Electrostatic Point Charge Model Research Articles

Morphology of polar ASO 3·6H 2O crystals (A = Ni, Co, Mg) and solvent interaction

The PBC analysis of the polar ASO 3·6H 2O structure leads to the F-forms {001}, {00 1 }, {111}, { 1 1 1 }, {011}, {0 1 1 }, {0 1 1} and {01 1 }. Attachment energies and slice energies were calculated using an electrostatic point charge model. Two centrosymmetric theoretical habits are derived. One, based on slice energies, is prismatic with {0 1 1} and {01 1 } as main forms, the other, based on attachment energies, is isometric with only {001} and {00 1 }. The observed polar habit is explained in terms of the interaction of water molecules with the exposed oxygens of the sulphite ion. This interaction decreases the growth rate of { 1 1 1 }, {0 1 1 } and {001}, while the {01 1 } prisms is more affected than {0 1 1}, in qualitative agreement with the observed habit.

Librations and ordering in NH4AIF4. A heat capacity study

Abstract The heat capacity of NH4AIF4 has been measured from 5 K to 330 K. An anomalous peak at 156.9 K and a broad shoulder above 100 K are discussed in relation with the NH4 +-NH4 + direct and indirect interactions and the librations of the ammonium ions within an electrostatic point charge model.

Structural morphology of YBa 2Cu 3O 7- x

The structural morphology of YBa 2Cu 3O 7- x (YBCO) has been investigated by application of the periodic bond chain (PBC) theory. For x=1, the F forms were found to be {001}, {011}, {013}, {112} and {114}. Attachment energies have been calculated in broken bond model and in an electrostatic point charge model. For x=1 the theoretical growth habit is tabular to platy {001} with {011} as side faces. For x=0 {010} also becomes an F form. The habit is isometric with large {001} and {011} and small {010} faces. The outermost layer of {001} contains half of the Cu + ( x=1) or Cu 3+ and O 2- ( x=0) ions in an ordered arrangement based on a c(2x2) quadratic lattice. For the outermost layer of (010) ( x=0) an ordering scheme of the copper and oxygen ions is proposed. The occurrence of {010} rather than {011} on grown crystals has to be ascribed to external factors.

Structural morphology of crystals with the barite (BaSO 4) structure: A revision and extension

The structural morphology of crystals with the barite (BaSO 4) structure (sulphates, chromates, perchlorates, permanganates and tetrafluoroborates) has been determined with the use of computer programs. Uniquely defined F forms are {002}, {210}, {211}, {020} and {201}. Two different F slices were found for {101} and {200}, 33 for {011}. Attachment energies and specific surface energies have been calculated for an electrostatic point charge model as a function of the charge distribution in the anion. On this basis it is concluded that {101} behaves as an F form, {200} as an S form and {011} as a K form. The theoretical growth form shows {210}, {101} and {002} as main forms. A comparison is made with habits of natural and synthetic crystals. Experiments on KCIO 4 show that {011} appears at high supersaturations (>38;~;20%). It is shown that a broken bond model provides relative attachment energies that are higher by a factor of about three.

Ligand-field analysis of the ion VO2+: application of the angular overlap model to the electronic absorption spectrum of bis(acetylacetonato)oxovanadium(IV) in various solvents

A ligand-field analysis employing the angular overlap model of the electronic d–d spectrum of [VO(acac)2](acac = acetylacetonate) is presented. A consistent set of eλ values has been determined through statistical procedures. First, the constancy of the parameters was assumed when solid [VO(acac)2] is dissolved in different solvents. Then, the results were compared with those obtained when variability of the parameters with the solvent is allowed. Variations in the electronic spectra are primarily dependent on modifications in the chromophore topology induced by the solvent. Earlier calculations using the point-charge electrostatic model are discussed on the basis of the formal equivalence between the models.

Organic anions: IX. Applications of point charge and HSE force field models to group 1 organometallic terameric and hexameric aggregates

The relative dimensions of group 1 (RM) 4 tetramers can be accounted for in terms of a simple point charge electrostatic model. Such a model cannot be applied to the equivalent (RM) 6 hexamers, but for these a hard sphere electrostatic model is reasonably successful. The findings support the view that the structures of group 1 organometallics are determined principally by electrostatic factors but not the argument that bonding in these compounds is wholly ionic.

