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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.

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Effective Hamiltonian of Crystal Field (EHCF) is a hybrid quantum chemical method originally developed for an accurate treatment of highly correlated d-shells in molecular complexes of transition metals. In the present work, we generalise the EHCF method to periodic systems containing transition metal atoms with isolated d-shells, either as a part of their crystal structure or as point defects. A general solution is achieved by expressing the effective resonance interactions of an isolated d-shell with the band structure of the crystal in terms of the Green's functions represented in the basis of local atomic orbitals. Such representation can be obtained for perfect crystals and for periodic systems containing atomic scale defects. Our test results for transition metal oxides (MnO, FeO, CoO, and NiO) and MgO periodic solid containing transition metal impurities demonstrate the ability of the EHCF method to accurately reproduce the spin multiplicity and spatial symmetry of the ground state. For the studied materials, these results are in a good agreement with experimentally observed d-d transitions in optical spectra. The proposed method is discussed in the context of modern solid state quantum chemistry and physics.

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.

We present a standalone ΘΦ (ThetaPhi) package capable to read the results of ab initio DFT/PAW quantum‐chemical solid‐state calculations processed through various tools projecting them to the atomic basis states as an input and to perform on top of this an analysis of so derived electronic structure which includes (among other options) the possibility to obtain a superconducting (Bardeen‐Cooper‐Schrieffer, BCS), spin‐liquid (resonating valence bond, RVB) states/phases as solutions of the electronic structure problem along with the magnetically ordered phases with an arbitrary pitch (magnetic superstructure) vector. Remarkably, different solutions of electronic‐structure problems come out as temperature‐dependent (exemplified by various superconducting and spin‐liquid phases) which feature is as well implemented. All that is exemplified by model calculations on 1D chain, 2D square lattice as well as on more realistic superconducting doped graphene, magnetic phases of iron, and spin‐liquid and magnetically ordered states of a simplest nitrogen‐based copper pseudo‐oxide, CuNCN, resembling socalled metal‐oxide framework (MOF) phases by the atomic interlinkage. The available solid‐state electronic‐structure codes are devoid of hot topics of physics: incommensurate magnetic, superconducting, and spin‐liquid electronic states/phases. The temperature dependence of the solutions of electronic problem is not accessible either. These gaps are closed by the proposed ΘΦ package.

Local and angular momentum projected densities of states (DOS) are invaluable sources of information that can be obtained from density functional theory calculations. In this work, we describe a theoretical framework within ONETEP's linear-scaling DFT formalism that allows the calculation of local (atom-projected) and angular momentum projected density of states l-p-DOS. We describe four different bases that can be used for projecting the DOS with angular momentum resolution and perform a set of tests to compare them. We validate the results obtained with ONETEP's l-p-DOS against the plane-wave DFT code CASTEP. Comparable results between ONETEP's and CASTEP's charge spilling parameters are observed when we use pseudo-atomic orbitals as the projection basis sets. In general, the charge spilling parameters show remarkably low values for projections using non-contracted spherical waves as the angular momentum resolved basis. We also calculate the d-band and d-band centres for Pt atoms in (111) facets of cuboctahedral Pt nanoparticles of increasing size, which is an example of l-p-DOS application commonly used as an electronic descriptor in heterogeneous catalysis. Interestingly, the different projection bases lead to similar conclusions, showing the reliability of the implemented method for such studies. The implementation of these methods in a linear-scaling framework such as ONETEP provides another tool for analysing the electronic structure of complex nanostructured materials.

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.

In the present work, we revisit the problem of atomic orbitals from the positions mostly dictated by semiempirical approaches in quantum chemistry. To construct basis set, having proper nodal structure and simple functional form of orbitals and representing atomic properties with reasonable accuracy, authors propose an Ansatz based on gradual improvement of hydrogen atomic orbitals. According to it, several basis sets with different numbers of variable parameters are considered and forms of orbitals are obtained for the 2nd-row elements either by minimization of their ground state energy (direct problem) or by extracting from atomic spectra (inverse problem). It is shown that so-derived three- and four-parametric basis sets provide accurate description of atomic properties, being, however, substantially provident for computational requirements and, what is more important, simple to handle in analytic models of quantum chemistry. Since the discussed Ansatz allows a generalization for heavier atoms, our results may be considered not only as a solution for light elements, but also as a proof of concept with possible further extension to a wider range of elements.

