Abstract: The occupation of d orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition-metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations of the orbital occupation at surfaces and interfaces are believed to be responsible for massive variations of the magnetic and transport properties, but could not thus far be probed in a quantitative manner. Here we show that it is possible to derive quantitative, spatially resolved orbital polarization profiles from soft-X-ray reflectivity data, without resorting to model calculations. We demonstrate that the method is sensitive enough to resolve differences of ~3% in the occupation of Ni e(g) orbitals in adjacent atomic layers of a LaNiO(3)-LaAlO(3) superlattice, in good agreement with ab initio electronic-structure calculations. The possibility to quantitatively correlate theory and experiment on the atomic scale opens up many new perspectives for orbital physics in transition-metal oxides.

Abstract: The title compounds are studied with scalar relativistic, gradient-corrected (PBE) and hybrid (PBE0) density functional theory. The metal–Cp centroid distances shorten from ThCp3 to NpCp3, but lengthen again from PuCp3 to CmCp3. Examination of the valence molecular orbital structures reveals that the highest-lying Cp π2,3-based orbitals transform as 1e + 2e + 1a1 + 1a2. Above these levels come the predominantly metal-based 5f orbitals, which stabilise across the actinide series such that in CmCp3 the 5f manifold is at more negative energy than the Cp π2,3-based levels. Mulliken population analysis shows metal d orbital participation in the e symmetry Cp π2,3-based orbitals. Metal 5f character is found in the 1a1 and 1a2 levels, and this contribution increases significantly from ThCp3 to AmCp3. This is in agreement with the metal spin densities, which are enhanced above their formal value in NpCp3, PuCp3 and especially AmCp3 with both PBE and PBE0. However, atoms-in-molecules analysis of the electron densities indicates that the An–Cp bonding is very ionic, increasingly so as the actinide becomes heavier. It is concluded that the large metal orbital contributions to the Cp π2,3-based levels, and enhanced metal spin densities toward the middle of the actinide series arise from a coincidental energy match of metal and ligand orbitals, and do not reflect genuinely increased covalency (in the sense of appreciable overlap between metal and ligand levels and a build up of electron density in the region between the actinide and carbon nuclei).

Abstract: An explicit formulation of the Piris cumulant λΔ,Π matrix is described herein, and used to reconstruct the two-particle reduced density matrix (2-RDM). Then, we have derived a natural orbital functional, the Piris Natural Orbital Functional 5, PNOF5, constrained to fulfill the D, Q, and G positivity necessary conditions of the N-representable 2-RDM. This functional yields a remarkable accurate description of systems bearing substantial (near)degeneracy of one-particle states. The theory is applied to the homolitic dissociation of selected diatomic molecules and to the rotation barrier of ethylene, both paradigmatic cases of near-degeneracy effects. It is found that the method describes correctly the dissociation limit yielding an integer number of electrons on the dissociated atoms. PNOF5 predicts a barrier of 65.6 kcal/mol for the ethylene torsion in an outstanding agreement with Complete Active Space Second-order Perturbation Theory (CASPT2). The obtained occupation numbers and pseudo one-particle energies at the ethylene transition state account for fully degenerate π orbitals. The calculated equilibrium distances, dipole moments, and binding energies of the considered molecules are presented. The values obtained are accurate comparing those obtained by the complete active space self-consistent field method and the experimental data.

Abstract: Dynamical mean-field methods are used to calculate the phase diagram, many-body density of states, relative orbital occupancy, and Fermi-surface shape for a realistic model of LaNiO(3)-based superlattices. The model is derived from density-functional band calculations and includes oxygen orbitals. The combination of the on-site Hunds interaction and charge transfer between the transition metal and the oxygen orbitals is found to reduce the orbital polarization far below the levels predicted either by band-structure calculations or by many-body analyses of Hubbard-type models which do not explicitly include the oxygen orbitals. The findings indicate that heterostructuring is unlikely to produce one band-model physics and demonstrate the fundamental inadequacy of modeling the physics of late transition-metal oxides with Hubbard-like models.

