Coulomb Repulsion Energy Research Articles

Post-scission dissipative motion and fission-fragment kinetic energy

A dynamic model developed earlier is used to describe the last stage of nuclear fission: the postscission motion of fission fragments. In this process, Coulomb repulsive energy turns into the kinetic energy of fission fragments measured by experimenters. It is shown that the dissipated energy can be as high as 10% of the average experimental kinetic energy.

The influence of charge transfers effects in monazite-type LaVO4 and perovskite-type LaVO3 prepared by sol-gel acrylamide polymerization

Core-hole spectroscopy such as X-ray absorption spectroscopy (XAS) is useful to determine the electronic structure of strongly correlated and strongly hybridized compounds such as vanadates. Monazite-type LaVO4 and perovskite-type LaVO3 are good candidates to elucidate the electronic structure through the vanadium L2,3 edge. LaVO4 was prepared by sol-gel acrylamide polymerization and solid-state reaction. LaVO3 was obtained by reduction of LaVO4 using Zr as gatherer. Monoclinic crystal phase for LaVO4 and orthorhombic crystal phase for LaVO3 were confirmed by the Rietveld refinement of X-ray diffraction patterns. XAS comparison between Vanadium L2,3 edge confirms the presence of V5+ for the monazite and V3+ for the orthorhombic perovskite. Multiplet calculations including crystal field and charge transfer effects (CTM) were performed in order to elucidate the tetragonal (D4h symmetry) parameters Dq, Ds and Dt, the charge transfer energy Δ, and d-d Coulomb repulsion energy U parameters. CTM confirms for LaVO3 the strong V 3d–O 2p hybridization with a significant contribution of covalent character due to the delocalization of 3d electrons. For LaVO4 this work suggest the reclassification of this band insulator as charge transfer insulator that shows a significant contribution of ionic character.

Influence of hydrostatic pressure on the bulk magnetic properties ofEu2Ir2O7

We report on the magnetic properties of Eu$_{2}$Ir$_{2}$O$_{7}$ upon the application of hydrostatic pressure $P$ by means of macroscopic and local-probe techniques. In contrast to previously reported resistivity measurements, our dc magnetization data unambiguously demonstrate a non-monotonic $P$-dependence for $T_{N}$, i.~e., the critical transition temperature to the magnetic phase. More strikingly, we closely reproduce the recently calculated behaviour for $T_{N}$ under the assumption that $P$ lowers the $U/W$ ratio (i.~e., Coulomb repulsion energy over electronic bandwidth). Zero-field muon-spin spectroscopy measurements confirm that the local magnetic configuration is only weakly perturbed by low $P$ values, in agreement with theoretical predictions. The current results experimentally support the preservation of a $4$-in/$4$-out ground state and, simultaneously, a departure from the single-band $j_{\text{eff}} = 1/2$ model across the accessed region of the phase diagram.

Modeling thermionic emission from laser-heated nanoparticles

An adjusted form of thermionic emission is applied to calculate emitted current from laser-heated nanoparticles and to interpret time-resolved laser-induced incandescence (TR-LII) signals. This adjusted form of thermionic emission predicts significantly lower values of emitted current compared to the commonly used Richardson-Dushman equation, since the buildup of positive charge in a laser-heated nanoparticle increases the energy barrier for further emission of electrons. Thermionic emission influences the particle's energy balance equation, which can influence TR-LII signals. Additionally, reports suggest that thermionic emission can induce disintegration of nanoparticle aggregates when the electrostatic Coulomb repulsion energy between two positively charged primary particles is greater than the van der Waals bond energy. Since the presence and size of aggregates strongly influences the particle's energy balance equation, using an appropriate form of thermionic emission to calculate emitted current may improve interpretation of TR-LII signals.

