Electrostatic energy of disordered distributions of vacancies or altervalent ions

It is shown that the “average charge” model for calculating the Madelung energy of an ideally disordered crystal gives the correct mean lattice energy, and that only defect terms need be considered in deriving the energy of ordering of a distribution of vacancies or altervalent ions. A completely random arrangement of such defects results in a very large spread of electrostatic potentials at the ion sites, because of the possibility of unreasonable local charge aggregations. Many sites have highly unfavorable potentials, and it is concluded that a completely random disordered arrangement of vacancies or altervalent ions is only possible in very small domains, so that the magnitude of local charge unbalance is limited.     

Electrostatic energy of vacancy formation in crystals of polar molecules

An exact expression is derived for the electrostatic energy of a crystal of polar polarizable molecules containing an unrelaxed vacancy. The energy exceeds twice the electrostatic binding energy per molecule L by a polarization energy term, when changes in dielectric response due to the vacancy are ignored. The electrostatic energy of a molecule at a crystal surface is estimated from surface and bulk polarization energy measurements. It can be as high as 1.5 L. making the electrostatic energy of vacancy formation significantly less than L. the value for non-polarizable molecules. This may help to explain anomalous results for certain plastic crystals.     

Free energy partitioning analysis of the driving forces that determine ion density profiles near the water liquid-vapor interface

Free energy partitioning analysis is employed to explore the driving forces for ions interacting with the water liquid-vapor interface using recently optimized point charge models for the ions and SPC/E water. The Na(+) and I(-) ions are examined as an example kosmotrope/chaotrope pair. The absolute hydration free energy is partitioned into cavity formation, attractive van der Waals, local electrostatic, and far-field electrostatic contributions. We first compute the bulk hydration free energy of the ions, followed by the free energy to insert the ions at the center of a water slab. Shifts of the ion free energies occur in the slab geometry consistent with the SPC/E surface potential of the water liquid-vapor interface. Then the free energy profiles are examined for ion passage from the slab center to the dividing surface. The profiles show that, for the large chaotropic I(-) ion, the relatively flat total free energy profile results from the near cancellation of several large contributions. The far-field electrostatic part of the free energy, largely due to the water liquid-vapor interface potential, has an important effect on ion distributions near the surface in the classical model. We conclude, however, that the individual forms of the local and far-field electrostatic contributions are expected to be model dependent when comparing classical and quantum results. The substantial attractive cavity free energy contribution for the larger I(-) ion suggests that there is a hydrophobic component important for chaotropic ion interactions with the interface.     

Hydration of ions and formation of crystal hydrates

Effects of electrostatic and entropic factors on the dependence between the type of hydration of ions and their ability to form crystal hydrates from water solutions are discussed. It is shown that in the case of the single-charged ions because of the insignificant electrostatic interaction the crystal hydrates are formed mainly by the salts containing ions with different type of hydration. In the case of poly-charged ions the increase in the electrostatic interaction leads to formation of crystal hydrates mainly by the salts containing ions with the positive type of hydration. It was established also that the formation of salt crystal hydrates is influenced not only by the electrostatic and entropic factors, but also by the spatial arrangement and the electronic density distribution of ions.     

The electrostatic interaction energy between crystallographic shear planes in reduced tungsten trioxide

The contribution to the internal energy of slightly reduced WO₃ crystals containing CS planes due to electrostatic interactions between ions in the CS plane and ions in the surrounding crystal matrix or in neighboring CS planes has been investigated theoretically. Three CS plane geometries have been studied, {102}, {103}, and {001}. Using simple assumptions about the charge distribution in the CS planes, numerical values for these interaction energies have been estimated. It was found that the interaction energy between a CS plane and the surrounding matrix was negligible compared to the repulsive (coulomb) interaction energy between a pair of CS planes. The magnitude of this repulsive energy was in the order {103} < {102} < {001}. The possible significance of these results in controlling the microstructure of crystals containing CS planes is discussed.     