Theoretical growth and equilibrium forms of ADP (NH 4H 2PO 4)

The Hartman-Perdok theory enables one to establish the F forms of ammonium dihydrogen phosphate (ADP) as {100} and {011}. Although the {0 kl} forms are theoretically expected to be S faces, they nevertheless exhibit K face characteristics for k < l. The forms {0 kl}, with k > l, which are typical of the so-called tapering of the ADP crystals, are S faces. The attachment energy of a particular face, which is assumed to be directly proportional to its growth rate, can be computed in an electrostatic point charge model. As the ionic charge distribution in the crystallizing units is not known exactly, the calculations have been made in 36 models, with P-O and N-H bond varying from purely ionic to completely covalent. The theoretical growth forms comprise always the {011} and sometimes {100}. The presence of the latter is a function of the ionic charge of the oxygen, q o, and that of the hydrogen H 0 belonging to the [H 2PO 4] - group, q H 0 . The form {100} is present, if -0.9 < q o < 0, when q H 0 varies accordingly between 0 and 0.8. When halving of the elementary growth layer d 011 is applicable, the theoretical growth forms of all the models show {100} and {011} resulting in a very pronounced prismatic habit. The presence of impurities can explain the occurrence of {031} on the growth forms of all the models, which therefore resemble the so called tapered ADP crystals. The equilibrium forms show always {100} and {011}. The prismatic habit is more pronounced for models with a low q O and q H 0 . The hydrogens H 0 are situated just on the boundaries of the elementary growth layers. The effect of ordering of these H 0 ions on the theoretical growth and equilibrium forms is not substantial.

Band Structure Calculations of Two-Dimensional (2 D) Models of the Phases LiBC and CaAl2Si2

The electronic structures of the phases LiBC and CaAl2Si2 have been investigated by two dimensional crystal orbital calculations. The corresponding solid-state ensembles have been separated into anionic (e.g. [BC]-, [AlSi]- , [Al2Si2]2-) and cationic substructures. The employed fragmentation is topologically related to the electron counting schemes used in the classical Zintl approach. The band structures of the anionic fragments have been determined by a semiempirical Hartree-Fock crystal orbital (CO ) Hamiltonian on the basis of the tight-binding approximation. The adopted self-consistent-field variant is an intermediate neglect of differential overlap (INDO ) scheme. The influence of the cationic substructure has been simulated by an electrostatic point-charge model. The computational formalism allows for a suitable explanation of the conformations of the anionic subunits of the studied solids. In the CaAl2Si2 model the site symmetry in the anionic substructure has been studied in larger detail. The Al atoms show a tetrahedral coordination while an inverted tetrahedron (i.e. umbrella-like structure) is realized at the more electronegative Si centers. This local geometry is stabilized by the Coulomb interaction between the anionic [Al2Si2]2- layer and the cationic substructure. The energetic sources leading to the different conformations in LiBC and CaAl2Si2 are also quantified. The observed geometric preferences are rationalized by means of an energy fragmentation into covalent resonance (kinetic energy of the electrons) and classical Coulomb elements. This energy decomposition in the planar and chair-like conformations of LiBC and CaAl2Si2 shows that the kinetic energy favours the former, the electrostatic part the latter conformation. The dimerization of two anionic substructures (CaAl2Si2 structure) is also studied by the tight-binding formalism . The observed geometric differences between intra- and interlayer bonds are satisfactorily reproduced by the semiempirical CO model.

The electronic structure of organometallic complexes of the f elements. XIII. Comparison of the empirical and predicted crystalfield parameters of a cyclohexylisocyanide adduct derived from tris( η5-cyclopentadienyl)Praseodymium(III)

The previously derived crystal-field splitting pattern of a cyclohexylisocyanide adduct of tris( η 5-cyclopentadienyl)-praseodymium(III) has been fitted to the parameters of a semi-empirical Hamiltonian with an r.m.s. deviation of 31.7 cm −1 for 44 levels. The crystal-field parameters obtained are compared with those predicted on the basis of the electrostatic point charge model and the angular overlap model, respectively.