Recognizing the bonding situations in chemical compounds is of fundamental interest for materials design because this very knowledge allows us to understand the sheer existence of a material and the structural arrangement of its constituting atoms. Since its definition 25 years ago, the Crystal Orbital Hamilton Population (COHP) method has been established as an efficient and reliable tool to extract the chemical-bonding information based on electronic-structure calculations of various quantum-chemical types. In this review, we present a brief introduction into the theoretical background of the COHP method and illustrate the latter by diverse applications, in particular by looking at representatives of the class of (polar) intermetallic compounds, usually considered as “black sheep” in the light of valence-electron counting schemes.

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.

The effect of the linear approximation of the electronic spectrum of single-layer graphene (low-energy approximation) on the magnitude of charge transfer between an adatom and graphene has been investigated. It has been shown that the implementation of this approximation for adsorption of alkali metals and halogens leads to a change in the occupation numbers of local and band states as compared to the results obtained in the model taking into account the entire spectrum. However, the total occupation numbers agree quite well.

The Green’s functions for the Alexander-Anderson problem have been obtained using the previously proposed model density of states for graphene. Both the ferromagnetic and antiferromagnetic dimers have been considered. It has been shown that, in order to describe the density of states of the dimer adatom, the density of states of the isolated adatom with two positions of the gravity center of the quasi-level shifted in opposite directions can be used. It has been demonstrated that the approximate method of obtaining the Green’s function of the dimer proposed by us previously and consisting in that the Green’s function of the adatom rather than that of the atom is taken as the seed function gives the same result as the Alexander-Anderson approach. The dependences of the indirect interaction of dimer adatoms on the problem parameters have been evaluated in the limit of low energies.

The change in the local density of states δρg
of a single-sheet graphene due to adsorption of a single atom has been calculated in the framework of the M model proposed earlier. The dependence of the local density of states δρg
on the position of the adatom energy level ɛa
with respect to the Dirac point and other parameters of the problem has been analyzed. It has been shown that the largest changes in the local density of states δρg
are caused by adatoms with the ɛa
levels lying in the vicinity of the Dirac point, so that the minimum density of states of graphene remains equal to zero. An analytical expression has been derived for the energy of bonding W
ads of the adatom with graphene. The obtained estimates of the bonding energy W
ads in the weak and strong adatom-substrate bonding regimes are presented. Atoms of alkali metals and halogens have been considered as specific adsorbates.

The π-electron charge Qsh in alternant conjugated systems with one heteroatom is considered. A complete proof of the law of alternating polarity is presented. The integral expression for Qsh is decomposed into a number of relatively simple terms, which give some insight into the dependence of Qsh, on molecular topology.

A simple M-shaped model has been proposed for the density of states of the π bands of the graphene. The model has been used to derive
the expression for the local density of states on the adsorbed atom and to calculate the corresponding occupation numbers
for different model parameters. Additional simplifications have made it possible to represent the band contribution n
b
to the total occupation number of the adatom n
a
in the analytical form. The contributions of local states n
l
to n
a
= n
b
+ n
l
have been calculated for different parameters. The charge has been numerically evaluated for the case of adsorption of alkali
metal atoms on the graphene. The results obtained have been verified using the model of a surface diatomic molecule calculated
by the Harrison bond-orbital method. The verification has demonstrated that the charges calculated in terms of radically different
models are in good agreement.

