TL;DR: A new set of atomic partial charges of MeCN and MeSCN is obtained by using the MD simulation trajectories and the electrostatic potential model recently developed, and the CN and SCN stretching mode frequency trajectories were obtained and used to simulate the IR spectra.
Abstract: Nitrile- and thiocyanate-derivatized amino acids have been found to be useful IR probes for investigating their local electrostatic environments in proteins. To shed light on the CN stretch frequency shift and spectral lineshape change induced by interactions with hydrogen-bonding solvent molecules, we carried out both classical and quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations for MeCN and MeSCN in water. These QM/MM and conventional force field MD simulation results were found to be inconsistent with the experimental results as well as with the high-level ab initio calculation results of MeCN-water and MeSCN-water potential energies. Thus, a new set of atomic partial charges of MeCN and MeSCN is obtained. By using the MD simulation trajectories and the electrostatic potential model recently developed, the CN and SCN stretching mode frequency trajectories were obtained and used to simulate the IR spectra. The C[Triple Bond]N frequency blueshifts of MeCN and MeSCN in water are estimated to be 9.0 and 1.9 cm(-1), respectively, in comparison with those of gas phase values. These values are found to be in reasonable agreement with the experimentally measured IR spectra of MeCN, MeSCN, beta-cyano-L-alanine, and cyanylated cysteine in water and other polar solvents.
TL;DR: In this article, the authors examined the heterolytic dissociation process associated with the activation of Single Electron Transfer Living Radical Polymerization through the use of energy profile modeling.
TL;DR: The basic mechanism of the charge migration process in the studied molecules is analyzed in detail and is demonstrated to be due to electron correlation and relaxation effects.
Abstract: The ultrafast charge migration following outer-valence ionization in three different but related molecules, namely, 2-phenylethyl-N,N-dimethylamine (PENNA), and its butadiene (MePeNNA) and ethylene (BUNNA) derivates, is studied in detail. The molecules have different chromophore-donor sites, but nearly identical amine-acceptor sites. The results show that the charge migration process depends strongly on the particular donor site, varying from ultrafast migration of the charge from the donor to the acceptor site (4fs for MePeNNA) to no migration at all (for BUNNA). The influence of the geometrical structure of the molecule on the charge migration is also investigated. It is shown that energetically closely lying conformers may exhibit dramatically different charge migration behaviors. The basic mechanism of the charge migration process in the studied molecules is analyzed in detail and is demonstrated to be due to electron correlation and relaxation effects.
TL;DR: In this paper, the effect of ionic liquids on the formation of a partial positive charge on the surface of a silver nanoparticle and its subsequent effect on facilitated olefin transport were investigated.
TL;DR: In this article, new ideas about the electronic structure of amides and the peptide bond are presented, and the discussion is extended to include the presence of a negative charge on the nitrogen atom.
Abstract: A majority of the standard texts dealing with proteins portray the peptide link as a mixture of two resonance forms, in one of which the nitrogen atom has a positive charge. As a consequence, it is often believed that the nitrogen atom has a net positive charge. This is in apparent contradiction with the partial negative charge on the nitrogen that is used in force fields for molecular modeling. However, charges on resonance forms are best regarded as formal rather than actual charges and current evidence clearly favors a net negative charge for the nitrogen atom. In the course of the discussion, new ideas about the electronic structure of amides and the peptide bond are presented.
TL;DR: This paper elucidates the consequences of different charge sets on the structure and dynamics of the ionic liquid: 1-ethyl-3-methyl-imidazolium dicyanoamide and shows that all dynamical parameters presented in this work can be converted from one charge set to another by viscosity scaling.
Abstract: The vast majority of molecular dynamics simulations are based on nonpolarizable force fields with fixed partial charges for all atoms. The traditional way to obtain these charges are quantum-mechanical calculations performed prior to simulation. Unfortunately, the set of the partial charges heavily relies on the method and the basis set used. Therefore, investigations of the influence of charge variation on simulation data are necessary in order to validate various charge sets. This paper elucidates the consequences of different charge sets on the structure and dynamics of the ionic liquid: 1-ethyl-3-methyl-imidazolium dicyanoamide. The structural features seem to be more or less independent of the partial charge set pointing to a dominance of shape force as modeled by Lennard–Jones parameters. This can be seen in the radial distribution and orientational correlation functions. The role of electrostatic forces comes in when studying dynamical properties. Here, significant deviations between different charge sets can be observed. Overall, dynamics seems to be governed by viscosity. In fact, all dynamical parameters presented in this work can be converted from one charge set to another by viscosity scaling.
