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

I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

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Conceptual density functional theory.

Kohn-Sham Density Functional Theory: Predicting and Understanding Chemistry

Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared with coupling constants deduced from a number of different experimental techniques. It is discussed why ${\mathrm{A}}_{3}$${\mathrm{C}}_{60}$ are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$, describing the effect of the Coulomb repulsion on the superconductivity, as well as possible electronic mechanisms for the superconductivity, are reviewed. The calculation of various properties within the Migdal-Eliashberg theory and attempts to go beyond this theory are described.

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Superconductivity in fullerides

Atomic charges were obtained from ab initio molecular orbital calculations using a variety of procedures to compare them and assess their utility Two procedures based on the molecular orbitals were examined, the Mulliken population analysis and the Weinhold–Reed Natural Population Analysis Two procedures using the charge density distribution were included; the Hirshfeld procedure and Bader's Atoms in Molecules method Charges also were derived by fitting the electrostatic potential (CHELPG) and making use of the atomic polar tensors (GAPT) The procedures were first examined for basis set independence, and then applied to a group of hydrocarbons The dipole moments for these molecules were computed from the various atomic charges and compared to the total SCF dipole moments This was followed by an examination of a series of substituted methanes, simple hydrides, and a group of typical organic compounds such as carbonyl derivatives, nitriles, and nitro compounds In some cases, the ability of the charges to reproduce electrostatic potentials was examined © John Wiley & Sons, Inc

Comparison of atomic charges derived via different procedures

Accurate and efficient integration of the electron density function over arbitrary regions has been previously achieved by exploiting a separation of variables. Recently, a computer program has been written that calculates ρ, ρ, and ∇2ρ in an expeditious fashion, taking advantage of the separation of variables in the electron density function. Accurate integrations of ∇2ρ over arbitrary regions can also be accomplished. The structure of the program is suited especially to vector processors. As a result of the efficiencies of these programs, functions of the electron density, such as the density itself, the surrounding electrostatic potential, ∇ρ, and ∇2ρ have been calculated in three dimensions. Results of calculations for nitrated cubanes are presented illustrating how the effects of the nitro groups are manifested in the electron density and associated properties.

Some methods and applications of electron density distribution analysis

Calculs a l'aide d'une variante simple de l'algorithme de Streitweiser pour evaluer la densite electronique projetee sur un plan unique

Electron density distribution analysis for nitromethane, nitromethide, and nitramide

Twenty-three organolithium compounds were analyzed by using the topological theory of molecular structure. The geometry of each compound was first optimized, making use of the 3-21G basis set. Then integrated lithium charges and quantities characterizing the carbon-lithium bond critical point, such as rho/sub c/ (C-Li), del/sup 2/rho/sub c/(C-Li), and the local energy density, were calculated. The results confirm the nature of the carbon-lithium bond to be primarily ionic. Bond path networks of these compounds were also calculated and proved surprising. Coordination numbers of lithium, as assigned by the topological theory, range from one to four. Similarly defined coordination numbers of carbon range as high as nine. Unexpectedly, some putatively bridging lithiums are not bridging in a topological sense. Additional unexpected features of the bond path networks are bond paths connecting essentially neutral carbons with lithiums and bond paths connecting highly negatively charged carbons that are widely separated. No lithium-lithium bond paths are found. Finally, unstable topological structures occur at potential energy minima. Polarization of electrons toward what are essentially lithium cations accounts for the carbon-lithium bond paths observed.

Bond paths and bond properties of carbon-lithium bonds

Semiempirical modified-neglect-of-differential-overlap (MNDO) quantum chemistry calculations are performed for the negative ions of an isolated ${\mathrm{C}}_{60}$. The value computed for the first electron affinity is in excellent agreement with experiment. MNDO predictions of the energies of the low-lying states of ${\mathrm{C}}_{60}^{2\mathrm{\ensuremath{-}}}$ and ${\mathrm{C}}_{60}^{3\mathrm{\ensuremath{-}}}$ allow us to extract an effective on-site repulsion ${\mathit{U}}_{0}$\ensuremath{\sim}3 eV, and a direct exchange interaction K\ensuremath{\sim}50 meV for ${\mathrm{C}}_{60}$. These values are used to estimate the effective on-site repulsion and dielectric constant of solid ${\mathrm{C}}_{60}$, with results in good agreement with experiment. A similar approach is used to determine ``partially'' screened parameters appropriate to a model of ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$. We find that both the on-site (${\mathit{U}}_{0}$\ensuremath{\sim}1.3 eV) and near-neighbor (V\ensuremath{\sim}0.3 eV) Coulomb terms are significant relative to the bandwidth (W\ensuremath{\sim}0.6 eV).

Coulomb and exchange interactions in C60n

The isomeric pairs 1-picryl-1,2,3-triazole, 2-picryl-1,2,3-triazole and 4-nitro-1-picryl-1,2,3-triazole, 4-nitro-1-picryl-1,2,3-triazole differ dramatically in their impact sensitivity. Since these pairs of compounds have identical oxygen balance this strongly suggests that there is a difference in the decomposition mechanism. The authors report here the x-ray crystal structure, molecular orbital calculations, and {sup 13}C and {sup 1}H NMR spectra of the four compounds. The picryl substituents are essentially identical in all four cases. The most significant structural difference in the X-ray structures and in the molecular orbital calculations is a decrease in the N2-N3 bond length, accompanied by a lengthening of the adjacent bonds, in the two 1-picryl isomers relative to the corresponding bond lengths in the 2-picryl isomers. Molecular orbital calculations show that this leads to a low activation energy for the elimination of N{sub 2} from the 1-picryl isomers. They suggest that this initial step then leads to a reactive intermediate and is responsible for the large difference in sensitivity.

Structural basis of the impact sensitivities of 1-picryl-1,2,3-triazole, 2-picryl-1,2,3-triazole, 4-nitro-1-picryl-1,2,3-triazole, and 4-nitro-2-picryl-1,2,3-triazole

James P. Ritchie

Papers

Some methods and applications of electron density distribution analysis

Electron density distribution analysis for nitromethane, nitromethide, and nitramide

Bond paths and bond properties of carbon-lithium bonds

Coulomb and exchange interactions in C60n

Structural basis of the impact sensitivities of 1-picryl-1,2,3-triazole, 2-picryl-1,2,3-triazole, 4-nitro-1-picryl-1,2,3-triazole, and 4-nitro-2-picryl-1,2,3-triazole