Electrostatic Point Charge Model Research Articles

Analytical crystal-field models applied to compounds doped with Eu3+

The point charge electrostatic model (PCEM) and the simple overlap model (SOM), both purely analytical crystal field models, are being briefly revisited, in order to show the evolution of their application to Eu doped compounds. Calculations are made through the method of equivalent nearest neighbours (MENN), and applied to the Eu(dipivaloylmethanate)31,10-phenanthroline [Eu(DPM)3o-phen] complex, with the aim of discussing the Eu–O and Eu–N interactions. The charge of the Eu ion is calculated using the Batista-Longo improved model (BLIM) to give gBLIM = 3,64e around the Eu-NN midpoint. The 7F1 crystal-field levels and level splitting were satisfactorily reproduced with two charge factors, namely, g1 = 0.495 and g2 = 0.415, assuming the luminescent site in a tetragonal point symmetry slightly distorted. In particular, it is shown that the Eu3+, itself, is satisfied by attracting an amount of charge, which neutralize/stabilize its own site electrostatically, no matter what the ligating ions are. The Eu-NN overlap (ρ = <4f|2s2p>) is assumed to be 0.1, which is physically plausible both as a limit in respect to β, the SOM correction factor to the PCEM, and describes the covalent contribution to the Ln-NN interaction, the latter is the most important contribution of the SOM to the crystal-field theory of lanthanide containing compounds. An eloquent comparison with crystal-field levels of the Eu:LiYF4 and Eu(btfa)3(4,4-bipy)(EtOH) is made. Finally, this paper is, indeed, a very simple tribute to Professor Oscar L. Malta, as an acknowledgement of his deep contribution to the author's apprenticeship about crystal-field theory of systems containing lanthanides.

Global Optimization of Dinitrogen Clusters Bound to Monolayer and Bilayer Graphene: A Swarm Intelligence Approach

Locating the global minimum of a potential energy surface is an arduous task. The complexity of the potential energy surface increases as the number of degrees of freedom of the system increases. The highly rugged nature of the potential energy surface makes the minimization of the total energy of the molecular clusters a difficult optimization problem. A solution to this conundrum is the use of metaheuristic techniques that efficiently track down the global minima through a trade-off between exploration and exploitation. Herein, we use the swarm intelligence technique, particle swarm optimization to locate the global minima geometries of N2 clusters of size 2-10, in free and adsorbed states. We have investigated the structures and energetics of bare N2 clusters, followed by N2 clusters adsorbed on graphene and intercalated between the layers in bilayer graphene. The noncovalent interactions between dinitrogen molecules are modeled using the Buckingham potential as well as the electrostatic point charge model, while those of the N2 molecules with the carbon atoms of graphene are modeled using the improved Lennard-Jones potential. The interactions of the carbon atoms belonging to different layers in a bilayer are modeled using the Lennard-Jones potential. The bare cluster geometries and intermolecular interaction energies obtained using particle swarm optimization are found to be the same as reported in the literature, validating the use of particle swarm optimization for studying molecular clusters. The N2 molecules are found to adsorb as a monolayer on top of the graphene sheet and intercalate themselves right in the middle of the two sheets of bilayer graphene. Our study establishes that particle swarm optimization is a feasible global optimization technique for performing the optimization of high-dimensional molecular clusters, both in pristine and in confined forms.

Theoretical and Experimental Studies of the Magnetostructural Correlations in Mononuclear DyIII Compounds Evidenced by Quantum Tunneling of Magnetization Time, Crystal Field Parameters, and Point Charge Electrostatic Model

Theoretical and Experimental Studies of the Magnetostructural Correlations in Mononuclear Dy^III Compounds Evidenced by Quantum Tunneling of Magnetization Time, Crystal Field Parameters, and Point Charge Electrostatic Model

Advanced x-ray spectroscopy of actinide trichlorides.