The nature of interactions in the ionic crystal of 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium

The hybrid variation -- perturbation many-body interaction energy decomposition scheme has been applied to analyze the physical nature of interactions in the ionic 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium crystal, which can be regarded as a model for a large group of aromatic quaternary nitrogen salts. In the crystal structure the sodium ions and water molecules of adjacent unit cells form a positively charged "inorganic layer" with the sodium ions clustered together along the ab faces with the organic (negative) part in between. This puzzling crystal packing is due to a strong favorable interaction between the water molecule and the sodium ions and a substantial charge transfer from the carbanions that balances out the destabilizing sodium-sodium ion repulsion. Although the majority of cohesion energy of the crystal structure comes from the electrostatic interactions of ions, the resulting net stabilization also depends heavily on the nonadditive delocalization components, due to a counterbalance between the two-body delocalization and exchange effects. The estimated nonadditivity of interactions varies between 12% and 22%.     

Computer simulation of defects in ammonium perchlorate

The electrical conductance of ammonium perchlorate has been theoretically investigated by a computer simulation technique using a polarizable point-ion model. The cohesive energy of the crystal was obtained from a Born-Harber cycle calculation. The Born-Mayer repulsive parameter was obtained from the crystal binding energy. The relaxation of approximately 50 ions was accounted for by exact calculation of the repulsive, electrostatic, and polarization energies. Twenty-one defect calculations were performed in all.Based on these calculations, a novel turnstile mechanism involving slow synchronous rotations of the perchlorate ions to allow passage of ammonium ions is proposed for vacancy migration, which accounts for the high-temperature electrical conductance.The energy of formation of a Schottky defect pair was calculated to be 1.66 eV, and the activation energy for migration of a vacancy was found to be 4.53 eV.     

Structure and charge-state dependence of the gas-phase ionization energy of proteins

Photoionization of protein ions: The ionization energy of polyprotonated protein cations in the gas phase measured using VUV synchrotron radiation appears to be correlated with the charge state z of the protein and its tertiary structure. A simple electrostatic model accounts for the results and also shows predictive capabilities to derive a mean radius R(m) of the protein ion from the ionization energy, and vice versa.     

Ion kinetic energy spectroscopy

Preliminary results indicate the value of ion kinetic energy (1KE) spectra in adding a new dimension to structural information obtained by mass spectrometry. These spectra are especially useful in the distinction of some isomer pairs. Energy spectra provide a summary of gaseous ion chemistry occurring as metastable transitions in the first-field free-drift region of the double-focusing (Mattauch-Herzog geometry) mass spectrometer and are produced by scanning the electrostatic sector voltage while recording the ions transmitted by the sector with the beam monitor electrometer.     

Kinetic energy measurements of molecular ions ejected into an electric field by matrix-assisted laser desorption.

Measurements of kinetic energy distributions of molecular ions ejected into an extraction field by matrix-assisted laser desorption are reported. The measurements were made in a time-of-flight mass spectrometer with an electrostatic mirror by measuring the reflected signal as a function of the difference between the accelerating voltage and the voltage applied to the mirror. The molecular ions were found to have less kinetic energy than the extraction field alone would normally provide, i.e., we observed an energy deficit. Under conditions typical for a matrix-assisted laser desorption experiment, the deficit is about 24 eV for molecular ions of insulin. The size of the deficit increases with the intensity of the molecular ion signal, and the molecular weight of the protein; it is also larger for negative molecular ions than for positive molecular ions.     

