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Sensitivity and uncertainty in the effective delayed neutron fraction ({beta}{sub eff})

Precise knowledge of effective delayed neutron fraction ({beta}{sub eff}) and of the corresponding uncertainty is important for reactor safety analysis. The interest in developing the methodology for estimating the uncertainty in {beta}{sub eff} was expressed in the scope of the UAM project of the OECD/NEA. A novel approach for the calculation of the nuclear data sensitivity and uncertainty of the effective delayed neutron fraction is proposed, based on the linear perturbation theory. The method allows the detailed analysis of components of {beta}{sub eff} uncertainty. The procedure was implemented in the SUSD3D sensitivity and uncertainty code applied to several fast neutron benchmark experiments from the ICSBEP and IRPhE databases. According to the JENDL-4 covariance matrices and taking into account the uncertainty in the cross sections and in the prompt and delayed fission spectra the total uncertainty in {beta}eff was found to be of the order of {approx}2 to {approx}3.5 % for the studied fast experiments. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Orbital-optimized MP2.5 and its analytic gradients: Approaching CCSD(T) quality for noncovalent interactions

Orbital-optimized MP2.5 [or simply “optimized MP2.5,” OMP2.5, for short] and its analytic energy gradients are presented. The cost of the presented method is as much as that of coupled-cluster singles and doubles (CCSD) [O(N{sup 6}) scaling] for energy computations. However, for analytic gradient computations the OMP2.5 method is only half as expensive as CCSD because there is no need to solve λ{sub 2}-amplitude equations for OMP2.5. The performance of the OMP2.5 method is compared with that of the standard second-order Møller–Plesset perturbation theory (MP2), MP2.5, CCSD, and coupled-cluster singles and doubles with perturbative triples (CCSD(T)) methods for equilibrium geometries, hydrogen transfer reactions between radicals, and noncovalent interactions. For bond lengths of both closed and open-shell molecules, the OMP2.5 method improves upon MP2.5 and CCSD by 38%–43% and 31%–28%, respectively, with Dunning's cc-pCVQZ basis set. For complete basis set (CBS) predictions of hydrogen transfer reaction energies, the OMP2.5 method exhibits a substantially better performance than MP2.5, providing a mean absolute error of 1.1 kcal mol{sup −1}, which is more than 10 times lower than that of MP2.5 (11.8 kcal mol{sup −1}), and comparing to MP2 (14.6 kcal mol{sup −1}) there is a more than 12-fold reduction in errors. For noncovalent interaction energies (at CBS limits), the OMP2.5 method maintains the very good performance of MP2.5 for closed-shell systems, and for open-shell systems it significantly outperforms MP2.5 and CCSD, and approaches CCSD(T) quality. The MP2.5 errors decrease by a factor of 5 when the optimized orbitals are used for open-shell noncovalent interactions, and comparing to CCSD there is a more than 3-fold reduction in errors. Overall, the present application results indicate that the OMP2.5 method is very promising for open-shell noncovalent interactions and other chemical systems with difficult electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A new approach to the propagation of light-like signals in perturbed cosmological backgrounds

We present a new method to compute the deflection of light rays in a perturbed FLRW geometry. We exploit the properties of the Geodesic Light Cone (GLC) gauge where null rays propagate at constant angular coordinates irrespectively of the given (inhomogeneous and/or anisotropic) geometry. The gravitational deflection of null geodesics can then be obtained, in any other gauge, simply by expressing the angular coordinates of the given gauge in terms of the GLC angular coordinates. We apply this method to the standard Poisson gauge, including scalar perturbations, and give the full result for the deflection effect in terms of the direction of observation and observed redshift up to second order, and up to third order for the leading lensing terms. We also compare our results with those presently available in the literature and, in particular, we provide a new non trivial check of a previous result on the luminosity-redshift relation up to second order in cosmological perturbation theory.