Field-induced quantum metal–insulator transition in the pyrochlore iridate Nd2Ir2O7

A combination of strong spin–orbit coupling and electronic correlations in pyrochlore iridates produces a quantum insulator–metal transition that can be induced by applying a magnetic field along specific crystalline axes. The metal–insulator transition (MIT) is a hallmark of strong correlation in solids1,2,3. Quantum MITs at zero temperature have been observed in various systems tuned by either carrier doping or bandwidth1. However, such transitions have rarely been induced by application of magnetic field, as normally the field scale is too small in comparison with the charge gap, whose size is a fraction of the Coulomb repulsion energy (∼1 eV). Here we report the discovery of a quantum MIT tuned by a field of ∼10 T, whose magnetoresistance exceeds 60,000%. In particular, our anisotropic magnetotransport measurements on the cubic insulator Nd2Ir2O7 (ref. 4) reveal that the insulating state can be suppressed by such a field to a zero-temperature quantum MIT, but only for fields near the [001] axis. The strong sensitivity to the field direction is remarkable for a cubic crystal, as is the fact that the MIT can be driven by such a small magnetic field, given the 45 meV gap energy5, which is of order of 50 times the Zeeman energy for an Ir4+ spin. The systematic change in the MIT from continuous near zero field to first order under fields indicates the existence of a tricritical point proximate to the quantum MIT. We argue that these phenomena imply both strong correlation effects on the Ir electrons and an active role for the Nd spins.

Effects of the defects on the half-metallic characters and magnetic properties in double perovskite Pb2FeMoO6

In point of view of the half-metallic character and magnetization reduction, the structural, electronic and magnetic properties of the disordered Pb2FeMoO6 compound containing seven different defects of FeMo and MoFe antisites, Fe–Mo interchange, and VFe, VMo, VO and VPb vacancies have been studied by using the first-principles projector augmented wave (PAW) potential within the generalized gradient approximation taking into account on-site Coulomb repulsive energy (GGA+U). No obvious structural changes are observed for the cases of the FeMo and MoFe antisites, Fe–Mo interchange, and VPb vacancy, however, the six (eight) nearest oxygen neighbors of the vacancy move away from (close to) VFe or VMo (VO) vacancy. The half-metallic character is maintained for the FeMo antisite, VFe, VO or VPb vacancy cases, while it vanishes in the MoFe antisite, Fe–Mo interchange or VMo vacancy cases even the defect concentration reduces down to C = 6.25%. So the MoFe antisite, Fe–Mo interchange or VMo vacancy defects have to be avoided in order to preserve the half-metallic character of the Pb2FeMoO6 compound and thus usable in magnetoresistive and spintronics devices. In FeMo or MoFe antisite cases, the spin moments of Fe (Mo) cations situated on Mo (Fe) antisites are in an antiferromagnetic coupling with those of Fe (Mo) cations on the regular sites. On the contrary, in Fe–Mo interchange case, the spin moments of Fe (Mo) cations situated on Mo (Fe) antisites are in a ferromagnetic coupling with those of Fe (Mo) cations on the regular sites. In VFe, VO or VPb vacancy cases, a ferromagnetic coupling is observed within each cation sublattice, while the two cation sublattices are coupled antiferromagneticly. But in VMo vacancy case, a ferromagnetic coupling is obtained not only within each cation sublattice but also between Fe and Mo sublattices. The saturation magnetization of the disordered Pb2FeMoO6 compound decreases in the sequence of VPb, VMo, Fe–Mo, VO, VFe, FeMo and MoFe cases.

Simple models for predicting correlation energy

A total of six different models that can account for the missing correlation energy in atomic systems were applied to the isoelectronic atomic series of two to ten electrons. Based on Rassolov’s linear correlation operator (Rassolov, 1999) we have defined a term, Xab=Jab/Taa+Tbb, where J and T are the Coulomb repulsion and kinetic energy associated with orbitals a and b. This supports the idea that electron correlation depends on the separation of electrons in both position space and in momentum space. Xab, especially where a=b, can account for the behaviour of electron correlation in these isoelectronic series. A model with only three terms (X11,X22 and J12) performed consistently well with the RMSD ranging from 9×10-4(N=3) to 6×10-5(N=5). This study also provides insight into the Liu–Parr model which relates the correlation energy to the density at the nucleus (Liu and Parr, 2007).

