Interatomic interactions in momentum space. Momentum density and kinetic energy in chemical bonding

On the basis of the virial theorem for a uniform scaling process of a polyatomic system, the total energy and its gradient are quantitatively related with the behavior of the electron density in momentum space through the kinetic energy of the system. For attractive and repulsive interactions, the behavior of the momentum density distribution and its effect on the stabilization energy and the interatomic force are examined. Some guiding principles are deduced for their interrelation. The results are used to clarify the role of kinetic energy in chemical bonding. Possible energy partitioning in this approach is also mentioned.     

Chemical bonding in view of electron charge density and kinetic energy density descriptors

Stalke's dilemma, stating that different chemical interpretations are obtained when one and the same density is interpreted either by means of natural bond orbital (NBO) and subsequent natural resonance theory (NRT) application or by the quantum theory of atoms in molecules (QTAIM), is reinvestigated. It is shown that within the framework of QTAIM, the question as to whether for a given molecule two atoms are bonded or not is only meaningful in the context of a well‐defined reference geometry. The localized‐orbital‐locator (LOL) is applied to map out patterns in covalent bonding interaction, and produces results that are consistent for a variety of reference geometries. Furthermore, LOL interpretations are in accord with NBO/NRT, and assist in an interpretation in terms of covalent bonding. © 2008 Wiley Periodicals, Inc.J Comput Chem, 2009.     

Computational methods in the theory of chemical bonding in solids

Popular techniques for analyzing the spatial and energy characteristics of chemical bonding in solids based on Hückel theory, Hartree-Fock method, and electron density functional theory are reviewed. Methods for calculating the total energies and dependent characteristics (cohesion energies, formation energies, partial pressures, etc.), the moments of the densities of states, bond occupations, and the pair potentials of electron density and localization function are considered. Examples of using these calculations for high-melting and laminated compounds are given. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 3, pp. 554–583, May–June, 1997.     

Constraint-based analysis of a physics-guided kinetic energy density expansion

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It has also been shown that any noninteracting KEDF must necessarily have a homogeneity degree of 2 in coordinate scaling, and that the ratio of the collective KED to electron density must approach the ionization energy as $r\to \infty$. This article demonstrates that the scaling condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint, and that the second condition places a restriction on the expansion terms of the KED. The discussion is extended as well for some known KEDs for comparison.     

An analysis of nonlocal density functionals in chemical bonding

In this work, we carry out an analysis of the gradient-corrected density functionals in molecules that are used in the Kohn–Sham density functional approach. We concentrate on the special features of the exchange and correlation energy densities and exchange and correlation potentials in the bond region. By comparing to the exact Kohn–Sham potential, it is shown that the gradient-corrected potentials build in the required peak in the bond midplane, but not completely correctly. The gradient-corrected potentials also exhibit wrong asymptotic behavior. Contributions from different regions of space (notably bond and outer regions) to nonlocal bonding energy contributions are investigated by integrating the exchange and correlation energy densities in various spatial regions. This provides an explanation of why the gradient corrections reduce the local density approximation (LDA ) overbinding of molecules. It explains the success of the presently used nonlocal corrections, although it is possible that there is a cancellation of errors, too much repulsion being derived from the bond region and too little from the outer region. © John Wiley & Sons, Inc.     

The role of kinetic energy in chemical binding

The wavefunctions and various partitions of the energy are examined for a variety of small molecules (H₂, H₃, H₄, HeH, HeH₂, He₂, LiH, and BH) in order to isolate the factors crucial for bond formation. We find that a natural partition of the energy leads to the conclusion that the crucial factor is the exchange, or nonclassical, part of the kinetic energy, T ^x. The change in T ^xupon pushing the atoms towards one another is the dominant term in the binding energy; it is negative when the resulting molecule is stable and positive when it is unstable. We show that T ^x is related to the interference kinetic energy considered by Ruedenberg.