79 ASTRONOMY AND ASTROPHYSICS↗

Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system

We study scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard model. In the free interaction case, using both analytical and numerical approaches, the metric operator for many-particle is constructed. The derived properties of the metric operator, similarity matrix and equivalent Hamiltonian reflect the fact that all the matrix elements change dramatically with diverging derivatives near the exceptional point. In the nonzero interaction case, it is found that even small on-site interaction can break the PT symmetry drastically. It is demonstrated that the scaling law can be established for the exceptional point in both small and large interaction limit. Based on perturbation and numerical methods, we also find that the phase diagram shows rich structure: there exist multiple regions of unbroken PT symmetry. - Highlights: Black-Right-Pointing-Pointer Generalization is done to many-particle sector of PT-symmetric non-Hermitian system. Black-Right-Pointing-Pointer The metric operator, similarity matrix and equivalent Hamiltonian possess diverging derivatives near the exceptional point. Black-Right-Pointing-Pointer The scaling law is established for the exceptional point of a PT-symmetric non-Hermitian Bose-Hubbard model. Black-Right-Pointing-Pointer The phase diagram shows that multiple regions of unbroken PT symmetry exist. Black-Right-Pointing-Pointer It is shown that even small on-site interaction can break the PT symmetry drastically.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Excitonic splitting and coherent electronic energy transfer in the gas-phase benzoic acid dimer

The benzoic acid dimer, (BZA){sub 2}, is a paradigmatic symmetric hydrogen bonded dimer with two strong antiparallel hydrogen bonds. The excitonic S{sub 1}/S{sub 2} state splitting and coherent electronic energy transfer within supersonically cooled (BZA){sub 2} and its {sup 13}C-, d{sub 1}-, d{sub 2}-, and {sup 13}C/d{sub 1}- isotopomers have been investigated by mass-resolved two-color resonant two-photon ionization spectroscopy. The (BZA){sub 2}-(h-h) and (BZA){sub 2}-(d-d) dimers are C{sub 2h} symmetric, hence only the S{sub 2} Leftwards-Arrow S{sub 0} transition can be observed, the S{sub 1} Leftwards-Arrow S{sub 0} transition being strictly electric-dipole forbidden. A single {sup 12}C/{sup 13}C or H/D isotopic substitution reduces the symmetry of the dimer to C{sub s}, so that the isotopic heterodimers (BZA){sub 2}-{sup 13}C, (BZA){sub 2}-(h-d), (BZA){sub 2}-(h{sup 13}C-d), and (BZA){sub 2}-(h-d{sup 13}C) show both S{sub 1} Leftwards-Arrow S{sub 0} and S{sub 2} Leftwards-Arrow S{sub 0} bands. The S{sub 1}/S{sub 2} exciton splitting inferred is {Delta}{sub exc}= 0.94 {+-} 0.1 cm{sup -1}. This is the smallest splitting observed so far for any H-bonded gas-phase dimer. Additional isotope-dependent contributions to the splittings, {Delta}{sub iso}, arise from the change of the zero-point vibrational energy upon electronic excitation and range from {Delta}{sub iso}= 3.3 cm{sup -1} upon {sup 12}C/{sup 13}C substitution to 14.8 cm{sup -1} for carboxy H/D substitution. The degree of excitonic localization/delocalization can be sensitively measured via the relative intensities of the S{sub 1} Leftwards-Arrow S{sub 0} and S{sub 2} Leftwards-Arrow S{sub 0} origin bands; near-complete localization is observed even for a single {sup 12}C/{sup 13}C substitution. The S{sub 1}/ S{sub 2} energy gap of (BZA){sub 2} is {Delta}{sub calc}{sup exc}=11 cm{sup -1} when calculated by the approximate second-order perturbation theory (CC2) method. Upon correction for vibronic quenching, this decreases to {Delta}{sub vibron}{sup exc}=2.1 cm{sup -1} [P. Ottiger et al., J. Chem. Phys. 136, 174308 (2012)], in good agreement with the observed {Delta}{sub exc}= 0.94 cm{sup -1}. The observed excitonic splittings can be converted to exciton hopping times {tau}{sub exc}. For the (BZA){sub 2}-(h-h) homodimer {tau}{sub exc}= 18 ps, which is nearly 40 times shorter than the double proton transfer time of (BZA){sub 2} in its excited state [Kalkman et al., ChemPhysChem 9, 1788 (2008)]. Thus, the electronic energy transfer is much faster than the proton-transfer in (BZA){sub 2}{sup *}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Calculations for energies, transition rates, and lifetimes in Al-like Kr XXIV

