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At least 991 records · Page 55

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe 2+ , Fe 3+ , and Co 3+ , including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. Furthermore, we find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method—in terms of computational cost and in terms of accuracy on monatomic systems—and therefore we chose this method for molecular benchmarks. Then Kohn–Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF 2 , FeCl 2 , and CoF 2 . We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The effect of bond functions on dissociation energies

The procedure employing bond functions recently suggested by Wright and Buenker has been applied to the N2 X 1 Sigma g + potential curve within the CAS SCF + MRSD CI treatment of electron correlation. The basis set used herein is identical to that employed by these authors in their SCF + CI calculations. The De and and the shape of the resulting potential curve, as judged by the computed vibrational levels, is not so accurate as would be expected from the results reported by Wright and Buenker (1984). The results indicate that using the CI superposition errors associated with bond functions to cancel basis set incompleteness depends on the treatment of the electron correlation.

Bauschlicher, C. W., Jr.↗

Discrete approximation methods for parameter identification in delay systems

Approximation schemes for parameter identification problems in which the governing state equation is a linear functional differential equation of retarded type are constructed. The basis of the schemes is the replacement of the parameter identification problem having an infinite dimensional state equation by a sequence of approximating parameter identification problems in which the states are given by finite dimensional discrete difference equations. The difference equations are constructed using linear semigroup theory and rational function approximations to the exponential. Sufficient conditions are given for the convergence of solutions to the approximating problems, which can be obtained using conventional methods, to solutions to the original parameter identification problem. Finite difference and spline based schemes using Paderational function approximations to the exponential are constructed, and shown to satisfy the sufficient conditions for convergence. A discussion and analysis of numerical results obtained through the application of the schemes to several examples is included.

Rosen, I. G.↗

The Solar Wind and Geomagnetic Activity as a Function of Time Relative to Corotating Interaction Regions

Corotating interaction regions during the declining phase of the solar cycle are the cause of recurrent geomagnetic storms and are responsible for the generation of high fluxes of relativistic electrons. These regions are produced by the collision of a high-speed stream of solar wind with a slow-speed stream. The interface between the two streams is easily identified with plasma and field data from a solar wind monitor upstream of the Earth. The properties of the solar wind and interplanetary magnetic field are systematic functions of time relative to the stream interface. Consequently the coupling of the solar wind to the Earth's magnetosphere produces a predictable sequence of events. Because the streams persist for many solar rotations it should be possible to use terrestrial observations of past magnetic activity to predict future activity. Also the high-speed streams are produced by large unipolar magnetic regions on the Sun so that empirical models can be used to predict the velocity profile of a stream expected at the Earth. In either case knowledge of the statistical properties of the solar wind and geomagnetic activity as a function of time relative to a stream interface provides the basis for medium term forecasting of geomagnetic activity. In this report we use lists of stream interfaces identified in solar wind data during the years 1995 and 2004 to develop probability distribution functions for a variety of different variables as a function of time relative to the interface. The results are presented as temporal profiles of the quartiles of the cumulative probability distributions of these variables. We demonstrate that the storms produced by these interaction regions are generally very weak. Despite this the fluxes of relativistic electrons produced during those storms are the highest seen in the solar cycle. We attribute this to the specific sequence of events produced by the organization of the solar wind relative to the stream interfaces. We also show that there are large quantitative differences in various parameters between the two cycles.

McPherron, Robert L.↗

Vacuum distillation/vapor filtration water recovery

The development and evaluation of a vacuum distillation/vapor filtration (VD/VF) water recovery system are considered. As a functional model, the system converts urine and condensates waste water from six men to potable water on a steady-state basis. The system is designed for 180-day operating durations and for function on the ground, on zero-g aircraft, and in orbit. Preparatory tasks are summarized for conducting low gravity tests of a vacuum distillation/vapor filtration system for recovering water from urine.

Honegger, R. J.↗

Theoretical study of NH2 - Potential curves, transition moments, and photodissociation cross sections

Photodissociation cross sections from the ground state of NH2 have been calculated using a pseudodiatomic model. The potential curves needed in these calculations, functions of one NH bond length, were obtained by ab initio MCSCF calculations on the five lowest doublet states of NH2 using a contracted Gaussian basis set of double zeta quality augmented by polarization and Rydberg functions. Transition dipole moments between the ground and excited states were evaluated using MCSCF wave functions.

