One-center Model Research Articles

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review.

The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.

Effect of radiation physics on inherent statistics of glow curves from small samples or low doses

A theory is developed to predict statistical noise in the trap populations of small samples or single grains subjected to high-energy ionizing irradiation. Using a model of the radiation process and a one-trap one-center model of a thermoluminescent (TL) material, the statistical behavior of the number of occupied traps during irradiation is predicted. The model focuses on the inherent physics of the process. Experimental sources of error are not considered. The interaction of radiation with the TL material is modeled in a simple way using the Bethe equation. The trap and center populations in the TL material are modeled both with the conventional phenomenological equations and also the more general Master Equation approach. The theory predicts, as the irradiation process proceeds, the mean, standard deviation, dispersion, skewness, and kurtosis of the probability distribution of occupied traps in the TL material. For the same applied dose, the standard deviation and dispersion of the trap population depend strongly on the type of radiation as well as the shape and orientation of the material. High-energy radiation sources, such as alpha, beta, or gamma rays, are found to produce standard deviations and dispersion much larger than low-energy sources, such as UV radiation. The results are summarized in tables which enable, for useful limiting cases, easy calculation of not just standard deviation but also skewness and kurtosis for various radiation sources and geometries.

Photosensitive center in CdTe:Sn: photorefractive, spectroscopic, and magneto-optical studies

Photorefractive properties of tin-doped CdTe crystals are studied. The material demonstrates sensitivity for low-intensity recording. A one-center model of the space-charge formation perfectly describes the experimental results. The tin impurity center is characterized using the data of optical absorption and light-induced absorption spectroscopy, pseudo-3D mapping of the photoabsorption, magnetic circular dichroism, and optical detection of magnetic resonance. Spectroscopic studies confirm appropriateness of the one-center model for describing the space-charge formation with tin as a main photorefractive center. Optical ionization (neutralization) energies are estimated for phototransitions from Sn+ (1.14 eV) and Sn0 (1.09 eV). Possible ways for improvement of the photorefractive performances are discussed.

First-principles study of the electronic structures and absorption spectrum of Fe:Mg:LiNbO3 crystals

In this paper, the electronic structures and absorption spectra of LiNbO3 (LN) and Fe:Mg:LiNbO3 crystals are studied by the first-principles under the generalized gradient approximation. The supercell structures of the LN crystal are established with 60 atoms, including four models: pure LN crystal, Fe:LiNbO3 crystal (Fe:LN), Fe:Mg:LiNbO3 crystal with Mg of 2 mol%-3 mol% (Fe:Mg(L):LN), and Fe:Mg:LiNbO3 crystal with Mg of 5.0 mol% (Fe:Mg(E):LN). The electronic structures show that the extrinsic defect levels (within forbidden band) of Fe:LN are contributed by Fe 3d orbital and O 2p orbital, and the band gap of Fe:LN (about 2.85 eV) is narrower than that of LN. For Fe:Mg:LN crystals, the band gap changes to 2.90 eV and 2.81 eV respectively for the Mg ion concentration less than and equal to the threshold (～5.0 mol%). The two absorption peaks at 2.3 eV and 2.6 eV are attributed to the Fe ions in crystal. Moreover, the intensities of these peaks vary with the concentration of Mg ion. It is revealed that the concentration of Mg ion influences the concentrations and the sites of Fe2+ and Fe3+ ions in crystal. From the absorption spectrum, the values of ratio Fe2+/Fe3+ in Fe:Mg(E):LN and Fe:Mg(L):LN can be obtained, and the ratio of first sample is smaller than that of the second one. With the one-center model, one can distinctly deduce that the photoconductivity of Fe:Mg(E):LN is relatively weak compared with that of Fe:Mg(L):LN, but this is inconsistent with many experimental results. One notices the contribution of O 2p orbital to extrinsic defect level in electronic structure. Therefore, it is reasonable to presume that the one-center model is not suitable enough for this condition. Based on the research work, we find that the formations of photoelectrons are related to orbital electron states of iron ions and oxygen atoms at extrinsic defect levels in Fe:LN and Fe:Mg:LN crystals.

