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Abstract

Deductive molecular mechanics is applied to study the relative stability and mechanical properties of carbon allotropes containing isolated σ-bonds. Our approach demonstrates the numerical accuracy comparable to that of density-functional theory, but achieved with dramatically lower computational costs. We also show how the relative stability of carbon allotropes may be explained from a chemical perspective using the concept of strain of bonds (or rings) in close analogy to theoretical organic chemistry. Besides that, the role of nonbonding electrostatic interactions as the key factor causing the differences in mechanical properties (in particular, hardness) of the allotropes is emphasized and discussed. The adamas program developed on the basis of this study fairly reproduces spatial and electronic structure as well as mechanical properties of carbon allotropes.

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... P6 3 /mmc P6 3 /mmc В настоящем обзоре представлен один из таких квантово-химических методов -дедуктивная молекулярная механика и ее реализация в программном пакете Adamas [15,16], обеспечивающем эффективное квантово-химическое моделирование электронной структуры и механических свойств аллотропов углерода. Метод использует представление групповых функций [17], позволяющее разделить σи π-электронные подсистемы и описывать их волновыми функциями различных функциональных форм, отвечающими их химической природе: локальными валентными связями для σ-подсистемы [18] и делокализованными молекулярными орбиталями для π-подсистемы [19]. ...
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We present a software package GoGreenGo -- aimed to model local perturbations of periodic systems due to either chemisorption or point defects. The electronic structure of an ideal crystal is obtained by worldwide distributed standard quantum physics/chemistry codes, then processed by various tools performing projection to atomic orbital basis sets. Starting from this, the perturbation is addressed by GoGreenGo with use of the Green's functions formalism, which allows to evaluate its effect on the electronic structure, density matrix and energy of the system. In the present contribution the main accent is made on processes of chemical nature such as chemisorption or doping. We address a general theory and its computational implementation supported by a series of test calculations for benchmark model solids: simple, face-centered and body-centered cubium systems. In addition, more realistic problems of local perturbations in graphene lattice such as lattice substitution, vacancy and "on-top" chemisorption are considered.
... Notably, although TB parameters have been derived from first principles based on the maximally localized Wannier function [42][43][44][45][46][47] or atomic orbitals [48][49][50][51] constructed from KS states over the years, attempts to calculate TB parameters in the basis of directed hybrid orbital has been primarily limited so far to analytical models [52,53]. Self-energy corrected TB parameters ...
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Quantum-chemical computations of solids benefit enormously from numerically efficient plane-wave (PW) basis sets, and together with the projector augmented-wave (PAW) method, the latter have risen to one of the predominant standards in computational solid-state sciences. Despite their advantages, plane waves lack local information, which makes the interpretation of local densities-of-states (DOS) difficult and precludes the direct use of atom-resolved chemical bonding indicators such as the crystal orbital overlap population (COOP) and the crystal orbital Hamilton population (COHP) techniques. Recently, a number of methods have been proposed to overcome this fundamental issue, built around the concept of basis-set projection onto a local auxiliary basis. In this work, we propose a novel computational technique toward this goal by transferring the PW/PAW wavefunctions to a properly chosen local basis using analytically derived expressions. In particular, we describe a general approach to project both PW and PAW eigenstates onto given custom orbitals, which we then exemplify at the hand of contracted multiple-ζ Slater-type orbitals. The validity of the method presented here is illustrated by applications to chemical textbook examples-diamond, gallium arsenide, the transition-metal titanium-as well as nanoscale allotropes of carbon: a nanotube and the C60 fullerene. Remarkably, the analytical approach not only recovers the total and projected electronic DOS with a high degree of confidence, but it also yields a realistic chemical-bonding picture in the framework of the projected COHP method. Copyright © 2013 Wiley Periodicals, Inc.