The application of core-to-core (3d-to-4f) resonant inelastic x-ray scattering (RIXS) and high-energy-resolution fluorescence-detected x-ray absorption (HERFD-XAS) at actinide M4,5 edges, as techniques with the enhanced sensitivity to changes in the chemical state, was analyzed for trivalent actinide compounds. As an example, a series of actinide chlorides AnCl3 (An = U, Np, Pu, Am, Cm, Bk, and Cf) was used. The crystal-field multiplet formalism was applied to calculate the 3d-4f RIXS maps, and the HERFD-XAS spectra were extracted as cuts of these RIXS maps along the incident energy axis at the constant emitted energy, corresponding to the maximum of the RIXS intensity. A relation between HERFD and conventional XAS methods was also examined. Despite some differences between profiles of the An M5 HERFD and conventional XAS spectra of trivalent actinides, the results of calculations indicate that the HERFD method can be used at the An M5 edge for monitoring even small variations in the An chemical state. As a whole, better agreement between the HERFD and XAS spectra was found for the An M4 edges as compared to the An M5 edges. By using the pointcharge electrostatic model, the dependence of the An M4,5 HERFD-XAS spectra on the An coordination number was studied, which indicates the significant sensitivity of the distribution of the An 5f states to the ligand structural arrangement around the An sites.

Crystal field parameters of the C2 site in Eu2O3

We studied the energy levels of Eu3+ at the C2 lattice site of cubic Eu2O3. We identified 29 Lorentzian lines corresponding to 5D0 → 7F0-6 transitions obtained from photoluminescence spectra at 10 K. The levels were analyzed in terms of the 14 crystal field parameters corresponding to the site symmetry. The energy-level fit yielded a final standard deviation of 12.0 cm−1. The resulting crystal field strength parameter is Nv = 3869 ± 185. This value confirms the linear dependence on the host atomic radius predicted by the extended point charge electrostatic model (PCEM). The present study considered the highest number of transitions to date for Eu3+ in Eu2O3 to the authors’ knowledge.

Ab Initio Crystal Field for Lanthanides.

An ab initio methodology for the first-principle derivation of crystal-field (CF) parameters for lanthanides is described. The methodology is applied to the analysis of CF parameters in [Tb(Pc)2 ]- (Pc=phthalocyanine) and Dy4 K2 ([Dy4 K2 O(OtBu)12 ]) complexes, and compared with often used approximate and model descriptions. It is found that the application of geometry symmetrization, and the use of electrostatic point-charge and phenomenological CF models, lead to unacceptably large deviations from predictions based on ab initio calculations for experimental geometry. It is shown how the predictions of standard CASSCF (Complete Active Space Self-Consistent Field) calculations (with 4f orbitals in the active space) can be systematically improved by including effects of dynamical electronic correlation (CASPT2 step) and by admixing electronic configurations of the 5d shell. This is exemplified for the well-studied Er-trensal complex (H3 trensal=2,2',2"-tris(salicylideneimido)trimethylamine). The electrostatic contributions to CF parameters in this complex, calculated with true charge distributions in the ligands, yield less than half of the total CF splitting, thus pointing to the dominant role of covalent effects. This analysis allows the conclusion that ab initio crystal field is an essential tool for the decent description of lanthanides.

A direct route for the investigation of crystalline field effects on the spectral properties of Eu3+ ions in designed nanostructures

The spectral properties of lanthanide ions doped in a solid-state matrix, especially the Stark splitting and emission shifts, are strongly influenced by the local crystalline field. Here, we use a direct approach to quantitatively investigate the crystalline field effect on these spectral properties of Eu3+ ions in our designed β-PbF2:Eu3+ and BaF2:Eu3+ nanostructures. The extremely similar structures in which the central Eu3+ ions have the same site symmetry allow the local crystalline field to be simplified as the same point charge electrostatic field model. In this model, the direction and intensity of the electrostatic field are related to the distortion and expansion degree of the charge cloud of the luminescent center, respectively, and further determine the Stark splitting and emission shift. The theoretical analysis and charge-cloud stimulations were in good agreement with the experimental results. The direction and intensity of the crystalline field were calculated, and showed that the emission spectra shift to red with the increase in intensity. This work provides a comprehensive understanding of the spectral changes induced by a crystalline field, which is of great significance for the design of materials with the desired spectral properties.