Landau-Pekar Bipolaron in Singlet and Triplet States

We give an overview of studies a bipolaron stability by variational method. For bipolaron formations, a relation is established between the variational principle and the virial theorem optimizing the electronic wave functions. We present a large number of qualitative and quantitative arguments, which indicate that the Landau-Pekar bipolaron is an axially-symmetrical formation. Much attention is paid to the analysis of the influence of the Coulomb electron-electron correlations on the stability of a large bipolaron. In detail we analyzed the criteria for determining the optimal wave functions. It is established that a step-by-step increase in the flexibility of the electronic wave function due to the electron correlations does not stabilize a one-center bipolaron. We show after into account of electron-electron correlations a singlet bipolaron retains spatial axially-symmetrical. At the same time, the electron-excited triplet states of Landau-Pekar bipolaron have spherical symmetry. The results of Kasirina and Lakhno are based on the one-center bipolaron model are incorrect. Presented evidence that the correct application of the variational method and correct account of electron-electron correlations only increase the binding energy of the bipolaron but symmetry of Hartree-Fock approximation can not change. We adduce proofs which point to methodological errors of one-center bipolaron model as well as arising from their calculations incorrect physical consequences. As illustrated in this review the axially symmetric Landau-Pekar bipolaron can correctly interpret the experimentally detected spectroscopic data.

Carbon 1s photoelectron spectroscopy of the chlorinated methanes: Lifetimes and accurate vibrational lineshape models

Construction of accurate lineshape models for chlorosubstituted hydrocarbons is challenging. In this account the problem has been investigated thoroughly for the chloromethane series, CH4−nCln, n=1–4, using high-resolution experimental data and extensive theoretical calculations. The CCl bond contraction following ionization is a key parameter for a quantitative description of the vibrational excitation for all four molecules. We determine this quantity accurately for the title molecules and also propose approximate approaches that may applied to larger molecules. Having developed accurate vibrational lineshape models as well as reliable estimates of the instrumental broadening in each case, the carbon 1s hole lifetime broadening is determined from a fit to the experimental spectrum for each molecule. The resulting values for the lifetime broadening are 88±5meV for CH3Cl, 80±5meV for CH2Cl2, 74±5meV for CHCl3 and 62±5meV for CCl4. The lifetime widths decrease systematically with the number of chlorine substituents and correlate excellently with the valence occupancy of the core-ionized carbon. This indicates that the one-center model for Auger decay of the core hole is valid for the present series of molecules.

Simple One-Center Model for Linear Molecules: Application to Carbon Dioxide

With computational efficacy in mind, a one-center model for linear molecules is heuristically sketched. When parametrized for CO(2), all parameters save for two are supplied from literature quantum chemistry calculation or, in one case, heuristic argument. Using the remaining two adjustable parameters, the mean unsigned relative errors (predicted/observed) over the temperature range 220-290 K are 4.7% for the energy of vaporization, 0.6% for the liquid, and 8.0% for the vapor coexistence densities, respectively. The critical temperature is estimated at T(c) = 308 K, the critical density at ρ(c) = 0.460 g/cm(3), and the critical pressure at p(c) = 8.26 ± 0.11 MPa. This order of accuracy is comparable to that of many all-atom potential descriptions of CO(2) but is obtained at roughly nine times the speed. When supplied with the experimental bond length, somewhat worse agreement with experiment is exhibited for the neutron-weighted atomic pair distribution function of the liquid. This disparity is tentatively attributed to an overestimated electrostatic quadrupole-quadrupole interaction relative to the other forces present.

