Binding Energies Of Orbitals Research Articles

More than the sum of its parts: Combining parametrized tests of extreme gravity

We connect two formalisms that describe deformations away from general relativity, one valid in the strong-field regime of neutrons stars and another valid in the radiative regime of gravitational waves: the post-Tolman-Oppenheimer-Volkoff and the parametrized-post-Einsteinian formalisms respectively. We find that post-Tolman-Oppenheimer-Volkoff deformations of the exterior metric of an isolated neutron star induce deformations in the orbital binding energy of a neutron star binary. Such a modification to the binding energy then percolates into the gravitational waves emitted by such a binary, with the leading-order post-Tolman-Oppenheimer-Volkoff modifications introducing a second post-Newtonian order correction to the gravitational wave phase. The lack of support in gravitational wave data for general relativity deformations at this post-Newtonian order can then be used to place constraints post-Tolman-Oppenheimer-Volkoff parameters. As an application, we use the binary neutron star merger event GW170817 to place the constraint $-2.4 \leq \chi \leq 44$ (at 90% credibility) on a combination of post-Tolman-Oppenheimer-Volkoff parameters. We also explore the implications of this result to the possible deformations of the mass-radius relation of neutron stars allowed within this formalism. This work opens the path towards theory-independent tests of gravity, combining astronomical observations of neutron stars and gravitational wave observations.

Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions

Orbital binding energies in the ground state of many-electron elements obtained in experiments or in quantum-mechanical-calculations are studied. Their dependences on the atomic number and on the degree of ionization are analyzed. The Bohr – Sommerfeld semiclassical quantization condition is used and filled-shell orbital binding energy approximate scaling is shown. The scaling is similar to the one in the Thomas – Fermi model, but with two other functions-coefficients. The effective method of the demonstration of binding energies in a large number of atoms through these two functions is proposed. As a result, special features of the elements of the main and transition groups and the influence of relativistic effects are vividly manifested. Simple interpolation expressions are built for the two functions. One can use them to estimate orbital binding energies in the filled shells of many-electron atoms and ions to within 10% for middle elements and from 10% to 30% for heavy ones. The estimate can be used as the initial approximation in precessional atomic computations and also for rough calculations of the ionization cross sections of many-electron atoms and ions by electrons and heavy particles, failing more precise data.

Квазиклассический метод анализа и оценки орбитальных энергий связи в многоэлектронных атомах и ионах

Квазиклассический метод анализа и оценки орбитальных энергий связи в многоэлектронных атомах и ионах

Solid state NMR and XPS of ternary fluorido-zirconates of various coordination modes

Extended information is provided about 19F MAS NMR and XPS spectroscopic data on 11 ternary fluorido-zirconates (Li2ZrF6, Rb2ZrF6, Cs2ZrF6, Na3ZrF7, (NH4)3ZrF7, K3ZrF7, Li4ZrF8, K2ZrF6, Na5Zr2F13, Na7Zr6F31, and (NH4)2ZrF6), which display different coordination numbers of the zirconium atom as well as different modes of fluorine atom bonding. XPS data show that binding energies on fluorine 1s electrons are sensitive to its coordination properties (ionic, terminal or bridging coordination mode) while the binding energies of zirconium orbitals are not sensitive to its coordination properties (six-, seven- or eightfold coordination). 19F chemical shifts correlate with the ionic radii of counter cations along the series Li2ZrF6, Rb2ZrF6, Cs2ZrF6 and K3ZrF7, (NH4)3ZrF7 and Na3ZrF7. This reflects the polarizability properties and shielding potential of the cations surrounding the fluorine atoms. Additionally, calculations of NMR parameters for the compounds were also carried out using the CASTEP DFT code. The correlation between the experimental isotropic chemical shifts and calculated isotropic chemical shieldings established for the studied compounds allows us to predict the 19F NMR spectrum of crystalline compounds with good accuracy. A unique technique of low temperature 19F MAS NMR experiments combined with CASTEP calculation on (NH4)2ZrF6 enabled the assignment of all 12 crystallographically non-equivalent fluorine atoms to NMR signals.

Magnetic properties and core electron binding energies of liquid water.