Abstract: Density functional theory is based on the two Hohenberg-Kohn theorems, which state that the ground-state properties of an atom or molecule are determined by its electron density function, and that a trial electron density must give an energy greater than or equal to the true energy (the latter theorem is true only if the exact functional could be used). In the Kohn-Sham approach the energy of a system in formulated as a deviation from the energy of an idealized system with noninteracting electrons. From the energy equation, by minimizing the energy with respect to the Kohn-Sham orbitals the Kohn-Sham equations can be derived, analogously to the Hartree-Fock equations. Finding good functionals is the main problem in DFT. Various levels of DFT and kinds of functionals are discussed. The mutually related concepts of electronic chemical potential, electronegativity, hardness, softness, and the Fukui function are discussed.

Abstract: Quantum phases provide us with important information for understanding the fundamental properties of a system. However, the observation of quantum phases, such as Berry's phase and the sign of the matrix element of the Hamiltonian between two nonequivalent localized orbitals in a tight-binding formalism, has been challenged by the presence of other factors, e.g. , dynamic phases and spin or valley degeneracy, and the absence of methodology. Here, we report a way to directly access these quantum phases, through polarization-dependent angle-resolved photoemission spectroscopy (ARPES), using graphene as a prototypical two-dimensional material. We show that the momentum- and polarization-dependent spectral intensity provides direct measurements of (i) the phase of the band wavefunction and (ii) the sign of matrix elements for nonequivalent orbitals. Upon rotating light polarization by $\ensuremath{\pi}/2$, we found that graphene with a Berry's phase of $n\ensuremath{\pi}$ ($n=1$ for single- and $n=2$ for double-layer graphene for Bloch wavefunction in the commonly used form) exhibits the rotation of ARPES intensity by $\ensuremath{\pi}/n$, and that ARPES signals reveal the signs of the matrix elements in both single- and double-layer graphene. The method provides a technique to directly extract fundamental quantum electronic information on a variety of materials.

Abstract: We have carried out first-principles calculations on electronic properties of graphene quantum dots embedded in hexagonal boron nitride monolayer sheets. The calculations with density functional theory show that the band gaps of quantum dots are determined by the quantum confinement effects and the hybridization of π orbitals from B, N, and C atoms. The energy states near the Fermi level are found to be strongly localized within and in the vicinity of the quantum dots.

Abstract: Quantum interference (QI) in molecular transport junctions can lead to dramatic reductions of the electron transmission at certain energies. In a recent work [Markussen et al., Nano Lett., 2010, 10, 4260] we showed how the presence of such transmission nodes near the Fermi energy can be predicted solely from the structure of a conjugated molecule when the energies of the atomic pz orbitals do not vary too much. Here we relax the assumption of equal on-site energies and generalize the graphical scheme to molecules containing different atomic species. We use this diagrammatic scheme together with tight-binding and density functional theory calculations to investigate QI in linear molecular chains and aromatic molecules with different side groups. For the molecular chains we find a linear relation between the position of the transmission nodes and the side group π orbital energy. In contrast, the transmission functions of functionalized aromatic molecules generally display a rather complex nodal structure due to the interplay between molecular topology and the energy of the side group orbital.