Structural, electronic, and elastic properties of CuFeS2: first-principles study

The structural, electronic, and elastic properties of CuFeS2 have been investigated by using the generalized gradient approximation (GGA), GGA + U (on-site Coulomb repulsion energy), the local density approximation (LDA), and the LDA + U approach in the frame of density functional theory. It is shown that when the GGA + U formalism is selected with a U value of 3 eV for the 3d state of Fe, the calculated lattice constants agree well with the available experimental and other theoretical data. Our GGA + U calculations indicate that CuFeS2 is a semiconductor with a band gap of 0.552 eV and with a magnetic moment of 3.64 µB per Fe atom, which are well consistent with the experimental results. Combined with the density of states, the band structure characteristics of CuFeS2 have been analyzed and their origins have been specified, which reveals a hybridization existing between Fe-3d, Cu-3s, and S-3p, respectively. The charge and Mulliken population analyses indicate that CuFeS2 is a covalent crystal. Moreover, the calculated elastic constants prove that CuFeS2 is mechanically stable but anisotropic. The bulk modulus obtained from elastic constants is 87.1 GPa, which agrees well with the experimental value of 91 ± 15 GPa and better than the theoretical bulk modulus 74 GPa obtained from GGA method by Lazewski et al. The obtained shear modulus and Debye temperature are 21.0 GPa and 287 K, respectively, and the latter accords well with the available experimental value. It is expected that our work can provide useful information to further investigate CuFeS2 from both the experimental and theoretical sides.

Electron binding energies and how it relates to activator luminescence and bonding in compounds

Methods and models to determine the vacuum referred binding energy (VRBE) of electrons in luminescence impurity states and in host band states are briefly reviewed. Special attention is focussed on how electron bonding within anion ligands of the host compound and bonding between luminescence center and those ligands affect VRBEs, electronic properties, and luminescence properties. The chemical shift of 4f-electron VRBE, the centroid shift of 5d-electron VRBE and the Coulomb repulsion energy U for Eu appear strongly correlated with bonding and one may predict one from the other. Also conduction band and valence band energies of different compounds can be compared with each other and with reference to the common vacuum energy level. How that provides new insight in luminescence properties will be addressed. All models were derived from lanthanide spectroscopy. First results on the VRBE in transition metal impurities with single d-electron states are also reviewed.

Optical freezing of charge motion in an organic conductor.

Dynamical localization, that is, reduction of the intersite electronic transfer integral t by an alternating electric field, E(ω), is a promising strategy for controlling strongly correlated systems with a competing energy balance between t and the Coulomb repulsion energy. Here we describe a charge localization induced by the 9.3 MV cm(-1) instantaneous electric field of a 1.5 cycle (7 fs) infrared pulse in an organic conductor α-(bis[ethylenedithio]-tetrathiafulvalene)(2)I(3). A large reflectivity change of >25% and a coherent charge oscillation along the time axis reflect the opening of the charge ordering gap in the metallic phase. This optical freezing of charges, which is the reverse of the photoinduced melting of electronic orders, is attributed to the ~10% reduction of t driven by the strong, high-frequency (ω ≧ t/ħ) electric field.

Photodissociation ofBr2molecules in an intense femtosecond laser field

We experimentally demonstrate the photodissociation process of ${\mathrm{Br}}_{2}$ molecules in the intense femtosecond laser field by a dc-sliced ion velocity map imaging technique. We show that four fragment ions $\mathrm{B}{\mathrm{r}}^{n+}\phantom{\rule{0.16em}{0ex}}\left(n=1--4\right)$ are observed, and their kinetic energy increases while their angular distribution decreases with the increase of the charge number. We prove that the low (or high) charged fragment ions result from the photodissociation of the low (or high) charged parent ions. We explain the changes of the kinetic energy and angular distribution in these fragment ions by considering the potential energy curves of these parent ions that involve both the interaction of the Coulomb repulsive energy and chemical bonding energy. We also explain the experimental observation that the measured kinetic energy release in the experiment is much smaller than the theoretical calculation by enhanced ionization at a critical distance.