The problem of developing an exact form of the junction between the quantum and classical parts in a hybrid QC/MM approach is considered. We start from the full Hamiltonian for the whole system and assume a specific form of the electron wavefunction, which allows us to separate the electron variables relevant to the reactive (quantum) part of the system from those related to the inert (classical) part. Applying the Löwdin partition to the full Hamiltonian for the molecular system results in general formulae for the potential energy surfaces of a molecular system composed of different parts provided some of these parts are treated quantum mechanically whereas others are treated with use of molecular mechanics. These principles of separating electron variables have been applied to construct an efficient method for analysis of electronic structure and d-electron excitation spectra of transition metal complexes. This method has been also combined with the MM approximation in order to get a description for potential energy surfaces of the complexes and to develop a consistent approach to the known problem of extending molecular mechanics to transition metals.

Simulating the incommensurate spin density waves (ISDW) states is not a simple task within the standard ab initio methods. Moreover, in the context of new material discovery, there is a need for fast and reliable tool capable to scan and optimize the total energy as a function of the pitch vector, thus allowing to automatize the search for new materials. In this paper we show how the ISDW can be efficiently obtained within the recently released ΘΦ program. We illustrate this on an example of the single orbital Hubbard model and of γ-Fe, where the ISDW emerge within the mean-field approximation and by using the twisted boundary conditions. We show the excellent agreement of the ΘΦ with the previously published ones and discuss possible extensions. Finally, we generalize the previously given framework for spin quantization axis rotation to the most general case of spin-dependent hopping matrix elements.

We propose the ΘΦ package which addresses two of the most important extensions of the essentially single-particle mean-field paradigm of the computational solid state physics: the admission of the Bardeen–Cooper–Schrieffer electronic ground state and allowance of the magnetically ordered states with an arbitrary superstructure (pitch) wave vector. Both features are implemented in the context of multi-band systems which paves the way to an interplay with the solid state quantum physics packages eventually providing access to the first-principles estimates of the relevant matrix elements of the model Hamiltonians derived from the standard DFT calculations. Several examples showing the workability of the proposed code are given.

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.

ConspectusComplex chemical systems present challenges to electronic structure theory stemming from large system sizes, subtle interactions, coupled dynamical time scales, and electronically nonadiabatic effects. New methods are needed to perform reliable, rigorous, and affordable electronic structure calculations for simulating the properties and dynamics of such systems.This Account reviews projection-based quantum embedding for electronic structure, which provides a formally exact method for density functional theory (DFT) embedding. The method also provides a rigorous and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction (WF) method while the remainder of the system is described at the level of DFT. A key advantage of projection-based embedding is that it can be formulated in terms of an extremely simple level-shift projection operator, which eliminates the need for any optimized effective potential calculation or kinetic energy functional approximation while simultaneously ensuring that no extra programming is needed to perform WF-in-DFT embedding with an arbitrary WF method. The current work presents the theoretical underpinnings of projection-based embedding, describes use of the method for combining wavefunction and density functional theories, and discusses technical refinements that have improved the applicability and robustness of the method.Applications of projection-based WF-in-DFT embedding are also reviewed, with particular focus on recent work on transition-metal catalysis, enzyme reactivity, and battery electrolyte decomposition. In particular, we review the application of projection-based embedding for the prediction of electrochemical potentials and reaction pathways in a Co-centered hydrogen evolution catalyst. Projection-based WF-in-DFT calculations are shown to provide quantitative accuracy while greatly reducing the computational cost compared with a reference coupled cluster calculation on the full system. Additionally, projection-based WF-in-DFT embedding is used to study the mechanism of citrate synthase; it is shown that projection-based WF-in-DFT largely eliminates the sensitivity of the potential energy landscape to the employed DFT exchange-correlation functional. Finally, we demonstrate the use of projection-based WF-in-DFT to study electron transfer reactions associated with battery electrolyte decomposition. Projection-based WF-in-DFT embedding is used to calculate the oxidation potentials of neat ethylene carbonate (EC), neat dimethyl carbonate (DMC), and 1:1 mixtures of EC and DMC in order to overcome qualitative inaccuracies in the electron densities and ionization energies obtained from conventional DFT methods. By further embedding the WF-in-DFT description in a molecular mechanics point-charge environment, this work enables an explicit description of the solvent and ensemble averaging of the solvent configurations.Looking forward, we anticipate continued refinement of the projection-based embedding methodology as well as its increasingly widespread application in diverse areas of chemistry, biology, and materials science.

