Density functional embedding approach to the Mn impurities in NaBr crystals

We have performed density functional calculations for three 19‐atom clusters, two 25‐atom clusters, and one 18‐atom cluster, each embedded in a Madelung potential that takes into account the long‐range electrostatic interactions of the ion lattice of a NaBr crystal. One of the three 19‐atom and one of the two 25‐atom clusters model bulk crystalline NaBr; the others model a Mn²⁺ impurity trapped in a cubically symmetric crystalline electric field (CEF) site of the NaBr host. One of the latter has the NaBr bulk interatomic distance, while in the others relaxation of the Br atoms around the metallic impurity has been considered. The 18‐atom cluster models a relaxed Mn impurity Na vacancy system. All of our calculated clusters have a Na site at the center, and they all include at least first and second nearest‐neighbor host atoms. In the center of the doped clusters the Mn impurity replaces the missing Na ion. The electronic structure of the embedded impurity ion in its local environment was computed self‐consistently by means of all‐electron density functional theory (DFT) techniques. We have examined the lattice relaxation around the impurity and calculated the hyperfine coupling constants (HFCC). The results for the Mn electronic structure and for the HFCC are in agreement with experimental results using electron paramagnetic resonance measurements. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 34–46, 2000     

Quantum chemical cluster modeling of boundary conditions for metal azides

An approach to crystal field modeling for solids with a predominantly ionic type of bond is suggested. The approach uses Evjen 's method of iteratively selecting point charges in such a way that the net charge on the crystal fragment be close to zero. The MNDO quantum chemical program is modified to include electron interactions of a point charge system in the Fock operator. The approach is tested on potassium azide. The calculated charges on potassium atoms agree well with the results of band structure calculations. Translated fromZhurnal Strukturnoi Khimii, Vol. 41, No. 3, pp. 605-608, May-June, 2000.     

Importance of Madelung potential in quantum chemical modeling of ionic surfaces

The importance of the inclusion of the Madelung potential in cluster models of ionic surfaces is the subject of this work. We have determined Hartree-Fock all electron wave functions for a series of MgO clusters with and without a large array of surrounding point charges (PC) chosen to reproduce the Madelung potential. The phenomena investigated include: the reactivity of surface oxygens toward CO₂, atomic hydrogen, and H⁺; the geometry and adsorption energy of water and the vibrational shift of CO adsorbed at Mg²⁺ sites; the electronic structure and the hyperfine coupling constants of oxygen vacancies, the paramagnetic F_s⁺ centers. While some clusters give results which are virtually independent of the presence of the PCs, other clusters, typically of small size, give physically incorrect results when the PCs are not included. The embedding of the cluster in PCs guarantees a similar response for clusters of different size, at variance with the bare clusters, where the long range coulombic interactions are not included. © 1997 by John Wiley & Sons, Inc.     

Madelung fields from optimized point charges for ab initio cluster model calculations on ionic systems

A simple procedure devised to obtain optimized point charges to represent the Madelung potential is reported and applied to six different crystal structures occurring in ionic systems. Their use in ab initio cluster model calculations is discussed through some selected examples and results compared with those arising from the use of the well-known Evjen method. © 1993 John Wiley & Sons, Inc.     

Electron density distributions calculated for the nickel sulfides millerite, vaesite, and heazlewoodite and nickel metal: a case for the importance of ni-ni bond paths for electron transport