Coulomb repulsion, point-like nuclear charges, Dirac paradox, soft nuclear charge density and hypermultiplet nuclear repulsion

A discussion about the classical Coulomb repulsion via point-like nuclear charges, usually employed within Born–Oppenheimer approximation, leads to the description of Dirac paradox: an inconsistency found when describing nuclear charges by means of Dirac’s distributions and computing with them nuclear Coulomb repulsion integrals. The way of overcoming Dirac paradox is bound to the description of soft Gaussian nuclear charge density and also to adopting a nuclear hypermultiplet Coulomb repulsion formulation. Such theoretical prospect produces a quantum mechanically compliant but simple algorithm in order to compute nuclear repulsion, which also appears to be consistently related to classical Coulomb repulsion energy, while avoiding singularities when nuclei collapse.

Metropolis Evaluation of the Hartree-Fock Exchange Energy.

We examine the possibility of using a Metropolis algorithm for computing the exchange energy in a large molecular system. Following ideas set forth in a recent publication (Baer, Neuhauser, and Rabani, Phys. Rev. Lett. 111, 106402 (2013)) we focus on obtaining the exchange energy per particle (ExPE, as opposed to the total exchange energy) to a predefined statistical error and on determining the numerical scaling of the calculation achieving this. For this we assume that the occupied molecular orbitals (MOs) are known and given in terms of a standard Gaussian atomic basis set. The Metropolis random walk produces a sequence of pairs of three-dimensional points (x,x'), which are distributed in proportion to ρ(x,x')(2), where ρ(x,x') is the density matrix. The exchange energy per particle is then simply the average of the Coulomb repulsion energy υC(|x-x'|) over these pairs. To reduce the statistical error we separate the exchange energy into a short-range term that can be calculated deterministically in a linear scaling fashion and a long-range term that is treated by the Metropolis method. We demonstrate the method on water clusters and silicon nanocrystals showing the magnitude of the ExPE standard deviation is independent of system size. In the water clusters a longer random walk was necessary to obtain full ergodicity as Metropolis walkers tended to get stuck for a while in localized regions. We developed a diagnostic tool that can alert a user when such a situation occurs. The calculation effort scales linearly with system size if one uses an atom screening procedure that can be made numerically exact. In systems where the MOs can be localized efficiently the ExPE can even be computed with "sublinear scaling" as the MOs themselves can be screened.

Electronic screening-enhanced hole pairing in two-leg spin ladders studied by high-resolution resonant inelastic x-ray scattering at Cu M edges.

We study the electronic screening mechanisms of the effective Coulomb on-site repulsion in hole-doped Sr(14)Cu(24)O(41) compared to undoped La(6)Ca(8)Cu(24)O(41) using polarization dependent high-resolution resonant inelastic x-ray scattering at Cu M edges. By measuring the energy of the effective Coulomb on-site repulsion and the spin excitations, we estimate superexchange and hopping matrix element energies along rungs and legs, respectively. Interestingly, hole doping locally screens the Coulomb on-site repulsion reducing it by as much as 25%. We suggest that the increased ratio of the electronic kinetic to the electronic correlation energy contributes to the local superexchange mediated pairing between holes.

