LiF与MgF_2晶体中离子簇CoF_6~（4－）的电子光谱和吸收光谱的从头算

用量子化学的从头算方法对ＬｉＦ与ＭｇＦ_２晶体中的离子簇ＣｏＦ_６~（４－）的电子结构与吸收光谱进行了计算。计算结果与实验基本一致，说明把ＣｏＦ_６~（４－）放在ＬｉＦ与ＭｇＦ_２的马德隆场中进行从头计算的理论模型是可取的；并澄清了文献用Ｘ_ａ方法对ＣｏＦ_６~（４－）的光谱项对称分类不清楚的地方。     

Setting the boundary conditions by the potential shift in the self-consistent field (Xα-scattered wave) cluster calculations

Potential shifts given by the Madelung potentials in different regions of a molecular cluster are determined in the MT approximation. Nickel and zinc oxides are employed to consider the interrelation between the approaches to the calculation of the boundary conditions in terms of the Watson sphere and the potential shift in the cluster calculations of perfect and imperfect ionic crystals using the self-consistent field (Xα-scattered wave) method. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 1, pp. 23–31, January–February, 1997. Original article submitted February 12, 1996.     

Cluster and periodic DFT calculations of MgO/Pd(CO) and MgO/Pd(CO)(2) surface complexes

The bonding and vibrational properties of Pd(CO) and Pd(CO)(2) complexes formed at the (100) surface of MgO have been investigated using the gradient-corrected DFT approach and have been compared to the results of infrared and thermal desorption experiments performed on ultrathin MgO films. Two complementary approaches have been used for the calculation of the electronic properties: the embedded cluster method using localized atomic orbital basis sets and supercell periodic calculations using plane waves. The results show that the two methods provide very similar answers, provided that sufficiently large supercells are used. Various regular and defect adsorption sites for the Pd(CO) and Pd(CO)(2) have been considered: terraces, steps, neutral and charged oxygen vacancies (F and F(+) centers), and divacancies. From the comparison of the computed and experimental results, it is concluded that the most likely site where the Pd atoms are stabilized and where carbonyl complexes are formed are the F(+) centers, paramagnetic defects consisting of a single electron trapped in an anion vacancy.     

A combined molecular dynamics+quantum mechanics method for investigation of dynamic effects on local surface structures

A combined molecular dynamics (MD)+quantum mechanics (QM) method for studying processes on ionic surfaces is presented. Through the combination of classical MD and ab initio embedded-cluster calculations, this method allows the modeling of surface processes involving both the structural and dynamic features of the substrate, even for large-scale systems. The embedding approach used to link the information from the MD simulation to the cluster calculation is presented, and rigorous tests have been carried out to ensure the feasibility of the method. The electrostatic potential and electron density resulting from our embedded-cluster model have been compared with periodic slab results, and confirm the satisfying quality of our embedding scheme as well as the importance of applying embedding in our combined MD+QM approach. We show that a highly accurate representation of the Madelung potential becomes a prerequisite when the embedded-cluster approach is applied to temperature-distorted surface snapshots from the MD simulation.     

Oxygen adsorption at anionic free and supported Au clusters

The structure, stability, and O2 adsorption properties of anionic Au(n) (n=1-11) clusters either free or supported at defected MgO100 surfaces are investigated using density-functional theory. O2 adsorption is strong whenever unpaired electrons are present, except for at some small, supported, planar, high-band-gap clusters. These clusters have the unpaired electrons pinned by the Madelung potential of the support. Larger clusters (starting at Au7-Au8) become three dimensional and metallic. This ensures that while one cluster orbital is pinned to the defect, another orbital at comparable energy can undergo depletion, thus binding O2 with charge transfer.     