Graphene is one of the most promising materials for post-silicon electronics and has outstanding physical and electronic properties. In particular, its unique 2D sp²-hybridized networks of carbon atoms arranged in a honeycomb lattice make graphene potential for exceptional electronic quality. However, in order to use graphene in possible applications such as photodetector, photovoltaics, sensors, organic light-emitting diodes, organic thin-film transistors, supercapacitor, and catalytic applications, it is essential to precisely modulate its electronic properties, i.e. doping. In this review, we present various strategies for engineering the Fermi level in graphene, including heteroatom substitution, molecular adsorption, introducing functional molecules for external stimuli responsiveness. We anticipate that the current review provides a concise information on the methods to probe doping level, effective doping approaches, and achievable doping type and charge carrier concentration ranges so that an appropriate doping approach can be readily designed.

It is widely recognized that an understanding of the physical and chemical properties of clusters will give a great deal of important information relevant to surface and bulk properties of condensed matter. This relevance of clusters for condensed matter is one of the major motivations for the study of atomic and molecular clusters. The changes of properties with cluster size, from small clusters containing only a few atoms to large clusters containing tens of thousands of atoms, provides a unique way to understand and to control the development of bulk properties as separated units are brought together to form an extended system. Another important use of clusters is as theoretical models of surfaces and bulk materials. The electronic wavefunctions for these cluster models have special advantages for understanding, in particular, the local properties of condensed matter. The cluster wavefunctions, obtained with molecular orbital theory, make it possible to relate chemical concepts developed to describe chemical bonds in molecules to the very closely related chemical bonding at the surface and in the bulk of condensed matter. The applications of clusters to phenomena in condensed matter is a cross-disciplinary activity which requires the interaction and collaboration of researchers in traditionally separate areas. For example, it is necessary to bring together workers whose background and expertise is molecular chemistry with those whose background is solid state physics. It is also necessary to bring together experimentalists and theoreticians.

I. The Born-Oppenheimer Hamiltonian. 1. Separating the center of mass motion in quantum mechanics. 1.1. Reducing the two-body problem to two one-body ones. 1.2. The center of mass in quantum mechanics 1.3. Free atoms and atomcules. 2. The Born--Oppenheimer approximation. 2.1. Introductory remarks. 2.2. The Born-Oppenheimer separation. 2.3. Why the Born-Oppenheimer separation is not exact? 2.4. Approximate decoupling. 2.5. A note on the Born-Oppenheimer separation. II. General Theorems And Principles. 1. The variation principle. 1.1. The Rayleigh quotient. 1.2. The variation principle for the ground state. 1.3. The variation principle as an equivalent of the Schrodinger equation: a useful formulation of the variation principle. 1.4. Eckart's inequality. 1.5. Excited states. 2. The Hellmann - Feynman theorem. 2.1. The differential Hellmann - Feynman theorem. 2.2. The integral Hellmann -Feynman theorem. 3. The virial theorem in quantum mechanics. 3.1. Time dependence of a physical quantity. 3.2. The virial theorem. 3.3. Scaling - a connection with the variation principle. 3.4. The virial theorem in the Born-Oppenheimer approximation. 3.5. The virial theorem and the chemical bonding. III. The Linear Variational Method And Lowdin's Orthogonalization Schemes. 1. The linear variational method (Ritz -method) 2. Lowdin's symmetric orthogonalization. 2.1. Matrix SAND-1/2. 2.2. The S∧-1/2 transformation. 2.3. The Lowdin basis. 2.4. The stationary property of Lowdin's symmetric orthogonalization scheme. 2.5. Lowdin-orthogonalization: a two-dimensional example. 3. Linear independence of the basis and Lowdin's canonic orthogonalization. 3.1. Eigenvalues of the overlap matrix: a measure for the linear. 3.2. Lowdin's canonic orthogonalization. IV. Perturbational Methods. 1. Non-degenerate Rayleigh-Schrodinger perturbation theory. 1.1. The problem. 1.2. 'Algebraic' expansion. 1.3. The use of the reduced resolvent in the Rayleigh-Schrodinger perturbation theory. 1.4. Wigner's 2n+1 theorem. 2. Variational-perturbational method: the Hylleraas-functional.3. Degenerate Rayleigh-Schrodinger perturbation theory. 4. Brillouin-Wigner perturbation theory. 4.1. The size-consistency problem. 5. Size consistency of the Rayleigh-Schrodinger perturbation. 5.1. Formal considerations based on the properties of power series. 5.2. Size consistency of the perturbational expansions. 6. Lowdin's partitioning method. V. Determinant Wave Functions. 1. Spin-orbitals. 2. Many-electron spin states. 3. Slater determinants. 3.1. Two-electron examples. 4. The antisymmetrizing operator. 4.1. The projection character of the antisymmetrizing operator. 4.2. Commutation properties of the antisymmetrizing operator. 5. Invariance of the determinant wave function with respect of. 6. Matrix elements between determinant wave functions. 6.1. Overlap. 6.2. One-electron operators. 6.3.

