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The density matrix functional approach to electron correlation: Dynamic and nondynamic correlation along the full dissociation coordinate
For chemistry an accurate description of bond weakening and breaking is vital. The great advantage of density matrix functionals, as opposed to density functionals, is their ability to describe such processes since they naturally cover both nondynamical and dynamical correlation. This is obvious in the Löwdin-Shull functional, the exact natural orbital functional for two-electron systems. We present in this paper extensions of this functional for the breaking of a single electron pair bond in N-electron molecules, using LiH, BeH{sup +}, and Li{sub 2} molecules as prototypes. Attention is given to the proper formulation of the functional in terms of not just J and K integrals but also the two-electron L integrals (K integrals with a different distribution of the complex conjugation of the orbitals), which is crucial for the calculation of response functions. Accurate energy curves are obtained with extended Löwdin-Shull functionals along the complete dissociation coordinate using full CI calculations as benchmark.
A COMPREHENSIVE ANALYSIS OF FERMI GAMMA-RAY BURST DATA. III. ENERGY-DEPENDENT T {sub 90} DISTRIBUTIONS OF GBM GRBs AND INSTRUMENTAL SELECTION EFFECT ON DURATION CLASSIFICATION
The durations (T {sub 90}) of 315 gamma-ray bursts (GRBs) detected with Fermi/GBM (8-1000 keV) up to 2011 September are calculated using the Bayesian Block method. We compare the T {sub 90} distributions between this sample and those derived from previous/current GRB missions. We show that the T {sub 90} distribution of this GRB sample is bimodal, with a statistical significance level comparable to those derived from the BeppoSAX/GRBM sample and the Swift/BAT sample, but lower than that derived from the CGRO/BATSE sample. The short-to-long GRB number ratio is also much lower than that derived from the BATSE sample, i.e., 1:6.5 versus 1:3. We measure T {sub 90} in several bands, i.e., 8-15, 15-25, 25-50, 50-100, 100-350, and 350-1000 keV, to investigate the energy-dependence effect of the bimodal T {sub 90} distribution. It is found that the bimodal feature is well observed in the 50-100 and 100-350 keV bands, but is only marginally acceptable in the 25-50 keV and 350-1000 keV bands. The hypothesis of bimodality is confidently rejected in the 8-15 and 15-25 keV bands. The T {sub 90} distributions in these bands are roughly consistent with those observed by missions with similar energy bands. The parameter T {sub 90} as a function of energy follows T-bar {sub 90}{proportional_to}E{sup -0.20{+-}0.02} for long GRBs. Considering the erratic X-ray and optical flares, the duration of a burst would be even longer for most GRBs. Our results, together with the observed extended emission of some short GRBs, indicate that the central engine activity timescale would be much longer than T {sub 90} for both long and short GRBs and the observed bimodal T {sub 90} distribution may be due to an instrumental selection effect.
Accurate Infrared Line Lists for 20 Isotopologues of CS 2 at Room Temperature
To facilitate atmospheric and spectroscopic studies of carbon disulfide, or CS 2 , in both planetary and exoplanetary atmospheres, we adopt the “Best Theory + Reliable High-resolution Experiment” algorithm to generate semiempirical IR line lists for the 20 most abundant CS 2 isotopologues, denoted as Ames-296K. The IR lists are computed using the Ames-1 potential energy surface, refined using the experimental transition set and an ab initio dipole moment surface fitted from CCSD(T)/aug-cc-pV(T/Q/5+d)Z dipoles extrapolated to a one-particle basis set limit. The IR lists cover the range of 0–10,000 cm -1 , with an S 296K cutoff at 10 -31 cm -1 /molecule·cm -2 (abundance included). A “natural” IR line list at 296 K includes about 10 million lines of the 20 isotopologues, with their intensities scaled by the corresponding abundances. The zero-point energy, partition functions, and abundances are reported for each isotopologue. The energy levels in the global effective Hamiltonian model for 12 C 32 S 2 are adopted to improve the line position accuracy. This new IR list for the main isotopologue is denoted as A+I.296K. Reliable HITRAN2020 line positions are also utilized to improve the accuracy of the 32 S 12 C 34 S, 32 S 12 C 33 S, and 32 S 13 C 32 S isotopologue line lists. The final composite line list is validated against Pacific Northwest National Laboratory experimental cross sections, showing excellent agreement. The agreement supports the quality of the composite line list and the power of synergy between experiment and theory. The new data are proposed for use in updating and expanding the CS 2 data in HITRAN and other high-resolution IR databases. Supplementary files are available in Zenodo and AHED.
Influence of Deformation on the Energy and Optical Absorption Spectra of Fullerene C{sub 20} within the Hubbard Model
Abstract—Anticommutator Green’s functions and energy spectra of fullerene C{sub 20} with the I{sub h}, D{sub 5d}, and D{sub 3d} symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C{sub 20} with the I{sub h}, D{sub 5d}, and D{sub 3d} symmetry groups have been determined. It is also shown how the energy levels of fullerene C{sub 20} with the I{sub h} symmetry group are split with the symmetry reduction.