Improved embedded molecular cluster model

We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the problem of varied subsystem in the field of the frozen remaining part of the whole electron system” is investigated in the framework of a one-electron approximation. The consideration is general for every task of this type. Homogeneous equations resulting directly from variation of the total energy expression are obtained and transformed to the eigenvalue problem equations. Orthogonality constraints are not imposed during variation. A particular case of the equations describing mutually orthogonal one-electron wave functions of the cluster staying nonorthogonal to those of the remaining crystal is found. A proposed embedding scheme is realized in the CLUSTER code based on the calculation scheme of the semiempirical INDO method. Boundary effects both in the standard (cluster in the field of the infinite lattice of nonpoint spherical charges) and new embedding scheme are investigated, calculating the clusters of LiF, MgO, NaCl, KCl, and AgCl crystals. Significant reduction of the boundary effects in the new embedding scheme is achieved. Reasons for the boundary effects are discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

群分解EHMO计算机程序的编制及GaN晶体能谱的计算

本文把变换算符对原子轨道的作用概括成两个法则,还给出了一个求属于某个高阶不可约表示的基分子轨道的简便方法,即用投影算符求出其中一个分子轨道,然后用这个轨道在变换算符作用下的变换性质来求其余的分子轨道。用这种算法编制EHMO计算机程序在文中也作了扼要的说明。作为程序应用的示例,计算了GaN“分子簇”(包括不同原子数目、掺杂和空位等各种情况)的单电子能级,为实验工作者对GaN(Zn)中什么是施主和什么是受主的推测提供了量子化学的解释。     

Applications of the group-function theory to the field of materials science

The group-function theory, as proposed by McWeeny for the study of weak intermolecular interactions and developed by Huzinaga in the context of valence-electron methods, is shown to be applicable to the ab initio study of tunable solid-state laser materials made of defective ionic crystals. The applicability of the theory relies on the existence of local electronic states (to which the demonstrated/potential laser activity is ascribed), which are essentially localized in a small cluster of atoms including the defect and whose electron correlation interactions with the surrounding crystal components are negligible. According to the group-function formalism, it is possible (a) to neglect electron correlation effects beyond the defect cluster and (b) to define a quantum mechanical embedding potential which embodies the rest of the so-called host effects. Computationally, the theory becomes applicable as the embedding potential is approximated through ab initio model potentials (AIMP). The results of AIMP embedded-cluster calculations demonstrate that it is possible to calculate the local structure and spectroscopy of the active defect at an ab initio level, the attainable accuracy being comparable to the usual one in molecular ab initio studies in the gas phase. Also, in this article, we present a systematic study of the local distortions produced upon doping divalent first-series transition-metal ions in rock-salt oxides, MO:Me²⁺ (M=Mg, Ca, Sr; Me=Sc-Zn) and Tl⁺ in KMgF₃ and KF hosts. This study leads to the calculation of the local structures of the defects in these materials, which have not been measured. The results suggest that the use of the mismatch of the empirical ionic radii of the impurity and the substituted ion in order to predict local distortions in doped ionic crystals is not significant when it is smaller than 0.1 Å, and when it is larger, it should be weighted by a reduction factor depending on the host. For the first-series divalent transition-metal ion impurities, this factor is shown to be 0.15 for SrO, 0.25 for CaO, and around 0.50 for MgO. © 1996 John Wiley & Sons, Inc.     

Ground-state degeneracy and slip energy in fractional-valency donor-acceptor molecular crystals

Slip energies have been calculated as the differences of the Madelung energies for Wigner lattices with identical values for the ionic valences for highly conducting TTF-TCNQ and NMP-TCNQ donor-acceptor molecular crystals in the region of the observed ionic valences. It is found that these energies are small, i.e., there are degenerate Wigner structures, which allow the occurrence of specific electronic excitations (kinks) responsible for the high electronic conductivities of molecular crystals with fractional valences.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 4, pp. 464–469, July–August, 1986.     

Spin quenching of Mn in complexes and CO binding with Mn deposited on MgO and CaO supports: DFT calculations