Abstract: Historically, two important approaches to the concept of electronegativity have been in terms of: (a) an atom in a molecule (e.g., Pauling) and (b) the chemical potential. An approximate form of the latter is now widely used for this purpose, although it includes a number of deviations from chemical experience. More recently, Allen introduced an atomic electronegativity scale based upon the spectroscopic average ionization energies of the valence electrons. This has gained considerable acceptance. However it does not take into account the interpenetration of valence and low-lying subshells, and it also involves some ambiguity in enumerating d valence electrons. In this paper, we analyze and characterize a formulation of relative atomic electronegativities that is conceptually the same as Allen's but avoids the aforementioned problems. It involves the property known as the average local ionization energy, I(r), defined as [Formula: see text], where ρi(r) is the electronic density of the i(th) orbital, having energy ei, and ρ(r) is the total electronic density. I(r) is interpreted as the average energy required to remove an electron at the point r. When I(r) is averaged over the outer surfaces of atoms, taken to be the 0.001 au contours of their electronic densities, a chemically meaningful scale of relative atomic electronegativities is obtained. Since the summation giving I(r) is over all occupied orbitals, the issues of subshell interpenetration and enumeration of valence electrons do not arise. The procedure is purely computational, and all of the atoms are treated in the same straightforward manner. The results of several different Hartree-Fock and density functional methods are compared and evaluated; those produced by the Perdew-Burke-Ernzerhof functional are chemically the most realistic.

Abstract: We report an analytical scheme for the calculation of first-order electrical properties using the spin-free Dirac-Coulomb (SFDC) Hamiltonian, thereby exploiting the well-developed density-matrix formulations in nonrelativistic coupled-cluster (CC) derivative theory. Orbital relaxation effects are fully accounted for by including the relaxation of the correlated orbitals with respect to orbitals of all types, viz., frozen-core, occupied, virtual, and negative energy state orbitals. To demonstrate the applicability of the presented scheme, we report benchmark calculations for first-order electrical properties of the hydrogen halides, HX with X = F, Cl, Br, I, At, and a first application to the iodo(fluoro)methanes, CHnF3 − nI, n = 0–3. The results obtained from the SFDC calculations are compared to those from nonrelativistic calculations, those obtained via leading-order direct perturbation theory as well as those from full Dirac-Coulomb calculations. It is shown that the full inclusion of spin-free (SF) re...

Abstract: The quantum chemistry of finite aperiodic graphene flakes is a matter of considerable interest because of the anticipated technological importance of such objects. Since real aperiodic graphene flakes will in general be composed of many thousands of carbon atoms, theoretical methods appropriate to such large molecules would need to be used for the ab initio quantum calculation of their properties. The Kernel energy method is discussed here, and it is shown to be accurately applicable to graphenes and analogous extended aromatic molecules. It is necessary to define the kernels of a graphene molecule in a new way because of the extensive aromaticity, which defines its electronic structure. The kernels used in the reconstruction of the full graphene sheet preserve the total number of π-electrons, Clar sextets, and the approximate overall aromaticity. Sivaramakrishnan et al. [J Phys Chem A, 2005, 109, 1621] define similar “ring conserved isodesmic reactions (RCIR).” The principal innovation of this article is the suggestion that kernels may be mathematically extracted from an extended aromatic molecule such as graphene by a fissioning of aromatic bonds. Hartree Fock (HF) and Moller-Plesset (MP2) chemical models using a Gaussian basis of 3-21G orbitals are used to calculate the total energy of a graphene flake. This demonstration calculation is performed on a graphene flake in which dangling bonds are saturated with hydrogens (C78H26) composed of a total of 104 atoms arranged in 27 benzenoid rings. The KEM with both types of chemical model are shown to be accurate to nearly 1 kcal/mol, of a total energy, which is nearly 3000 atomic units, that is, with an absolute error within “chemical accuracy” and a relative error of the order of 5 × 105% of the total energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Abstract: We present a novel technique for the manipulation of the energy spectrum of hard-wall InAs/InP nanowire quantum dots. By using two local gate electrodes, we induce a strong transverse electric field in the dot and demonstrate the controlled modification of its electronic orbitals. Our approach allows us to dramatically enhance the single-particle energy spacing between the first two quantum levels in the dot and thus to increment the working temperature of our InAs/InP single-electron transistors. Our devices display a very robust modulation of the conductance even at liquid nitrogen temperature, while allowing an ultimate control of the electron filling down to the last free carrier. Potential further applications of the technique to time-resolved spin manipulation are also discussed.

