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Deductive molecular mechanics of four-coordinated carbon allotropes
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.
Supplementary resource (1)
Data
August 2019
... 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]. ...
... Все расчеты проведены с учетом корреляции (11), позволяющей получать наиболее точные относительные энергии аллотропов. Полные таблицы с результатами расчета геометрий, плотностей, относительных энергий и объемных модулей упругости могут быть найдены в Приложении к работе [16]. На рис. ...
... Рис. 8. Результаты расчетов плотностей (а), относительных энергий (б) и объемных модулей упругости (в) для серии аллотропов углерода в программе Adamas в сравнении с DFT данными из SACADA. (Воспроизведено из [16] с разрешения PCCP Owner Societies.) Рис. 9. (Онлайн в цвете) Зависимость электронных энергий связей от межатомного расстояния. ...
The relative stability of diamond and graphite is readdressed from the new perspective of deductive molecular mechanics. Unlike most theoretical studies that are conducted numerically, this article uses an analytical model to gain insight into the fundamental reasons behind the quasi-degeneracy of these allotropes with very different bonding patterns. The relative energies of the allotropes are derived and several general statements about the structure of these materials are proven. This analysis yields a quasi-degenerate electronic ground state for graphite and diamond at 0 K. Numerical estimates based on this analysis are in astonishingly good agreement with experimental data and recent results of numeric modeling, despite the fact that they were obtained with a drastically smaller numerical effort. An extension of the proposed interpretation to silicon allotropes proves to be very successful as well. The proposed approach is also expanded to four-coordinated carbon allotropes, and the software package Adamas is developed, which is able to calculate allotrope energies and elastic properties (elastic moduli). In the case of diamond and graphene, some general statements could be proven from deductive molecular mechanics parameters. Specifically, it is shown that among the four-coordinated allotropes the cubic diamond structure represents the true minimum. In the cases of allotropes with some C—C bonds that are stronger than those in diamond, the energy gain is compensated by the mandatory presence of weaker bonds in the same allotrope, which leads to the overall increase of the energy relative to the diamond.
... Thus, the DMM contains variables characterizing the electronic structure in addition to purely geometric ones of the usual force fields. Applied originally in the low-symmetry molecular context [25,26,30], later DMM has been extended to crystalline systems [16,[31][32][33]. In addition to significant reduction of computational costs it allowed us to develop analytical models for the structure-energy dependencies of the corresponding species, that could qualitatively (and even semi-quantitatively) reproduce phase diagrams of some fundamental elements (stoicheia) of ancients, namely, fire [34] (actually, of C 2 occurring in flames) and water [16] (of which we considered solid water phases-ices). ...
... In addition to significant reduction of computational costs it allowed us to develop analytical models for the structure-energy dependencies of the corresponding species, that could qualitatively (and even semi-quantitatively) reproduce phase diagrams of some fundamental elements (stoicheia) of ancients, namely, fire [34] (actually, of C 2 occurring in flames) and water [16] (of which we considered solid water phases-ices). Furthermore, we applied similar ideas to carbon allotropes [31][32][33] comparing diamond and graphite and being able to reproduce the energy difference of the order of 1 kJ/mol between them. ...
In the present paper we apply an analytical approach based on the (Quantum) deductive molecular mechanical (DMM) to the principal component of upper and middle Earth crust—silica (SiO2) to study its polymorphs, trying to cover different coordination patterns occurring, respectively at ambient and somewhat higher pressures. Some characteristic structure features of either family of polymorphs are reproduced with a reasonable precision within a very simple physically sensible model. Specifically, the microscopic nature of the instability of the low-pressure phases towards Si–O–Si bending is revealed eventually paving a way towards understanding the entire field of “tetrahedral” polymorphs. As for higher-pressure “octahedral” polymorphs, some “proof-of-concept” estimates are performed, showing a perspective way of extending DMM technique towards higher pressures in a more numerical than analytical fashion.
... Complete treatment of such process can be performed in σ − π approximation by considering π-bonds breaking as a vacancy forms (as described above) and a rigorous evaluation of the σ-system reorganization energy. Although theoretical basis for that has been already established in our previous works [57,75,76,77], full analysis of the problem goes beyond the scope of the present paper. Here, we restrict ourselves by testing the eect of interaction of hydrogen atom only with the graphene π-system, neglecting possible distortion of graphene geometry and not touching the σ-core. ...
