A reference‐free stockholder partitioning method based on the force on electrons

We argue that when one divides a molecular property into atom‐in‐a‐molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms‐in‐a‐molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference‐free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an “arbitrary” choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc.     

A relationship between the sizes and energies of localized molecular orbitals. I. A study of selected first-row hydrides

Ab initio calculations have been performed on selected first-row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMO 'S ) were computed and analysed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with an MO , and the relationship between the sizes and energies of such orbitals was examined. It was found that a simple energy–size relationship exists for core LMO 'S but only approximately holds for bond LMO 'S .     

On the “Wolfsberg–Helmholz Conjecture” of “Extended‐Hückel Theory”

After having reviewed some pioneer integral approximations closely related to Rüdenberg's expansions of one‐ and two‐electron orbital products, we apply the previously described “Implicit Multi‐Center Integration” techniques on Roothaan's “restricted” Fock‐matrix components over standard atomic orbital bases. The resulting compact forms are very similar to the well‐known “Wolfsberg–Helmholz Conjecture” of “Extended‐Hückel Theory,” which relates the various off‐diagonal matrix elements of “restricted” Fock‐type to their corresponding diagonal counterparts. In this way, a “nonempirical Extended‐Hückel Theory” can be created. © 2012 Wiley Periodicals, Inc.     

Paradigms and paradoxes: Hess’ law and the thermodynamic validity of Jolly’s method for estimating bond dissociation energies

This study evaluates Jolly’s method to estimate the difference in homolytic bond dissociation energy between two isoelectronic molecules by the use of atomic and ionic electronegativities. The use of intermediate species as an energetic “stepping stone” between the two diatomic species in question is discussed, particularly within the context of Hess’ law. We also show a sample calculation for a pair of diatomic species that is fully consistent with data from atomic physics.     

Advances in electric field and atomic surface derived properties from experimental electron densities

The present study is devoted to a general use of the Gauss law. This is applied to the atomic surfaces derived from the topological analysis of the electron density. The method proposed here is entirely numerical, robust and does not necessitate any specific parametrization of the atomic surfaces. We focus on two fundamental properties: the atomic charges and the electrostatic forces acting on atoms in molecules. Application is made on experimental electron densities modelized by the Hansen-Coppens model from which the electric field is derived for a heterogenic set of compounds: water molecule, NO(3) anion, bis-triazine molecule and MgO cluster. Charges and electrostatic forces are estimated by the atomic surface flux of the electric field and the Maxwell stress tensor, respectively. The charges obtained from the present method are in good agreement with those issued from the conventional volume integration. Both Feynman and Ehrenfest forces as well as the electrostatic potential at the nuclei (EPN) are here estimated from the experimental electron densities. The values found for the molecular compounds are presented and discussed in the scope of the mechanics of atomic interactions.     

“Surface water” and “strong-bonded water” in cyclodextrins: a Karl Fischer titration approach

Cyclodextrins are some of the most used carriers for bioactive compounds (as host–guest complex) and many factors influence the association–dissociation of this complex, some of them being related to hydrophobicity. In the solid state, cyclodextrins contain two types of water molecules: “surface” water molecules (especially close to the crystal surface) and “strong-bonded” water molecules (especially from the cyclodextrin cavity), but the classification is hard to do, and the concentration of these water molecules are relatively difficult to estimate by simple methods. In the present study we used the volumetric Karl Fischer titration to estimate these types of water molecules in cyclodextrins by means of the rate of water reaction (related to diffusion from cyclodextrin crystals). “Surface” water molecules are titrated with rates between 1.8–2.8 mM/s for α-cyclodextrin, while for β-cyclodextrin these rates are little bit higher (2.9–3.4 mM/s). The rates corresponding to “strong-bonded” water molecules are approximately tens fold lower (0.05–0.3 mM/s for α-cyclodextrin and 0.15–0.33 mM/s for β-cyclodextrin). The approximate ratio between “surface” and “strong-bonded” water molecules could also be estimated by this simple and rapid method.     

On the formation of the so-called arsanthrene

The structure of Kalb's “arsanthrene oxide” and “arsanthrene” have been reinvestigated. The “arsanth-rene oxide” is monomeric and is therefore properly termed 5,10-epoxy-5,10-dihydroarsanthrene(6). A spectroscopic study of “arsanthrene” revealed that this compound has the dimeric structure 12 corresponding to the photodimer of anthracene. Mechanisms of formation of dimeric “arsanthrene” and the possible dissociation of dimeric “arsanthrene” into its monomer by reaction with a dienophile at elevated temperature are discussed. An attempt to synthesize arsanthrene (7) by dehalogenation of 5,10-dichloro-5,10-dihydroarsanthrene (5) was unsuccessful. The mass spectral fragmentation patterns of some 5,10-dihydroarsanthrenes are recorded.     