TL;DR: In this article, the effects of solvent nature, partial charge distribution and polarity index on the preparation of uniform silane self-assembly monolayers were investigated and the results can be applied to other monolayer-solvent systems.
TL;DR: The results demonstrate that liquid-phase partial charges are capable of improving the quality of ionic liquid force fields substantially and that their utilization led to a model that can be applied to predict structural, energetic, and dynamic properties of GILs.
Abstract: We propose a new all-atom force field for guanidinium-based ionic liquids (GILs) which is based on the charge distribution in the actual liquid. It comprises all cations that can be built by attaching alkyl chains of variable length to an acyclic or cyclic guanidinium compound and that are paired with nitrate or perchlorate anions. We based the parametrization of the force field on liquid-phase charge distributions to improve the prediction of energetic and dynamic properties of GILs. The impact of electron charge transfer and polarization on various properties of GILs is systematically assessed. A significant average electron charge transfer between -0.12 and -0.06 e from anions to the central guanidinium group of the cations and a strong polarization of acyclic cations are observed by applying a combined quantum mechanical/molecular mechanical (QM/MM) approach. Molecular dynamics simulations of GILs are performed, utilizing the proposed force field. Derived structures approach the accuracy of QM/MM structures, and a previously reported crystal structure remains stable throughout the simulations. Mass densities are reproduced with a deviation of only 1.4% from experimental data. The calculated melting point of a GIL crystal deviates only 8% from the measured value. Self-diffusion coefficients of various GILs are reported, and a comparison with a diffusion coefficient derived from experimental data indicates that the values are within a reasonable range. We observe that the melting point of a GIL crystal was lowered up to 60 K and that diffusion coefficients are substantially increased by a factor of up to 3.5 upon consideration of charge transfer and polarization. The results demonstrate that liquid-phase partial charges are capable of improving the quality of ionic liquid force fields substantially and that their utilization led to a model that can be applied to predict structural, energetic, and dynamic properties of GILs.
TL;DR: Molecular dynamics simulations of alkyl nitrate liquids and two polymorphs of PETN crystal demonstrate the ability of the quantum-chemistry-based force fields to accurately predict thermophysical and mechanical properties of these materials.
Abstract: Quantum-chemistry-based many-body polarizable and two-body nonpolarizable atomic force fields were developed for alkyl nitrate liquids and pentaerythritol tetranitrate (PETN) crystal. Bonding, bending, and torsional parameters, partial charges, and atomic polarizabilities for the polarizable force field were determined from gas-phase quantum chemistry calculations for alkyl nitrate oligomers and PETN performed at the MP2/aug-cc-pvDz level of theory. Partial charges for the nonpolarizable force field were determined by fitting the dipole moments and electrostatic potential to values for PETN molecules in the crystal phase obtained from molecular dynamics simulations using the polarizable force field. Molecular dynamics simulations of alkyl nitrate liquids and two polymorphs of PETN crystal demonstrate the ability of the quantum-chemistry-based force fields to accurately predict thermophysical and mechanical properties of these materials.
TL;DR: Optimization of the hydrated Cu(II)(N7-guanine) structures revealed a number of minima on the potential energy surface, and the energetic preference of diaqua-Cu-(N7,O6-guansine) over triaqua- Cu-(N 7-guAnine) was found for the four-coordinate structures.
Abstract: Optimization of the hydrated Cu(II)(N7−guanine) structures revealed a number of minima on the potential energy surface. For selected structures, energy decompositions together with the determination of electronic properties (partial charges and electron spin densities) were performed. In the complexes of guanine with the bare copper cation and that with the monoaqua ligated cation, an electron transfer from guanine to Cu(II) was observed, resulting in a Cu(I)−guanine+ type of complex. Conformers with two aqua ligands are borderline systems characterized by a Cu partial charge of +0.7e and a similar value of the spin density (0.6e) localized on guanine. When tetracoordination of copper was achieved, only then the prevailing electron spin density is unambiguously localized on copper. The energetic preference of diaqua-Cu−(N7,O6−guanine) over triaqua-Cu−(N7−guanine) was found for the four-coordinate structures. However, the energy difference between these two conformations decreases with the number of water ...