Bond paths and the bond critical point properties (the electron density (rho) and the Hessian of rho at the bond critical points (bcp's)) have been calculated for the bonded interactions comprising the nickel sulfide minerals millerite, NiS, vaesite, NiS(2), and heazlewoodite, Ni(3)S(2), and Ni metal. The experimental Ni-S bond lengths decrease linearly as the magnitudes of the properties each increases in value. Bond paths exist between the Ni atoms in heazlewoodite and millerite for the Ni-Ni separations that match the shortest separation in Ni metal, an indicator that the Ni atoms are bonded. The bcp properties of the bonded interactions in Ni metal are virtually the same as those in heazlewoodite and millerite. Ni-Ni bond paths are absent in vaesite where the Ni-Ni separations are 60% greater than those in Ni metal. The bcp properties for the Ni-Ni bonded interactions scatter along protractions of the Ni-S bond length-bcp property trends, suggesting that the two bonded interactions have similar characteristics. Ni-Ni bond paths radiate throughout Ni metal and the metallic heazlewoodite structures as continuous networks whereas the Ni-Ni paths in millerite, a p,d-metal displaying ionic and covalent features, are restricted to isolated Ni(3) rings. Electron transport in Ni metal and heazlewoodite is pictured as occurring along the bond paths, which behave as networks of atomic size wires that radiate in a contiguous circuit throughout the two structures. Unlike heazlewoodite, the electron transport in millerite is pictured as involving a cooperative hopping of the d-orbital electrons from the Ni(3) rings comprising Ni(3)S(9) clusters to Ni(3) rings in adjacent clusters via the p-orbitals on the interconnecting S atoms. Vaesite, an insulator at low temperatures and a doped semiconductor at higher temperatures, lacks Ni-Ni bond paths. The net charges conferred on the Ni and S atoms are about a quarter of their nominal charges for the atoms in millerite and vaesite with the net charge on Ni increasing with increasing Ni-S bond length. Reduced net charges are observed on the Ni atoms in heazlewoodite and are related to its Ni-Ni metal bonded interactions and to the greater covalent character of its bonds. Local energy density and bond critical point properties of the electron density distributions indicate that the Ni-S and Ni-Ni bonded interactions are intermediate in character between ionic and covalent.     

Interaction of similarly charged surfaces mediated by nanoparticles

We study the interaction between two like charged surfaces embedded in a solution of oppositely charged multivalent rod-like counterions.The counterions consist of two rigidly bonded point charges,each of valency Z.The strength of the electrostatic coupling increases with increasing surface charge density or valency of the charges.The system is analyzed by employing a self-consistent field theory,which treats the short and long range interactions of the counterions within different approximations.We find that in the weak coupling limit,the interactions are only repulsive.In the intermediate coupling regime,the multivalent rod-like counterions can mediate attractive interactions between the surfaces. For sufficiently long rods,bridging contributes to the attractive interaction.In the strong coupling limit,the charge correlations can contribute to the attractive interactions at short separations between the charged surfaces.Two minima can then appear in the force curve between surfaces.     

Size and shape dependence of the electrostatic potential in cluster models of the MgO(100) surface

We investigated the dependence of the electrostatic potential on the size and the shape of various cluster models of the MgO(100) surface. Both Mg²⁺ and O²⁻ adsorption sites have been considered. The clusters were embedded in a large array of point charges to provide a representation of the Madelung potential. We found that the electrostatic potential in the adsorption region shows a marked dependence on the size of the cluster, in particular, for non-stoichiometric clusters where the number of cations and anions differs considerably. These oscillations are due to (a) the different contribution to the electrostatic potential given by a point charge or by an extended ion, and (b) by the polarization of the ions at the cluster border. The effect of the oscillations in the electrostatic potential on the chemisorption properties was investigated for the case of CO₂ interacting with surface and defect O²⁻ sites of the MgO surface. © 1996 John Wiley & Sons, Inc.     

Theoretical electron density distributions for Fe- and Cu-sulfide earth materials: a connection between bond length, bond critical point properties, local energy densities, and bonded interactions