Parameter-free one-center model potential for an effective one-electron description of molecular hydrogen

For the description of an ${\mathrm{H}}_{2}$ molecule, an effective one-electron model potential is proposed which is fully determined by the exact ionization potential of the ${\mathrm{H}}_{2}$ molecule. In order to test the model potential and examine its properties, it is employed to determine excitation energies, transition moments, and oscillator strengths in a range of internuclear distances, $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}<R<2.5\phantom{\rule{0.3em}{0ex}}\mathrm{a.u}$. In addition, it is used as a description of an ${\mathrm{H}}_{2}$ target in calculations of the cross sections for photoionization and for partial excitation in collisions with singly charged ions. The comparison of the results obtained with the model potential with literature data for ${\mathrm{H}}_{2}$ molecules yields a good agreement and encourages therefore an extended use of the potential in various other applications or in order to consider the importance of two-electron and anisotropy effects.

Dynamics of photodeformations and space charge field in photorefractive Fe:LiNbO3 studied with synchrotron area diffractometry

The method of synchrotron area diffractometry has been used to map with a high spatial resolution in real time the distribution over the crystal surface of the lattice deformation tensor components induced by a macroscopic visible light beam on a z-cut iron-doped photorefractive LiNbO3 crystal. The xy planes exhibit a tensile strain, on the order of 10−4, in the center and long range, extending up to 780μm, shear deformations at the borders of the illuminated region, respectively. Photodeformations evolve with illumination time with relaxation type, time dependence, and time constants of the order of minutes. The observed lateral distribution of deformation tensor components, as well as their temporal evolution, has been examined, considering the coupling of the converse piezoelectric effect with the strong space charge field generated by the damage inducing beam along the z axis due to the bulk photovoltaic effect. The observed strain in the center can be attributed to the bulk photovoltaic field of the order of 107V∕m, while the long range shear deformations are mainly associated with the lateral components of the electric field which are present at the borders of the space charge regions. Both photodeformations and space charge field evolve at the same time scale, the dependence of time constants on the incident light intensity following the predictions of the one-center model charge redistribution due to the bulk photovoltaic effect. This work demonstrates that the method of synchrotron area diffractometry is a very powerful tool to study in situ the dynamics and spatial variation of microstuctural changes (deformations) induced by an external field (electric, magnetic, or temperature).

Vectorial solution of Kukhtarev equations for doubly doped crystals and optimal choice of recording directions in nonvolatile holographic storage

Vectorial Kukhtarev equations modified for the nonvolatile holographic recording in doubly doped crystals are analyzed, in which the bulk photovoltaic effect and the external electrical field are both considered. On the basis of small modulation approximation, both the analytic solution to the space-charge field with time in the recording phase and in the readout phase are deduced. The analytic solutions can be easily simplified to adapt the one-center model, and they have the same analytic expressions given those when the grating vector is along the optical axis. Based on the vectorial analyses of the band transport model an optimal recording direction is given to maximize the refractive index change in doubly doped LiNbO3:Fe:Mn crystals.

Charge transport in highly iron-doped oxidized lithium niobate single crystals

The photorefractive properties of highly iron-doped lithium niobate crystals in as-grown and completely oxidized states are investigated. Iron concentrations range from 0.5 to 3 wt. %. Measurements of light-induced refractive-index changes, two-beam coupling gain, bulk-photovoltaic current densities, and conductivities are performed with visible light. Absorption spectra and the bulk photovoltaic currents are used to determine the Fe2+ concentration. The dark conductivity confirms the tunneling model for charge-carrier migration. Beam-coupling experiments as well as photocurrent measurements with highly oxidized samples indicate that the one-center model is valid in such highly doped crystals, but that hole conductivity dominates the charge transport.

Stability of bipolarons, electron-electron correlations, the variational principle, and the virial theorem

For bipolaron states, a relation is established between the variational principle and the virial theorem optimizing the electronic wave functions. It is shown that a bipolaron one-center state is unstable under any conditions that do not violate basic physical principles. It is established that a stage-by-stage increase in the flexibility of the electronic wave function due to the electron-electron correlations does not stabilize a one-center bipolaron. It is argued that the results of calculations based on the one-center bipolaron model are incorrect.