The use of population localised orbitals to interpret molecular orbital calculations

An efficient and general method is derived to calculate population localised molecular orbitals (LMO's) from a given SCF eigenvector matrix, by reduction to an eigenvalue problem. Applications to both localised molecules (NH₃ and C₂H₂) and delocalised ones (B₂H₆, C₆H₆ and butadiene) are discussed in some detail. It is shown that unequal occupation of atomic energy levels leads to non-orthogonal LMO's. The consequences of non-orthogonal atomic hybrid orbitals are discussed, formulas for their overlap in terms of atomic occupation numbers are derived and it is shown that the occupation numbers are connected to LMO atomic orbital coefficients by various sum rules.     

Ab initioMODPOT/VRDDO/MERGE calculations on energetic compounds. III. Nitroexplosives: Polyaminopolynitrobenzenes (including DATB,TATB, and tetryl)

Quantum chemical ab initio MODPOT /VRDDO calculations have been carried out on the following aminonitrobenzenes for which crystal structures had been determined experimentally: 4-nitroaniline; N,N-dimethyl-p-nitroaniline; 2,4,6-trinitroaniline; 1,3-diamino-2,4,6-trinitrobenzene (DATB—Form I); 1,3,5-triamino-2,4,6-trinitrobenzene (TATB); 2,3,4,6-tetranitroaniline; N-methyl-N,2,4,6-tetranitroaniline (Tetryl); and N-(β,β,β-trifluoroethyl)-N,2,4,6-tetranitroaniline. These quantum chemical calculations were performed on the molecules in their conformations as found in their crystal structures. The calculations were carried out with our own ab initio programs which also incorporate as options several desirable features for calculations on large molecules: ab initio effective core model potentials (MODPOT) which enable calculations of valence electrons only explicitly, yet accurately, and a charge conserving integral prescreening evaluation (which we named VRDDO-variable retention of diatomic differential overlap) especially effective for spatially extended molecules. Aminonitrobenzenes are especially interesting since there are inherent intramolecular ring distortions and deviations from planarity and intramolecular hydrogen bonds as well as intermolecular hydrogen bonds causing further deviations from planarity. The theoretical indices resulting from the quantum chemical calculations are relevant to a number of properties and behavioral characteristics of these molecules, both intramolecular and intermolecular. The charges on the atoms [from the gross atomic populations (GAP 's)] are needed for calculation of the atomic multipole–atomic multipole electrostatic contributions (a dominant factor) to the intermolecular interaction energies. These electrostatic interaction energies are part of the input necessary for calculations on the crystal packing and densities of these molecules. These GAP 's are also of value in interpreting the experimental photoelectron and ESCA spectra of these molecules. The total overlap populations (TOP 's) between atoms are related to the inherent bond strengths and can serve as a quantitative replacement for the old empirical bond length-bond order-bond energy relationship still used by explosives chemists to identify the “target bonds” (the weakest bonds). The TOP 's are of considerable value in predicting and tracing initiation and subsequent steps of explosive phenomena. The molecular orbital energies of the lowest unoccupied orbitals are of interest since nitroexplosives have been implicated in testicular toxicity and the initial metabolic activation appears to proceed through a one-electron reduction of the nitroexplosive.     

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model

The model of the full optimized reaction space describes the electronic structure of a molecule in terms of the best wave-function that can be obtained as a superposition of all those configurations which are generate possible occupancies and couplings from a “formal minimal basis” of valence, orbitals on the constituent atoms. These configurations span a “full reaction space”, and MC SCF optimization of the orbitals in terms of an extended set of quantitative basis orbitals determines the full optimized reaction space (FORS). Basic justifications, methodological specifics and sample applications are discussed.     

Variational Properties of Adiabatic Molecular Wave Functions and Their Generalizations for Collision States

Born-Oppenheimer wave functions are shown to be variationally stable with respect to all other approximations to unbound-state molecular wave functions that are products of an electronic factor, and a function of nuclear coordinates only. The validity of this result is verified for functions having an “outgoing wave” or “ingoing wave” or “standing wave” behaviour. In the case of either of the first two classes of wave functions we use a variational principle associated with the transition matrix to derive our conclusion, whereas in the treatment of the third class, of “standing waves”, a variational principle for the reaction operator is employed. We then extend our investigations to the set of wave functions that are a finite sum of terms, each of which is a product of an electronic factor and an arbitrary function of nuclear coordinates. The result that emerges is that the variationally stable functions of this set are those whose nuclear functions satisfy Born's set of coupled equations for nuclear motions. On démontre que les fonctions d'onde de type Born-Oppenheimer sont stables du point de vue variationnel, par rapport à toute autre approximation d'une fonction d'onde moléculaire pour un état non lié, qui est le produit d'un facteur électronique et d'une fonction des coordonnées nucléaires seules. On vérifie ce résultat-ci pour des fonctions de type “onde sortante”, “onde incidente” ou “onde stationnaire”. Dans le cas d'une des deux premières classes de fonctions d'onde on déduit ce résultat d'un principe de variation associé à la matrice de transition, tandis que pour la troisième classe le même résultat est obtenu d'un principe de variation pour l'opérateur de réaction. Enfin on considère des fonctions d'onde, qui peuvent être écrites comme une somme finie de produits d'un facteur électronique et d'une fonction arbitraire des coordonnées nucléaires. On en déduit une condition pour les fonctions de cette classe-ci, qui sont stables du point de vue variationnel: ce sont celles dont les fonctions nucléaires satisfont au système d'équations couplées de Born pour les mouvements nucléaires. Es wird bewiesen, dass Born-Oppenheimer Wellenfunktionen von variationaler Standpunkte aus stabil sind mit Rücksicht auf alle andere Approximationen einer molekularen Wellenfunktion für einen nicht-gebundenen Zustand, die Produkte von einem elektronischen Faktor und einer Funktion der Kernkoordinaten sind. Dieses Resultat wurde für Funktionen, die sich als “ausgehende Wellen”, “einfallende Wellen” oder “stehende Wellen” verhalten, bestätigt. Für die zwei ersten Klassen wurde dabei ein Variationsprinzip für die Ubergangsmatrize, für die dritte Klasse eines für den Reaktionsoperator, angewendet. Schliesslich wurden solche Wellenfunktionen betrachtet, die eine endliche Summe von Produkten eines elektronischen Faktors und einer willkürlichen Funktion der Kernkoordinaten sind. Davon wurde eine Bedingung für von variationaler Standpunkte aus stabile Funktionen dieser Klasse hergeleitet: solche Funktionen müssen Lösungen von Born's gekoppelten Gleichungen für Kernbewegungen sein.     