Abstract: A rationale for the removal of the hybrid atomic orbital from the chemistry curriculum is examined. Although the hybrid atomic orbital model does not accurately predict spectroscopic energies, many chemical educators continue to use and teach the model despite the confusion it can cause for students. Three arguments for retaining the model in the chemical curriculum are presented. These arguments are then refuted and methods for teaching chemistry without invoking the hybrid atomic orbital model are presented to show how the model can be removed from the chemistry curriculum with little negative effect.

Abstract: We derive a realistic spin-orbital model at finite Hund's exchange for alkali hyperoxides. We find that, due to the geometric frustration of the oxygen lattice, spin and orbital waves destabilize both spin and p-orbital order in almost all potential ground states. We show that the orbital order induced by the lattice overrules the one favoured by superexchange and that this, together with the large interorbital hopping, leads to generalized Goodenough-Kanamori rules. They i) lift the geometric frustration of the lattice, and ii) explain the observed layered C-type antiferromagnetic order in alkali hyperoxides. This is confirmed by a spin-wave dispersion with no soft-mode behavior presented here as a prediction for future experiments.

Abstract: We consider the use in quantum Monte Carlo calculations of two types of valence bond wave functions based on strictly localized active orbitals, namely valence bond self-consistent-field and breathing-orbital valence bond wave functions. Complemented by a Jastrow factor, these Jastrow-valence-bond wave functions are tested by computing the equilibrium well depths of the four diatomic molecules C2, N2, O2, and F2 in both variational Monte Carlo and diffusion Monte Carlo. We show that it is possible to design compact wave functions based on chemical grounds that are capable of describing both static and dynamic electron correlations. These wave functions can be systematically improved by inclusion of valence bond structures corresponding to additional bonding patterns.

Abstract: A combined strategy that unifies our interacting quantum atoms approach (IQA), a chemically intuitive energetic perspective within the quantum theory of atoms in molecules (QTAIM), the domain natural orbitals obtained by the diagonalization of the charge-weighted domain-averaged Fermi hole (DAFH), and the statistical analyses of chemical bonding provided by the electron number distribution functions (EDF) is presented. As shown, it allows for recovering traditional orbital images from the orbital invariant descriptions of QTAIM. It does also provide bonding indices (like bond orders) and bond energetics, all in a per orbital basis, still invariant manner, using a single unified framework. The procedure is applied to show how the Dewar, Chatt, and Ducanson model of bonding in simple transition metal carbonyls may be recovered in the real space. The balance between the number of σ-donated and π-backdonated electrons is negative in classical compounds and positive in non-classical ones. The energetic strength of backdonation is, however, smaller than that of donation. Our technique surpasses conventional orbital models by providing physically sound, quantitative energetics of chemical bonds (or interactions) together with effective one-electron pictures, all for arbitrary wavefunctions.

Abstract: Ab initio molecular dynamics (MD) and relativistic density functional NMR methods were applied to calculate the one-bond Hg-C NMR indirect nuclear spin-spin coupling constants (J) of [Hg(CN)(2) ] and [CH(3) HgCl] in solution. The MD averages were obtained as J((199) Hg-(13) C)=3200 and 1575 Hz, respectively. The experimental Hg-C spin-spin coupling constants of [Hg(CN)(2) ] in methanol and [CH(3) HgCl] in DMSO are 3143 and 1674 Hz, respectively. To deal with solvent effects in the calculations, finite "droplet" models of the two systems were set up. Solvent effects in both systems lead to a strong increase of the Hg-C coupling constant. From a relativistic natural localized molecular orbital (NLMO) analysis, it was found that the degree of delocalization of the Hg 5d(σ) nonbonding orbital and of the HgC bonding orbital between the two coupled atoms, the nature of the trans Hg-C/Cl bonding orbital, and the s character of these orbitals, exhibit trends upon solvation of the complexes that, when combined, lead to the strong increase of J(Hg-C).