稀土离子对溶液体系中碳酸钙生成的影响

用X射线粉末衍射、XPS光电子能谱、红外光谱以及ICP-MS等技术研究不同浓度的Ce3+,Nd3+,Tb3+,Gd3+,Lu3+对碳酸钙结晶状况的影响.稀土离子的加入有利于热力学稳定态的方解石型碳酸钙的生成,并且稀土离子能够部分的取代晶格中的钙离子,改变碳酸钙的结晶习性,在宏观上形成有序规则的排列.     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

Accurate modeling of the intramolecular electrostatic energy of proteins

The (?, ψ) energy surface of blocked alanine (N-acetyl–N′-methyl alanineamide) was calculated at the Hartree-Fock (HF)/6-31G* level using ab initio molecular orbital theory. A collection of six electrostatic models was constructed, and the term electrostatic model was used to refer to (1) a set of atomic charge densities, each unable to deform with conformation; and (2) a rule for estimating the electrostatic interaction energy between a pair of atomic charge densities. In addition to two partial charge and three multipole electrostatic models, this collection includes one extremely detailed model, which we refer to as nonspherical CPK. For each of these six electrostatic models, parameters—in the form of partial charges, atomic multipoles, or generalized atomic densities—were calculated from the HF/6-31G* wave functions whose energies define the ab initio energy surface. This calculation of parameters was complicated by a problem that was found to originate from the locking in of a set of atomic charge densities, each of which contains a small polarization-induced deformation from its idealized unpolarized state. It was observed that the collective contribution of these small polarization-induced deformations to electrostatic energy differences between conformations can become large relative to ab initio energy differences between conformations. For each of the six electrostatic models, this contribution was reduced by an averaging of atomic charge densities (or electrostatic energy surfaces) over a large collection of conformations. The ab initio energy surface was used as a target with respect to which relative accuracies were determined for the six electrostatic models. A collection of 42 more complete molecular mechanics models was created by combining each of our six electrostatic models with a collection of seven models of repulsion + dispersion + intrinsic torsional energy, chosen to provide a representative sample of functional forms and parameter sets. A measure of distance was defined between model and ab initio energy surfaces; and distances were calculated for each of our 42 molecular mechanics models. For most of our 12 standard molecular mechanics models, the average error between model and ab initio energy surfaces is greater than 1.5 kcal/mol. This error is decreased by (1) careful treatment of the nonspherical nature of atomic charge densities, and (2) accurate representation of electrostatic interaction energies of types 1—2 and 1—3. This result suggests an electrostatic origin for at least part of the error between standard model and ab initio energy surfaces. Given the range of functional forms that is used by the current generation of protein potential functions, these errors cannot be corrected by compensating for errors in other energy components. © 1995 by John Wiley & Sons, Inc.     

First-principles calculations of migration energy of lithium ions in halides and chalcogenides

Migration of Li+ ions via the vacancy mechanism in LiX (X = F, Cl, Br, and I) with the rocksalt and hypothetical zinc blende structures and Li2X (X = O, S, Se, and Te) with the antifluorite structure has been investigated using first-principles projector augmented wave calculations with the generalized gradient approximation. The migration paths and energies, determined by the nudged-elastic-band method, are discussed on the basis of two idealized models: the rigid-sphere and charged-sphere models. The trajectories and energy profiles of the migration in these lithium compounds vary between these two models, depending on the anion species and crystal structure. The migration energies in LiX with both the rocksalt and hypothetical zinc blende structures show a tendency to decrease with increasing periodic number of the anion species in the periodic table. This is consistent with the widely accepted view that anion species with large ionic radii and high polarizabilities are favorable for good ionic conduction. In contrast, Li2O exhibits the lowest migration energy among Li2X compounds, although O is the smallest among the chalcogens, indicating that electrostatic attractive interactions play the dominant role in the inter-ion interactions in Li2O and, therefore, in the ion migration.     

Surface energy of talc and chlorite: Comparison between electronegativity calculation and immersion results

The surface energies of talc and chlorite is computed using a simple model, which uses the calculation of the electrostatic energy of the crystal. It is necessary to calculate the atomic charges. We have chosen to follow Henry's model of determination of partial charges using scales of electronegativity and hardness. The results are in correct agreement with a determination of the surface energy obtained from an analysis of the heat of immersion data. Both results indicate that the surface energy of talc is lower than the surface energy of chlorite, in agreement with observed behavior of wettability. The influence of Al and Fe on this phenomenon is discussed. Surface energy of this type of solids seems to depend more strongly on the geometry of the crystal than on the type of atoms pointing out of the surface; i.e., the surface energy depends more on the physics of the system than on its chemistry.     

