Finite-mass helium atoms. i - the 2 super 1 p state.
Variational wave functions of 2 P states of helium isoelectronic series, finding isotope shifts
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Variational wave functions of 2 P states of helium isoelectronic series, finding isotope shifts
Two triplet P states of helium isoelectronic series investigated via 50-term variational wave functions with isotopic shift determinations
Polarized orbital method for calculating electron-atom scattering amplitudes, noting discontinuous wave function, nonvariational technique and strong dependence on parameter
The states considered lie below the n = 2 threshold of He(+) and decay radiatively to the lower states. The most general D-state wave function of odd parity of two electrons is examined. The results presented are optimized with respect to four nonlinear parameters for 112 terms. A mass-polarization correction is given for all the states listed. The positions of the D states, including the reduced mass and the mass-polarization corrections, with respect to the ground state of He are reported.
The theory of perturbations, giving the diatomic effective Hamiltonian, is used for calculating actual molecular wave functions and intensity factors involved in transitions between states arising from Hund's coupling cases a,b, intermediate a-b, and c tendency. The Herman and Wallis corrections are derived, without any knowledge of the analytical expressions of the wave functions, and generalized to transitions between electronic states with whatever symmetry and multiplicity. A general method for studying perturbed intensities is presented using primarily modern spectroscopic numerical approaches. The method is used in the study of the ScO optical emission spectrum.
The present paper is concerned with an analysis of the bonding in Fe2(CO)9, taking into account the results of self-consistent-field (SCF) calculations. The basis sets used are the same as those employed in the study of Fe(CO)5 conducted by Bauschlicher and Bagus (1985). The Fe basis set starts with the 14s9p5d primitive set optimized by Wachters (1970), which is contracted to 8s4p5d. An SCF wave function, consisting of only the core electrons, was determined, and then electrons were slowly added to the virtual orbitals with the lowest eigenvalues. The conducted calculations show no direct Fe-Fe bonding, but rather bonding resulting from the bridging CO's. The bonding is found to involve both the 5 sigma and 2 pi(asterisk) orbitals of the bridging CO's.
Ab initio quantum chemical techniques have been used to investigate covalently-bonded and hydrogen-bonded species that may be important intermediates in the reaction of hydroxyl and hydroperoxyl radicals. Stable structures of both types were identified. Basic sets of polarized double-zeta quality and large scale configuration interaction wave functions have been utilized. Based upon electronic energies, the covalently-bonded HOOOH species is found to be 26.4 kcal/mol more stable than the OH and HO2 radicals. Similarly, the hydrogen-bonded HO-HO2 species is found to have an electronic energy 4.7 kcal/mol below that of the component radicals, after correction is made for the basis set superposition error. The hydrogen-bonded form is found to be planar, to possess one relatively 'normal' hydrogen bond, and to have lowest energy 3A-prime and 1A-prime states that are essentially degenerate. The 1A-double prime and 3A-double prime excited states produced by rotation of the unpaired OH electron into the molecular plane are found to be very slightly bound.
The operating principles, design, and development histories of three image correlation systems, the Portable Correlator Unit (PCU), the Miniature Correlator Unit (MCU), and the Coherence Interferometer (CI) are reviewed. The PCU and MCU are compact versions of the classical Vander Lught filter optical correlator, essentially parallel optical processors by light valve; the CI is a white-light correlator which functions entirely by interfering light waves, with electronic detection only at the final output, and thus represents a parallel optical processor by rotational-shear interferometer. Details of the design and construction are discussed and illustrated with drawings and photographs. Also considered are applications of the MCU to NASA tasks such as rendezvous and docking on the Mars Rover and Sample Return mission, autonomous robotic exploration of planetary surfaces, and compression and pattern-recognition of remote-sensing data.