It is shown that the standard formulas of reducing elliptic integrals to the normal forms are useful in expressing the lattice Green's functions for the cubic lattices as a sum of simple integrals of the complete elliptic integrals.

Heterogeneous catalysts are ‘high tech’ materials, of huge economical and societal stake. Density Functional Theory (DFT) of electronic structure in molecules and solids has been playing a growing role in the science behind applied heterogeneous catalysis for the past 25 years, and it is the purpose of this article to explain why and how. The main characteristics of heterogeneous catalysts are first recalled, as well as the typical conceptual gaps hampering the rational design and synthesis of these key materials for fuels and chemicals production. A wish list of the basic requirements for an adapted computational chemistry approach follows. In view of this list, the specificities of DFT help explain why this approach became so overwhelmingly popular for addressing heterogeneous catalysis research issues. This adequacy is illustrated by a few examples.

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This is the first book to present both classical and quantum-chemical approaches to computational methods, incorporating the many new developments in this field from the last few years. Written especially for "non"-theoretical readers in a readily comprehensible and implemental style, it includes numerous practical examples of varying degrees of difficulty. Similarly, the use of mathematical equations is reduced to a minimum, focusing only on those important for experimentalists. Backed by many extensive tables containing detailed data for direct use in the calculations, this is the ideal companion for all those wishing to improve their work in solid state research.

A simple and accurate algorithm to evaluate the Hilbert transform of a real function is proposed using interpolations with piecewise–linear functions. An appropriate matrix representation reduces the complexity of this algorithm to the complexity of matrix-vector multiplication. Since the core matrix is an antisymmetric Toeplitz matrix, the discrete trigonometric transform can be exploited to calculate the matrix–vector multiplication with a reduction of the complexity to O(N log N), with N being the dimension of the core matrix. This algorithm has been originally envisaged for self-consistent simulations of radio-frequency wave propagation and absorption in fusion plasmas.

The lattice Green’s function of the simple cubic lattice
\includegraphics{dummy.eps} is considered for the following ranges of
the parameters; t{=}s-i\varepsilon, -∞<s<∞,
0≤l+m+n≤5. The function Gsc(t;l, 0, 0) along an axis is
expressed as a sum of simple integrals of the complete elliptic integral
of the first kind and the integrals are evaluated numerically. The
function Gsc(t;l, m, n) at a general position (l, m, n) is
calculated with the aid of the recurrence formula which is satisfied by
the Green’s function. The behaviors of the function
Gsc(t;l, m, n) are shown by figures. Discussions of the
divergent behavior of the derivative of Gsc(t;l, 0, 0) with
respect to s, are given at the singular points, s{=}0, 1 and 3.