The magnetic properties and the core and inner valence electron binding energies of liquid water are investigated. The adopted methodology relies on the combination of molecular dynamics and electronic structure calculations. Born-Oppenheimer molecular dynamics with the Becke and Lee-Yang-Parr functionals for exchange and correlation, respectively, and includes an empirical correction (BLYP-D3) functional and classical molecular dynamics with the TIP4P/2005-F model were carried out. The Keal-Tozer functional was applied for predicting magnetic shielding and spin-spin coupling constants. Core and inner valence electron binding energies in liquid water were calculated with symmetry adapted cluster-configuration interaction. The relationship between the magnetic shielding constant σ(17O), the role played by the oxygen atom as a proton acceptor and donor, and the tetrahedral organisation of liquid water are investigated. The results indicate that the deshielding of the oxygen atom in water is very dependent on the order parameter (q) describing the tetrahedral organisation of the hydrogen bond network. The strong sensitivity of magnetic properties on changes of the electronic density in the nuclei environment is illustrated by a correlation between σ(17O) and the energy gap between the 1a1[O1s] (core) and the 2a1 (inner valence) orbitals of water. Although several studies discussed the eventual connection between magnetic properties and core electron binding energies, such a correlation could not be clearly established. Here, we demonstrate that for liquid water this correlation exists although involving the gap between electron binding energies of core and inner valence orbitals.

Determination of Dark Matter Halo Mass from Dynamics of Satellite Galaxies

Abstract We show that the mass of a dark matter halo can be inferred from the dynamical status of its satellite galaxies. Using nine dark matter simulations of halos like the Milky Way (MW), we find that the present-day substructures in each halo follow a characteristic distribution in the phase space of orbital binding energy and angular momentum, and that this distribution is similar from halo to halo, but has an intrinsic dependence on the halo formation history. We construct this distribution directly from the simulations for a specific halo and extend the result to halos of similar formation history but different masses by scaling. The mass of an observed halo can then be estimated by maximizing the likelihood in comparing the measured kinematic parameters of its satellite galaxies with these distributions. We test the validity and accuracy of this method with mock samples taken from the simulations. Using the positions, radial velocities, and proper motions of nine tracers and assuming observational uncertainties comparable to those of MW satellite galaxies, we find that the halo mass can be recovered to within . The accuracy can be improved to within ∼25% if 30 tracers are used. However, the dependence of the phase-space distribution on the halo formation history sets a minimum uncertainty of that cannot be reduced by using more tracers. We believe that this minimum uncertainty also applies to any mass determination for a halo when the phase-space information of other kinematic tracers is used.

Valence Electronic Structure of Aqueous Solutions: Insights from Photoelectron Spectroscopy.

The valence orbital electron binding energies of water and of embedded solutes are crucial quantities for understanding chemical reactions taking place in aqueous solution, including oxidation/reduction, transition-metal coordination, and radiation chemistry. Their experimental determination based on liquid-photoelectron spectroscopy using soft X-rays is described, and we provide an overview of valence photoelectron spectroscopy studies reported to date. We discuss principal experimental aspects and several theoretical approaches to compute the measured binding energies of the least tightly bound molecular orbitals. Solutes studied are presented chronologically, from simple electrolytes, via transition-metal ion solutions and several organic and inorganic molecules, to biologically relevant molecules, including aqueous nucleotides and their components. In addition to the lowest vertical ionization energies, the measured valence photoelectron spectra also provide information on adiabatic ionization energies and reorganization energies for the oxidation (ionization) half-reaction. For solutes with low solubility, resonantly enhanced ionization provides a promising alternative pathway.

Size-dependent electronic structure controls activity for ethanol electro-oxidation at Ptn/indium tin oxide (n = 1 to 14).

Understanding the factors that control electrochemical catalysis is essential to improving performance. We report a study of electrocatalytic ethanol oxidation - a process important for direct ethanol fuel cells - over size-selected Pt centers ranging from single atoms to Pt14. Model electrodes were prepared by soft-landing of mass-selected Ptn(+) on indium tin oxide (ITO) supports in ultrahigh vacuum, and transferred to an in situ electrochemical cell without exposure to air. Each electrode had identical Pt coverage, and differed only in the size of Pt clusters deposited. The small Ptn have activities that vary strongly, and non-monotonically with deposited size. Activity per gram Pt ranges up to ten times higher than that of 5 to 10 nm Pt particles dispersed on ITO. Activity is anti-correlated with the Pt 4d core orbital binding energy, indicating that electron rich clusters are essential for high activity.