Intertwined charge and spin correlations are ubiquitous in a wide range of transition metal oxides and are often perceived as intimately related to unconventional superconductivity. Theoretically envisioned as driven by strong electronic correlations, the intertwined order is usually found to be strongly coupled to the lattice as signaled by pronounced phonon softening. Recently, both charge and spin density waves (CDW and SDW) and superconductivity have been discovered in several Ruddlesden-Popper (RP) nickelates, in particular trilayer nickelates 𝑅𝐸 4 Ni 3 O 10 (𝑅𝐸 = Pr, La). The nature of the intertwined order and the role of lattice-charge coupling are at the heart of the debate about these materials. Using inelastic x-ray scattering, we mapped the low-energy phonon dispersions in 𝑅𝐸 4 Ni 3 O 10 and found no evidence of softening near the CDW wave vector over a wide temperature range, which contrasts with the pronounced anomalies frequently observed in cuprate superconductors. Calculations of the electronic susceptibility revealed a peak at the observed SDW ordering vector but not at the CDW wave vector. Our experimental and theoretical findings highlight the crucial role of the spin degree of freedom and establish a foundation for understanding the interplay between superconductivity and density-wave transitions in RP nickelate superconductors and beyond.
The non-orthogonal configuration interaction with fragments (NOCI-F) approach is extended opening the possibility to study intramolecular processes and materials with covalent or ionic lattices. So far, NOCI-F has been applied to study intermolecular energy and electron transfer employing ensembles of fragments that do not have atoms or bonds in common. The here presented approach divides the target system into two overlapping fragments that share one or more atoms and/or one or more bonds. After the construction of a collection of (multiconfigurational) fragment wave functions in a state specific optimization procedure, the fragment wave functions are combined to form many-electron basis functions for the non-orthogonal configuration interaction of the whole system. The orbitals in the overlapping fragment are defined by a corresponding orbital transformation of the fragment orbitals through a singular value decomposition. The overlapping fragments approach is first illustrated for a model system and then used to highlight some possible applications of NOCI with overlapping fragments. In conclusion, the results of excited state diffusion in transition metal oxide, intramolecular singlet fission and magnetic interactions in organic biradicals and ionic compounds are discussed.
Here, we present a statistical analysis of electrostatic solitary waves observed aboard Magnetospheric Multiscale spacecraft in the Earth's magnetosheath. Applying single-spacecraft interferometry to several hundred solitary waves collected in about 2-minute interval, we show that almost all of them have the electrostatic potential of positive polarity and propagate quasi-parallel to the local magnetic field with plasma frame velocities of the order of 100 km/s. The solitary waves have typical parallel half-widths from 10 to 100 m that is between 1 and 10 Debye lengths and typical amplitudes of the electrostatic potential from 10 to 200 mV that is between 0.01% and 1% of local electron temperature. The solitary waves are associated with quasi-Maxwellian ion velocity distribution functions, and their plasma frame velocities are comparable with ion thermal speed and well below electron thermal speed. We argue that the solitary waves of positive polarity are slow electron holes and estimate the time scale of their acceleration, which occurs due to interaction with ions, to be of the order of one second. The observation of slow electron holes indicates that their lifetime was shorter than the acceleration time scale. We argue that multi-spacecraft interferometry applied previously to these solitary waves is not applicable because of their too-short spatial scales. The source of the slow electron holes and the role in electron-ion energy exchange remain to be established.
Consideration is given to a possible explanation for the one-dimensional anomalous resistivity and breakdown of runaway acceleration observed in the auroral zones. It is shown that under conditions existing along auroral field lines, where the cyclotron frequency is greater than the plasma frequency and density fluctuations exceed 0.25, trapping of a major portion of the electron distribution function by large-amplitude ion cyclotron waves can inhibit the free acceleration of runaways and act to violate the conservation of the first adiabatic invariant for electrons above a certain threshold velocity. Particle simulations combining the effects of finite ion cavities and pitch angle scattering at the anomalous Doppler resonance are then presented which demonstrate the formation of a runaway distribution upon the application of a constant dc field and the effects of the instability at the anomalous Doppler resonance in preventing it. The necessity for further large-scale macrophysics simulations to gain a fuller understanding of the total system dynamics is pointed out.
