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 topological and energetic properties of the electron density distribution ρ(r) of the isolated pairwise H⋯F interaction have been theoretically calculated at several geometries (0.8<d<2.5 A) and represented against the corresponding internuclear distances. From long to short geometries, the results presented here lead to three characteristic regions, which correspond to three different interaction states. While the extreme regions are associated to pure closed-shell (CS) and shared-shell (SS) interactions, the middle one has been related to the redistribution of ρ(r) between those electronic states. The analysis carried out with this system has permitted to associate the transit region between pure CS and SS interactions to internuclear geometries involved in the building of the H–F bonding molecular orbital. A comparative analysis between the formation of this orbital and the behavior of some characteristic ρ(r) properties has indicated their intrinsic correspondence, leading to the definition of a bond degree parameter [BD=HCP/ρCP; HCP and ρCP being the total electron energy density and the electron density value at the H⋯F (3,−1) critical point]. Along with the isolated pairwise H⋯F interaction, 79 X–H⋯F–Y (neutral, positively and negatively charged) complexes have been also theoretically considered and analyzed in terms of relevant topological and energetic properties of ρ(r) found at their H⋯F critical points. In particular, the interaction energies of X–H⋯F–Y pure CS interactions have been estimated by using the bond degree parameter. On the other hand, the [F⋯H⋯F]− proton transfer geometry has been related to the local maximum of the electron kinetic energy density (GCP)max.

From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving X–H⋯F–Y systems

The theoretical description of charge distribution, and related properties, such as chemical reactivity descriptors of chemical compounds, has greatly benefited from the development of density functional theory (DFT) methods. Indeed, most concepts stemmed from DFT but, up to now, they have been used mostly within semiempirical MO methods, Hartree–Fock, or post-Hartree–Fock methods. During the last decade, however, DFT has enabled theoretical chemistry to predict accurately structures and energetics of clusters and molecules. Therefore, more attention should also now be paid to these reactivity descriptors determined directly from DFT calculations. In this work, chemical reactivity is explored in DFT through a functional Taylor expansion of energy that introduces various energy derivatives of chemical significance. This review summarizes their main features and examines the limitations of some indexes presently used for the characterization of reactivity. Also, several perspectives are given. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 129–154, 1999

Chemical reactivity indexes in density functional theory

Hydrogen bonding is an important interaction playing a key role in chemical, physical, and biochemical processes. One can mention numerous examples such as the role of hydrogen bonding in enzymatic catalysis, arrangement of molecules in crystals, crystal engineering, proton transfer reactions, and also its important role in life processes. Hence, its nature is often the subject of investigations and polemics. One of the first definitions of hydrogen bonding was formulated by Pauling who stated that “under certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms, instead of only one, so that it may be considered to be acting as a bond between them. This is called the hydrogen bond”. Pauling also pointed out that the hydrogen atom is situated only between the most electronegative atoms and it usually interacts much stronger with one of them. The latter interaction is a typical covalent bond (A-H). The interaction between hydrogen and another electronegative atom is much weaker and mostly electrostatic in nature; it is a nonbonding interaction (H 3 3 3B). This system is often designated as AH 3 3 3B where the B-center (acceptor of proton) should possess at least one lone electron pair; A-H is called the protondonating bond. Pauling stated that sometimes the H 3 3 3B interaction possesses characteristics of the covalent bond. The [FHF] ion is an example where the proton is inserted between two negative fluorine ions, accurately in the middle of the F 3 3 3 F distance. Hence, both H 3 3 3 F interactions are equivalent. This is in line with an early conclusion of Lewis that “an atom of hydrogen may at times be attached to two electron pairs of two different atoms” and with the statement of Latimer and Rodebush that “the hydrogen nucleus held by two octets constitutes a weak bond”. The latter statements correspond to recent studies on proton bound homodimers, that is, systems where the proton is inserted between two closed-shell moieties and where it often interacts equivalently with both of them. Chan and co-workers analyzed recently what factors determine whether the protonbound homodimer has a symmetric or an asymmetric hydrogen bond. In the other study, it is discussed what conditions should be fulfilled for the proton situated accurately in the midpoint of the donor-acceptor distance. The high level calculations up to CCSD(T)/6-311þþ(3df,3pd)//CCSD/6-311þþ(3df,3pd) were performed on the [FHF] ion and systems with O-H 3 3 3O or N-H 3 3 3N hydrogen bonds. The latter study is supported by the experimental X-ray and neutron diffraction data because there are numerous crystal structures with short O-H 3 3 3O hydrogen bonds and the proton situated in the central position or nearly so. Also recently, homogeneous and heterogeneous short and strong hydrogen bonds (SSHBs) as well as the proton bound homodimers were analyzed theoretically at MP2/aug-ccpVDZ þ diffuse(2s,2p) level. Among various topics, the matter was raised if hydrogen bonding is an electrostatic or covalent interaction. The following question arises: what does the covalency of hydrogen bonding mean? The decomposition of the interaction energy is useful to analyze hydrogen bonding and particularly to answer the latter question. One of the first decomposition schemes introduced is one of Morokuma and Kitaura, where the interaction energy is calculated within the Hartree-Fock one-electron approximation and it is decomposed into the following components: the exchange energy, EEX (arising from repulsive forces), and the other components, which might be a result of attractive forces: the polarization energy, EPL, the charge transfer energy, ECT, and the electrostatic energy, EES. If a method is applied where the correlation of electrons is taken into account, then the correlation energy may be included. One of the most important attractive components of the correlation energy is the dispersive energy. Different H-bonded systems were analyzed early by Umeyama and Morokuma who stated that: “The energy components are strongly distance dependent. At a relatively small separation, ES, CT, and PL can all be important attractive components, competing against a large EX repulsion. At larger distances for the same complex the short-range attractions CT and PL are usually unimportant and ES is the only important attraction.” One can see that the “covalency of interaction”may be connected with short H 3 3 3B distances where terms other than the electrostatic attractive one are important.