Free energy of adsorption of water and metal ions on the [1014] calcite surface

We calculated the free energy profiles of water and three metal ions (magnesium, calcium, and strontium) adsorbing on the [1014] calcite surface in aqueous solution. The approach uses molecular dynamics with parametrized equations to describe the interatomic forces. The potential model is able to reproduce the interactions between water and the metal ions regardless of whether they are at the mineral surface or in bulk water. The simulations predict that the free energy of adsorption of water is relatively small compared to the enthalpy of adsorption calculated in previous papers. This suggests a large change in entropy associated with the water adsorption on the surface. We also demonstrate that the free energy profile of a metal ion adsorbing on the surface correlates with the solvent density and that the rate of formation of an innersphere complex depends on overcoming a large free energy barrier, which is mainly electrostatic in nature. Furthermore, comparison among the rates of desorption of magnesium, calcium, and strontium from the calcite surface suggests that magnesium has a much lower rate of desorption due to its strong interactions with both water and the surface.     

Photoelectron energy analysis in a strong magnetic field: The role of elastic scattering

A new photoelectron spectroscopic method is described directed towards the measurement of the photoelectron spectra of trapped ions. An electrostatic retarding field electron energy analyser incorporating a channel plate is included with an ion trap in a strong magnetic field. The form of photoelectron spectrum is shown to be strongly influenced by a elastic scattering effects which can be enhanced by using an electron trapping potential well. The resultant spectra then have a particularly simple and useful form.     

Comparison of methods to estimate the free energy of solvation:Importance in the modulation of the affinity of 3-benzazepines for the D1receptor

We computed the free energy of solvation for a series of ions and neutral molecules using two different continuum approaches. First, we used the AM1–SM1 technique, where the AM1 Fock matrix is modified to include a generalized Born contribution. Second, we applied the DelPhi approach, where the electrostatic component of the free energy of solvation is evaluated by resolving the Poisson–Boltzman equation by a finite difference method. Both methods appear equally reliable for ionic systems. For neutral compounds, AM1–SM1 performs better than DelPhi; however, the differences become less pronounced for compounds with larger free energies of solvation. In parallel, both methods were applied to study the influence of the solvation process in the overall drug receptor interaction for a series of closely related ligands for the D₁ dopamine receptor. An inverse linear relationship was found between the free energy of solvation and the logarithm of the affinity of the ligands; nevertheless, electrostatic properties are likely to modulate affinity as well. © 1993 John Wiley & Sons, Inc.     

Positive and negative ions of the amino acid histidine formed in low‐energy electron collisions

Histidine is an aromatic amino acid crucial for the biological functioning of proteins and enzymes. When biological matter is exposed to ionising radiation, highly energetic particles interact with the surrounding tissue which leads to efficient formation of low‐energy electrons. In the present study, the interaction of low‐energy electrons with gas‐phase histidine is studied at a molecular level in order to extend the knowledge of electron‐induced reactions with amino acids. We report both on the formation of positive ions formed by electron ionisation and negative ions induced by electron attachment. The experimental data were complemented by quantum chemical calculations. Specifically, the free energies for possible fragmentation reactions were derived for the τ and the π tautomer of histidine to get insight into the structures of the formed ions and the corresponding neutrals. We report the experimental ionisation energy of (8.48 ± 0.03) eV for histidine which is in good agreement with the calculated vertical ionisation energy. In the case of negative ions, the dehydrogenated parent anion is the anion with the highest mass observed upon dissociative electron attachment. The comparison of experimental and computational results was also performed in view of a possible thermal decomposition of histidine during the experiments, since the sample was sublimated in the experiment by resistive heating of an oven. Overall, the present study demonstrates the effects of electrons as secondary particles in the chemical degradation of histidine. The reactions induced by those electrons differ when comparing positive and negative ion formation. While for negative ions, simple bond cleav ages prevail, the observed fragment cations exhibit partly restructuring of the molecule during the dissociation process.