Using the second-order many-body perturbation theory (MBPT) method, a complete and accurate data set of excitation energies, lifetimes, wavelengths, and electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) line strengths, transition rates, and oscillator strengths for the lowest 880 levels arising from the 3l{sup 3} (0≤l≤2), 3l{sup 2}4l{sup ′} (0≤l≤2, 0≤l{sup ′}≤3), 3s{sup 2}5l (0≤l≤4), 3p{sup 2}5l (0≤l≤1), and 3s3p5l (0≤l≤4) configurations in Al-like Kr XXIV is provided. Comparisons are made with available experimental and theoretical results. Our calculated energies are expected to be accurate enough to facilitate identifications of observed lines involving the n=4,5 levels. The complete data set is also useful for modeling and diagnosing fusion plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimal Control of Evolution Mixed Variational Inclusions

Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Unraveling Excitonic Effects for the First Hyperpolarizabilities of Chromophore Aggregates

Excitonic interactions often significantly affect the optoelectronic properties of molecular materials. However, their role in determining the nonlinear optical response of organic electro-optic materials remains poorly understood. In this paper, we explore the effects of excitonic interactions on the first hyperpolarizability for aggregates of donor–acceptor chromophores. We show that calculations of the first hyperpolarizabilty of chromophore aggregates based on a two-state model agree well with the more rigorous coupled perturbed Hartree–Fock method. We then use both time-dependent density functional theory calculations and the molecular exciton approximation to parametrize the two-state model. Use of the molecular exciton approximation to the two-state model (i) is appropriate for disordered aggregates (unlike band theory), (ii) is computationally efficient enough for calculating the first hyperpolarizability of materials that consist of thousands of interacting chromophores, and (iii) allows the unraveling of the effects of both excitonic interactions and electrostatic polarization of the chromophore electron density by its environment on the first hyperpolarizability of molecular materials. We find that use of the molecular exciton approximation to the two-state model does not introduce significant additional errors compared to those introduced by applying the two-state model alone. We determine that the absolute change to the first hyperpolarizability of chromophore aggregates due to excitonic interactions increases with the size of the aggregate. For all sizes of disordered aggregates of chromophores considered in this paper, the inclusion of excitonic interactions on average decreases the magnitude of the first hyperpolarizability by 12–14% compared to the case of non-interacting chromophores. Lastly, we present a method for analytically calculating the first hyperpolarizability of a one-dimensional periodic array of chromophores within the molecular exciton approximation to the two-state model. This technique can be used to include an approximate correction for excitonic effects when simulating the electro-optic response of disordered and ordered organic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct Measurements of Carrier Transport in Polycrystalline Methylammonium Lead Iodide Perovskite Films with Transient Grating Spectroscopy

Hybrid organic-inorganic halide perovskites have been proposed in many optoelectronic applications, but critical to their increasing functionality and utility is understanding and controlling carrier transport. Here, we use light-induced transient grating spectroscopy to probe directly carrier transport in polycrystalline methylammonium lead iodide perovskite thin films using a weakly perturbative and noncontact method. The data reveal intrinsic diffusion characteristics of the charge carriers in the material and agree well with a simulated model of charge transport in which grain boundaries act as barriers to carrier movement.