The theoretical growth morphology of calcium oxalate dihydrate

A qualitative PBC analysis of the COD structure results in five F forms: {110}, {101}, {100}, {121} and {211}. In order to quantify the morphological importance of these forms, their attachment energies are computed in an electrostatic point charge model. This model is derived for the oxalate ion from theoretical chemical considerations and simplified for the purpose to C 2 +1O 4 -1. The growth forms are constructed from the attachment energies, assumed to be proportional to the growth rates. Contrary to the observed morphology, the theoretical morphology is dominated by {110}. This discrepancy can be accounted for by noting that the elementary growth layer d 110 can be subdivided into two equivalent F slices with thickness 1 2 d 110 . Both have the same slice energy, which is furthermore smaller than the d 110 slice energy. When spiral and/or 2D growth mechanism occurs by means of both 1 2 d 110 F slices alternatingly in space and in time, the corresponding rate is higher than in the convential case of step thickness d 110. The presence of this growth mechanism, viewed as an extension of the original PBC theory, leads to an improved theoretical morphology in better agreement with the observed one.

A unified ligand field model comprising the effects of electrostatics and covalence on molecular electronic energies

The relevance of models describing molecular electronic energies including electrostatic as well as covalence effects is outlined and a summary of developments resulting in the present formulation is given. A simple, semi-empirical model based on a LCAO-MO approximation and comprising the point charge electrostatic model and angular overlap model is formulated. Although the present formulation is restricted to the antibonding effects of covalence it is applicable to p, d, f and g orbital energies. The mathematical and conceptual simplicity of the model derives from the application of a re-parameterized ionic model and the superposition principle for ligand contributions, the latter applied in the case of ionic as well as antibonding effects. A physical interpretation of the model, for diatomic as well as polyatomic molecules, is presented and the results of its application to the pentachlorovanadate(IV) ion are cited.

An electrostatic approach to the thermochemistry of fluorocarbons

The often used predictive schemes, notably bond and group additivites, work well for the prediction of heats of formation of compounds not containing polar groups. However, as halogens are introduced into the molecule, the additivity schemes may be in error by as much as 7–10 kcal mol /t-1. An electrostatic point charge model will be described which shows marked improvement in the prediction of heats of formation of fluorine and chlorine containing organic molecules. Intrinsic point charges are assigned to each atom at infinite distances. As these charges are brought to molecular dimensions, polarization occurs due to the electric fields generated. The heats of formation are then considered to be the sum of three terms - a bond contribution, an electrostatic work contribution, and a polarization work contribution.

On the equivalence between the point-charge electrostatic model and the angular-overlap model

The parametric equivalence between the point-charge electrostatic model and the angular-overlap model previously derived by the author for the n/N configuration in arbitrary symmetry is extended to the case of the n/Nn'l'N' configuration. The equivalence between the two models is discussed from a practical viewpoint.

X-ray photoelectron spectroscopy of polymorphous thallous halides

A comparative x-ray photoelectron spectroscopy study of thallous chloride and thallous bromide in their simple cubic and face centered cubic crystallographic structures is reported. Simple cubic structure is the normal phase and a face centered structure is obtained by epitaxial growth of thin layers on potassium bromide substrate. The x-ray photoelectron spectroscopy appears to be able to distinguish these structural modifications. From one structure to another slight differences are found between the separation of cation and anion core energy levels; the use of an electrostatic point charge model leads us to attribute a more covalent bond in the fcc structures as compared to the sc ones. The evolution of the main structures in the valence band from sc to fcc crystals and from compound to compound are discussed in comparison with available KKR density of states calculations; the general shape of the valence bands as well as the trends in the sequences are fairly well reproduced.

Relations entre la morphologie théorique et la morphologie observée des cristaux de CdCl 2 · 2.5 H 2O

Growth habit of CdCl 2 · 2.5 H 2O crystals is described. The most important forms are: {011}, {110} and {101}. The relations between the crystal structure and the crystal morphology have been investigated according to the PBC theory of Hartman and Perdok. In this structure two types of bond are present, on the one hand Cd-Cl and Cd-O bonds, on the other hand hydrogen bond O-H ⋯ O and O-H ⋯ Cl. The PBC directions are [100], 〈111〉, 〈111〉, [10 1 ], [010] and [001]. The F faces containing at least two PBCs within a growth layer are {110}, {011}, {101}, {010} and {10 1 }. Starting from an electrostatic point charge model, the electrostatic chain, attachment, crystal and specific surface energies are calculated for the F faces and two S faces. By application of the Wulff plot method the structural growth form is drawn from the attachment energy values, and the equilibrium form from the specific energy values. The structural growth form contains {101}, {011} and {110} forms, the equilibrium form has {010} in addition. This agrees with the observed morphology.