What is the covalency of hydrogen bonding

Among many various kinds of molecular interactions, the H-bond has a special position. The term is ubiquitous in the world that surrounds us, but also it is often applied in different ways. The H-bond is of great importance in natural sciences. This relates particularly to biological aspects, such as molecular recognition that could be a basis for the creation of life,1-4 formation of higher order structures of peptides and nucleic acids,5 and biochemical processes, particularly the enzymes catalyzed.6,7 One can say that the H-bond plays a double role in biological systems: on one hand, as a relatively strong directional interaction, it leads to relatively stable supramolecular structures, and on the other hand, because of dynamic features of the proton, it is an active site for initiation of chemical reactions. H-bonds are the source of specific properties of associated liquids, with water being the most popular among them.8 Water as a medium in which life was most probably created is saturated by H-bonds with highly mobile protons in between, even in the solid state.9 In many crystal lattices of organic compounds, the H-bonds are a decisive factor governing packing.10 In designing new interesting crystal structures, which is the subject of fast developing crystal engineer* To whom correspondence should be addressed. E-mail: slagra@ uni.lodz.pl or slagra@ccmsi.us. Fax: +48-42-6790447. 3513 Chem. Rev. 2005, 105, 3513−3560

Interrelation between H-bond and Pi-electron delocalization.

The variation with the intermolecular distance of features in hydrogen bond (HB) dimers dependent on the electron density ρ(r) are studied in four complexes representative of weak/medium HB interactions. Topological properties, energy densities and integrated atomic properties are obtained with ρ(r) of dimers at B3LYP/6-311++G(d,p) optimized structures obtained upon fully relaxing the geometry of monomers. The dependence of A–H⋯B bond properties on intermolecular R(H⋯B) distances allows to characterize the nature of the interaction as monomers move nearer from infinite separation. At long distances the interaction is only electrostatic while for separations about 1 A larger than the equilibrium distance Req, quantum effects arising from ρ(r) begin to dominate. In the immediate neighborhood of Req the interaction is mainly led by the stabilization of the H-donor due in turn to energy lowerings in A and B atoms associated to polarization effects. The mutual penetration of electron densities of donor and acc...

Variation with the intermolecular distance of properties dependent on the electron density in hydrogen bond dimers

The variation with the intermolecular distance of geometries, energies, and other properties dependent on the electron density ρ(r) are studied in three cyclic dimers linked by two hydrogen bonds: formic acid and formamide homodimers and the heterodimer formamide/formic acid complex. Topological features, energy densities and integrated atomic properties provided by AIM theory are calculated with ρ(r) obtained at B3LYP/6-311++G(d,p) optimized geometries for a number of intermonomer distances covering large separations, equilibrium, and short distances. The variation with these distances of properties studied allows to characterize the nature of the interaction in A–H⋯B (A=N, O and B=O) hydrogen bonds. Whereas at large distances the attraction is purely electrostatic, quantum effects associated with redistributions of ρ(r) mainly around H and B atoms dominate the interaction in the neighborhood of equilibrium. Mutual penetration of the electron densities of these atoms leads to considerable reductions of their atomic volumes and associated polarization effects as well as energetic stabilization of atom A. Although the interaction in this range of intermonomer separations displays noncovalent features, when the dimers move at distances shorter than equilibrium, characteristics typical of covalent interactions begin to appear while the systems leave the planar structures presented until then. This work complements our previous study [O. Galvez, P. C. Gomez, and L. F. Pacios, J. Chem. Phys. 115, 11166 (2001)] of dimers with one single hydrogen bond.

Variation with the intermolecular distance of properties dependent on the electron density in cyclic dimers with two hydrogen bonds

Approximate kinetic energy density for intermolecular regions in hydrogen bond dimers

Thirteen conformers of nonionized glycine identified previously in ab initio correlated calculations at the MP2/6-311++G** level of theory are investigated by means of the atoms in molecules (AIM) ...

Intramolecular Effects and Relative Stabilities of Conformers of Gaseous Glycine

Ab initio calculations at the MP2/6‐311++G** level of theory led recently to the identification of 13 stable conformers of gaseous glycine with relative energies within 11 kcal/mol. The stability of every structure depends on subtle intramolecular effects arising from conformational changes. These intramolecular interactions are examined with the tools provided by the Atoms In Molecules (AIM) theory, which allows obtaining a wealth of quantum mechanics information from the molecular electron density ρ(r). The analysis of the topological features of ρ(r) on one side and the atomic properties integrated in the basins defined by the gradient vector field of the density on the other side makes possible to explore the different intramolecular effects in every conformer. The existence of intramolecular hydrogen bonds on some conformers is demonstrated, while the presence of other stabilizing interactions arising from favorable conformations is shown to explain the stability of other structures in the potential energy surface of glycine. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 702–716, 2001

Pedro C. Gómez

Papers

Variation with the intermolecular distance of properties dependent on the electron density in hydrogen bond dimers

Variation with the intermolecular distance of properties dependent on the electron density in cyclic dimers with two hydrogen bonds

Approximate kinetic energy density for intermolecular regions in hydrogen bond dimers

Intramolecular Effects and Relative Stabilities of Conformers of Gaseous Glycine

Intramolecular interactions and intramolecular hydrogen bonding in conformers of gaseous glycine