A comparison of the transition metal 3d1 crystal field splitting with the lanthanide 5d1 crystal field splitting in compounds

Spectroscopic data on the 3d1 transition metal activators Ti3+, V4+ and Cr5+ in compounds were collected and analysed in order to obtain an overview on the size of the 3d1 level crystal field splitting. Results are compared with data on the 5d1 activators Ce3+ and Eu2+. Trends earlier observed for the 5d1 lanthanides also apply to the 3d1 transition metals. They will be interpreted with the point charge electrostatic model and a modified version thereof.

Unification of the point charge electrostatic model with the chemical shift model for lanthanide 5d states

The relationship between the chemical shift of the 5d-electron binding energy and the 5d-electron 10Dq crystal field splitting for Ce3+ and Eu2+ in octahedral, cubic and cuboctahedral configuration has been investigated. The traditional point charge electrostatic model (PCEM) largely underestimates the size of the 10Dq crystal field splitting, and it also does not correctly reproduce how 10Dq changes with lanthanide charge. In the recently proposed chemical shift model to determine the absolute 4f and 5d electron binding energies a screening charge of equal but opposite size than the lanthanide charge, that is located at a screening distance slightly larger than the radius of the lanthanide, was introduced to derive electron binding energies. Here we will demonstrate that when similar concepts are introduced for the PCEM, much better 10Dq values are obtained. We will further establish that trends in chemical shift with varying chemical environment, that are strongly related to the nephelauxetic effect, also appear in the value for 10Dq.

Polarization-enhanced bonding process of halogen bond, a theoretical study on F–H/F–X (X = F, Cl, Br, I) and ammonia

Polarization plays an important role in halogen bond formation process. In this work, we proposed a polarization-enhanced bonding process of halogen bonds. Firstly, the energy differences between electrostatic interaction and point charge model are linearly correlated with polarization effects in studied dimers. The contribution of polarization to electrostatic interaction was 23.9% for the hydrogen bonded dimers, while it varied from 2.5 to 50.5% for the halogen bonded dimers. Secondly, we observed that the dominant term of polarization effects is different for hydrogen bonds, weak halogen bonds, and strong halogen bonds. In this study the dominant terms in the bonds change from the dispersion component to induction component gradually. Finally, we found that polarization and charge transfers are cooperated mutually. We feel these findings will be beneficial to designing better halogen bonded materials and lead to the development of polarizable force fields of halogen bonds.

The dependence of 10 Dq crystal field parameter for Mn4+ (3d3 configuration) and the magnitude of 7F1 level splitting for Eu3+ (4f6 configuration) on pyrochlore compositions

The excitation spectra of the six-coordinated Mn4+ ion in the pyrochlores Ln2Sn2O7 (Ln=Lu3+, Y3+, and Gd3+) have been determined to examine the variation in the crystal field splitting parameter (10 Dq) on the Mn4+–O48f2- distance. The results obtained are entirely consistent with the expectation of the electrostatic point charge model since 10 Dq progressively increase with decreasing Mn4+–O48f2- distance. A comparative study pertaining to the behavior of the Eu3+ (4f6) and Mn4+ (3d3) ions in the pyrochlores, Ln2(Ti,Sn)2O7 (Ln=Lu3+, Y3+, and Gd3+) is presented. The results show that the crystal-field strength that are experienced by the Mn4+ and Eu3+ ions in the Ln2Sn2O7 (Ln=Lu3+, Y3+, and Gd3+) family of materials, are anti-correlated. Thus, for the Mn4+ ion with 3d3 configuration, the crystal-field strength increases with decreasing ionic radii of the Ln3+ cation, while for the Eu3+ ion with 4f6 configuration, an increase with increasing ionic radii of the Ln3+ cation is observed. However, when the Sn4+ ion of the Y2Sn2O7 lattice are replaced by the Ti4+ ion, the crystal-field strength is reduced to the extent that the exposed Mn4+ 3d3 electrons and the screened Eu3+4f6 electrons start to behave similarly. These results are explained by the variations in the covalent mixing between the ligand (O48f2-) and the activator (Mn4+ and Eu3+) cations, which is driven by the competition for the O48f2- electron density by the Ln3+, Sn4+, and Ti4+ ions of the Ln2(Ti,Sn)2O7 lattice.