Projected constraints on scalarization with gravitational waves from neutron star binaries

Certain scalar-tensor theories have the property of endowing stars with scalar hair, sourced either by the star's own compactness (spontaneous scalarization) or, for binary systems, by the companion's scalar hair (induced scalarization) or by the orbital binding energy (dynamical scalarization). Scalarized stars in binaries present different conservative dynamics than in General Relativity, and can also excite a scalar mode in the metric perturbation that carries away dipolar radiation. As a result, the binary orbit shrinks faster than predicted in General Relativity, modifying the rate of decay of the orbital period. In spite of this, scalar-tensor theories can pass existing binary pulsar tests, because observed pulsars may not be compact enough or sufficiently orbitally bound to activate scalarization. Gravitational waves emitted during the last stages of compact binary inspirals are thus ideal probes of scalarization effects. For the standard projected sensitivity of advanced LIGO, we here show that, if neutron stars are sufficiently compact to enter the detector's sensitivity band already scalarized, then gravitational waves could place constraints at least comparable to binary pulsars. If the stars dynamically scalarize while inspiraling in band, then constraints are still possible provided the scalarization occurs sufficiently early in the inspiral, roughly below an orbital frequency of 50Hz. In performing these studies, we derive an easy-to-calculate data analysis measure, an integrated phase difference between a General Relativistic and a modified signal, that maps directly to the Bayes factor so as to determine whether a modified gravity effect is detectable. Finally, we find that custom-made templates are equally effective as model-independent, parameterized post-Einsteinian waveforms at detecting such modified gravity effects at realistic signal-to-noise ratios.

Why observable space is solely three dimensional

Quantum (and classical) binding energy considerations in n-dimensional space indicate that atoms (and planets) can only exist in three-dimensional space. This is why observable space is solely 3-dimensional. Both a novel Virial theorem analysis, and detailed classical and quantum energy calculations for 3-space circular and elliptical orbits indicate that they have no orbital binding energy in greater than 3-space. The same energy equation also excludes the possibility of atom-like bodies in strictly 1 and 2-dimensions. A prediction is made that in the search for deviations from r^-2 of the gravitational force at sub-millimeter distances such a deviation must occur at < ~ 10^-10 m (or < ~10^-12 m considering muoniom), since atoms would disintegrate if the curled up dimensions of string theory were larger than this. Callender asserts that the often-repeated claim in previous work that stable orbits are possible in only three dimensions is not even remotely established. The binding energy analysis herein avoids the pitfalls that Callender points out, as it circumvents stability issues. An uncanny quantum surprise is present in very high dimensions.

Investigation of superhalogen behaviour of RuF n (n = 1–7) clusters: density functional theory (DFT) study

In the present investigation, interaction of ruthenium (Ru) atoms with fluorine (F) atoms was studied using the density functional theory utilizing B3LYP method. It was found that up to seven F atoms can bind to a single Ru atom which results in increase of electron affinities successively, reaching a peak value of 6·95 eV for RuF6. Its stability and reactivity were also examined by using HOMO–LUMO gap, molecular orbital analysis and binding energy of these clusters. It is found that energy required for dissociation of F2 molecules are higher than energy required for dissociation of F atoms. The unusual properties are attributed to the involvement of inner shell 4d-electrons, which not only allow RuF n clusters to belong to the class of superhalogens but also show that its valence can exceed the nominal value of 1. The interaction of RuF4 superhalogen with an alkali atom lithium (Li) were also studied which suggests that a new class of salt can be synthesized by reacting RuF4 with Li.

Aligned spins: orbital elements, decaying orbits, and last stable circular orbit to high post-Newtonian orders

In this paper, the quasi-Keplerian parameterization for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin–orbit, next-to-next-to-leading order spin(1)–spin(2) and next-to-leading order spin-squared dynamics in the conservative regime. In a further step, we use the expressions for the radiative multipole moments with spin to leading order linear and quadratic in both spins to compute radiation losses of the orbital binding energy and angular momentum. Orbital averaged expressions for the decay of energy and eccentricity are provided. An expression for the last stable circular orbit is given in terms of the angular velocity-type variable x.