We present a software package GoGreenGo—an overlay 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, and 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 evaluating 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 of the electronic structure perturbations 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. Point defects in crystals form a wide class of processes being of great importance in solid‐state chemistry. Only by considering surface chemistry one can propose a numerous examples ‐ from formation of isolated surface defects to single particle chemisorption and elementary reactions on catalysts' surfaces. Theoretical investigation of these processes, aiming to understand their mechanisms from the electronic structure perspective, presents one of many important branches of solid‐state chemistry deserving close attention. In this work we present a new software package GoGreenGo specifically designed to perform computationally effective quantum chemical calculations of local processes in solids and to provide results in “chemical” terms.
... Complete treatment of such process can be performed in σ − π approximation by considering π-bonds breaking as a vacancy forms (as described above) and a rigorous evaluation of the σ-system reorganization energy. Although theoretical basis for that has been already established in our previous works [56,74,75,76], full analysis of the problem goes beyond the scope of the present paper. Here, we restrict ourselves by testing the effect of interaction of "hydrogen" atom only with the graphene π-system, neglecting possible distortion of graphene geometry and not touching the σ-core. ...
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 ...
We present self-energy corrected tight-binging(TB) parameters in the basis of the directed hybridised atomic orbitals constructed from first principles, for nano-diamonds as well as bulk diamond and zinc blende structures made of elements of group 13, 14 and 15 in the 2p, 3p and 4p blocks. With increasing principal quantum number of frontier orbitals, the lowering of self-energy corrections(SEC) to the band-gap and consequently to the dominant inter-atomic TB parameters, is much faster in bulk than in nano-diamonds and hence not transferable from bulks to nano-structures. However, TB parameters transfered from smaller nano-diamonds to much larger ones exclusively through mapping of neighbourhoods of atoms not limited to nearest neighbours, are found to render HOMO-LUMO gaps of the larger nano-diamonds with few hundreds of atoms in good agreement with their explicitly computed values at the DFT as well as DFT+G0W0 levels. TB parameters and their SEC are found to vary significantly from 2p to 3p block but negligibly from 3p to 4p, while varying rather slowly within each block, implying the possibility of transfer of SEC across block with increasing principal quantum number. The demonstrated easy transferability of self-energy corrected TB parameters in the hybrid orbital basis thus promises computationally inexpensive estimation of quasi-particle electronic structure of large finite systems with thousands of atoms.
Modeling of structure and properties of molecules and materials (crystals/solids) on the basis of their electronic structure is one of the most important consumers of computer resources (processor time, memory and storage). The known attempts to improve its efficiency reduce to massive parallelization. This approach ignores enormous diversity of types of structures and behaviors of molecules and materials. Moreover, this diversity is by no means reflected in the paradigm currently dominating the field of molecular/material modeling.
The relative stability of the two most important forms of elemental carbon, diamond and graphite, is readdressed from a newly developed perspective as derived from historically well-known roots. Unlike other theoretical studies mostly relying on numerical methods, we consider an analytical model to gain fundamental insight into the reasons for the quasi-degeneracy of diamond and graphite despite their extremely different covalent bonding patterns. We derive the allotropes' relative energies and provide a qualitative picture predicting a quasi-degenerate electronic ground state for graphite (graphene) and diamond at zero temperature. Our approach also gives numerical estimates of the energy difference and interatomic separations in good agreement with experimental data and recent results of hybrid DFT modeling, although obtained with a much smaller numerical but highly transparent effort. An attempt to extend this treatment to the lowest energy allotropes of silicon proves to be successful as well.
We explore the thermodynamic properties of the layered copper(II) carbodiimide CuNCN by heat-capacity measurements and investigate the corresponding thermal atomic motions by means of neutron powder diffraction as well as inelastic neutron scattering. The experiments are complemented by a combination of density-functional calculations, phonon analysis and analytic theory. The existence of a soft flexural mode-bending of the layers, characteristic for the material structure-is established in the phonon spectrum of CuNCN by giving characteristic temperature-dependent contributions to the heat capacity and atomic displacement parameters. The agreement with the neutron data allows us to extract a residual-on top of the lattice-presumably spinon contribution to the heat capacity ∝ T 2, speaking in favor of the spin-liquid picture of the electronic phases of CuNCN.