14 SOLAR ENERGY↗

Competition between Hydrogen and Chalcogen Bonding in Homodimers of Chalcogen Hydrides (H 2 X) 2 , X = O, S, Se, Te

The structural and chemical bonding motifs manifested by the competition between hydrogen and chalcogen bonding in the homodimers of chalcogen hydrides (H 2 X) 2 , where X = O, S, Se, Te have been characterized using high-level electronic structure calculations and analysis of the electron density based on Quasi-atomic orbital (QUAO) and the Symmetry-adapted perturbation theory (SAPT) methods. The QUAO analysis clearly identifies a three-center interaction responsible for either hydrogen or chalcogen bonds: in the former, the σ-bond connecting the donor and hydrogen atom participating in the hydrogen bond interacts with the lone pair on the nucleophile acceptor via the hydrogen atom, while in the latter this same σ-bond interacts with the nucleophile lone pair via the donor chalcogen. The number of minimum energy structures increase dramatically from one for (H 2 O) 2 , three for (H 2 S) 2 , four for (H 2 Se) 2 , and finally six for (H 2 Te) 2 . Furthermore, the emergence of the chalcogen-bonded arrangements appears for (H 2 S) 2 with their subsequent energetic stabilization over the hydrogen-bonded minima manifesting in (H 2 Se) 2 and (H 2 Te) 2 . In particular, one of the (H 2 S) 2 , two of the (H 2 Se) 2 , and three of the (H 2 Te) 2 dimers are chalcogen bonded. Induction plays a small but important role in stabilizing hydrogen over chalcogen-bonded structures, while dispersion is more important for chalcogen bonds.

Chemical structure↗

Adsorption of a water molecule on the MgO(100) surface as described by cluster and slab models

The interaction of a water molecule with the (100) surface of MgO as described by cluster models is studied using MP2, coupled MP2 (MP2C) and symmetry–adapted perturbation theory (SAPT) methods. In addition, diffusion Monte Carlo (DMC) results are presented for several slab models as well as for the smallest, 2X2 cluster model. For the 2X2 model it is found that the MP2C, DMC, and CCSD(T) methods give nearly the same potential energy curve for the water–cluster interaction, whereas the potential energy curve from the SAPT calculations differs slightly from those of the other methods. The interaction of the water molecule with the cluster models of the MgO(100) surface is weakened upon expanding the number of layers from one to two and also upon expanding the description of the layers from 2X2 to 4X4 to 6X6. The SAPT calculations reveal that both these expansions of the cluster model are accompanied by reductions in the magnitudes of the induction and dispersion constributions. The best estimate of the energy for binding an isolated water molecule to the surface obtained from the cluster model calculations is in good agreement with that obtained from the DMC calculations using a 2–layer slab model with periodic boundary conditions.

Chemistry↗

Near-resonant rotational energy transfer in HCl–H{sub 2} inelastic collisions

We present a new four-dimensional (4D) potential energy surface for the HCl–H{sub 2} van der Waals system. Both molecules were treated as rigid rotors. Potential energy surface was obtained from electronic structure calculations using a coupled cluster with single, double, and perturbative triple excitations method. The four atoms were described using the augmented correlation-consistent quadruple zeta basis set and bond functions were placed at mid-distance between the HCl and H{sub 2} centers of mass for a better description of the van der Waals interaction. The global minimum is characterized by the well depth of 213.38 cm{sup −1} corresponding to the T-shape structure with H{sub 2} molecule on the H side of the HCl molecule. The dissociation energies D{sub 0} are 34.7 cm{sup −1} and 42.3 cm{sup −1} for the complex with para- and ortho-H{sub 2}, respectively. These theoretical results obtained using our new PES are in good agreement with experimental values [D. T. Anderson, M. Schuder, and D. J. Nesbitt, Chem. Phys. 239, 253 (1998)]. Close coupling calculations of the inelastic integral rotational cross sections of HCl in collisions with para-H{sub 2} and ortho-H{sub 2} were performed at low and intermediate collisional energies. Significant differences exist between para- and ortho-H{sub 2} results. The strongest collision-induced rotational HCl transitions are the transitions with Δj = 1 for collisions with both para-H{sub 2} and ortho-H{sub 2}. Rotational relaxation of HCl in collision with para-H{sub 2} in the rotationally excited states j = 2 is dominated by near-resonant energy transfer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lattice location and local magnetism of recoil implanted Fe impurities in wide and narrow band semiconductors CdTe, CdSe, and InSb: Experiment and theory

