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.

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Oxygen vacancies in transition metal and rare earth oxides: Current state of understanding and remaining challenges

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Studies in Surface Science and Catalysis

ion step. The reactivity of pMMO has been also explored by Chan,525 by means of DFT calculations on small models of Figure 116. Nonradical mechanism proposed in the Yoshizawa model of sMMO. Figure 117. Mononuclear and dinuclear models of the copper active sites of pMMO. CsH Bond Activation in Transition Metal Species Chemical Reviews, 2010, Vol. 110, No. 2 813

C-H bond activation in transition metal species from a computational perspective

Results presented in this account show that the quantum-chemical description of intermediate complexes formed in the course of the catalytic reactions may supply valuable information concerning catalysis. Modification of the reactivity of different bonds of the reacting molecule as the result of its interaction with the active center of the catalyst, have been found. This may contribute to an important degree to the understanding of the mechanism of the catalytic reaction and to identification of factors influencing its selectivity. At present, exact discussion of the interaction of an adsorbed molecule with the group of atoms of the solid forming the active center is not yet possible, and many approximations must be introduced. The model choosen and the quantum-chemical method used depends on the particular problem to be solved. Advantages and limitations of various quantum chemical methods usually used to solve catalytic problems are summarized. It may be hoped that with the development of quantum chemistry on one hand, and with further improvement in the knowledge of the mechanism of elementary acts in catalysis on the other hand, it will become possible to give a full description of the interactions between the reacting molecules and the catalyst as a basis formore » the development of the theory of catalysis.« less

Quantum-chemistry and catalysis in oxidation of hydrocarbons

Copyright (c) 1997 Elsevier Science B.V. All rights reserved. Structure and properties of V 2 O 5 are described and the role of three types of oxygen atoms present in the lattice: vanadyl oxygen atoms O(1) coordinated only to one vanadium atom, and bridging oxygen atoms O(2) and O(3) coordinated to two and three vanadium atoms, respectively, is discussed. Equilibration of gas phase oxygen with vanadium oxides results in the formation of the intrinsic defect structure of V 2 O 5 consisting of oxygen vacancies. Discussion of the properties of vacancies as deduced from measurements of electrical conductivity, EPR and IR spectra and the stability of different oxygen vacant sites as obtained from quantum-chemical calculations is given. Mechanism of the reduction of V 2 O 5 through crystallographic shear, resulting in the formation of V 6 O 13 or V 4 O 9 , is illustrated. It is shown that because of a pronounced anisotropy of V 2 O 5 crystal structure sensitivity of catalytic reactions appears. Two types of crystal planes are exposed. The (0 1 0) basal plane has all chemical bonds almost fully saturated. The non-bonding d-orbitals of V ions have the LUMO character and act as Lewis acid sites, whereas the lone electron pairs of bridging oxygen atoms have the HOMO character and behave as Lewis basic sites. On the (1 0 0) and (0 0 1) planes cleavage leaves coordinatively unsaturated vanadium and oxygen ions, which develop Bronsted acid-base interactions with reacting molecules, causing the heterolytic chemisorption. Oxygen vacancies in the lattice are replenished through oxidation by gas phase oxygen, which sometimes is considered as oxygen chemisorption.

Vanadium pentoxide I. Structures and properties

Density-functional theory (DFT) studies are performed to examine geometric and electronic properties of orthorhombic bulk ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ as well as of its (010) oriented surface. Electronic states, total energies, as well as atom forces (used to obtain equilibrium geometries) are computed with the ab initio full-potential linear augmented plane wave method. The ${\mathrm{V}}_{2}{\mathrm{O}}_{5}(010)$ surface is modeled by periodic single layers in a repeated slab geometry, which is justified by the weak electronic interlayer coupling found in the bulk calculations. The electronic structure of the ${\mathrm{V}}_{2}{\mathrm{O}}_{5}(010)$ single-layer slabs, represented by their valence densities of states (DOS) and its atom contributions, is compared with results of bulk ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ and with previous results obtained by DFT surface cluster studies. The comparison yields good qualitative agreement between the different approaches, which confirms the local nature of interatomic binding in ${\mathrm{V}}_{2}{\mathrm{O}}_{5}.$ Further, the computed valence DOS is used to interpret recent experimental results from photoemission on ${\mathrm{V}}_{2}{\mathrm{O}}_{5}(010),$ which suggests that differently coordinated oxygen sites at the surface can be identified in the spectrum. Thus, ${\mathrm{V}}_{2}{\mathrm{O}}_{5}(010)$ photoemission spectra may be used to monitor the participation of oxygen ions in respective surface reactions.

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Geometric and electronic structure of vanadium pentoxide: A density functional bulk and surface study

Properties of oxygen sites at the MoO_3(010) surface: density functional theory cluster studies and photoemission experiments

Sixth International Symposium. Effects of surface heterogeneity in adsorption and catalysis on solids—ISSHAC VI, Zakopane, Poland, 28th August-2nd September 2006

Malgorzata Witko

Papers

Quantum-chemistry and catalysis in oxidation of hydrocarbons

Vanadium pentoxide I. Structures and properties

Geometric and electronic structure of vanadium pentoxide: A density functional bulk and surface study

Properties of oxygen sites at the MoO_3(010) surface: density functional theory cluster studies and photoemission experiments

Sixth International Symposium. Effects of surface heterogeneity in adsorption and catalysis on solids—ISSHAC VI, Zakopane, Poland, 28th August-2nd September 2006