An attempt has been made to analyze the spin quenching properties of Mn, as a representative of transition metals, in Mn·MgO, Mn·CaO, OC·Mn·MgO, and OC·Mn·CaO complexes formed at the regular (001) surfaces of MgO and CaO, as well as the adsorption of CO on Mn deposited on MgO and CaO by means of hybrid density functional theory calculations and embedded cluster model. Clusters of moderate sizes were embedded in the simulated Coulomb fields that closely approximate the Madelung fields of the host surfaces. A test has been made to examine the effect of artificial flow of charge. While the spin states of Mn in Mn·MgO and Mn·CaO complexes are preserved, the combined effects of adsorbate and substrate in OC·Mn·MgO and OC·Mn·CaO complexes are strong enough to favor the low spin states and to quench the spin. The deposited Mn atoms enhance the adsorption of CO on MgO and CaO surfaces. The significant weakening of bond strength between OC and Mn in complexes supports the concept of bond order conservation. The relation between the strength of CO adsorption and the basicity of the support is verified. The natural bond orbital analysis reveals that the electronic structure of the adsorbed metal represents a qualitative change with respect to that of the free metal. The effects of spin contamination on the geometry, Mulliken charges, and adsorption energy are examined. The binding of CO precursor is dominated by the E(i)^Mn···CO pairwise additive components in MgO and CaO complexs, and the role of the support is not restricted to supporting the metal. The adsorbed CO molecules exhibit no remarkable deviation from linearity. Finally, relations are established between the process of spin quenching and the energy gaps between frontier orbitals. The results show that the spin state of adsorbed metal atoms on oxide supports and the role of precursor molecules on the magnetic and binding properties of complexes need to be explicitly taken into account. © 2012 Wiley Periodicals, Inc.     

SPC cluster modeling of metal oxides: ways of determining the values of point charges in the embedded cluster model

Ｍｅｔａｌｏｘｉｄｅｓａｒｅｏｎｅｋｉｎｄｏｆｍａｔｅｒｉａｌｏｆｉｍｐｏｒｔａｎｔａｐｐｌｉｃａｔｉｏｎｓ[1,2].Ｆｏｒｔｈｅｃｌｕｓｔｅｒｍｏｄｅｌｉｎｇｏｆｍｅｔａｌｏｘｉｄｅｓｗｉｔｈｑｕａｎｔｕｍｃｈｅｍｉｃａｌｍｅｔｈｏｄｓ,ｔｈｅｗａｙｓｇｏｉｎｔｏｔｈｒｅｅｇｒｏｕｐｓ[3,4],ｉ.ｅ.ｔｈｅｂａｒｅｃｌｕｓｔｅｒｍｏｄｅｌ,ｔｈｅｓａｔｕｒａｔｅｄｃｌｕｓｔｅｒｍｏｄｅｌａｎｄｔｈｅｅｍｂｅｄｄｅｄｃｌｕｓｔｅｒｍｏｄｅｌ.Ｔｈｅｂａｒｅｃｌｕｓｔｅｒｍｏｄｅｌｉｓｓｉｍｐｌｙａｓｍａｌ…     

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.     

Experimental and theoretical studies of the structure of alkali halide clusters

We have investigated the structures and properties of alkali halide cluster ions produced by laser vaporization of solid samples. In many alkali halide cluster ions, we observe the appearances of bulk-like characteristics even at sub-nanometer sizes:fcc crystalline structures (including surface terraces), ionic binding, and a susceptibility to common bulk defects such as F and H color-centers. To understand the origins of cluster structures, we have made calculations of ground state energetics, high-temperature molecular dynamics, and the electronic structure of clusters having excess electrons.     

Brueckner coupled cluster response functions

A derivation of the linear response function for the Brueckner coupled cluster method is presented that enables the calculation of second-order molecular properties such as frequency-dependent polarizabilities. By using the Brueckner orbital variant of coupled cluster theory, the spurious pole structure inherent in the standard coupled cluster approach with orbital relaxation is avoided. © 1994 John Wiley & Sons, Inc.     

Solid-state energetics and electrostatics: Madelung constants and Madelung energies

The Madelung constants of ionic solids relate to their geometry and electrostatic interactions. Furthermore, because of issues in their evaluation, they are also of considerable mathematical interest. The corresponding Madelung (electrostatic, coulomb) energy is the principal contributor to the lattice energies of ionic systems, and these energies largely influence many of their physical properties. The Madelung constants are here defined and their properties considered. A difficulty with their application is that they may be defined relative to various lattice distances, and with various conventions for inclusion of the charges, leading to possible confusion in their use. Instead, the unambiguous Madelung energy, E(M), is to be preferred in chemistry. An extensive list of Madelung energies is presented. From this data set, it is observed that there is a strong linear correlation between the lattice energies of ionic solids, U(POT), and their Madelung energies: U(POT)/kJ mol(-1) = 0.8519E(M) + 293.9. This correlation establishes that the lattice energy, U(POT), for ionic solids is about 15% smaller than the attractive Madelung energy, the difference arising from the repulsions unaccounted for by the solely coulombic Madelung energy calculation. Correlations of U(POT) against E(M) for alkali metal hydrides and transition metal compounds, each having considerable covalency, show much reduced Madelung contributions to the lattice energy. These correlations permit ready estimation of lattice energies, and are the first to be based on actual data rather than a broad analysis. The independent volume-based thermodynamic (VBT) method, which relies on a separate correlation with the formula unit volume of the ionic material, complements these correlations.     