Calculations of nuclear excitation by electron capture (NEET) in nonlocal thermodynamic equilibrium plasmas

The nuclear excitation by electron capture (NEET) process may occur when the energy differences between two nuclear levels and between two electronic states are nearly equal, provided the quantum selection rules are fulfilled. These resonant conditions drastically limit the number of possible candidates, even though thermodynamic conditions encountered in hot dense plasmas do modify the orbital electronic binding energy and the resonance conditions. $^{201}\mathrm{Hg}$, with a low-lying isomeric state located at $1.565$ keV, can be excited by NEET process in a laser-created plasma. However, its correct calculation requires nonlocal thermodynamic equilibrium (non-LTE) atomic physics treatment because current laser-created plasmas do not reach high-enough temperature in the area at LTE. In this article, we describe the calculation leading to an estimated excitation rate and discuss the influence of LTE$/$non-LTE physics with an average-atom model and the use of a Gaussian variance calculation to estimate the broadening around the mean energy mismatch.

An experimental and computational study of the valence photoelectron spectra of halogenated pyrimidines

The electronic structures of pyrimidine and a selection of its halogen-substituted derivatives have been investigated using ultraviolet photoelectron spectroscopy and ab initio quantum chemical methods. Assignments are proposed for all of the features in the PES spectra by comparison with the vertical ionization energies of the molecular orbitals calculated using the partial third-order quasiparticle approximation as applied to electron propagator theory and a corrected density functional method based on the B3LYP functional. The shifts of the outermost five molecular orbitals of the pyrimidine ring structure in the halogen-substituted derivatives with respect to the binding energies of the equivalent orbitals in the parent pyrimidine molecule are discussed as a function of the identity and ring position of the halogen atom.

N-K spectra of adenine amino tautomers

Adenine tautomeric process is not a small perturbation but a significant change of the inner shell configuration. For canonical adenine, ade n9, the inner-shell configuration in the ground electronic states (X1A′) is given by 1a′(N(9))2a′(N(10))3a′(N(7))4a′(N(3))5a′(N(1)) 6a′(C(6))7a′(C(8))8a′(C(4))9a′(C(2))10a′(C(5)). Although the five N1s orbitals in the core shell of all adenine amino tautomers are always given as 1a′2a′3a′4a′5a′. The profound tautomer dependent inner-shell electronic reconfiguration has been largely masked by small net differences in their total electronic energies and subtle differences in their valence shell electronic structures. The present quantum mechanical spectral study demonstrates that inner-shell chemical shift of N1s orbitals of adenine amino tautomers is atomic site and tautomer specific: the orbital binding energy shifts of the amino N1s sites (-N-) are smaller than those of the imino N1s sites (-N=) in the same tautomer. The nitrogen N@1s site (an amino site) which connects the mobile hydrogen exhibits the smallest energy shift within a tautomer and therefore, is an indicator of the specific tautomer. The preferential adenine (ade n9) protonation sites are the imino sites in the order of 5a′(N(1)), 4a′(N(3)) and 3a′(N(7)) which agrees with previous observations.

Absorption spectra and electronic structures of Au mAg n ( m + n = 8) clusters

The electronic structures and absorption spectra of Au m Ag n ( m + n = 8) clusters have been investigated using time-dependent density functional response theory. We have discovered that the vertical ionization potentials, highest occupied molecular orbital level, lowest unoccupied molecular orbital level and binding energies of the most stable binary Au m Ag n are intermediate between those of Ag 8 and Au 8 clusters. The analysis of the low-energy absorption spectra shows that the dominant excitation energies and the corresponding oscillator strengths exhibit an obvious odd–even oscillation with the variation of the number of Au atoms. The odd–even oscillation character indicates that the optical properties of Au m Ag n can be tuned by changing the stoichiometries. The excitation of electrons to exterior atoms plays a key role in optical responses of Au m Ag n clusters.

Study of the chemical mechanism of color reactions of selenium(IV) with o-arylenediamines

o-Arylenediamines are promising for the photometric determination of selenium. The search for new reagents of this group is desirable. To obtain information necessary for this purpose, the chemical mechanism of color reactions of selenium(IV) with o-arylenediamines was studied. The optimum conditions of these reactions and the spectrophotometric characteristics of reagents and complexes were found. The ratio of components in the reaction products (piazoselenols) of 1: 1 was determined by elemental analysis, NMR spectroscopy, and the isomolar series method. The formation of the selenium-nitrogen bond was confirmed and the quasiaromatic character of piazoselenols was revealed by IR and NMR spectroscopy. Binding energies of valence orbitals, electron density distribution, and charges of nitrogen and selenium atoms were estimated by x-ray photoelectron spectroscopy. In the case of piazoselenol from 1,2-phenylenediamine, the existence of two tautomeric forms with the oxidation numbers of selenium close to +2 and +4 were found. Piazoselenol based on N-phenyl-1,2-phenylenediamine predominantly occurs as a single compound with the oxidation number of selenium close to +2. The most probable structures of the resulting piazoselenols were proposed, and the probable schemes of the reactions of selenium(IV) with 1,2-phenylenediamine and N-phenyl-1,2-phenylenediamine were justified.