TL;DR: The linear absorbance of a particular chromophore complex P(4) dissolved in ethanol is computed using an improved exciton model, where the charge and transition densities of the chromophores are described by atomic partial charges, derived from a fit of the respective ab initio electrostatic potentials.
Abstract: The linear absorbance of a particular chromophore complex P4 dissolved in ethanol is computed. P4 is formed by a butanediamine dendrimer to which four pheophorbide-a molecules are covalently linked. The computations utilize a mixed quantum classical methodology and different approximations are compared. The electronic states of the P4 chromophores which form Frenkel excitons in the excited states are treated quantum mechanically, whereas the intramolecular, intermolecular, as well as solvent coordinates are described classically. The computations use an improved exciton model, where the charge and transition densities of the chromophores are described by atomic partial charges, derived from a fit of the respective ab initio electrostatic potentials. Room temperature molecular dynamics simulations of all nuclear coordinates result in a time-dependent exciton model. It includes modulations of chromophore excitation energies due to charge density coupling between all chromophores as well as between the chrom...
TL;DR: Result obtained showed that nonlinear model can simulate the relationship between structural descriptors and the partition coefficients of the molecules in data set accurately.
TL;DR: In this article, the CHARMM charge equilibration force field is applied to molecular dynamics simulations of liquid straight-chain alkylamine systems, and the importance of defining the extent of molecular charge transfer via judicious selection of charge normalization units is considered and evaluated.
TL;DR: Test calculations on the gas-phase glucagon and solvated alpha-conotoxin GI demonstrate that the present polarization model is capable of describing the structural properties with accuracy comparable to some other polarizable force fields and the quantum mechanics/molecular mechanics (QM/MM) hybrid model.
Abstract: The solution conformation of alpha-conotoxin GI and its two single disulfide analogues are simulated using a polarizable force field in combination with the molecular fragmentation quantum chemical calculation. The polarizability is explicitly described by allowing the partial charges and fragment dipole moments to be variables, with values coming from the linear-scaling energy-based molecular fragmentation calculations at the B3LYP/6-31G(d) level. In comparison with the full quantum chemical calculations, the fragmentation approaches can yield precise ground-state energies, dipole moments, and static polarizabilities for peptides. The B3LYP/6-31G(d) charges and fragment-centered dipole moments are introduced in calculations of electrostatic terms in both AmberFF03 and OPLS force fields. Our test calculations on the gas-phase glucagon (PDB code: 1gcn) and solvated alpha-conotoxin GI (PDB code: 1not) demonstrate that the present polarization model is capable of describing the structural properties (such as the relative conformational energies, intramolecular hydrogen bonds, and disulfide bonds) with accuracy comparable to some other polarizable force fields (ABEEM/MM and OPLS-PFF) and the quantum mechanics/molecular mechanics (QM/MM) hybrid model. The employment of fragment-centered dipole moments in calculations of dipole-dipole interactions can save computational time in comparison with those polarization models using atom-centered dipole moments without much loss of accuracy. The molecular dynamics simulations using the polarizable force field demonstrate that two single disulfide GI analogues are more flexible and less structured than the native alpha-conotoxin GI, in agreement with NMR experiments. The polarization effect is important in simulations of the folding/unfolding process of solvated proteins.
TL;DR: In this paper, the authors showed that iron is incorporated at the [Zr,Ti]-site, acting as an acceptor and building a charged defect dipole with a directly coordinated oxygen vacancy for partial charge compensation.
Abstract: Ferroelectric 1 mol% Gd3+ and 0.5 mol% Fe3+ codoped "soft" Pb[Zr0.525Ti0.475]O3 ceramics were studied by means of multifrequency electron paramagnetic resonance (EPR) spectroscopy. The obtained results prove that iron is incorporated at the [Zr,Ti]-site, acting as an acceptor and building a charged defect dipole with a directly coordinated oxygen vacancy for partial charge compensation. As the La3+ ion is diamagnetic, no information is accessible about the donor. Gd3+ is an isoelectronic and paramagnetic probe for studying A-site. On the other hand, the donor forms no defect associates with lattice vacancies and rather exists as an "isolated" functional center. Consequently, also the lead vacancies that are created for charge compensation have to exist as isolated centers in compound.