Solid surfaces are used extensively as catalysts throughout the chemical industry, in the energy sector, and in environmental protection. Recently, density functional theory has started providing new insight into the atomic-scale mechanisms of heterogeneous catalysis, helping to interpret the large amount of experimental data gathered during the last decades. This article shows how density functional theory can be used to describe the state of the surface during reactions and the rate of catalytic reactions. It will also show how we are beginning to understand the variation in catalytic activity from one transition metal to the next. Finally, the prospects of using calculations to guide the development of new catalysts in industry will be discussed.

The indirect interaction between adatom pairs on the (100) surface of a simple-cubic tight-binding solid is investigated within a molecular-orbital approach. A general scheme for calculating the surface-density-of-states change and the interaction energy of one and two single-level adatoms is presented, and contact (and a correction) is made with Grimley's formulation. The method permits binding above surface atoms, at bridge sites, or at centered positions, and yields interaction energy as a function of band filling, adatom energy level, and a general hopping potential V between an adatom and the nearest surface atom(s). Calculations have been carried out for V/Wb in the range 1/12-1/2, the upper limit giving split-off states (Wb≡bandwidth). The single-atom interaction shows little dependence on binding type, in all three cases being most attractive when the Fermi energy equals the noninteracting adatom level, with a strongly V-dependent strength. For the pair interaction, one finds a strength at nearest-neighbor separation of about an order of magnitude smaller than the absorption energy of a single adatom. This interaction has an exponentiallike dropoff and sign alternations as one moves along the 〈10〉 direction. Under reasonable conditions, the nearest-neighbor interaction is often repulsive while the next nearest, third nearest, or fourth nearest is attractive, suggesting the patterns c(2×2), (2 × 2), and c(4×2), respectively, which are frequently observed in the adsorption of simple gases on the (100) surfaces of transition metals. On the basis of two-dimensional Ising-model calculations including second-neighbor interactions, one can estimate the strength of V from the observed disordering temperature of the adatom lattice; the result is similar to that obtained from estimates based on the heat of adsorption.

The effect of dilute impurities on the spin-wave spectrum of ferromagnetic insulators has been studied. The theory of spin-wave impurity states is developed from the Heisenberg exchange Hamiltonian using Green's function techniques. The low-lying, s-like, impurity states for cubic crystals are discussed and shown to depend only upon the unperturbed spin-wave density of states. Numerical results are obtained for simple cubic crystals. It is shown that localized states lying outside of the spin-wave band as well as virtual states which decay into the continuum can exist. The energy of the s-, p-, and d-like states is obtained as a function of the ratios of the impurity spin and effective exchange to those of the host atoms. The nature of the virtual states is discussed and a general expression for the width is obtained by considering the change in the density of states due to the impurities. Low-lying, s-like, virtual states with long lifetimes are found to exist, and it is suggested that these states may cause significant effects in the spin-wave specific heat and thermal conductivity of impure ferroinsulators.

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.

Quantum chemical aspects of chemical bonding to metal surfaces are discussed. It is demonstrated that a Frontier Orbital Theory of chemisorption can be developed in which the group orbital local density of states at the Fermi level replaces the HOMO and LUMO interactions familiar in organic or organo-metallic chemistry. This appears to be a useful tool to describe elementary reactions at metal surfaces. Dissociation of the H2 molecule and hydrogen atom recombination is analysed in detail. Symmetry considerations can be applied. It is shown that the interaction with antisymmetric group orbitais lowers the activation energies. Such orbitais are also available at s-valence electron metal surfaces as long as the molecule interacts in bridging coordination sites.One finds that the interaction with metal d-valence electrons stabilizes coordination in the atop position. The relative contribution to bonding of metal s and d-valence electrons differs significantly for the transition metals. It is not only a function of metal-electron occupation, number, but also of the row in the periodic system in which the metal is placed. This information is used to explain the different hydrogenolysis behaviour of Ni and Pt.