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The pi‐electron approximation is defined to be the approximation in which the following two restrictions are imposed upon the total approximate electronic wave functions for some group of molecular states:(I) The wave function for each state satisfies the sigma‐pi separability conditions: (A) the wave function has the form Ψ = [(Σ) (II)], where (Σ) and (II) are antisymmetrized functions describing the so‐called sigma and pi electrons, respectively, and the outer brackets connote antisymmetrization with respect to sigma‐pi exchange; (B) each of (Σ), (II), and Ψ is normalized to unity; (C) each of (Σ), (II), and Ψ is well‐behaved.(II) The sigma description is the same for all states.Imposition of these restrictions is shown to be sufficient to validate the customary procedure in which the pi electrons in a molecule are treated apart from the rest.A formula is given for the pi‐electron Hamiltonian to be used when the pi‐electron approximation is invoked. Present day pi‐electron theories are examined, and lines for carrying out improved calculations are suggested. An iterative procedure is proposed for treating both sigma and pi electrons wherein first a sigma function is assumed (which defines a ``core'' in the field of which the pi electrons move), then a pi function is computed (which defines a ``peel'' in the field of which the sigma electrons move), then a new sigma function is computed, and so on.Certain generalizations of the quantum‐mechanical argument are made which give it wider applicability, and several illustrations are drawn from pi‐electron theory and elsewhere.
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“Die Ringschließung ist offenbar diejenige Erscheinung, welche am meisten über die räumliche Anordnung der Atome Auskunft geben kann. Wenn eine Kette von 5 und 6 Gliedern sich leicht, eine von weniger oder mehr Gliedern sich schwierig oder auch gar nicht schließen läßt, so müssen dafür offenbar räumliche Gründe vorhanden sein.… Die vier Valenzen des Kohlenstoffatoms wirken in den Richtungen, welche den Mittelpunkt der Kugel mit den Tetraederecken verbinden, und welche miteinander einen Winkel von 109°28′ machen. Die Richtung der Anziehung kann eine Ablenkung erfahren, die jedoch eine mit der Größe der Letzteren wachsende Spannung zur Folge hat,”[† ] This is the quintessence of the “ring-strain theory” formulated by Adolf von Baeyer over one hundred years ago. Although it is today only one facet of the many aspects of strain theory, it has repeatedly stimulated experimental and theoretical chemists. Among the most spectacular of the recent successes in synthetic chemistry are the syntheses of tetra-tert-butyltetrahedrane and [1.1.1]propellane. The reasons for the great stability of these two highly strained compounds are completely different. The experimental findings as well as the results of theoretical analysis by means of molecular mechanics and ab initio calculations have contributed decisively to our present state of knowledge of the structure, energy, and reactivity of organic compounds.
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Das Kräftespiel zwischen neutralen Atomen zeigt eine charakteristische quantenmechanische Mehrdeutigkeit. Diese Mehrdeutigkeit scheint geeignet zu sein, die verschiedenen Verhaltungsweisen zu umfassen, welche die Erfahrung liefert: Bei Wasserstoff z. B. die Möglichkeit einer homöopolaren Bindung, bzw. elastischer Reflexion, bei den Edelgasen dagegen nur die letztere — und zwar dies bereits als Effekte erster Näherung von ungefähr der richtigen Größe. Bei der Auswahl und Diskussion der verschiedenen Verhaltungsweisen bewährt sich das Pauliprinzip auch hier, in Anwendung auf Systeme von mehreren Atomen.
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The theory of electronic spectra and electronic structure, the elucidation of which was begun in the first paper of this series, is further developed and applied to ethylene, butadiene, benzene, pyridine, pyrimidine, pyrazine, and s-triazine.A realistic and consistent LCAO-MO π-electron theory should allow the σ-electrons to adjust themselves to the instantaneous positions of the mobile π-electrons. This is accomplished in the theory by assignment of empirical values to the Coulomb electronic repulsion integrals and Coulomb penetration integrals which enter the formulas, these values being obtained in a prescribed way from valence state ionization potentials and electron affinities of atoms. Use of the empirical values in the molecular orbital theory reduces the magnitude of computed singlet-triplet splittings and the effects of configuration interaction without complicating the mathematics. From the valence-bond point of view, ionic structures may be said to be enhanced.The applications to hydrocarbons and heteromolecules which are considered show that the theory can correlate known π-electron spectral wavelengths and intensities very successfully, which, together with the simple structure of the theory, signals that manifold applications of the theory are in order elsewhere.
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Tables are given of the specific heat and the enthalpy of 28 metals, 3 alloys, 8 other inorganic substances, and 8 organic materials, in the temperature range of 1 to 300 f K. (auth)
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Analysis of electronic structure of organic molecules performed on the basis of the APSLG trial electronic wave function with use of the biquaternion parameterization of the SO(4) hybridization manifold of nonhydrogen atoms provided a logical framework for deductive transition from quantum mechanical (QM) description of molecular electronic structure to molecular mechanical (MM) description of molecular potential energy surface. This derivation resulted in an alternative form of MM in which atoms are not considered as interacting point masses (‘balls’), but manifest more complex structure reflecting their valence state. The latter may be correlated with the atom ‘types’ introduced in standard MM on the basis of analysis of failed attempts to reproduce certain sets of experimental data in the respective model frameworks.