Gradient of molecular Hartree–Fock–Bogoliubov energy with a linear combination of atomic orbital quasiparticle wave functions
The analytical gradient for the atomic-orbital-based Hartree–Fock–Bogoliubov (HFB) energy functional, the modified form of which was proposed by Staroverov and Scuseria to account for the static electron correlation [J. Chem. Phys. 117, 11107 (2002)], is derived. Interestingly, the Pulay force for the HFB energy is expressed with the same formula as that for the Hartree–Fock method. The efficiency of the present HFB energy gradient is demonstrated in the geometry optimizations of conjugated and biradical systems. The geometries optimized by using the HFB method with the appropriate factor ζ, which controls the degree of static correlation included, are found to show good agreement with those obtained by using a complete active-space self-consistent field method, although they are significantly dependent on ζ.
Information content of the differences in the charge radii of mirror nuclei
Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, $ΔR$$^{mir}_{ch}$, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability α D . In particular, this quantity correlates poorly with both the neutron skin and L. Here, we demonstrate that $ΔR$$^{mir}_{ch}$ is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on $ΔR$$^{mir}_{ch}$, we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.
A reverse Monte Carlo method for deriving optical constants of solids from reflection electron energy-loss spectroscopy spectra
A reverse Monte Carlo (RMC) method is developed to obtain the energy loss function (ELF) and optical constants from a measured reflection electron energy-loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC) simulation procedure. The method combines the simulated annealing method, i.e., a Markov chain Monte Carlo (MCMC) sampling of oscillator parameters, surface and bulk excitation weighting factors, and band gap energy, with a conventional MC simulation of electron interaction with solids, which acts as a single step of MCMC sampling in this RMC method. To examine the reliability of this method, we have verified that the output data of the dielectric function are essentially independent of the initial values of the trial parameters, which is a basic property of a MCMC method. The optical constants derived for SiO{sub 2} in the energy loss range of 8-90 eV are in good agreement with other available data, and relevant bulk ELFs are checked by oscillator strength-sum and perfect-screening-sum rules. Our results show that the dielectric function can be obtained by the RMC method even with a wide range of initial trial parameters. The RMC method is thus a general and effective method for determining the optical properties of solids from REELS measurements.
Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function
Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.
Towards improved local hybrid functionals by calibration of exchange-energy densities
A new approach for the calibration of (semi-)local and exact exchange-energy densities in the context of local hybrid functionals is reported. The calibration functions are derived from only the electron density and its spatial derivatives, avoiding spatial derivatives of the exact-exchange energy density or other computationally unfavorable contributions. The calibration functions fulfill the seven more important out of nine known exact constraints. It is shown that calibration improves substantially the definition of a non-dynamical correlation energy term for generalized gradient approximation (GGA)-based local hybrids. Moreover, gauge artifacts in the potential-energy curves of noble-gas dimers may be corrected by calibration. The developed calibration functions are then evaluated for a large range of energy-related properties (atomization energies, reaction barriers, ionization potentials, electron affinities, and total atomic energies) of three sets of local hybrids, using a simple one-parameter local-mixing. The functionals are based on (a) local spin-density approximation (LSDA) or (b) Perdew-Burke-Ernzerhof (PBE) exchange and correlation, and on (c) Becke-88 (B88) exchange and Lee-Yang-Parr (LYP) correlation. While the uncalibrated GGA-based functionals usually provide very poor thermochemical data, calibration allows a dramatic improvement, accompanied by only a small deterioration of reaction barriers. In particular, an optimized BLYP-based local-hybrid functional has been found that is a substantial improvement over the underlying global hybrids, as well as over previously reported LSDA-based local hybrids. It is expected that the present calibration approach will pave the way towards new generations of more accurate hyper-GGA functionals based on a local mixing of exchange-energy densities.
Electron heating mode transition induced by mixing radio frequency and ultrahigh frequency dual frequency powers in capacitive discharges
Electron heating mode transitions induced by mixing the low- and high-frequency power in dual-frequency nitrogen discharges at 400 mTorr pressure are presented. As the low-frequency (13.56 MHz) power decreases and high-frequency (320 MHz) power increases for the fixed power of 200 W, there is a transition of electron energy distribution function (EEDF) from Druyvesteyn to bi-Maxwellian type characterized by a distinguished warm electron population. It is shown that this EEDF evolution is attributed to the transition from collisional to collisionless stochastic heating of the low-energy electrons.
Quasi-particle energy spectra in local reduced density matrix functional theory
Recently, we introduced [N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A 90, 032511 (2014)] local reduced density matrix functional theory (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C{sub 20} isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solids.