TL;DR: It is found that the partial charges of the solutes in the force field simulations are lower than the localized electron densities for the quantum simulations, which decreases the hydrogen bond strength.
Abstract: We present molecular dynamics simulations of glutamic acid and glutamate solvated in water, using both density functional theory (DFT) and the Gromos96 force field. We focus on the microscopic aspects of the solvation-particularly on the hydrogen bond structures and dynamics-and investigate the influence of the protonation state and of the simulation method. Radial distribution functions show that the hydrogen bonds are longer in the force field systems. We find that the partial charges of the solutes in the force field simulations are lower than the localized electron densities for the quantum simulations. This lower polarization decreases the hydrogen bond strength. Protonation of the carboxylate group renders glutamic acid a very strong and stable hydrogen bond donor. The donated hydrogen bond is shorter and lives longer than any of the other hydrogen bonds. The solute molecules simulated by the force field accept on average three more hydrogen bonds than their quantum counterparts. The life times of these bonds show the opposite result: the residence times are much longer (up to a factor 4) in the ab initio simulations.
TL;DR: In this article, the point of zero charge (pzc) of a metal oxide in contact with water in an operational way was estimated by performing potentiometric titrations.
Abstract: After performing this experiment, the student shall be able to:
Understand the concept of point of zero charge (pzc) of a metal oxide in contact with water in an operational way.
Estimate the pzc of a simple metal oxide by performing potentiometric titrations.
Visualize the importance and applications of the pzc.
TL;DR: In this article, the growth of crystalline Li4C60 films was demonstrated and the low-energy electron diffraction pattern of the films indicated the formation of polymer chains in the plane of the surface, consistent with the reported crystal structure.
Abstract: We demonstrate the growth of crystalline Li4C60 films. The low-energy electron diffraction pattern of the films indicates the formation of polymer chains in the plane of the surface, consistent with the reported crystal structure. Electron energy loss and photoemission spectra identify the Li4C60 polymer as a low band gap semiconductor, with a relatively strong coupling of electrons to low-frequency stretching modes of the polymer bonds and alkali phonons. No evidence is found for hybridization between the Li- and fullerene-derived electronic states. Instead, a partial charge transfer takes place, which is the same for different Li concentrations. This result rationalizes the stability of the polymer phase over a wide range of stoichiometries.
TL;DR: In this article, an optimized force field for the simulation of crystalline phases of resorcinol was proposed and the parameters for the van der Waals interactions were optimized using sensitivity analysis.
Abstract: The two known crystalline phases of resorcinol and their phase transitions are of considerable interest. The crystals exhibit pyro- and piezo-electricity and, remarkably, the higher temperature β phase is the denser phase. Furthermore, crystals of the α phase, by virtue of having a polar axis, have played a crucial role in investigating fundamental issues of crystal growth. We report an optimized force field for the molecular simulation of crystalline phases of resorcinol. The hydroxyl groups of the resorcinol molecule have a torsional degree of freedom and the molecule adopts a different conformation in each of the two phases of resorcinol. The torsional barrier, therefore, was considered to be critical and has been characterized using ab initio methods. Although the atomic partial charges showed some dependence on the molecular conformation, a single set of partial charges was found to be sufficient in describing the electrostatic potential for all conformations. The parameters for the van der Waals interactions were optimized using sensitivity analysis. The proposed force field reproduces not only the static structures but also the stability of the crystalline phases in extended molecular dynamics simulations.
TL;DR: Several widely available and economical semiempirical molecular orbital methods and molecular mechanical force fields are tested for their ability to accurately predict the partial charges, binding energies to a water molecule, and molecular geometries of representative fragments of methotrexate in the gaseous and aqueous phases.
Abstract: We have tested a variety of approximate methods for modeling 30 systems containing mixtures of nitrogen heterocycles and exocyclic amines, each of which is studied with up to 31 methods in one or two phases (gaseous and aqueous). Fifteen of the systems are protonated, and fifteen are not. We consider a data set consisting of geometric parameters, partial atomic charges, and water binding energies for the methotrexate fragments 2-(aminomethyl)pyrazine and 2,4-diaminopyrimidine, as well as their cationic forms 1H-2-(aminomethyl)pyrazine and 1H-2,4-diaminopyrimidine. We first evaluated the suitability of several density functionals with the 6−31+G(d,p) basis set to serve as a benchmark by comparing calculated molecular geometries to results obtained from coupled-cluster [CCSD/6−31+G(d,p)] wave function theory (WFT). We found that the M05-2X density functional can be used to obtain reliable geometries for our data set. To accurately model partial charges in our molecules, we elected to use the well-validated ...
