been calculated using both experimental and optimized geometries. For experimental geometries, good qualitative agreement with experiment is obtained. Quantitatively, the calculated results deviate from experiment on average by 163 ppm, which is approximately 3% of the range of 199Hg NMR. The experimental effects of an electron donating solvent on the mercury shifts have been reproduced with calculations on HgCl2(NH3)2, HgBr2(NH3)2, and HgI2(NH3)2. In addition, it is shown that the mercury NMR shieldings are sensitive to geometry with changes for HgCl2 of a...

/pdf/density-functional-calculations-of-nuclear-magnetic-1f8gmicb8a.pdf

Density functional calculations of nuclear magnetic shieldings using the zeroth-order regular approximation (ZORA) for relativistic effects: ZORA nuclear magnetic resonance

Relativistic time dependent density functional calculations have been performed on the excited states of the M(CO)6 (M = Cr, Mo, W) series. Our results, in agreement with previous density functional1 and ab initio2 calculations on Cr(CO)6, indicate that in all members of the series the lowest excited states in the spectra do not correspond to ligand field (LF) excitations, as has been accepted in the past. Instead they correspond to charge transfer (CT) states. The LF excitations are calculated at much higher energy than suggested by the original assignment by Beach and Gray3 and at different energy along the M(CO)6 series, being much higher in the heavier carbonyls than in Cr(CO)6. These results lead to a definitive reassessment of the role of the LF states in the photochemical dissociation of the metal−CO bonds in the M(CO)6 series, suggesting that the experimentally observed photodissociation of the M−CO bond upon irradiation into the lowest energy bands occurs in the heavier carbonyls, as it does in C...

Electronic Spectra of M(CO)6 (M = Cr, Mo, W) Revisited by a Relativistic TDDFT Approach

A scheme of approximation of the Kohn-Sham exchange potential ${\mathit{v}}_{\mathit{x}}$ is proposed, making use of a partitioning of ${\mathit{v}}_{\mathit{x}}$ into the long-range Slater ${\mathit{v}}_{\mathit{S}}$ and the short-range response ${\mathit{v}}_{\mathrm{resp}}$ components. A model potential ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ has been derived from dimensional arguments. It possesses the proper short-range behavior and the atomic-shell stepped structure characteristic for ${\mathit{v}}_{\mathrm{resp}}$. When combined with the accurate ${\mathit{v}}_{\mathit{S}}$, ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ provides an excellent approximation to the exchange potential of the optimized potential model ${\mathit{v}}_{\mathit{x}}^{\mathrm{OPM}}$. With the generalized-gradient approximation to ${\mathit{v}}_{\mathit{S}}$ ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ provides an efficient density-functional-theory approach that fits closely the form of the accurate exchange potential and yields reasonably accurate exchange and total energies as well as the energy of the highest occupied orbital.

/pdf/self-consistent-approximation-to-the-kohn-sham-exchange-hz49356y1h.pdf

Self-consistent approximation to the Kohn-Sham exchange potential.

In this paper we first describe the implementation of the zeroth-order regular approximation (ZORA) for relativistic effects in our density-functional program for extended systems. The ZORA formalism affords approximations, which are discussed and tested, that reduce the computational effort of scalar relativistic calculations to that of nonrelativistic calculations, the inclusion of spin-orbit coupling requiring additional effort. Second, we present the outcome of nonrelativistic, scalar relativistic, and spin-orbit coupling calculations on the adsorption energy of CO on the (111) surfaces of Ni, Pd, and Pt. Relativity has a modest effect for CO on Pd, but proves to be essential for CO on Pt. The relativistic correction for the CO/Pt adsorption energy is as large as 70% at the scalar relativistic level and 55% when including spin-orbit coupling. In addition, relativity changes the preferred adsorption site for CO/Pt from hollow to top. We have examined the effects of spin polarization and of different exchange-correlation functionals, i.e., the local-density approximation (LDA) versus two generalized gradient approximations (GGA). The GGA's correct the severe overbinding by LDA of CO to the metal surfaces, and yield good agreement with experiment for adsorption energies and sites.

/pdf/relativistic-calculations-on-the-adsorption-of-co-on-the-111-3iip18t3sv.pdf

E. van Lenthe

Papers

Density functional calculations of nuclear magnetic shieldings using the zeroth-order regular approximation (ZORA) for relativistic effects: ZORA nuclear magnetic resonance

Electronic Spectra of M(CO)6 (M = Cr, Mo, W) Revisited by a Relativistic TDDFT Approach

Self-consistent approximation to the Kohn-Sham exchange potential.

Relativistic calculations on the adsorption of CO on the (111) surfaces of Ni, Pd, and Pt within the zeroth-order regular approximation

The ZORA formalism applied to the Dirac-Fock equation