In 1996 Sir Harold W. Kroto, Robert F. Curl and Richard E. Smalley were honored with the Nobel Prize in Chemistry for the discovery of fullerenes. The advent of these new forms of carbon heralded a race to understand the physical and chemical properties. C60 is virtually insoluble in polar solvents but is partially soluble in benzene, toluene, and carbon disulfide. This made the processing of fullerenes for new applications fairly problematic. However, the physical and chemical properties of these cage structures may be tailored for a wide range of applications. Some of the difficulties in processing have been overcome by using novel fullerene derivatives. The functionalization of the fullerene core with different chemical moieties provided a vector toward potential applications in drug delivery, optoelectronics, electrochemistry and organic photovoltaics. In this review, we will take a closer look at the features of some of the fullerene derivatives that have reinvigorated the field of fullerene research. Water-soluble polyhydroxylated fullerenes such as fullerenol have demonstrated the potential for good electron transfer and optical transmission, while hydrophobic fullerene derivatives have shown promising avenues for catalytic applications. 2015 marked the 30th anniversary of the discovery of fullerenes, with celebrations around the world including an event by the Royal Society of Chemistry, bringing together many of Sir Harold Kroto's former students. The event also coincided with the recent discovery of C60+ in space after a complex twenty-year search. It is with sadness that we, Harry's Research Group at Florida State University, and his international collaborators, reflect on the passing of Sir Harold Kroto. His dedication to science and commitment to science communication through the VEGA Science Trust and the Global Educational Outreach for Science Engineering and Technology (GEOSET) initiative help to raise awareness of the challenges for science in the modern world. We will continue to inspire young students through outreach activities he initiated.
Cite we must, cite we do. We cite because we are links in a chain, using properties and methods validated by others. We also cite to negotiate the anxiety of influence. And to be fair. After outlining the reasons for citation, we use two case studies of citation amnesia in the field of hypothetical carbon allotropes to present a computer-age search tool (SACADA) in that subsubfield. Finally, we advise on good search practice, including what to do if you miss a citation.
The computer program LOBSTER (Local Orbital Basis Suite Towards Electronic-Structure Reconstruction) enables chemical-bonding analysis based on periodic plane-wave (PAW) density-functional theory (DFT) output and is applicable to a wide range of first-principles simulations in solid-state and materials chemistry. LOBSTER incorporates analytic projection routines described previously in this very journal [J. Comput. Chem. 2013, 34, 2557] and offers improved functionality. It calculates, among others, atom-projected densities of states (pDOS), projected crystal orbital Hamilton population (pCOHP) curves, and the recently introduced bond-weighted distribution function (BWDF). The software is offered free-of-charge for non-commercial research. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
Diamond has the highest number density (i.e., the number of atoms per unit volume) of all known substances and a remarkably high valence electron density (rws = 0.697 Å). Searching for possible superdense carbon allotropes, we have found three structures (hP3, tI12, and tP12) that have significantly greater density. The hP3 and tP12 phases have strong analogy with two polymorphs of silica (β-quartz and keatite), while the tI12 phase is related to the high-pressure SiS2 polymorph. Furthermore, we found a collection of other superdense structures based on the motifs of the aforementioned structures, but with different ways of packing carbon tetrahedra, and among these the hP3 and tI12 structures are the densest. At ambient conditions, the hP3 phase is a semiconductor with the GW band gap of 3.0 eV, tI12 is an insulator with the band gap of 5.5 eV, while tP12 is an insulator, the band gap of which is remarkably high (7.3 eV), making it the widest-gap carbon allotrope. These allotropes are metastable and have comparable to diamond or slightly higher bulk moduli; their Vickers hardnesses are calculated to be 87.6 GPa for hP3, 87.2 GPa for tI12, and 88.3 GPa for tP12, respectively, thus making these allotropes nearly as hard as diamond (for which the same model gives the hardness of 94.3 GPa). Superdense carbon allotropes are predicted to have remarkably high refractive indices and strong dispersion of light.
The basal plane cleavage energy (CE) of graphite is a key material parameter
for understanding many of the unusual properties of graphite, graphene, and
carbon nanotubes. The CE is equal to twice the surface energy and is closely
related to the interlayer binding energy and exfoliation energy of graphite.