Laser-induced polarized fluorescence in cubic yttrium sesquioxide doped with trivalent europium

The fluorescence spectrum of ${\mathrm{Eu}}^{3+}$ in the ${C}_{2}$---approximately ${C}_{2v}$---site of the $C$-${\mathrm{Y}}_{2}$${\mathrm{O}}_{3}$ structure was recorded using a tunable dye laser to populate the $^{5}D_{0}$ level of the $4{f}^{6}$ configuration. Because the active ion occupies an anisotropic point site in an overall cubic unit cell one can make use of the Feofilov theory to interpret the experimental polarization of the emission lines. The polarized laser beam was applied perpendicular to the (111) plane of a single crystal and the polarization for each line of the $^{5}D_{0}\ensuremath{\rightarrow}^{7}F_{1,2,3,4}$ transitions was measured. From the data the irreducible representations associated with the Stark levels can be found. In particular the transitions ${A}_{1}\ensuremath{\rightarrow}{A}_{1}$ and ${A}_{1}\ensuremath{\rightarrow}{A}_{2}$ can be unambiguously distinguished from ${A}_{1}\ensuremath{\rightarrow}{B}_{1}$ and ${A}_{1}\ensuremath{\rightarrow}{B}_{2}$. A preliminary crystal-field analysis was undertaken on the basis of the 49 $^{7}F_{J}$ states using an Hamiltonian (including spin-orbit coupling) written in true ${C}_{2}$ symmetry, that is including imaginary crystal-field parameters. To derive approximate values of the crystal-field parameters the electrostatic point-charge model was applied.

The thermodynamics of ionization of gaseous oxides; the first ionization potentials of the lanthanide metals and monoxides

The first ionization potentials of the gaseous lanthanide metals and monoxides have been determined by electron impact from the appearance potentials of ionization efficiency curves. A method of simultaneous and intercomparative measurements with known standards was used and the results for the lanthanide metals are in excellent agreement with values obtained previously from spectroscopic and surface ionization studies. In the early part of the lanthanide sequence the ionization potentials of LnO(g) are less than those of Ln(g), whereas the converse is true in the latter part. The differences in the ionization potentials of LnO(g) and Ln(g) are simply related to the differences in the dissociation energies of LnO(g) and LnO+(g). Values of D0(LnO+) are derived. The nature of the chemical bonding in LnO(g) and LnO+(g) is examined for the lanthanide sequence by means of an electrostatic point-charge model. The assumption of monotonic variation of the interatomic distance and the electrostatic repulsion parameter and the nonmonotonic variation of the polarization energy derived from the known f-to-d electronic transitions are all mutually consistent and describe rather closely the variation in bonding in LnO(g); a similar scheme without the f-to-d transition energies is shown to describe the variation in the bonding of LnO+(g).

The crystal field at Er3+ in copper doped zinc selenide

AbstractAn empirical LCAO‐MO calculation of the magnitude of the overlap contribution to the crystal field at Er3+ at an interstitial site in copper doped ZnSe is reported. The success of the point charge electrostatic model in calculating the magnitude of the crystal field at such sites is discussed.

Ligand field splitting in square planar, trigonal bipyramidal, and octahedral structures by the diffuse charge model

The electrostatic point charge model of the ligand field theory is extended by representing each ligand by 2635 points uniformly distributed at the position of the ligands. Application to a square planar, trigonal bipyramidal and octahedral structure is considered. The orders of d-orbitals are found to be the same as those based on the simple point charge model, for the examples examined. However, the centre of the splitting is at somewhat higher values in the diffuse charge model and the overall magnitude has decreased. Moreover the relative magnitude of the separation of individual d-orbitals has also been altered. The diffuse charge model thus introduces new features which merit attention.

Comparison between the point charge electrostatic model and the Ξ 2 model

Relationships between crystal-field radial integrals which lead to an effective crystal-field hamiltonian of the same type as the one postulated in the Ξ 2 approach are given in this letter. The angular overlap model in its Ξ 2 restriction then appears as a particular case of the electrostatic model.