Validation of intermolecular pair potential model of SiH4: Molecular-dynamics simulation for saturated liquid density and thermal transport properties

We demonstrate a validation of the intermolecular pair potential model of SiH(4), which is constructed from ab initio molecular-orbital calculations and expressed as the sum of the exponential and the London dispersion terms. The saturated liquid densities of SiH(4) are calculated for temperatures from 100 to 225 K by molecular-dynamics (MD) simulation. The average deviation between the experiment and the MD simulation using the present potential model is 3.9%, while the deviations exceed 10% for other well-known potential models such as the five-center Lennard-Jones (LJ) model. Subsequently, the shear viscosity, the thermal conductivity, and the self-diffusion coefficient of liquid SiH(4) are calculated by an equilibrium MD simulation with the Green-Kubo formula from 100 to 225 K. The average deviations from experiment are 11.8% and 13.7% for the shear viscosity and the thermal conductivity, respectively. Comparing the present model with an empirical one-center LJ model, it turns out that the rotational energy transfer through the intermolecular potential energy, which comes from the anisotropic potential energy, plays an important role in the thermal conductivity of liquid SiH(4). These results indicate that the present intermolecular potential model has an ability to give realistic pictures for liquid SiH(4) through molecular simulations.

Adsorption of ethylene on graphitized thermal carbon black and in slit pores: a computer simulation study.

In this paper, we studied vapor-liquid equilibria (VLE) and adsorption of ethylene on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers. Simple models of a one-center Lennard-Jones (LJ) potential and a two-center united atom (UA)-LJ potential are investigated to study the impact of the choice of potential models in the description of VLE and adsorption behavior. Here, we used a Monte Carlo simulation method with grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo ensembles. The one-center potential model cannot describe adequately the VLE over the practical range of temperature from the triple point to the critical point. On the other hand, the two-center potential model (Wick et al. J. Phys. Chem. B 2000, 104, 8008-8016) performs well in the description of VLE (saturated vapor and liquid densities and vapor pressure) over the wide range of temperature. This UA-LJ model is then used in the study of adsorption of ethylene on graphitized thermal carbon black and in slit pores. Agreement between the GCMC simulation results and the experimental data on graphitized thermal carbon black for moderate temperatures is excellent, demonstrating that the potential of the GCMC method and the proper choice of potential model are essential to investigate adsorption. For slit pores of various sizes, we have found that the behavior of ethylene exhibits a number of features that are not manifested in the study of spherical LJ particles. In particular, the singlet density distribution versus distance across the pore and the angle between the molecular axis and the z direction provide rich information about the way molecules arrange themselves when the pore width is varied. Such an arrangement has been found to be very sensitive to the pore width.

Intensity and wavelength dependence of the photoconductivity in Cr-doped Sr $\mathsf{_{0.61}}$ Ba $\mathsf{_{0.39}}$ Nb $\mathsf{_2}$ O $\mathsf{_6}$

We examine the light-induced charge transport properties of a series of chromium-doped \(\rm {Sr}_{0.61}\rm {Ba}_{0.39}\rm {Nb}_2\rm {O}_6\) single crystals by measurements of the optical absorption and the electric conductivity. By comparing the wavelength dependence of the specific photoconductivity and the optical absorption we show that both effects stem from the same center. The intensity dependence of the photoconductivity shows the applicability of a one-center charge transport model for high doping concentrations, while for low doping concentrations a more sophisticated model is needed. The validity of a one-center model is exemplarily verified for a crystal doped with 0.51 mol % Cr over a wide intensity range using a holographic method. The product of mobility and recombination time of photoexcited electrons is deduced from the specific photoconductivity.

Anomalous natural linewidth in the 2p photoelectron spectrum of SiF4.