Nonetheless, a wide range of values for these properties have been reported and
no consensus has yet emerged as to their magnitude. Here, we report the first
direct, accurate experimental measurement of the CE of graphite using a novel
method based on the recently discovered self-retraction phenomenon in graphite.
The measured value, 0.37 +/- 0.01 J/m2 for the incommensurate state of
bicrystal graphite, is nearly invariant with respect to temperature (from
22{\deg}C to 198{\deg}C) and bicrystal twist angle, and insensitive to
impurities (from the atmosphere). The cleavage energy for the ideal ABAB
graphite stacking, 0.39 +/- 0.02 J/m2, is calculated based upon a combination
of the measured CE and a theoretical calculation. These experimental
measurements are ideal for use in evaluating the efficacy of competing
theoretical approaches.
The transition from diamond to graphite is a key equilibrium for interpreting ultrahigh-pressure metamorphic rocks. Despite widespread interest, there remain significant systematic differences between the best available experimental determinations of P and T(Kennedy and Kennedy 1976) and numerous thermodynamic calculations of the transition. At temperatures below 1400 K, calculated equilibrium pressures are lower than extrapolations of the experiments by as much as 5 kbar. At 3000 K, calculated pressures vary from more than 8 kbar above to almost 20 kbar below the position of the extrapolated transition. A revised curve based on a critical review of the experimental and thermodynamic data is consistent with expanded experimental brackets and the preferred calorimetric data. It is steeper than the transition proposed by Kennedy and Kennedy (1976) and previous calculations and passes through 16.2 kbar, 298 K; 33.9 kbar, 1000 K; 63.5 kbar, 2000 K; and 98.4 kbar, 3000 K. The revised curve implies that the minimum pressure for formation of diamond-bearing crustal rocks is 3-4 kbar less than implied by extrapolation of the experiments. Because the revised transition is steeper than most previous calculations, the triple point among graphite, diamond, and liquid carbon may be as much as 40 kbar higher than previously estimated.
We present a comprehensive computational study of sp3-carbon allotropes based on the topologies proposed for zeolites. From ≈600000 zeolite nets we identified six new allotropes, lying by at most 0.12 eV per atom above diamond. The analysis of cages in the allotropes has revealed close structural relations to diamond and lonsdaleite phases. Besides the energetic and mechanical stability of new allotropes, three of them show band gaps by ca. 1 eV larger than that of diamond, and therefore represent an interesting technological target as hard and transparent materials. A structural relation of new allotropes to continuous random networks is pointed out and possible engineering from diamond thin films and graphene is suggested.
Graphene research has accelerated exponentially since 2004 when graphene was isolated and characterized for the first time utilizing the ‘Scotch Tape’ method by Geim and Novoselov and given the reports of unique electronic properties that followed. The number of academic publications reporting the use of graphene was so substantial in 2013 that it equates to over 40 publications per day. With such an enormous interest in graphene it is imperative for both experts and the layman to keep up with both current graphene technology and the history of graphene technology. Consequently, this review addresses the latter point, with a primary focus upon disseminating graphene research with a more applicatory approach and the addition of our own personal graphene perspectives; the future outlook of graphene is also considered.
The enthalpy of gem diamonds has been measured from 273° to 1073°K using a ``drop'' method and a Bunsen ice calorimeter. The derived heat‐capacity values, which are believed to be accurate to ±0.5%, are used to calculate the thermal functions of diamond above 298.15°K. Values of Cv0 (harmonic) derived from the present investigation and recent measurements of the thermal expansion and the elastic constants of diamond are compared with theoretical treatments. Reasonably good agreement in the temperature range of this study can be obtained with a single Debye function (ΘD=1860) obtained from the measured elastic constants. Extrapolation of the data gives Θ∞=1880±10.
We performed a systematic structural search of high-pressure carbon allotropes for unit cells containing from
6 to 24 atoms using the minima hopping method. We discovered a series of new structures that are consistently
lower in enthalpy than the ones previously reported. Most of these include (5+7)- or (4+8)-membered rings
and can therefore be placed in the families proposed by H. Niu et al. [Phys. Rev. Lett. 108, 135501 (2012)].
However, we also found three more families with competitive enthalpies that contain (5+5+8)-membered
rings, sp2
motives, or buckled hexagons. These structures are likely to play an important role in dislocation
planes and structural defects of diamond and hexagonal diamond.