Optical characterization and crystal field calculation of Er3+ in AlN epilayers

We report on cathodoluminescence (CL) characterization and crystal field (CF) energy levels calculation of Er3+ ions doped in AlN hosts having different morphologies. The CL spectra of crystalline AlN:Er epilayers grown by molecular beam epitaxy and subsequently implanted with erbium were compared with amorphous AlN:Er3+ in situ doped with erbium grown by rf sputtering on (100) silicon. The high resolution CL spectra show a great similarity of Er3+ ion 4f-shell emission line pattern between all studied AlN:Er3+ samples. Assuming that Er3+ ion substitute for Al3+ ion in C3V site symmetry, the majority of emission lines were attributed to transitions between 4F9/2, 4S3/2, 2H11/2, 4F7/2, 2H9/2 and 2P3/2 excited multiplets to the 4I15/2 Stark energy levels. Simulations are carried out using Bkq crystal field parameters determined using electrostatic point charge modelstatic point charge model (PCEM) and crystal field theory. The simulations involved 23 Stark levels resulted in an average r.m.s deviation of 3.8cm−1. The comparison between the CL spectra of c-AlN:Er3+ epilayers grown on sapphire and silicon with amorphous AlN:Er3+ grown on silicon leads to a discussion on the effect of the substrate on the spectral feature of studied crystalline AlN:Er3+ epilayers.

A general trend of rare earth ions in the KRE(WO4)2 double tungstates (RE=Y, Yb, Gd, Lu)

Crystal-field energy levels of Er3+ ions doped in KYb(WO4)2, KY(WO4)2 and KLu(WO4)2 laser crystals were fitted to the parameters of semi-empirical Hamiltonian including J-mixing. A simulation of the energy level scheme is carried out. The crystal-field effect is introduced through the 14 non-zero crystal-field parameters allowed by C2 symmetry site occupied by the rare earth. Very satisfactory correlations were obtained between 58, 64 and 15 calculated and experimental Stark energy levels, with an r.m.s. of 8.7 cm−1, 9.3 cm−1 and 2.6 cm−1 for Er3+ ions doped in KYb(WO4)2, KY(WO4)2 and KLu(WO4)2 respectively. These results are compared with those reported for other rare earth ions in the same hosts and with Er3+ ions in KGd(WO4)2 crystal. Furthermore, based on the extended electrostatic point charge model, interesting results are obtained for Yb3+ ions doped KYb(WO4)2, KY(WO4)2, KLu(WO4)2 and KGd(WO4)2 crystals. The concordance between the crystal-field strength parameters indicates the consistence of our analysis. A general trend is then proposed for the rare earth ions in the KRE(WO4)2 double tungstates.

Chemical bonding and crystal field splitting of the Eu 3+7F 1 level in the pyrochlores Ln 2B 2O 7 (Ln = La 3+, Gd 3+, Y 3+, Lu 3+; B = Sn 4+, Ti 4+)

The crystal field splitting of Eu 3+ 7F 1 level in the pyrochlore’s Ln 2Sn 2O 7 (Ln = La 3+, Gd 3+, Y 3+and Lu 3+) and Ln 2Ti 2O 7 (Ln = Gd 3+, Y 3+ and Lu 3+) has been systematically examined. Since the splitting of the Eu 3+ 7F 1 manifold in these materials increases with increasing size of the rare earth cation, the electrostatic point charge model is inadequate to account for the observed splitting. It is pointed out that covalency/ligand polarizability contributions to the crystal field splitting are significant. It is shown that the host lattice dependent changes in the polarizability of the oxygen ions occupying the 48 f sites of the pyrochlore lattice is responsible for the variation in the splitting of the Eu 3+ 7F 1 manifold in these materials. Further, the splitting of the Eu 3+ 7F 1 manifold is larger in Ln 2Sn 2O 7 than in Ln 2Ti 2O 7. This is explained by the differences in the nature of the chemical bonding between Ti 4+ (3d 0)/Sn 4+(4d 10) cations and O 2−(2p) ligands. The importance of anion polarization towards the Eu 3+ ion in determining the magnitude of the Eu 3+ 7F 1 manifold splitting is demonstrated in this work.