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Zusammenfassung Die Wellenfunktionen und verschiedene Zerlegungen der Energie werden für eine Reihe kleiner Moleküle untersucht (H₂, H₃, H₄, HeH, HeH₂, He₂, LiH und BH), um die Faktoren zu finden, die für die Bindungsbildung ausschlaggebend sind. Die natürliche Zerlegung der Energie läßt die Folgerung zu, daß der bestimmende Faktor der Austauschanteil T ^x(oder nichtklassische Anteil) der kinetischen Energie ist. Die Änderung von T ^xbeim Zusammenführen der Atome ist der dominierende Term für die Bindungsenergie; er ist negativ, wenn das resultierende Molekül stabil ist, und positiv, falls es instabil ist. Es wird gezeigt, daß T ^x im Zusammenhang zum Wechselwirkungsanteil der kinetischen Energie nach Ruedenberg steht.

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Partially supported by a grant (GP-15423) from the National Science Foundation. This paper is based on a portion of the PhD thesis (California Institute of Technology, 1970) by CWW.

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National Science Foundation Predoctoral Trainee.

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Alfred P. Sloan Foundation Research Fellow.

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Contribution No. 3917.     

Experimental and theoretical charge density study of chemical bonding in a Co dimer complex

The charge density of Co2(CO)6(HC[triple bond]CC6H10OH) (1) in the crystalline state has been determined using multipolar refinement of single-crystal X-ray diffraction data collected (i) with a synchrotron source at very low temperatures (15 K) and (ii) using a conventional source with the crystal at intermediate temperature (100 K). The X-ray charge density model is augmented by complete active space and density functional theory calculations. Topological analyses of the different charge distributions show that the two Co atoms are not bonded to each other in the quantum theory of atoms in molecules (QTAIM) sense of the word. However, the behavior of the source function and the total energy density indicate that there is some bond-like character in the Co-Co interaction. The bridging alkyne fragment provides an unusual bonding situation, with extremely small electron density differences between the two Co-C bond critical points and the "CoC2" ring critical point. Thus, the structure is close to a topological catastrophe point. Comparison of the results obtained from the two diffraction data sets and ab initio theory suggests that the topology of the experimental electron density in this special atomic environment is highly sensitive to subtle effects of measurement errors and potential shortcomings of the multipole model, or to effects of the crystal field. Thus, even the two identical molecules in the asymmetric unit show altered bonding patterns.     

Theoretical study of atoms by the electronic kinetic energy density and stress tensor density

The electronic structure of atoms in the first, second, and third periods were analyzed using the electronic kinetic energy density and stress tensor density, which are local quantities motivated by quantum field theoretic consideration, specifically the rigged quantum electrodynamics. The zero surfaces of the electronic kinetic energy density, which are called as the electronic interfaces, of the atoms were computed. It was found that their sizes exhibited clear periodicity and were comparable to the conventional atomic and ionic radii. The electronic stress tensor density and its divergence, tension density, of the atoms, were also computed and how their electronic structures were characterized by them was discussed. © 2016 Wiley Periodicals, Inc.     

The chemical interpretation and practice of linear solvation energy relationships in chromatography

This review focuses on the use of linear solvation energy relationships (LSERs) to understand the types and relative strength of the chemical interactions that control retention and selectivity in the various modes of chromatography ranging from gas chromatography to reversed phase and micellar electrokinetic capillary chromatography. The most recent, widely accepted symbolic representation of the LSER model, as proposed by Abraham, is given by the equation: SP=c + eE + sS + aA + bB + vV, in which, SP can be any free energy related property. In chromatography, SP is most often taken as logk' where k' is the retention factor. The letters E, S, A, B, and V denote solute dependent input parameters that come from scales related to a solute's polarizability, dipolarity (with some contribution from polarizability), hydrogen bond donating ability, hydrogen bond accepting ability, and molecular size, respectively. The e-, s-, a-, b-, and v-coefficients and the constant, c, are determined via multiparameter linear least squares regression analysis of a data set comprised of solutes with known E, S, A, B, and V values and which span a reasonably wide range in interaction abilities. Thus, LSERs are designed to probe the type and relative importance of the interactions that govern solute retention. In this review, we include a synopsis of the various solvent and solute scales in common use in chromatography. More importantly, we emphasize the development and physico-chemical basis of - and thus meaning of - the solute parameters. After establishing the meaning of the parameters, we discuss their use in LSERs as applied to understanding the intermolecular interactions governing various gas-liquid and liquid-liquid phase equilibria. The gas-liquid partition process is modeled as the sum of an endoergic cavity formation/solvent reorganization process and exoergic solute-solvent attractive forces, whereas the partitioning of a solute between two solvents is thermodynamically equivalent to the difference in two gas/liquid solution processes. We end with a set of recommendations and advisories for conducting LSER studies, stressing the proper chemical and statistical application of the methodology. We intend that these recommendations serve as a guide for future studies involving the execution, statistical evaluation, and chemical interpretation of LSERs.     