A general systematic method of predicting hypothetical crystal structures could enable important advances in many areas of science. We describe a recently developed approach based on graph theory and density functional theory and apply it to enumerate systematically a number of sp3 -hybridized carbon polymorphs with four atoms per unit cell. The calculations predict three unknown structures that are potentially metastable under appropriate pressure and temperature conditions. The theoretical properties of these hypothetical polymorphs and their relative stability with respect to diamond are discussed.
The electronic properties of the regular graphite lattice are investigated within self-consistent LCAO (linear combination of atomic orbitals) scheme based as a modified extended-Hückel approximation. The band structure and interband transition energies agree favorably with previous first-principles calculations. Good agreement with experimental data on the density of valence states, energetic position of the lowest conduction states, equilibrium unit-cell parameters, cohesive energy and vibration force constants, is obtained. The McClure band parameters that were previously adjusted to obtain agreement with Fermi-surface data and the electronic specific heat, are reasonably reproduced. The charge distribution and bonding characteristics of the covalent graphite structure, are discussed. The same calculation scheme is used in part II of this article (following paper) to discuss properties associated with point defects in graphite. The correlation between the electronic properties of the regular and point-defect-containing lattice is studied.
On the basis of first-principles calculations, we contrast the favorable total energies of certain carbon allotropes with their uncompetitive bonding strengths as compared with those of graphite or diamond. Clearly, our tentative approach draws from ideas of organic synthesis and retrosynthesis by focusing at those bonds that have to be formed and stabilized or cleaved for preparing a certain C-based material. In particular, the covalent C–C bonds of the carbon allotropes are studied by extracting their crystal orbital Hamilton population (COHP) energies from plane-wave density-functional theory because this quantum-mechanical measure of covalent bond strength allows for a simple, yet numerically precise allotropic ranking including graphite and diamond. While many of the lowest-energy allotropes feature plainly imperfect bonding, we found a single one (topology 3².4T203 in SACADA) with both strong bonding and favorable total energy at the same time. To help experimentalists in distinguishing this very allotrope from all the other predicted carbon allotropes, we propose IR spectroscopy and predict certain vibrational fingerprints such as to identify 3².4T203 in exploratory syntheses.
Utilizing first-principles electronic-structure calculations, we present the chemical-bonding analyses of hypothetical carbon allotropes based on tetrahedral structure motifs such as T-carbon, TY-carbon and T-graphene. While previous publications on these novel allotropes have dealt with ab initio phonon, band structure and DOS calculations, the focus of this work is the partitioning of the band-structure energy in terms of bonding, nonbonding and antibonding contributions. We re-evaluate the chance of making such allotropes by careful bond analyses and compare them to already known equivalents, namely diamond, graphene and the Buckminsterfullerene molecule. A synthetic route is proposed to a new compound, called TY-carbodiimide, that exhibits similar structure and bonding properties as TY-carbon.
The Front Cover picture visualizes the strong binding of intermediate states to covalent attachment, so called precursors, for ethylene on Si(001). This is in stark contrast to the common picture of precursors, in which they are considered to be physisorbed and mobile. More information can be found in the Communication by J. Pecher and R. Tonner on page 34 in Issue 1, 2017 (DOI: 10.1002/cphc.201601129).
Silicene is a two-dimensional allotrope of silicon with a puckered hexagonal structure closely related to the structure of graphene and that has been predicted to be stable. To date, it has been successfully grown in solution (functionalized) and on substrates. The goal of this review is to provide a summary of recent theoretical advances in the properties of both free-standing silicene as well as in interaction with molecules and substrates, and of proposed device applications.
The story of C_2 continues to fascinate chemists spinning around a possibility of quadruple bonds for p-elements and discussing a wealth of options for the nature of an unconventional fourth bond. This led to lively discussions about the ways of counting or measuring bonds, and the interplay between the bond strength (energy), its length, and rigidity/stiffness (elasticity). Even old concerns about the possibility of theorems in chemistry and thus of the place of chemistry among ‘true’ sciences had been revived. We show that under some mild conditions certain exact statements (lemmas and theorems) about the C_2 molecule can be relatively easily proven which, if not resolves the controversy entirely, at least provides some theoretical reference points to the discussion. Some more general consequences from this experience are discussed as well.