Methane C–H activation at transition-metal sites often involves electronic structures that challenge conventional single-reference electronic structure descriptions. Although Kohn–Sham density functional theory (DFT) is widely used to study catalytic trends, its reliability for reactions involving strongly correlated species remains uncertain. Here we present a systematic multireference investigation of methane activation at metal–organic framework (MOF) node catalysts across the 3d transition-metal series. We introduce an automated workflow for active space selection to enable consistent application of multireference methods, including multiconfiguration pair-density functional theory and n-electron valence state perturbation theory, to these catalytic systems. These calculations show substantial static correlation in the C–H activation reaction step and predict activation barriers that differ from DFT by 30–70 kJ mol–1, with DFT often qualitatively disagreeing in barrier height trends across transition metals. Analysis of multireference wave functions shows that reactivity is governed by the electronic structure of the M–O moiety along a continuum from metal–oxo to oxyl radical and O biradical character. Increased oxygen-centered spin density and weakened M–O bonding are identified as descriptors of catalytic activity which correlate with lower activation barriers.
The electron density (n e ) and argon metastable density (1 s 5 ) of a 43GHz microplasma are obtained using the zero-dimensional plasma kinetics solver (ZDPlasKin®) for an incident power of 160 and 1000mW and argon pressures of 10–600Torr (1.3 ×10 3 to 8.0 × 10 4 Pa). These simulations are compared with previously published experimental data. To determine the self-consistent electric field in the modeled plasma, the three-dimensional millimeter wave fields are computed as a function of electron density using ANSYS EM19.2, HFSS®. This electromagnetic field model is coupled to ZDPlasKin such that any increase in the simulated plasma density correctly attenuates the simulated electric field within the microplasma. The electron density is found to be sensitive to argon gas temperature, so a two-zone temperature model was needed to obtain agreement with experimental measurements. The temperature in the central core of the microplasma was determined by a previous experimental study. That temperature was used as an input to the model for the simulation of volume recombination losses. The outer regions of the microplasma are assumed to be in equilibrium with the walls (300K). This second temperature was used in the model to determine diffusion losses. The modeled electron and metastable densities are of the order 10 20 and 10 18 m –3 , respectively. This is in good agreement with those measured experimentally as long as the two-zone temperature model is used. In the absence of a hot gas core, the modeled three-body recombination rates are excessive and the simulation severely under-predicts the electron density and over-estimates the metastable density. We conclude that the millimeter wave microplasma has a hot core (2500K at 600 Torr) that rarifies the argon gas and effectively reduces three-body recombination. Furthermore, this allows one to achieve high electron density on the order of 10 20 m –3 with only 100mW of wave power.
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This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.
An investigation of the generation of plasmaspheric hiss by the whistler mode instability has been carried out. Using combined ray-tracing and growth rate calculations, the path-integrated growth rates of a large number of waves have been calculated using a distribution function. In general, the waves damp out before being magnetospherically reflected, or soon after. This is true of all the waves traced, independent of the distribution functions used for the energetic (resonant) electrons. Thus the growth rates are generally low, since the waves undergo few equatorial transits. A comparison of these results with observed spectra indicates that while some spectral characteristics are in qualitative agreement, there is a major discrepancy in the intensity levels.
An overview is given of the microscopic state of the solar wind with emphasis on recent Ulysses high-latitude observations and previous Helios in-ecliptic observations. The possible links between composition, ionization state. velocity distribution functions of electrons, protons and heavy ions. kinetic plasma waves and MHD-scale turbulence are elaborated. Emphasis is placed on a connection of interplanetary kinetic-scale phenomena with their generating microscopic processes in the corona. The fast streams seem to consist of mesoscale pressure-balanced plasma filaments and magnetic flux tubes, reminiscent of the supergranular-size structures building the open corona, from which copious Alfven waves emanate. The wind from the magnetically structured and active corona shows developed compressive turbulence and considerable abundance and ionization state variations. Some modelling attempts to explain the observed element fractionation are briefly reviewed. The causes of the nonthermal particle features. such as proton-ion differential streaming, ion beams. temperature anisotropies, and skewed distributions associated with collisionless heat conduction, are ultimately to be searched in the fact, that the corona is never quiescent but fundamentally variable in space and time. Consequently, the radial evolution of the internal state of the wind resembles at all latitudes a complicated relaxation process, in the course of which the free (in comparison with LTE conditions) particle kinetic energy is converted into plasma waves and MHD turbulence on a wide range of scales. This leads to intermittent wave-particle interactions and unsteady anomalous transport, mixed with the weak effects of the rare Coulomb collisions. Spherical expansion and large-scale inhomogeneity forces the wind to attain microscopically a complex internal state of dynamic statistical equilibrium.