Bond critical point and local energy density properties together with net atomic charges were calculated for theoretical electron density distributions, rho(r), generated for a variety of Fe and Cu metal-sulfide materials with high- and low-spin Fe atoms in octahedral coordination and high-spin Fe atoms in tetrahedral coordination. The electron density, rho(rc), the Laplacian, triangle down2rho(rc), the local kinetic energy, G(rc), and the oxidation state of Fe increase as the local potential energy density, V(rc), the Fe-S bond lengths, and the coordination numbers of the Fe atoms decrease. The properties of the bonded interactions for the octahedrally coordinated low-spin Fe atoms for pyrite and marcasite are distinct from those for high-spin Fe atoms for troilite, smythite, and greigite. The Fe-S bond lengths are shorter and the values of rho(rc) and triangle down2rho(rc) are larger for pyrite and marcasite, indicating that the accumulation and local concentration of rho(r) in the internuclear region are greater than those involving the longer, high-spin Fe-S bonded interactions. The net atomic charges and the bonded radii calculated for the Fe and S atoms in pyrite and marcasite are also smaller than those for sulfides with high-spin octahedrally coordinated Fe atoms. Collectively, the Fe-S interactions are indicated to be intermediate in character with the low-spin Fe-S interactions having greater shared character than the high-spin interactions. The bond lengths observed for chalcopyrite together with the calculated bond critical point properties are consistent with the formula Cu+Fe3+S2. The bond length is shorter and the rho(rc) value is larger for the FeS4 tetrahedron displayed by metastable greigite than those displayed by chalcopyrite and cubanite, consistent with a proposal that the Fe atom in greigite is tetravalent. S-S bond paths exist between each of the surface S atoms of adjacent slabs of FeS6 octahedra comprising the layer sulfide smythite, suggesting that the neutral Fe3S4 slabs are linked together and stabilized by the pathways of electron density comprising S-S bonded interactions. Such interactions not only exist between the S atoms for adjacent S8 rings in native sulfur, but their bond critical point properties are similar to those displayed by the metal sulfides.     

Hydrogen‐Bond Cooperative Effects in Small Cyclic Water Clusters as Revealed by the Interacting Quantum Atoms Approach

The cooperative effects of hydrogen bonding in small water clusters (H₂O)_n (n=3–6) have been studied by using the partition of the electronic energy in accordance with the interacting quantum atoms (IQA) approach. The IQA energy splitting is complemented by a topological analysis of the electron density (ρ( r )) compliant with the quantum theory of atoms‐in‐molecules (QTAIM) and the calculation of electrostatic interactions by using one‐ and two‐electron integrals, thereby avoiding convergence issues inherent to a multipolar expansion. The results show that the cooperative effects of hydrogen bonding in small water clusters arise from a compromise between: 1) the deformation energy (i.e., the energy necessary to modify the electron density and the configuration of the nuclei of the isolated water molecules to those within the water clusters), and 2) the interaction energy (E_int) of these contorted molecules in (H₂O)_n. Whereas the magnitude of both deformation and interaction energies is enhanced as water molecules are added to the system, the augmentation of the latter becomes dominant when the size of the cluster is increased. In addition, the electrostatic, classic, and exchange components of E_int for a pair of water molecules in the cluster (H₂O)_n?1 become more attractive when a new H₂O unit is incorporated to generate the system (H₂O)_n with the last‐mentioned contribution being consistently the most important part of E_int throughout the hydrogen bonds under consideration. This is opposed to the traditional view, which regards hydrogen bonding in water as an electrostatically driven interaction. Overall, the trends of the delocalization indices, δ(Ω,Ω′), the QTAIM atomic charges, the topology of ρ( r ), and the IQA results altogether show how polarization, charge transfer, electrostatics, and covalency contribute to the cooperative effects of hydrogen bonding in small water clusters. It is our hope that the analysis presented in this paper could offer insight into the different intra‐ and intermolecular interactions present in hydrogen‐bonded systems.     

Treatment of delocalized electron transfer in periodic and embedded cluster DFT calculations: The case of Cu on ZnO (10 0)