On the evaluation of the non-interacting kinetic energy in density functional theory

The utility of both an orbital-free and a single-orbital expression for computing the non-interacting kinetic energy in density functional theory is investigated for simple atomic systems. The accuracy of both expressions is governed by the extent to which the Kohn-Sham equation is solved for the given exchange-correlation functional and so special attention is paid to the influence of finite Gaussian basis sets. The orbital-free expression is a statement of the virial theorem and its accuracy is quantified. The accuracy of the single-orbital expression is sensitive to the choice of Kohn-Sham orbital. The use of particularly compact orbitals is problematic because the failure to solve the Kohn-Sham equation exactly in regions where the orbital has decayed to near-zero leads to unphysical behaviour in regions that contribute to the kinetic energy, rendering it inaccurate. This problem is particularly severe for core orbitals, which would otherwise appear attractive due to their formally nodeless nature. The most accurate results from the single-orbital expression are obtained using the relatively diffuse, highest occupied orbitals, although special care is required at orbital nodes.     

Theoretical study of lithium ionic conductors by electronic stress tensor density and electronic kinetic energy density

We analyze the electronic structure of lithium ionic conductors, and , using the electronic stress tensor density and kinetic energy density with special focus on the ionic bonds among them. We find that, as long as we examine the pattern of the eigenvalues of the electronic stress tensor density, we cannot distinguish between the ionic bonds and bonds among metalloid atoms. We then show that they can be distinguished by looking at the morphology of the electronic interface, the zero surface of the electronic kinetic energy density. © 2016 Wiley Periodicals, Inc.     

Automatic comparison of thermodynamic data for species in detailed chemical kinetic modeling

This article describes the performance of an automatic comparator of thermochemical databases and demonstrates the use of a hypertext preprocessor to link chemical names with a three‐dimensional molecular viewer thus providing an unambiguous identification of species in a facile manner over the Internet. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 341–345, 2005     

Review paper: Design of a mass and ion kinetic energy spectrometer for organic chemical work

The design of a mass spectrometer for the determination of the structural formulae of organic compounds is discussed. The ion-optical characteristics of electric and magnetic sectors and also of quadrupole mass analysers are considered and the additional information that can be gleaned when such components are combined in various ways is listed. The advantages of using collision cells for inducing fragmentation of selected ion species are listed including those that result when the collision cell is floated at an electrical potential different from that of the incident ion beam. Important performance characteristics are the resolution with which a particular ion may be selected and the resolution with which daughter ions formed from it can be separated. It is concluded, that for instruments comprising three analysing units together with the appropriate collision cells, the most versatile combinations and those with the highest performance are an arrangement consisting of a magnetic sector followed by an electric sector, this being followed either by a further magnetic sector or a quadrupole. The properties of these two systems are compared in detail.     

Insight into the chemical bonding and electrostatic potential: A charge density study on a quinazoline derivative

2,3-Trimethylene-3,4-dihydroquinazoline shares the heterocyclic core with natural compounds and synthetic drugs. The hydrochloride of the compound forms excellent dihydrate crystals which have allowed us to collect high-resolution X-ray diffraction data and obtain the experimental charge density. The solid may be understood as built up from pairs of heterocyclic cations and chloride anions; a direct hydrogen bond links the halide to the formally cationic pyrimidine NH group. The hydrate water molecules interact with the anions, forming an infinite chain along the crystallographic a axis between the stacks of the heterocyclic cations. Based on the experimental charge density, a dipole moment of 16.1 Debye is calculated for a pair of the hydrogen-bonded quinazolinium cation and the chloride anion in the extended crystal structure.