Theoretical investigation of the 7F1 level splitting in a series of Eu3+ doped oxides matrixes

The point charge electrostatic model (PCEM) and the simple overlap model (SOM) are applied to a series of oxide crystals (Gd2O3, Y2O3, Lu2O3, In2O3 and Sc2O3) and a silicate glass (Al2O3–SiO2) doped with the Eu3+ ion. The SOM factor ρ(2β)k+1 is input as the shielding factor for all Bqk expressions, which enters in the calculations of the crystal-field strength parameter, NV. The maximum splitting ΔE of the 7F1 manifold of the Eu3+ ion is then obtained as a function of NV. It has been developed another way to calculate alpha, which is an expansion factor in the ΔE expression. For the glass, as the mean metal-ligating ions distances are larger than for the crystals, NV and ΔE are smaller, as expected. The prediction of the PCEM shows a linear dependence between ΔE and NV, even though the known mismatch in respect to the experimental splitting is kept. In the case of the SOM, two situations have been analyzed: firstly the charge factor varies in order to reproduce the experimental splitting (a phenomenological procedure); secondly the charge factor is the valence of the oxygen ions. The agreement between the experimental results and theoretical predictions for all investigated systems is very satisfactory in respect to both the linearity between ΔE and NV and the ΔE splitting.

Analysis of surface effect on luminescent properties of Eu3+ in YVO4 nanocrystals

In this Letter, 7F2 crystal field (CF) levels of surface Eu3+ in YVO4 nanocrystals are calculated employing a refined electrostatic point charge model, where surface states are simulated by point charges. Based on the theoretical 7F2 CF levels, emission spectra of YVO4: Eu3+ nanocrystals are assigned to Eu3+ under different local environments. and relaxation of selection rules by surface effect is discussed.

Surface state analysis of YVO 4:Eu 3+ nanocrystals by electrostatic point charge model

In this paper, surface state is simulated by charge compensation in nanocrystalline YVO 4:Eu 3+ according to electrostatic point charge model. The calculated evolutions of 7F 2 crystal field (CF) levels of surface Eu 3+ ions are compared with the experimental 5D 0→ 7F 2 emissions in nanocrystals. Surface adsorbates following broken Eu–O 2 bonds are proved to be the main reason that cause the splitting of two-fold 7F 2 level and the shift of 5D 0→ 7F 2 (A 1, B 2) emission.

Dynamic Breaking and Restoring of Finite Water Chains inside Carbon Nanotubes

Car-Parrinello molecular dynamics simulations combined with an electrostatic point charge model reveal that quasi one-dimensional (1D) water chains break down and restore dynamically inside the carbon nanotube (6, 6). The models of finite water chains include a pair of hydronium and hydroxyl ions separated by several water molecules. Fluctuations of the hydrogen-bonded path interrupt the continuous proton transport along the 1D water chains considerably. Driven by electrostatics, protons can move either toward or away from the breaking point of the water chains depending on the dipole orientation of the end water. As a result, both the hydronium and the hydroxyl ions are repelled by the breaking point of the water chains.

Nanoelectromechanics of piezoresponse force microscopy

To achieve quantitative interpretation of Piezoresponse Force Microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, analytical representations for tip-induced electroelastic fields inside the material are derived for the cases of weak and strong indentation. In the weak indentation case, electrostatic field distribution is calculated using image charge model. In the strong indentation case, the solution of the coupled electroelastic problem for piezoelectric indentation is used to obtain the electric field and strain distribution in the ferroelectric material. This establishes a complete continuum mechanics description of the PFM contact mechanics and imaging mechanism. The electroelastic field distribution allows signal generation volume in PFM to be determined. These rigorous solutions are compared with the electrostatic point charge and sphere-plane models, and the applicability limits for asymptotic point charge and point force models are established. The implications of these results for ferroelectric polarization switching processes are analyzed.

Growth form of TiO2

AbstractComputation of attachment energies, which are considered to be directly related to the growth rates of the corresponding F faces of the TiO2 crystal structure, have been calculated in an electrostatic point charge model. Corrections using van der Waals attractions and Born repulsions were used in normal calculations and then in calculations of attachment energies, crystal energies and surface energies using Buckingam potentials potentials and short range potentials according to Post. With this were constructed growth and equilibrium form of TiO2 crystals.