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The Brillouin spectrum of diamond excited with either the Ar+ or He-Ne laser radiation is measured with a triple-passed piezoelectrically scanned Fabry-Perot interferometer. The polarization features and the selection rules have been verified for a number of scattering geometries. From the measured frequency shifts of the Brillouin components, the following values are obtained for the elastic moduli: c11=10.764±0.002, c12=1.252±0.023, and c44=5.774±0.014 in units of 1012 dyn/cm2. The relative intensities of the observed Brillouin components for a variety of scattering geometries are consistent with the following elasto-optic contants: p44=-0.172 and p11-p12=-0.292 determined by Denning et al. and p11+2p12=-0.1640 obtained by Schneider. From a comparison of the Brillouin spectrum and the Raman spectrum associated with the zone-center optical phonon, observed under identical conditions, we obtain a value for the single independent component characterizing the Raman tensor per unit cell, viz., |a|=4.4±0.3 Å2.
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Graphene is a two-dimensional (2D) material with over 100-fold anisotropy of heat flow between the in-plane and out-of-plane directions. High in-plane thermal conductivity is due to covalent sp 2bonding between carbon atoms, whereas out-of-plane heat flow is limited by weak van der Waals coupling. Herein, we review the thermal properties of graphene, including its specific heat and thermal conductivity (from diffusive to ballistic limits) and the influence of substrates, defects, and other atomic modifications. We also highlight practical applications in which the thermal properties of graphene play a role. For instance, graphene transistors and interconnects benefit from the high in-plane thermal conductivity, up to a certain channel length. However, weak thermal coupling with substrates implies that interfaces and contacts remain significant dissipation bottlenecks. Heat flow in graphene or graphene composites could also be tunable through a variety of means, including phonon scattering by substrates, edges, or interfaces. Ultimately, the unusual thermal properties of graphene stem from its 2D nature, forming a rich playground for new discoveries of heat-flow physics and potentially leading to novel thermal management applications.
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A new crystalline form of carbon—hexagonal diamond—has been synthesized in the laboratory under conditions of static pressure exceeding about 130 kbar and temperature greater than about 1000°C. It is necessary to start with well‐crystallized graphite in which the c axes of the crystallites are parallel to each other and to the direction of compression. There is electrical evidence that the transformation starts at room temperature but hexagonal diamond is not retrieved unless a setting temperature exceeding about 1000°C is applied. The electrical and crystal characteristics have been studied. The crystal structure is hexagonal with a=2.52 Å and c=4.12 Å. The theoretical density is 3.51+g/cm3, same as cubic diamond. It has also been prepared recently in another laboratory from crystalline graphite by a method involving intense shock compression and strong thermal quenching. More recently it has been discovered to be present to the extent of over 30% in the Canyon Diablo meteorite diamonds.
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Convenient formulas have been obtained for the overlap integrals ∫χaχbdv, kinetic energy integrals —☒∫χaΔχbdv, nuclear attraction integrals Z∫χa(1/ra)χbdv and Z∫χb(1/ra)χb′dv, and coulomb repulsion integrals ∫ ∫ χa(1)χb(2)(1/r12)χa′(1)χb′(2)dv1dv2, where χa, χa′, χb, χb′ are Slater‐type AO's on the centers a and b. Explicit formulas are given for all the integrals arising from the principal quantum numbers 1 and 2, for arbitrary values of the effective nuclear charges and the interatomic distance.
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A detailed account is given of a quantum-mechanical treatment of the lower cycloparaffins, cyclobutadiene and ethylene. It is found that strained bonds (in the original sense of Baeyer) are to be described as bent. Strain energies comparable with those derived from thermochemical data are calculated; the properties of strained systems are discussed; and, in particular, a detailed description of the bonds in cyclopropane is given. The stability of cyclobutadiene has been considered with respect to that of the related molecules benzene, cyclooctatetraene and diphenylene; and hybridization in ethylene has been re-examined. The pairing approximation is used throughout, but an Appendix is added, in which the molecular orbital method is applied qualitatively to cyclopropane.