Protonation of Pyridyl‐Substituted TTF Derivatives: Substituent Effects in Solution and in the Proton–Electron Correlated Charge‐Transfer Complexes

Protonated pyridyl-substituted tetrathiafulvalene electron-donor molecules (PyH(+)-TTF) showed significant changes in the electron-donating ability and HOMO-LUMO energy gap compared to the neutral analogues and gave a unique N(+)-H⋅⋅⋅N hydrogen-bonded (H-bonded) dimer unit in the proton-electron correlated charge-transfer (CT) complex crystals. We have evaluated these features from the viewpoint of the molecular structure of the PyH(+)-TTF derivatives, that is, the substitution position of the Py group and/or the presence or absence of the ethylenedithio (EDT) group. Among 2-PyH(+)-TTF (1 oH(+)), 3-PyH(+)-TTF (1 mH(+)), 4-PyH(+)-TTF (1 pH(+)), and 4-PyH(+)-EDT-TTF (2 pH(+)) systems, the para-pyridyl-substituted donors 1 pH(+) and 2 pH(+) exhibit more marked changes upon protonation in solution; a larger redshift in the intramolecular CT absorption band and a larger decrease in the electron-donating ability. Furthermore, the EDT system 2 pH(+) has the smallest intramolecular Coulombic repulsion energy. These differences are reasonably interpreted by considering the energy levels and distributions of the HOMO and LUMO obtained by quantum chemical calculations. Such substituent effects related to protonation were also examined by comparing the structure and properties of a new H-bonded CT complex crystal based on 2 pH(+) with those of its 1 pH(+) analogue recently prepared by us: Both of them form a similar type of H-bonded dimer unit, however, its charge distribution as well as the overall molecular arrangement, electronic structure, and conductivity were significantly modulated by the introduction of the EDT group. These results provide a new insight into the structural and electronic features of the PyH(+)-TTF-based proton-electron correlated molecular conductors.

Properties of the internal excited state of the strong-coupling magneto-bipolaron in a parabolic quantum dot

The properties of the internal excited state of the strong coupling magneto-bipolarons in a parabolic quantum dot are studied by using the variational method of Pekar type based on the Lee-Low-Pines’ unitary transformation. With the influences of the electronic spin and the external magnetic field taken into consideration, the change law of ground state energy E0, the average number of phonon N0, the first excited state energy E1 and the average number of phonon N1 of the magneto-bipolarons with the confinement strength ω0, the dielectric constant ratio η, the electron-phonon coupling α, and the cyclotron frequency ωc are derived in two-dimensional quantum dot. Numerical results indicate that the ground state energy E0 and the first excited state energy E1 consist of four parts: the single-article energy Ee of two electrons, the Coulomb interaction energy EC between two electrons, the interaction energy Es between the electronic spin and the external magnetic field, and the interaction energy Ee-ph of the electron with the longitudinalo optical phonons. The energy E1 of the first excited state splits into two lines, i.e., E1(1+1) and E1(1-1) due to the interaction between the “orbital” motion of the single-particle and the magnetic field, and each level of the ground-state energy and the first excited state energies set produces three “fine structures” due to the interaction between the electronic spin and the magnetic field. N0 and N1 increase with ω0, α and ωc increasing; Ee-ph is always less than zero, and absolute value |Ee-ph| increases with ω0, α and ωc increasing. The electron-phonon interaction has an important influence on the formation of bound state of the magneto-bipolaron; but the confinement potential and coulomb repulsive energy between electrons are unfavorable for the formation of magneto-bipolaron in the bound state.

Hellmann–Feynman Forces in the DFT+UMethod with Ultrasoft Pseudopotentials

Density functional theory (DFT) with on-site Coulomb repulsion (DFT+U) is a conventional tool to study strongly-correlated electron systems, which cannot be described properly with semilocal approximations to DFT. In many cases, the on-site Coulomb repulsion (U) and the exchange (J) energies are given as an adjustable parameter, so as to reproduce desired physical properties (such as band gap), but by determining the effective on-site Coulomb repulsion energy from first-principles, a nonempirical DFT+U calculation is also possible. Furthermore, because the total energy can be determined variationally, the Hellmann–Feynman forces are available, which allows geometry optimization and molecular dynamics simulation within DFT+U. However, the so-called double-counting correction is not defined uniquely, and as a result, formulation of the Hellmann–Feynman forces depends on the particular implementation of DFT+U energy. Here, I present an implementation of the Hellmann– Feynman forces within DFT+U scheme adopted in the STATE code, which employs the ultrasoft pseudopotentials and plane-wave basis sets. In the present implementation of DFT+U, the diagonal representation of the density matrix is employed, which differs from previous ones. Interaction energy between localized electrons is assumed to be given by the Hubbard-like expression as