Saxon, R. P.↗

Range‐separated density functional theory using multiresolution analysis and quantum computing

Quantum computers are expected to outperform classical computers for specific problems in quantum chemistry. Such calculations remain expensive, but costs can be lowered through the partition of the molecular system. In the present study, partition was achieved with range-separated density functional theory (RS-DFT). The use of RS-DFT reduces both the basis set size and the active space size dependence of the ground state energy in comparison with the use of wave function theory (WFT) alone. The utilization of pair natural orbitals (PNOs) in place of canonical molecular orbitals (MOs) results in more compact qubit Hamiltonians. To test this strategy, a basis-set independent framework, known as multiresolution analysis (MRA), was employed to generate PNOs. Tests were conducted with the variational quantum eigensolver for a number of molecules. The results show that the proposed approach reduces the number of qubits needed to reach a target energy accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Frequency analysis via the method of moment functionals

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Pearson, A. E.↗

Frequency analysis via the method of moment functionals

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Pearson, A. E.↗

New Determinations of the UV Luminosity Functions from z ~ 9 to 2 Show a Remarkable Consistency with Halo Growth and a Constant Star Formation Efficiency

Here we provide the most comprehensive determinations of the rest-frame UV luminosity function (LF) available to date with the Hubble Space Telescope (HST) at z ~ 2–9. Essentially all of the noncluster extragalactic legacy fields are utilized, including the Hubble Ultra Deep Field, the Hubble Frontier Fields parallel fields, and all five CANDELS fields, for a total survey area of 1136 arcmin{sup 2}. Our determinations include galaxies at z ~ 2–3 leveraging the deep HDUV, UVUDF, and ERS WFC3/UVIS observations available over an ~150 arcmin{sup 2} area in the GOODS-North and GOODS-South regions. All together, our collective samples include >24,000 sources, >2.3× larger than previous selections with HST. We identify 5766, 6332, 7240, 3449, 1066, 601, 246, and 33 sources at z ~ 2, 3, 4, 5, 6, 7, 8, and 9, respectively. Combining our results with an earlier z ~ 10 LF determination by Oesch et al., we quantify the evolution of the UV LF. Our results indicate that there is (1) a smooth flattening of the faint-end slope α from α ~ -2.4 at z ~ 10 to α ~ -1.5 at z ~ 2, (2) minimal evolution in the characteristic luminosity M* at z ≥ 2.5, and (3) a monotonic increase in the normalization log{sub 10}ϕ* from z ~ 10 to 2, which can be well described by a simple second-order polynomial, consistent with an “accelerated” evolution scenario. We find that each of these trends (from z ~ 10 to 2.5 at least) can be readily explained on the basis of the evolution of the halo mass function and a simple constant star formation efficiency model.

47 OTHER INSTRUMENTATION↗

On the nature of macroradicals formed upon radiolysis of aqueous poly(N-vinylpyrrolidone) solutions

Herein we have explored the nature of macroradicals formed upon radiolysis of aqueous poly(N-vinylpyrrolidone) (PVP) solutions using pulse radiolysis, density functional theory (DFT) and literature data. On the basis of literature data on site-specific kinetics of hydrogen abstraction from simple amides and spectra corresponding to specific radical sites on the same amides we have assessed the distribution of H-atom abstraction by • OH radicals from different positions on the pyrrolidone ring and the polymer backbone. Pulse radiolysis experiments performed at different doses per pulse and different PVP concentrations demonstrate that the H-abstracting radiolysis products are not quantitatively scavenged by the polymer when the dose per pulse exceeds ≈40 Gy. The implications of this are discussed in the context of radical-initiated crosslinking reactions. At a mass fraction of 0.1% PVP and doses per pulse ranging from 7 Gy to 117 Gy, the overall radical decay observed at 390 nm follows second order kinetics with rate constants on the order of 10 9 dm 3 mol -1 s -1 .