X-ray and electron scattering factors for many-electron atomic system

Analytical expressions are developed for the x-ray and electron scattering factors for a many-electron atomic system when the single configuration wave function of the system is written as a sum of Slater determinants of spin orbitals. The radial part of the orbital is expanded in terms of Slater-type orbitals (STO 's). The expressions so developed have been used to calculate the coherent and incoherent x-ray and electron scattering factors and intensities for all the neutral atoms up to krypton (Z = 36) and for some positive and negative ions of chemical interest. The results obtained are used to test the value of Hartree–Fock wave functions for the evaluation of “one-electron properties” of many-electron atomic systems.     

From amorphous solid to defective crystal. A study of structural peculiarities in close packings of hard spheres

The structure of models of close packings of hard spheres is examined, with density of the packings exceeding the maximum value for uniform disordered packings (η = 0.64). High densities are achieved due to regions of the closest packing (η = 0.74) emerging in the models. Spatial geometry of good tetrahedral atomic configurations and of simplest elements of the crystal structure identified by Delaunay simplices was studied using the Voronoi— Delaunay method. Models with a packing coefficient η varying from 0.639 to 0.706 were considered. At smaller densities, a well-known disordered close “Bernal packing” is realized. At η = 0.706 (the greatest density achieved), a unified crystal structure with numerous defects is formed. At intermediate densities, stochastically oriented crystalline nuclei are observed. Specific atomic aggregates — stacks of five-membered rings in good tetrahedral configurations of spheres — are revealed in models having a substantial fraction of crystalline phase (η = 0.664). Such non-trivial structures can occur only in packings that are intermediate between amorphous and crystalline phases.     

Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing ?ω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ?ω at the closed shells. These discontinuities diminish as N increases. For large N, ?ω becomes simply: ?ω?c₁N^?1/3+c₂N^?1. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Conformational properties and homolytic bond cleavage of organic peroxides. I. An empirical approach based upon molecular mechanics and ab initio calculations

The conformational features of a large number of hydroperoxides ROOH and peroxides ROOR′, where R and R′ are alkyl groups of different and increasing size and phenyl rings, including ortho substituted derivatives, were obtained from molecular mechanics calculations by employing a standard package. For the molecules of small molecular size, comparison was carried out with the results of ab initio calculations. Heats of formation were also obtained from molecular mechanics for hydroperoxides and peroxides: The values are, in general, overestimated. For the molecules containing the CF₃ group, the calculated values are subject to large errors and heats of formation were obtained from ab initio total energies in the “atom equivalents” scheme. To estimate the homolytic dissociation energies of the different bonds in the peroxide molecules, heats of formation of R·, ·OR, and ·OOR radicals were employed and several of them had to be calculated. Different approaches were employed—molecular mechanics calculations, ab initio energies within the atom equivalent and isodesmic reaction schemes, and Benson's group additivity rule; values consistent within the different calculation methods were chosen for estimating dissociation energies. The bond dissociation energies indicate different trends in these molecules as a function of the nature of the R and R′ groups and the possible electronic effects operating in these molecules are discussed. © 1993 John Wiley & Sons, Inc.     

A numerical integration scheme for the evaluation of correlation energy functionals

A numerical integration scheme is presented for three-dimensional integrals occurring in electronic structure calculations, concentrating attention on the evaluation of the correlation energy through a density-functional expression. The scheme is based on the choice of density-based weight functions that naturally partition the space into “atomic” volumes (in which the integration is performed in terms of spherical coordinates) and “diatomic” volumes (in which the integration is performed in terms of confocal elliptical coordinates). Such a choice is justified on the basis of the analytical behavior of the integrand. The attainable accuracy and the required computational effort within the proposed scheme are discussed in detail in a test application on the C₆₀ molecule in the symmetrical configuration. Finally, a comparison with previously proposed schemes is presented. © 1993 John Wiley & Sons, Inc.