TL;DR: In this paper, the authors compared theoretical and experimental valence charge densities for two crystalline planes and compared the strengths of various inter-and intra-icosahedral bonds in terms of the maximum charge density associated with the line joining the atoms.
Abstract: Improved crystal structure parameters are reported for α‐boron. Plots showing comparison of theoretical and experimental valence charge densities for two crystalline planes are given. Comparisons of the strengths of various inter‐ and intraicosahedral bonds are reported in terms of the maximum charge density associated with the line joining the atoms.
TL;DR: In this paper, the electronic structures of ZnO(0001)-Zn and (000−1)-O surfaces were investigated by means of first-principles calculations.
Abstract: We investigated the electronic structures of ZnO(0001)-Zn and (000−1)-O surfaces by means of first-principles calculations. According to the results of the relaxation and the electrostatic criterion, the surface geometric relaxations and the charge transfer almost take place on the outer four double layers. For the (0001)-Zn surface, steep surface states appear in the band gap of bulk ZnO and follow the bottom of bulk conduction band. Moreover, Fermi level shifts up into the conduction band, which leads to the n-type conduction behaviour of (0001)-Zn surface. The dispersed partial charge densities derived from the Zn-4s state spread evenly on the surface and apparently lead to difficulty of getting an atom-resolved STM image. For the (000−1)-O surface, flat surface states emerge above the top of the valence band of bulk ZnO as Fermi level shifts down a little into the valence band. Based on that, the (000−1)-O surface can be predicted to have the p-type conductivity. The localized partial charge densities derived from the O-2p state makes it possible to get an atom-resolved STM image within the low bias voltage.
TL;DR: In this paper, the same reaction may be classified as either PT or HT, depending on the used criterion, such as formal translocation of charge; the reaction mechanism, in particular the coupling between the motion of the proton and the electron density redistribution.
Abstract: The meaning of terms "proton transfer" (PT) and "hydrogen transfer" (HT), commonly encountered in the literature, is not always unambiguous, especially in the case of intramolecular tautomerization processes Depending on the used criterion, the same reaction may be classified as either PT or HT Two criteria for distinguishing between PT and HT are discussed: (a) formal translocation of charge; (b) the reaction mechanism, in particular the coupling between the motion of the proton and the electron density redistribution The analysis is illustrated using the values of ground and excited state partial charges calculated for three well-known examples of molecules that undergo photoinduced and/or ground state tautomerization: 2-hydroxyacetophenone, 2,2'-bipyridyl-3,3'-diol, and porphycene
TL;DR: In this paper, it was shown that when both mass and charge cross the interface, the charge must be carried by the ionic species, not by the electrons, as a result of the very large difference in the time scale for electron and ion transfer.
Abstract: Electrode reactions are characterized by charge transfer across the interface. The charge can be carried by electrons or by ions. It is shown here that when both mass and charge cross the interface, the charge must be carried by the ionic species, not by the electrons, as a result of the very large difference in the time scale for electron and ion transfer. A prime example of charge transfer by ions is metal deposition.
It is proposed that ion transfer occurs by migration of the ions across the interface, under the influence of the high electrostatic field in the double layer. The rate constants observed for metal deposition are comparable to those for outer-sphere charge transfer. These unexpectedly high rate constants for metal deposition are explained by a model in which removal of the solvation shell and reduction of the effective charge on the metal ion occur in many small steps, and a make-before-break mechanism exists, which lowers the total Gibbs energy of the system as it moves along the reaction coordinate from the initial to the final state.
TL;DR: In this paper, it was shown that due to H-bond formation, the total charges of the dianion and H5O2+ cation are substantially decreased and bond length distribution in the SO3 moiety can be directly related to the total energy of the cation-anion interactions and partial charges.
TL;DR: In this paper, a stack of plastic CR-39 Track Detectors were exposed to 158.A.GeV 207Pb ions at the CERN-SPS beam facility, and the exposure was performed at normal incidence with a fluence of about 1500 ions / cm 2.