Abstract: We have developed a method for analyzing the (hyper)polarizabilities of open-shell molecular systems. This method employs the (hyper)polarizability densities based on the natural orbitals and occupation numbers, which enables us to analyze the contributions of odd electrons having various open-shell (diradical) characters. Within broken-symmetry, i.e., spin-unrestricted, single-determinant molecular orbital and density functional theory approaches, we can also remove the spin contamination effects on these quantities through spin projection. To do that, an approximate spin projected method has been elaborated and applied to the analysis of the (hyper)polarizability of multi-radical systems. As examples, typical open-shell singlet systems, 1,3-dipoles and rectangular graphene nanoflakes, are examined.

Abstract: With the example of the non-resonant inelastic x-ray scattering (NIXS) at the O${}_{45}$ edges ($5d\ensuremath{\rightarrow}5f$) of the actinides, we develop the theory for shallow-core to valence excitations, where the multiplet spread is larger than the core-hole attraction, such as if the core and valence orbitals have the same principal quantum number. This involves very strong final state configuration interaction (CI), which manifests itself as huge reductions in the Slater-Condon integrals, needed to explain the spectral shapes within a simple renormalized atomic multiplet theory. But more importantly, this results in a cross-over from bound (excitonic) to virtual-bound excited states with increasing energy, within the same core-valance multiplet structure, and in large differences between the dipole and high-order multipole transitions, as observed in NIXS. While the bound states (often higher multipole allowed) can still be modeled using local cluster-like models, the virtual-bound resonances (often dipole-allowed) cannot be interpreted within such local approaches. This is in stark contrast to the more familiar core-valence transitions between different principal quantum number shells, where all the final excited states almost invariably form bound core-hole excitons and can be modeled using local approaches. The possibility of observing giant multipole resonances for systems with high angular momentum ground states is also predicted. The theory is important to obtain ground state information from core-level x-ray spectroscopies of strongly correlated transition metal, rare-earth, and actinide systems.

Abstract: The first-principles quantum mechanical investigation on CdS quantum dots (QDs) adsorbed on anatase TiO2 nanotubes (TiO2NTs) in quantum dot-sensitized solar cells (QDSSCs) was performed using the density functional theory (DFT) approach. The geometry and electronic coupling between a CdS QD and the TiO2NT have been examined for the first time, together with a detailed discussion of interfacial electron transfer and electron transport models along the TiO2NT. It has been found that adsorbate states are introduced in the band gap of the TiO2NT upon the adsorption of a CdS QD on the TiO2NT surface, and an electron transfers from the sulfur atoms of a CdS QD to the conduction band of the TiO2NT upon adsorption of visible light. The unique TiO2NT structure offers a one-dimensional directional pathway for electron transport across the semiconductor substrate through titanium dx2–y2 and dz2 orbitals. Our work is of great benefit for understanding the charge separation process at the heterogeneous interface and t...

Abstract: Density functional theory calculations (DFT), as well as hybrid methods (B3LYP) for B18N18-[CoF6]3− complex have been carried out to study the non-bonded interaction. The geometry of the B18N18 has been optimized at B3LYP method with EPR-II basis set and geometry of the [CoF6]3− have been optimized at B3LYP method with Def2-TZVP basis set and Stuttgart RSC 1997 Effective Core Potential. The electromagnetic interactions of the [CoF6]3− molecule embedded in the B18N18 Nano ring have been investigated at B3LYP and total atomic charges, spin densities, dipole moment and isotropic Fermi coupling constants parameters in different loops and bonds of the B18N18-[CoF6]3− system have been calculated. Also NBO analysis such as electronic delocalization between donor and acceptor bonds has been studied by DFT method. Then we have been investigated the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) for the lowest energy have been derived to estimate the structural stability of the B18N18-[CoF6]3− system, and the coefficients of s, p and d orbitals of Co-F bonds involved in B18N18-[CoF6]3−.Thus, hybridization of Co and F atoms can be distinguished based on these NBO data. The Gaussian quantum chemistry package is used for all calculations.