Searches for low-energy tetrahedral polymorphs of carbon and silicon have been performed using density functional theory computations and the ab initio random structure searching approach. Several of the hypothetical phases obtained in our searches have enthalpies that are lower or comparable to those of other polymorphs of group 14 elements that have either been experimentally synthesized or recently proposed as the structure of unknown phases obtained in experiments, and should thus be considered as particularly interesting candidates. A structure of Pbam symmetry with 24 atoms in the unit cell was found to be a low-energy, low-density metastable polymorph in carbon, silicon, and germanium. In silicon, Pbam is found to have a direct band gap at the zone center with an estimated value of 1.4 eV, which suggests applications as a photovoltaic material. We have also found a low-energy chiral framework structure of symmetry with 20 atoms per cell containing fivefold spirals of atoms, whose projected topology is that of the so-called Cairo-type two-dimensional pentagonal tiling. We suggest that is a likely candidate for the structure of the unknown phase XIII of silicon. We discuss Pbam and in detail, contrasting their energetics and structures with those of other group 14 elements, particularly the recently proposed structure, for which we also provide a detailed interpretation as a network of tilted diamondlike tetrahedra.
During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells1, graphite has been vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. Concerning the question of what kind of 60-carbon atom structure might give rise to a superstable species, we suggest a truncated icosahedron, a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. This object is commonly encountered as the football shown in Fig. 1. The C60 molecule which results when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond, has many resonance structures, and appears to be aromatic.
Using density functional theory, we investigate the structural, vibrational, and dielectric properties of titanium oxides and silicates, which have attracted considerable attention in the framework of the quest for alternative high-materials. For the oxides, three crystalline phases of titanium dioxide are considered. The first two are hypothetical; they are obtained by similarity with the cubic and tetragonal structure of zirconia ZrO 2 or hafnia HfO 2. The third is the rutile, a crystal that occurs naturally. For the silicates, we analyze a hypothetical TiSiO 4 structure constructed by analogy with crystalline ZrSiO 4 and HfSiO 4 (zircon and hafnon).
Substitutional heteroatom doping is a promising route to modulate the outstanding material properties of carbon nanotubes and graphene for customized applications. Recently, (nitrogen-) N-doping has been introduced to ensure tunable work-function, enhanced n-type carrier concentration, diminished surface energy, and manageable polarization. Along with the promising assessment of N-doping effects, research on the N-doped carbon based composite structures is emerging for the synergistic integration with various functional materials. This invited feature article reviews the current research progress, emerging trends, and opening opportunities in N-doped carbon based composite structures. Underlying basic principles are introduced for the effective modulation of material properties of graphitic carbons by N-doping. Composite structures of N-doped graphitic carbons with various functional materials, including (i) polymers, (ii) transition metals, (iii) metal oxides, nitrides, sulphides, and (iv) semiconducting quantum dots are highlighted. Practical benefits of the synergistic composite structures are investigated in energy and catalytic applications, such as organic photovoltaics, photo/electro-catalysts, lithium ion batteries and supercapacitors, with a particular emphasis on the optimized interfacial structures and properties.
The relative stability of graphite and diamond is revisited with hybrid density functional theory calculations. The electronic energy of diamond is computed to be more negative by 1.1 kJ-mol-1 than that of graphite at T=0 K and in the absence of external pressure. Graphite gains thermodynamic stability over diamond at 298 K only because of the differences in the zero-point energy, specific heat, and entropy terms for both polymorphs. Graphite or diamond? The relative stabilities of graphite and diamond are revisited with hybrid density functional theory calculations. The electronic energy of diamond is computed to be more negative by 1.1 kJ-mol-1 than that of graphite at a temperature of 0 K and in the absence of an external pressure.
The definition of bond orders for singlet correlated wave functions is improved by adding a term providing the correct dissociation behaviour if the system dissociates into open-shell fragments.
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.
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.
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,”[ Ring formation is evidently the reaction that can provide the most important information on the spatial arrangement of atoms. Steric reasons should explain the observation that 5‐ or 6‐membered chain undergoes ready closure, whereas a shorter or longer chain undergoes difficult or no closure.… The four valences of the carbon atom act in the directions that connect the center of a sphere with the corners of a tetrahedron and form angles of 109°28′ with one another. The direction of the attraction can deviate, but this in increasing strain as the sizes of the latter increase.
] 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.
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.
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.
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)
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.
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.
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.
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.
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.