Theoretical study on structures and aromaticities of a new series of sandwich complexes: [M 2(η 5[sbnd]P 5) 2] and [M(η 5[sbnd]P 5) 2] (M = Be, Mg, and Ca)

Structures and magnetic properties [nucleus independent chemical shifts (NICS)] of [M 2(η 5–P 5) 2] and [M(η 5–P 5) 2] (M = Be, Mg, and Ca) are studied with density functional theory at B3LYP level using the 6-311+G(d, p) basis sets. The M 2 2 + and M 2+ sandwich complexes with D 5 symmetry are minima. The D 5 h and D 5 d symmetry conformations are saddle points on the flat potential energy surface. Analyses of molecular orbital correlation and binding energy for the two series of complexes reveal that the M–M bond is a weak σ covalent bond. In addition to electrostatic interactions, there are also covalent bonds between the M and the P 5 - ring. The M–M bond plays a dominant role in the stability of both series of complexes. The M–M and M–P 5 bond strength decreases as M varies from Be to Ca. The P–P bond length in these complexes is slightly elongated with respect to that in P 5 - . The NICS computed with GIAO-B3LYP/6-311+G(d,p) indicates that the P 5 rings in both series of complexes are aromatic, and the aromaticity decreases as M varies from Be to Ca. In these complexes, the NICS at the P 5 ring center slightly decreases and it increases at the outer side of the P 5 ring, thus resulting in the elongation of P–P bond and the significant flow of π-electron from the ring towards the bonding of the P 5 ring with the M 2 2 + unit or M and leading to the strengthening of the M–P 5 bonding. The dissected NICS of the P 5 - ring of these complexes shows that the large total NICS is mainly due to the P–P π bond contribution of the P 5 ring. The NICS of the P–P π bond decreases as the metal varies from Be to Ca.

Synchrotron-Induced Photoelectron Spectroscopy of the Dye-Sensitized Nanocrystalline TiO2/Electrolyte Interface: Band Gap States and Their Interaction with Dye and Solvent Molecules

The adsorption of Ru dye N3 [RuII(2,2‘-bipyridyl-4,4‘-dicarboxylate)2(NCS)2] from ethanol solution and gas-phase adsorption and coadsorption of the solvent acetonitrile on liquid nitrogen cooled nanocrystalline (nc) TiO2 films have been investigated using highly surface sensitive synchrotron-induced photoelectron spectroscopy. Resonantly excited Ti3+-related band gap states form a peak 2.2 eV above the leading edge of the valence band, and additional states up to the Fermi level are found. The intensities of the gap states and related Ti3+ 2p emissions of pristine samples depend strongly on sample preparation and history. Gap-state-related emissions are partially quenched by dye as well as acetonitrile adsorption. Quenching of gap states due to acetonitrile is reversible. The maximum of the highest occupied molecular orbital (HOMO) emission of the dye is found 1.6 eV above the leading edge of the nc-TiO2 valence band. The binding energies of dye orbitals are increased upon acetonitrile coadsorption. The H...

Investigation of a polythiophene interface using photoemission spectroscopy in combination with electrospray thin-film deposition

The conjugated polymer poly(3-hexylthiophene) (P3HT) was deposited in several steps onto a highly oriented pyrolytic graphite (HOPG) substrate directly from solution in high vacuum, using an electrospray thin-film deposition system. The deposition system was attached to a photoemission spectroscopy setup via in situ sample transfer, allowing characterization in between deposition steps with x-ray and ultraviolet photoemission spectroscopy. The resultant series of spectra enabled the determination of the ionization energy, work function, and highest occupied molecular orbital binding energy of the P3HT overlayer, while giving detailed insight into the orbital alignment and dipole formation at the P3HT/HOPG contact.