QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

Multiwfn is a multifunctional program for wavefunction analysis. Its main functions are: (1) Calculating and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population analysis. (3) Bond order analysis. (4) Orbital composition analysis. (5) Plot density-of-states and spectrum. (6) Topology analysis for electron density. Some other useful utilities involved in quantum chemistry studies are also provided. The built-in graph module enables the results of wavefunction analysis to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and analysis methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com.

Multiwfn: a multifunctional wavefunction analyzer.

Molecular structure does not easily identify the intricate noncovalent interactions that govern many areas of biology and chemistry, including design of new materials and drugs. We develop an approach to detect noncovalent interactions in real space, based on the electron density and its derivatives. Our approach reveals the underlying chemistry that compliments the covalent structure. It provides a rich representation of van der Waals interactions, hydrogen bonds, and steric repulsion in small molecules, molecular complexes, and solids. Most importantly, the method, requiring only knowledge of the atomic coordinates, is efficient and applicable to large systems, such as proteins or DNA. Across these applications, a view of nonbonded interactions emerges as continuous surfaces rather than close contacts between atom pairs, offering rich insight into the design of new and improved ligands.

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Revealing noncovalent interactions.

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 definitions currently used to classify chemical bonds (in terms of bond order, covalency versus ionicity and so forth) are derived from approximate theories1–3 and are often imprecise. Here we outline a first step towards a more rigorous means of classification based on topological analysis of local quantum-mechanical functions related to the Pauli exclusion principle. The local maxima of these functions define 'localization attractors', of which there are only three basic types: bonding, non-bonding and core. Bonding attractors lie between the core attractors (which themselves surround the atomic nuclei) and characterize the shared-electron interactions. The number of bond attractors is related to the bond multiplicity. The spatial organization of localization attractors provides a basis for a well-defined classification of bonds, allowing an absolute characterization of covalency versus ionicity to be obtained from observable properties such as electron densities.

Classification of chemical bonds based on topological analysis of electron localization functions

We introduce in this work a new approach to the identification of localized electronic groups in atomic and molecular systems. Our approach is based on local behavior of the Hartree–Fock parallel‐spin pair probability and is completely independent of unitary orbital transformations. We derive a simple ‘‘electron localization function’’ (ELF) which easily reveals atomic shell structure and core, binding, and lone electron pairs in simple molecular systems as well.

A Simple Measure of Electron Localization in Atomic and Molecular-Systems

Cr2 in density-functional theory: approximate spin projection

Studies of electronic structure of solids have concentrated mainly on Hilbert space properties such as energy-band structures and density of states, as well as some properties that can be reduced from them. Here, we report application of the topological charge density analysis to crystals. It is found that the pseudoatoms (or nonnuclear attractors, which are charge accumulations in nonnuclear regions), first found in Li 2 , exist in solid lithium and sodium as well. In the former, the pseudoatoms form a connected network; in the latter, they are separated from one another. Although such networks obey the space group symmetry of the corsesponding crystal, their existence is an intrinsic property of a specific crystal

Topological analysis of the charge density of solids: bcc sodium and lithium

The theory of molecular structure, developed by Bader and co‐workers, has met with considerable success and is now being applied to many aspects of chemistry. One finding, however, that has complicated the theory is that of non‐nuclear attractors, that is, pseudoatoms. In this study we examine basis set and to some extent electron correlation effects on the appearance and disappearance of non‐nuclear attractors in Li2, Na2, Na4, and Na5. The appearance of a pseudoatom in a lithium molecule correlates remarkably well with the size of the region, in an atomic calculation, of −∇2ρ(r) for the valence shell of the atom. This and the fact that the pseudoatom is also present in the promolecule indicates that the pseudoatoms are remnants of or, in fact, are portions of atoms that are not perturbed enough in the molecule to remove an essentially atomic characteristic.

Pseudoatoms of the electron density

The bonding in a number of σ‐bonded diatomic and linear triatomic molecules is interpreted in terms of the one‐particle density matrix (ODM) along the bond axis. Special attention is drawn to the off‐diagonal contributions of the ODM in a two‐dimensional position space representation, which are shown to be indicative of a bonding or antibonding covalent interaction between the atomic centers.

Kenneth E. Edgecombe

Papers

A Simple Measure of Electron Localization in Atomic and Molecular-Systems

Cr2 in density-functional theory: approximate spin projection

Topological analysis of the charge density of solids: bcc sodium and lithium

Pseudoatoms of the electron density

One‐particle density matrices along the molecular bonds in linear molecules