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Abstract

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.
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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.
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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.
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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.
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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.
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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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Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
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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.
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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.
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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.
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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.
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. 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.
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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.