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.     

Madelung Constants

Madelung constants are simple numbers which depend on the type of structure investigated. They are needed for the calculation (using the Born-Haber cycle) of lattice energies and enthalpies of formation of ionic compounds. Each Madelung constant is the sum of partial Madelung constants which represent the contributions of the individual ions to the total lattice energy. The partial Madelung constants depend on the ionic charge and, clearly though not stringently, on the coordination number. On the other hand, each Madelung constant can be represented by a sum of Madelung constants for related simple primitive AB structures. Surprisingly, these Madelung constants are numerically interrelated in a simple manner, and are related to the partial Madelung constants of interstitial sites. – Madelung constants of parameter-dependent structures (e.g. of the rutile or anatase type) and their variations with the structure-determining quantities are of particular interest. Madelung constants also yield information in the case of complex compounds and – surprisingly – of non-metal compounds (e.g. XeF₂, XeF₄, XeF₂·XeF₄).     

QM/MM investigation of the degradation mechanism of the electron-transporting layer

The mechanism of charge transfer among tris(8-hydroxyquinolinate)aluminum (Alq₃) molecules in the electron-transporting layer (ETL) under amorphous conditions was theoretically investigated using both quantum mechanical/molecular mechanical (QM/MM) calculations and molecular dynamics (MD) simulations. The rate constant of the electron transfer was estimated for the equilibrated structure taken from the QM/MM MD simulations, based on the hopping model and Marcus theory. It was found that the coordination of a (LiF)₄ cluster in ETL drastically lowers the energy of the lowest unoccupied molecular orbital in the Alq₃ molecule. The small rate constant, namely the slow charge mobility, in ETL is believed to be causally related to the low-lying delocalized unoccupied molecular orbital of Alq₃ coordinated by the (LiF)₄ cluster. The results suggest that their interaction has a considerable influence on efficiency and is attributed in part to ETL degradation in organic light-emitting diodes.     

Optical properties of Cu nanoclusters supported on MgO(100)

The vertical transitions of Cu atoms, dimers, and tetramers deposited on the MgO surface have been investigated by means of ab initio calculations based either on complete active space second-order perturbation theory or on time-dependent density functional theory. Three adsorption sites have been considered as representative of the complexity of the MgO surface: regular sites at flat (100) terraces, extended defects such as monoatomic steps, and point defects such as neutral oxygen vacancies (F or color centers). The optical properties of the supported Cu clusters have been compared with those of the corresponding gas-phase units. Upon deposition a substantial modification of the energy levels of the supported cluster is induced by the Pauli repulsion with the substrate. This causes shifts in the optical transitions going from free to supported clusters. The changes in cluster geometry induced by the substrate have a much smaller effect on the optical absorption bands. On F centers the presence of filled impurity levels in the band gap of MgO results in a strong mixing with the empty levels of the Cu atoms and clusters with consequent deep changes in the optical properties of the color centers. The results allow to interpret electron energy loss spectra of Cu atoms deposited on MgO thin films.     

Geometric and electronic structures of (BeO)(N) (N = 2-12, 16, 20, and 24): rings, double rings, and cages

The structure of (BeO)(N) clusters (N = 2-12, 16, 20, and 24) are investigated using the method combining the genetic algorithm with density function theory. Benchmark calculation indicates that THSSh functional is reliable to predict the structures of (BeO)(N) cluster. The global minimum structures of (BeO)(N) clusters are rings up to N = 5, double rings at N = 6 and 7 and cages at N ≥ 8. Besides, almost all of the structures of (BeO)(N) cluster are aromatic according to the NICS criterion. Adaptive natural density partitioning analysis reveals that C(6), (BN)(3), and (BeO)(3) rings (C(24) and (BeO)(12) fullerenes) are similar in bonding patterns. The building-up principle of (BeO)(N) is different from that of covalent (BN) and ionic (LiF and MgO) clusters.