TL;DR: The electrostatic and covalent contributions in the coordination bonds were investigated using quantum mechanical density functional theory and model complexes of glyoxal diimine and the 2+ cations of the first row transition metals to develop a molecular mechanics force field.
Abstract: To develop a molecular mechanics force field for modeling complexes of transition metals and organic ligands, the electrostatic and covalent contributions in the coordination bonds were investigated using quantum mechanical density functional theory and model complexes of glyoxal diimine and the 2+ cations of the first row transition metals. The VDD and Hirshfeld charges are found to be closely correlated with the extent of the electron transfer between the ligands and the cations. Assuming the electrostatic contribution can be represented by the atomic partial charges, the covalent contributions in the coordination bonds are estimated to be in a range of 54-92% for the systems calculated. A simple force field was parametrized to validate the partial charge representation.
TL;DR: In this article, the first ab initio study of molecular adsorption on the double hexagonal close-packed (dhcp) americium (Am) surface was performed using the FP-LAPW+lo method, and the corresponding distances of the oxygen molecule from the surface and oxygen-oxygen distance were found to be 0.953 and 3.731 A.
Abstract: In our continuing attempts to understand theoretically various surface properties such as corrosion and potential catalytic activity of actinide surfaces in the presence of environmental gases, we report here the first ab initio study of molecular adsorption on the double hexagonal close-packed (dhcp) americium (Am) (0 0 0 1) surface. Specifically, molecular oxygen adsorption on the (0 0 0 1) surface of dhcp Am has been studied in detail within the framework of density functional theory using a full-potential all-electron linearized augmented plane wave plus local orbitals (FP-LAPW+lo) method. Dissociative adsorption is found to be energetically more favorable compared to molecular adsorption. Chemisorption energies were optimized with respect to the distance of adsorbates from the surface for three approach positions at three adsorption sites, namely t1 (one-fold top), b2 (two-fold bridge), and h3 (three-fold hollow) sites. Chemisorption energies were computed at the scalar-relativistic-no-spin–orbit-coupling (SR-NSOC) and at the fully relativistic-with-spin–orbit-coupling (FR-SOC) levels of theory. The most stable configuration corresponds to a horizontal approach molecular dissociation with the oxygen atoms occupying neighboring h3 sites, with chemisorption energies at the NSOC and SOC theoretical levels being 9.395 and 9.886 eV, respectively. The corresponding distances of the oxygen molecule from the surface and oxygen–oxygen distance were found to be 0.953 and 3.731 A, respectively. Overall our calculations indicate that chemisorption energies in cases with SOC are slightly more stable than those with NSOC in the 0.089–0.493 eV range. The work functions and net magnetic moments, respectively, increased and decreased in all cases compared to corresponding quantities of the bare dhcp-Am (0 0 0 1) surface. Adsorbate–substrate interactions have been analyzed in detail using partial charges inside muffin-tin spheres, difference charge density distributions, and the local density of states. The effects, if any, of chemisorption on Am5f electron localization–delocalization characteristics in the vicinity of the Fermi level are also discussed.
TL;DR: In this paper, the authors study the possibility of charge ordered state in both single and bilayer graphene using a real space tight binding model and find that there is no charge ordered states in a single layer graphene.
Abstract: We study the possibility of charge ordered state in both single and bilayer graphene using a real space tight binding model. We argue that there is no charge ordered state in a single layer graphene. We also predict that the bilayer graphene can undergo a transition to a charge ordered state that is a commensurate CDW at low enough carrier density. We find that aside from the Coulomb interaction of the carriers of two layers that stabilizes the charge ordered state, so does the inter layer coupling.
TL;DR: The results show that although the variable charge model may not be advantageous in the study of ordered structures, it is important in describing structural disorders such as vacancies.
Abstract: In this paper, molecular dynamics simulations have been performed using both fixed charge and variable charge models. In the fixed charge model, partial charges are introduced to Si and C atoms to model the charge transfer observed in first principles studies. The calculated phonon dispersions, elastic constants, and lattice constants are in good accuracy. Variable charge model is also used to obtain geometry and connectivity dependent atomic charges. Our results show that although the variable charge model may not be advantageous in the study of ordered structures, it is important in describing structural disorders such as vacancies.