The electronic structure and binding energy of the 5d transition atoms on (100)W have been calculated in the Hartree-Fock approximation using Hubbard's Hamiltonian to describe the surface molecule. The experimental binding energy trend is reproduced.

The theory of Part I (Coulson & Longuet-Higgins 1947) is applied to hydrocarbons and their hetero-derivatives. An equation is given relating differences in activation energy to electron densities and atom polarizabilities (in the sense of Part I) for a heterolytic reaction at different positions in a conjugated system. The equations of Part I are then applied to hydrocarbons containing no odd-membered unsaturated rings. It has previously been shown that in such hydrocarbons all the electron densities are unity, and it is here proved that when one coulomb integral is altered slightly, the electron densities are alternately increased and decreased throughout the molecule. This fact is shown to provide a theoretical basis for the experimental law of alternating polarity in conjugated systems containing a hetero-atom.

The covariant quantum electrodynamics of Tomonaga, Schwinger, and Feynman is used as the basis for a general treatment of scattering problems involving electrons, positrons, and photons. Scattering processes, including the creation and annihilation of particles, are completely described by the $S$ matrix of Heisenberg. It is shown that the elements of this matrix can be calculated, by a consistent use of perturbation theory, to any desired order in the fine-structure constant. Detailed rules are given for carrying out such calculations, and it is shown that divergences arising from higher order radiative corrections can be removed from the $S$ matrix by a consistent use of the ideas of mass and charge renormalization.

Article de synthese montrant les similarites entre la structure electronique des molecules et des solides et suggerant le developpement d'idees destinees a l'etude des molecules, pour l'etude de l'etat solide

1. Periodic structure; 2. Lattice waves; 3. Electron states; 4. Static
properties of solids; 5. Electron-electron interaction; 6. Dynamics of
electrons; 7. Transport properties; 8. Optical properties; 9. The fermi
surface; 10. Magnetism; 11. Superconductivity; Bibliography; Index.

The chemisorption energy of an atom in the 5d series on a tungsten substrate is calculated on the basis of a two-center Hubbard model, for which the ground-state energy may be obtained exactly. The experimental data can be fitted with a choice of parameters consistent with independent estimates.

After a brief summary of the ideas underlying the quantum theory of dispersion it is shown that it can be applied to the refraction of x-rays, although the assumption that the number of atoms in a wave length cube is large is no longer satisfied. A general formula for the index of refraction in terms of the atomic absorption coefficient a and the critical frequencies is given. From the condition, experimentally verified, that the electrons in the atom for impressed frequencies, large compared to their natural frequencies, shall act like free electrons as far as the index of refraction is concerned, a relation is obtained for a. From the failure of this relation when applied to the groups of electrons separately, conclusions are drawn as to the coupling of the groups. Some considerations on the origin of the Compton shifted radiation are added, from which it appears that in the wave description this radiation must be regarded as coming from all the atoms and as being coherent with the incident waves; a result suited to stress the difficulty of harmonizing the wave picture with that of quantum processes in the atoms.

. Double- and triple-zeta basis sets of Slater-type functions (STFs) are developed for the 17 atoms from He to Ar. For computational
economy, the exponents of STFs corresponding to the same atomic subshell are restricted to be common. Instead, the principal
quantum numbers of the STFs are thoroughly optimized within the framework of integer values to reduce the energy loss due
to the common exponent restriction.

To make sense of the marvelous electronic properties of the solid state, chemists must learn the language of solid-state physics, of band structures. An attempt is made here to demystify that language, drawing explicit parallels to well-known concepts in theoretical chemistry To the joint search of physicists and chemists for understanding of the bonding in extended systems, the chemist brings a great deal of intuition and some simple but powerful notions. Most important among these is the idea of a bond, and the use of frontier-orbital arguments. How to find localized bonds among all those maximally delocalized bands? Interpretative constructs, such as the density of states, the decomposition of these densities, and crystal orbital overlap populations, allow a recovery of bonds, a finding of the frontier orbitals that control structure and reactivity in extended systems as well as discrete molecules.