We assess the consequences of the interface model—embedded‐cluster or periodic‐slab model—on the ability of DFT calculations to describe charge transfer (CT) in a particularly challenging case where periodic‐slab calculations indicate a delocalized charge‐transfer state. Our example is Cu atom adsorption on ZnO(10 0), and in fact the periodic slab calculations indicate three types of CT depending on the adsorption site: full CT, partial CT, and no CT. Interestingly, when full CT occurs in the periodic calculations, the calculated Cu atom adsorption energy depends on the underlying ZnO substrate supercell size, since when the electron enters the ZnO it delocalizes over as many atoms as possible. In the embedded‐cluster calculations, the electron transferred to the ZnO delocalizes over the entire cluster region, and as a result the calculated Cu atom adsorption energy does not agree with the value obtained using a large periodic supercell, but instead to the adsorption energy obtained for a periodic supercell of roughly the same size as the embedded cluster. Different density functionals (of GGA and hybrid types) and basis sets (local atom‐centered and plane‐waves) were assessed, and we show that embedded clusters can be used to model Cu adsorption on ZnO(10 0), as long as care is taken to account for the effects of CT. © 2015 Wiley Periodicals, Inc.     

Core excitations in MgO: a DFT study with cluster models

The time dependent density functional theory has been employed to calculate the absorption spectra relative to core excitation of Mg 1s, Mg 2p and O 1s orbitals of solid MgO. Cluster models of various size and shape are considered, embedded within an array of point charges to simulate the Madelung potential. Comparison with experimental data and previous theoretical calculations allows a precise assessment of the performances of the present method, which is competitive and promising for further application to more complex systems, like transition metal oxides.     

Simulation of ab initio results for palladium and rhodium clusters by tight‐binding calculations*

The study of metal clusters is nowadays a very active field of research using both experimental and theoretical techniques. Regular trends as well as unexpected behaviors have been observed regarding size‐dependent properties such as ionization potentials and atomization energies. Palladium and rhodium clusters of small size have been extensively studied at various semiempirical and ab initio levels of the theory, but the achievement and the interpretation of these calculations are generally difficult to be performed because of the incomplete shell structure of transition metal clusters. So we have tried to mimic the most important conclusions of the ab initio results available for Pd and Rh clusters by means of tight‐binding calculations, in the original Wolfsberg–Helmholz form, with appropriate parametrized repulsion terms. The occupation numbers of the one‐electron energy levels have been determined by taking into account some predictions of the graph theory. This enables us to study the variation of the atomization energies per atom for these clusters and to derive a bond‐energy systematics for Pd–Pd, Rh–Rh, and Pd–Rh linked atoms. Magic clusters with 13 atoms are considered. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 26–33, 2001     

Quantum chemical study of IrFn (n = 1–7) clusters: An investigation of superhalogen properties

In present investigation, the interactions of iridium (Ir) atom with fluorine (F) atoms have been studied using the density functional theory. Up to seven F atoms were able to bind to a single Ir atom which resulted in increase of electron affinities successively, reaching a peak value of 7.85 eV for IrF₇. The stability and reactivity of these clusters were analyzed by calculating highest occupied molecular orbital (HOMO)–LUMO gaps, molecular orbitals and binding energies of these clusters. The unusual properties of these clusters are due to the involvement of inner shell 5d‐electrons, which not only allows IrF_n clusters to belong to the class of superhalogens but also shows that its valence can exceed the nominal value of 2. © 2012 Wiley Periodicals, Inc.     

Electron-ion-coincidence spectra of K-shell excited Ne, Ar, and Kr clusters

Electron-ion-coincidence spectra were recorded for K-shell excited krypton, argon, and neon clusters covering the size range from 1 atom to about 3000 atoms by utilizing hard x-ray undulator beamlines. Multiply charged ions Rz+(z>or=2) and singly charged ions Rn+(n>or=1) are observed as cluster fragments, and their relative abundance exhibits a characteristic dependence on the average cluster size N. It is expected from these results that the charges generated on the cluster surface are strongly localized while those in the cluster core are more delocalized. The estimated charge separation distance increases with N, and it is longer for lighter elements.     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

Intact Four‐atom Organic Tetracation Stabilized by Charge Localization in the Gas Phase

Several features distinguish intact multiply charged molecular cations (MMCs) from other species such as monocations and polycations: high potential energy, high electron affinity, a high density of electronic states with various spin multiplicities, and charge‐dependent reactions. However, repulsive Coulombic interactions make MMCs quite unstable, and hence small organic MMCs are currently not readily available. Herein, we report that the isolated four‐atom molecule diiodoacetylene survives after the removal of four electrons via tunneling. We show that the tetracation remains metastable towards dissociation because of the localization (91–95 %) of the positive charges on the terminal iodine atoms, ensuring minimum Coulomb repulsion between adjacent atoms as well as maximum charge‐induced attractive dipole interactions between iodine and carbon. Our approach making use of iodines as the positively charged sites enables small organic MMCs to remain intact.     