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Prudhomme, C.↗

Luminosity function and cosmological evolution of X-ray selected quasars

The preliminary analysis of a complete sample of 55 X-ray sources is presented as part of the Medium Sensitivity Survey of the Einstein Observatory. A pure luminosity evolutionary law is derived in order to determine the uniform distribution of the sources and the rates of evolution for Active Galactic Nuclei (AGNs) observed by X-ray and optical techniques are compared. A nonparametric representation of the luminosity function is fitted to the observational data. On the basis of the reduced data, it is determined that: (1) AGNs evolve cosmologically; (2) less evolution is required to explain the X-ray data than the optical data; (3) the high-luminosity portion of the X-ray luminosity can be described by a power-law with a slope of gamma = 3.6; and (4) the X-ray luminosity function flattens at low luminosities. Some of the implications of the results for conventional theoretical models of the evolution of quasars and Seyfert galaxies are discussed.

Maccacaro, T.↗

A prescription for the asteroseismic surface correction

In asteroseismology, the surface effect refers to a disparity between the observed and the modelled frequencies in stars with solar-like oscillations. It originates from improper modelling of the surface layers. Correcting the surface effect usually requires using functions with free parameters, which are conventionally fitted to the observed frequencies. On the basis that the correction should vary smoothly across the H–R diagram, we parameterize it as a simple function of surface gravity, effective temperature, and metallicity. We determine this function by fitting a wide range of stars. The absolute amount of the surface correction decreases with luminosity, but the ratio between it and νmax increases, suggesting the surface effect is more important for red giants than dwarfs. Applying the prescription can eliminate unrealistic surface correction, which improves parameter estimations with stellar modelling. Using two open clusters, we found a reduction of scatter in the model-derived ages for each star in the same cluster. As an important application, we provide a new revision for the Δν scaling relation that, for the first time, accounts for the surface correction. The values of the correction factor, f Δν , are up to 2 percent smaller than those determined without the surface effect considered, suggesting decreases of up to 4 percent in radii and up to 8 percent in masses when using the asteroseismic scaling relations. This revision brings the asteroseismic properties into an agreement with those determined from eclipsing binaries. The new correction factor and the stellar models with the corrected frequencies are available at https://www.github.com/parallelpro/surface.

79 ASTRONOMY AND ASTROPHYSICS↗

Scattering by a groove in an impedance plane

An analysis of two-dimensional scattering from a narrow groove in an impedance plane is presented. The groove is represented by a impedance surface and the problem reduces to that of scattering from an impedance strip in an otherwise uniform impedance plane. On the basis of this model, appropriate integral equations are constructed using a form of the impedance plane Green's functions involving rapidly convergent integrals. The integral equations are solved by introducing a single basis representation of the equivalent current on the narrow impedance insert. Both transverse electric (TE) and transverse magnetic (TM) polarizations are treated. The resulting solution is validated by comparison with results from the standard boundary integral method (BIM) and a high frequency solution. It is found that the presented solution for narrow impedance inserts can be used in conjunction with the high frequency solution for the characterization of impedance inserts of any given width.

Bindiganavale, Sunil↗

Age-rotation relationship for late-type main-sequence stars

With advancing spectral type and increasing age, late main-sequence stars exhibit monotonic decrease in rotational velocity. It is of great interest to extend the rotation-age relationship to stars of later spectral type. In recent times it has become possible to measure directly the rotational periods from the photometric modulation by Ca II H and K line emission. There have also been successful attempts to relate the chromospheric activity as manifested through Ca II H and K lines to the rotation period, and it was shown that the fraction of total stellar luminosity in Ca II H and K lines, corrected for photospheric contribution, is a function of a single parameter related to P and B-V. In the present investigation, this rotation-activity relation is utilized to infer the rotation periods as a function of spectral type. The period versus B-V plot is employed as a basis to infer that the rotational period of main-sequence stars is a single-valued function of mass (B-V color) and age.

Rengarajan, T. N.↗

Systematic comparison and cross-validation of fixed-node diffusion Monte Carlo and phaseless auxiliary-field quantum Monte Carlo in solids

Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. Here, we investigate the compatibility, strengths, and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multideterminant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis-set full configuration interaction energies estimated with CIPSI are used as a reference in this comparative study between DMC and AFQMC. By focusing on a set of canonical finite–size solid-state systems, we show that both QMC methods can be made to systematically converge towards the same energy once basis-set effects and systematic biases have been removed. AFQMC shows a much smaller dependence on the trial wave function than DMC while simultaneously exhibiting a much larger basis-set dependence. We outline some of the remaining challenges and opportunities for improving these approaches.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