The silicon 2p photoelectron spectra for SiH4, SiF4, and SiCl4 have been analyzed to give the natural linewidths of the Si 2p hole states, which reflect the Auger decay rates of the states. For SiH4 the measured width of 38 meV is in approximate agreement with the prediction of the one-center model (32 meV), but that for SiF4 of 79 meV is more than 5 times the value of 14 meV predicted by this model. Approximate theoretical calculations indicate that valence electrons from the fluorine atoms of SiF4 play an important role in the Auger decay via interatomic processes.

Photorefractive and photochromic properties of Ru doped Sr 0.61Ba 0.39Nb 2O 6 crystal

We investigate the photorefractive properties of ruthenium doped strontium barium niobate by use of two-wave mixing experiments. Large gain coefficient of 19 cm −1 and fast response time of 0.4 s at 1 W/cm 2 are obtained at a wavelength of 476.5 nm. We estimate photorefractive parameters using one-center model and discuss wavelength dependence of these parameters. Furthermore, this crystal exhibits strong photochromic effect in the wide spectral range by the illumination of UV light. This photochromic effect can be bleached by red-light illumination.

Study of surface recombination velocity of Cd1−xZnxTe radiation detectors by direct current photoconductivity

The surface recombination velocity of a Cd1−xZnxTe (CZT) radiation detector treated by mechanical polishing and by a standard 5% bromine in methanol chemical etch is reported. The light power dependence of the surface recombination velocity was measured using dc photoconductivity. The results reveal that the surface recombination velocity is a function of the electron generation rate, which can be described by a Shockley–Read one-center model. It was observed that the surface recombination velocity of the CZT detector treated by polishing only is much larger than that treated with polishing followed by chemical etching. The correlation of dc photoconductivity and low-temperature photoluminescence measurements of the CZT detector is also discussed.

Carbon 1s photoelectron spectroscopy of CF4 and CO: Search for chemical effects on the carbon 1s hole-state lifetime

Carbon 1s photoelectron spectra for CF4 and CO have been measured at several photon energies near the carbon 1s threshold. The spectra have been analyzed in terms of the vibrational structure and the natural linewidth. For CO the vibrational structure shows evidence for anharmonicity in both the energy spacing and the intensity. Analysis of the results using an anharmonic model gives an equilibrium bond length for core-ionized CO that is 4.85 pm shorter than that of neutral CO. For CF4, the vibrational structure is very weak, and the analysis shows that the change in equilibrium CF bond length upon ionization is no more than 0.54 pm. Ab initio theoretical calculations give results in accord with these bond-length changes. The unusually small bond-length contraction in CF4 can be understood in terms of nonbonded fluorine–fluorine repulsion. The natural linewidth for core-ionized CO, 95±5 meV, is essentially the same as that of CH4. This result is in contrast with expectations based on the one-center model of Auger decay and earlier predictions based on semiempirical molecular orbital theory. More recent calculations indicate, however, that there is only a small difference between CO and CH4, in agreement with the observed result. For CF4, the natural linewidth is 77±6 meV. This value differs from that for CH4 in the direction expected from the electronegativities of hydrogen and fluorine, but is greater than the prediction based on semiempirical theory. The natural linewidth for CO with a carbon 1s electron excited to the 2π resonance is 83 meV, which is significantly less than is found for core-ionized CO. Although this difference is supported by theoretical calculations, the direction of the difference is counterintuitive. An overview is presented of the current state of experimental and theoretical knowledge on carbon 1s linewidths.

Growth and holographic characterization of nonstoichiometric sillenite-type crystals

We have grown Bi12GeO20 and Bi12SiO20 single crystals from melts with different GeO2 and SiO2 contents, respectively, to investigate the influence of an intrinsic defect, the antisite defect (Bi on Ge or Si site), on the light-induced charge transport. The optical absorption and the effective trap density of the crystals increase with decreasing GeO2 and SiO2 content in the melt. Furthermore, a variation of the photoconductivity is observed. Our results can be described by a one-center model with the antisite defect Bi3+/4+ on Ge or Si site as dominant photorefractive center.