Si-O bonded interactions in silicate crystals and molecules: a comparison

Bond critical point, local kinetic energy density, G(rc), and local potential energy density, V(rc), properties of the electron density distributions, rho(r), calculated for silicates such as quartz and gas-phase molecules such as disiloxane are similar, indicating that the forces that govern the Si-O bonded interactions in silica are short-ranged and molecular-like. Using the G(rc)/rho(rc) ratio as a measure of bond character, the ratio increases as the Si-O bond length, the local electronic energy density, H(rc)= G(rc) + V(rc), and the coordination number of the Si atom decrease and as the accumulation of the electron density at the bond critical point, rho(rc), and the Laplacian, inverted Delta2 rho(rc), increase. The G(rc)/rho(rc) and H(rc)/rho(rc) ratios categorize the bonded interaction as observed for other second row atom M-O bonds into discrete categories with the covalent character of each of the M-O bonds increasing with the H(rc)/rho(rc) ratio. The character of the bond is examined in terms of the large net atomic charges conferred on the Si atoms comprising disiloxane, stishovite, quartz, and forsterite and the domains of localized electron density along the Si-O bond vectors and on the reflex side of the Si-O-Si angle together with the close similarity of the Si-O bonded interactions observed for a variety of hydroxyacid silicate molecules and a large number of silicate crystals. The bond critical point and local energy density properties of the electron density distribution indicate that the bond is an intermediate interaction between Al-O and P-O bonded interactions rather than being a closed-shell or a shared interaction.     

CnB-的激光等离子体产生与质谱分析

Time-of-flight mass spectrum of C_nB~- has been recorded on a selfbuilt instrument with laser vaporization of tetraphenylboron sodium. By analysis of the com-position of the anions, it is found that number of the boron atoms in any of these ions equals to the number of the charges carried by the anion, and the sum of the numbers of the carbon and boron atoms in these species are always the odd numbers. The experimental results show that boron atom has a strong tendency to attract an electron so that those C_nB~- will have similar electronic structures as C_n, and carbon clusters with odd members are always more stable than their even neighbors.     

Multipolar electrostatics for proteins: Atom–atom electrostatic energies in crambin

Accurate electrostatics necessitates the use of multipole moments centered on nuclei or extra point charges centered away from the nuclei. Here, we follow the former alternative and investigate the convergence behavior of atom‐atom electrostatic interactions in the pilot protein crambin. Amino acids are cut out from a Protein Data Bank structure of crambin, as single amino acids, di, or tripeptides, and are then capped with a peptide bond at each side. The atoms in the amino acids are defined through Quantum Chemical Topology (QCT) as finite volume electron density fragments. Atom‐atom electrostatic energies are computed by means of a multipole expansion with regular spherical harmonics, up to a total interaction rank of L = ?_A+ ?_B + 1 = 10. The minimum internuclear distance in the convergent region of all the 15 possible types of atom‐atom interactions in crambin that were calculated based on single amino acids are close to the values calculated from di and tripeptides. Values obtained at B3LYP/aug‐cc‐pVTZ and MP2/aug‐cc‐pVTZ levels are only slightly larger than those calculated at HF/6‐31G(d,p) level. This convergence behavior is transferable to the well‐known amyloid beta polypeptide Aβ_1–42. Moreover, for a selected central atom, the influence of its neighbors on its multipole moments is investigated, and how far away this influence can be ignored is also determined. Finally, the convergence behavior of AMBER becomes closer to that of QCT with increasing internuclear distance. © 2013 Wiley Periodicals, Inc.