Abstract: The yrast states of nuclei that are spherical or weakly deformed in their ground states are described as quadrupole waves running over the nuclear surface, which we call "tidal waves". The energies and E2 transition probabilities of the yrast states in nuclides with Z= 44, 46, 48 and N= 56, 58,…, 66 are calculated by means of the cranking model in a microscopic way. The nonlinear response of the nucleonic orbitals results in a strong coupling between shape and single particle degrees of freedom.

Abstract: Spherical complex optical potential formalism and complex scattering potential–ionization contribution are used to generate electron impact total inelastic and total ionization cross section, respectively, for the atoms In, Sn, Sb, Te, I and Xe. Roothaan–Hartree–Fock calculations are used to approximate the atomic orbital wavefunction and hence to model the target charge densities and static potentials for these atoms. The results for the above targets are presented for energies ranging from ionization threshold to 2000 eV. Graphs are plotted with other theories and measurements wherever available. We have obtained a systematic and uniform result with an overall agreement with other data for all the elements presented here.

Abstract: In contrast with the single atom, atomic van der Waals clusters can form stable anions where the excess electron is bound due to long-range correlations with the electrons of the cluster. We report on extensive all-electron many-body ab initio studies on Xe clusters. Three-dimensional, planar, and linear structures of the clusters are investigated and compared. In particular, we find that the minimal number of Xe atoms in the cluster required to form a stable anion is 5 independently of the dimensionality of the cluster. We provide electron affinities for clusters made of 5, 6, and 7 atoms in all dimensions and find that the planar clusters form the most stable anions. The Dyson orbitals of the excess electrons are computed and analyzed.

Abstract: Preface Part I. 1D Problems: 1. Variational solution of the Schroedinger equation 2. Solution of bound state problems using a grid 3. Solution of the Schroedinger equation for scattering states 4. Periodic potentials: band structure in 1D 5. Solution of time-dependent problems in quantum mechanics 6. Solution of Poisson's equation Part II. 2D and 3D Systems: 7. 3D real space approach: from quantum dots to Bose-Einstein condensates 8. Variational calculations in 2D: quantum dots 9. Variational calculations in 3D: atoms and molecules 10. Monte Carlo calculations 11. Molecular dynamics simulations 12. Tight binding approach to electronic structure calculations 13. Plane wave density functional calculations 14. Density functional calculations with atomic orbitals 15. Real-space density functional calculations 16. Time-dependent density functional calculations 17. Scattering and transport in nanostructures 18. Numerical linear algebra Appendix: code descriptions References Index.

Abstract: Well-ordered and oriented monolayers of conjugated organic molecules can offer new perspectives on surface bonding. We will demonstrate the importance of the momentum distribution, or symmetry, of the adsorbate molecules' π orbitals in relation to the states available for hybridization at the metal surface. Here, the electronic band structure of the first monolayer of sexiphenyl on Cu(110) has been examined in detail with angle-resolved ultraviolet photoemission spectroscopy over a large momentum range and will be compared to measurements of a multilayer thin film and to density functional calculations. In the monolayer, the one-dimensional intramolecular band structure can still be recognized, allowing an accurate determination of orbital modification upon bonding and the relative energetic positions of the electronic levels. It is seen that the character of the molecular π orbitals is largely maintained despite strong mixing between Cu and molecular states and that the lowest unoccupied molecular orbital (LUMO) is filled by hybridization with Cu s,p states rather than through a charge transfer process. It is also shown that the momentum distribution of the substrate states involved and the periodicity of the molecular overlayer play a large role in the final E(k) distribution of the hybrid states. The distinct momentum distribution of the LUMO, interacting with the Cu substrate s,p valence bands around the gap in the surface projection of the bulk band structure, make this system a particularly illustrative example of momentum resolved hybridization. This system demonstrates that, for hybridization to occur, not only do states require overlap in energy and space, but also in momentum.