Photoinduced dynamics in spinel and pyrochlore vanadates as Mott-Hubbard insulators with magnetic ordering

We studied the photoinduced dynamics of spinel MnV${}_{1.8}$Al${}_{0.2}$O${}_{4}$ and pyrochlore Yb${}_{2}$V${}_{2}$O${}_{7}$ as prototypical Mott-Hubbard insulators with magnetic ordering. We found that the Mott excitation spectrum is suppressed much sooner than 1 ps after photoirradiation, and subsequently it shows an energy shift over several or several tens of picoseconds, which is caused by the melting of magnetic ordering. This indicates that the Mott excitation spectrum is dominated not only by the Coulomb repulsion energy but also by magnetic interactions, and their different energy scales lead to the different time scales in the photoinduced dynamics.

Excitation levels in ultra-dense hydrogen p(−1) and d(−1) clusters: Structure of spin-based Rydberg Matter

Laser-induced Coulomb explosions in ultra-dense hydrogen clusters prove that the interatomic distance in such clusters is a few picometers, since the well-defined kinetic energy release (Coulomb repulsion energy) is many hundred eV. In the best characterized case which is ultra-dense deuterium D(−1) or d(−1), the kinetic energy given to the fragments in a cluster is normally 630eV. This implies a D–D distance of 2.3±0.1pm (2.15±0.02pm measured in D4 clusters). A description based on theoretical work by J.E. Hirsch using only the electron spins predicts that several excitation levels of spin quantum number s exist in these quantum materials. The agreement with the experimental D–D distance is excellent at 2.23pm for s=2. Theory is now verified by experimentally detecting states with spin values s=1 and s=3. The D–D distance is only 0.56pm in the lowest excitation level s=1. The previously suggested “inverted” structure of D(−1) is obsolete since the new theory gives a better explanation of the accumulated experimental results.

Electronic structures and phonon free energies of LaCoO3using hybrid-exchange density functional theory

Hybrid-exchange density functional theory has been used to model the electronic structure of LaCoO${}_{3}$. Based on a rhombohedral unit cell of $R\overline{3}c$ symmetry containing two Co atoms we find a mixed spin phase, comprising alternating low and high spin Co${}^{+3}$ ions, with a total energy at 0 K just 57 meV per formula unit above that of a nonmagnetic semiconducting ground state. In the mixed spin phase the high-spin Co${}^{+3}$ ions have spin moments of $3.1\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ and the state is insulating with a band gap of 2.2 eV. Our calculations suggest that the effective on-site Coulomb repulsion energy ${U}_{\mathrm{eff}}$ on Co${}^{+3}$ ions is spin dependent. The ${U}_{\mathrm{eff}}$ on Co${}^{+3}$ ions is 7.1 eV and 8.5 eV for the nonmagnetic ground state and for the magnetic high spin state, respectively. For the mixed spin state, two different ${U}_{\mathrm{eff}}$ are estimated for two Co${}^{+3}$ ions in the unit cell having different spin states, 8.0 eV for the high-spin Co${}^{+3}$ ion and 7.0 eV for the low-spin Co${}^{+3}$ ion. An estimate of the harmonic phonon free energy suggests that this mixed spin phase would become the more stable phase as the temperature increases, which is consistent with experimental evidence. An alternative intermediate spin state is higher in energy at all temperatures.