Multi-Parameter Nonlinear Gain Correction of X-Ray Transition Edge Sensors for the X-Ray Integral Field Unit
With its array of 3840 Transition Edge Sensors (TESs), the Athena X-ray Integral Field Unit (X-IFU) will provide spatially resolved high-resolution spectroscopy (2.5 eV up to 7 keV) from 0.2 to 12 keV, with an absolute energy scale accuracy of 0.4 eV. Slight changes in the TES operating environment can cause significant variations in its energy response function, which may result in systematic errors in the absolute energy scale. We plan to monitor such changes at pixel level via onboard X-ray calibration sources and correct the energy scale accordingly using a linear or quadratic interpolation of gain curves obtained during ground calibration. However, this may not be sufficient to meet the 0.4 eV accuracy required for the XIFU. In this contribution, we introduce a newtwo-parameter gain correction technique, based on both the pulse-height estimate of a fiducial line and the baseline value of the pixels. Using gain functions that simulate ground calibration data, we show that this technique can accurately correct deviations in detector gain due to changes in TES operating conditions such as heat sink temperature, bias voltage, thermal radiation loading and linear amplifier gain. We also address potential optimisations of the onboard calibration source and compare the performance of this new technique with those previously used.
Kinetic simulations of ignited mode cesium vapor thermionic converters
Cesium vapor thermionic converters are an attractive method of converting high-temperature heat directly to electricity, but theoretical descriptions of the systems have been difficult due to the multi-step ionization of Cs through inelastic electron–neutral collisions. This work presents particle-in-cell simulations of these converters, using a direct simulation Monte Carlo collision model to track 52 excited states of Cs. Here, these simulations show the dominant role of multi-step ionization, which also varies significantly based on both the applied voltage bias and pressure. The electron energy distribution functions are shown to be highly non-Maxwellian in the cases analyzed here. A comparison with previous approaches is presented, and large differences are found in ionization rates due especially to the fact that previous approaches have assumed Maxwellian electron distributions. Finally, an open question regarding the nature of the plasma sheaths in the obstructed regime is discussed. The one-dimensional simulations did not produce stable obstructed regime operation and thereby do not support the double-sheath hypothesis.
Scaling of laser-driven electron and proton acceleration as a function of laser pulse duration, energy, and intensity in the multi-picosecond regime
A scaling study of short-pulse laser-driven proton and electron acceleration was conducted as a function of pulse duration, laser energy, and laser intensity in the multi-picosecond (ps) regime (~0.8 ps–20 ps). Furthermore, maximum proton energies significantly greater than established scaling laws were observed, consistent with observations at other multi-ps laser facilities. In addition, maximum proton energies and electron temperatures in this regime were found to be strongly dependent on the laser pulse duration and preplasma conditions. A modified proton scaling model is presented that is able to better represent the accelerated proton characteristics in this multi-ps regime.
Scaling of laser-driven electron and proton acceleration as a function of laser pulse duration, energy, and intensity in the multi-picosecond regime
A scaling study of short-pulse laser-driven proton and electron acceleration was conducted as a function of pulse duration, laser energy, and laser intensity in the multi-picosecond (ps) regime (∼0.8 ps–20 ps). Maximum proton energies significantly greater than established scaling laws were observed, consistent with observations at other multi-ps laser facilities. In addition, maximum proton energies and electron temperatures in this regime were found to be strongly dependent on the laser pulse duration and preplasma conditions. A modified proton scaling model is presented that is able to better represent the accelerated proton characteristics in this multi-ps regime.
Study of Atmospheric Nitric Oxide
We investigated the contribution of energetic nitrogen atoms to the production of nitric oxide in the thermosphere and their influence on the infrared emission spectrum. The nitric oxide molecules are important contributors to the cooling of the atmosphere. We first pointed out that in determining the energy distribution of the nitrogen atoms, it is important to take into account the thermal motion of the atmospheric gases. It had been ignored in all earlier studies. The source spectra are broadened considerably by the center of mass motion of the reactants. We worked out the consequences for the production of nitric oxide at night, using as sources of energetic N atoms, NO(+) + e yield N + O, N(D-2) + O yield N + O. The high energy tail is enhanced by orders of magnitude. We had earlier suggested (Sharma et al. 1993) that the reaction of energetic nitrogen atoms with O2 was responsible for the rotationally enhanced NO identified in the infrared spectrum. Our calculations provided quantitative confirmation of the suggestion. We proceeded to explore the validity of another approximation used in earlier analyses, the hard sphere approximation for the energy loss in elastic collisions. We carried out precise quantum mechanical calculations of the elastic 2 differential scattering of nitrogen atoms in collisions with oxygen atoms and showed that although the hard sphere approximation was nowhere of high precision, reasonable results could be obtained with an effective cross section of 6 x 10(exp 15)sq cm. We also initiated a program to include inelastic energy loss processes in the determination of the energy distribution function. We began a calculation of the rotation and vibrational excitation cross sections of molecular nitrogen and nitrogen atoms and developed a method for including inelastic energy loss as a function of scattering angle in the Boltzmann equation. A procedure for obtaining the solution of the Boltzman equation was worked out.