Employing the time differential perturbed angular distribution method, we have measured local susceptibility and spin relaxation rate of {sup 54}Fe nuclei implanted in III-V and II-VI semiconductors, CdTe, CdSe, and InSb. The magnetic response of Fe, identified to occupy the metal as well as the semi-metal atom sites, exhibit Curie-Weiss type susceptibility and Korringa like spin relaxation rate, revealing the existence of localized moments with small spin fluctuation temperature. The experimental results are supported by first principle electronic structure calculations performed within the frame work of density functional theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Communication: A mean field platform for excited state quantum chemistry

We present a mean field theory for excited states that is broadly analogous to ground state Hartree-Fock theory. Like Hartree-Fock, our approach is deterministic, state-specific, applies a variational principle to a minimally correlated ansatz, produces energy stationary points, relaxes the orbital basis, has a Fock-build cost-scaling, and can serve as the foundation for correlation methods such as perturbation theory and coupled cluster theory. To emphasize this last point, we pair our mean field approach with an excited state analog of second order Møller-Plesset theory and demonstrate that in water, formaldehyde, neon, and stretched lithium fluoride, the resulting accuracy far exceeds that of configuration interaction singles and rivals that of equation of motion coupled cluster.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fermi–Löwdin orbital self-interaction correction of adsorption energies on transition metal ions

Density functional theory (DFT)-based descriptions of the adsorption of small molecules on transition metal ions are prone to self-interaction errors. Here, we show that such errors lead to a large over-estimation of adsorption energies of small molecules on Cu + , Zn + , Zn 2+ , and Mn + in local spin density approximation (LSDA) and Perdew, Burke, Ernzerhof (PBE) generalized gradient approximation calculations compared to reference values computed using the coupled-cluster with single, doubles, and perturbative triple excitations method. These errors are significantly reduced by removing self-interaction using the Perdew–Zunger self-interaction correction (PZ-SIC) in the Fermi–Löwdin Orbital (FLO) SIC framework. In the case of FLO-PBE, typical errors are reduced to less than 0.1 eV. Furthermore, analysis of the results using DFT energies evaluated on self-interaction-corrected densities [DFT(@FLO)] indicates that the density-driven contributions to the FLO-DFT adsorption energy corrections are roughly the same size in DFT = LSDA and PBE, but the total corrections due to removing self-interaction are larger in LSDA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

POLARIZED LINE TRANSFER WITH F-STATE INTERFERENCE IN A NON-MAGNETIC MEDIUM: PARTIAL FREQUENCY REDISTRIBUTION EFFECTS IN THE COLLISIONLESS REGIME

Quantum interference phenomena manifest themselves in several ways in the polarized solar spectrum formed due to coherent scattering processes. One such effect arises due to interference between the fine structure (J) states giving rise to multiplets. Another effect is that which arises due to interference between the hyperfine structure (F) states. We extend the redistribution matrix derived for the J-state interference to the case of F-state interference. We then incorporate it into the polarized radiative transfer equation and solve it for isothermal constant property slab atmospheres. The relevant transfer equation is solved using a polarized approximate lambda iteration (PALI) technique based on operator perturbation. An alternative method derived from the Neumann series expansion is also proposed and is found to be relatively more efficient than the PALI method. The effects of partial frequency redistribution and the F-state interference on the shapes of the linearly polarized Stokes profiles are discussed. The emergent Stokes profiles are computed for hypothetical line transitions arising due to hyperfine structure splitting of the upper J = 3/2 and lower J = 1/2 levels of a two-level atom model with nuclear spin I{sub s} = 3/2. We confine our attention to the non-magnetic scattering in the collisionless regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SELF-CONSISTENT MAGNETIC STELLAR EVOLUTION MODELS OF THE DETACHED, SOLAR-TYPE ECLIPSING BINARY EF AQUARII

We introduce a new one-dimensional stellar evolution code, based on the existing Dartmouth code, that self-consistently accounts for the presence of a globally pervasive magnetic field. The methods involved in perturbing the equations of stellar structure, the equation of state, and the mixing-length theory of convection are presented and discussed. As a first test of the code's viability, stellar evolution models are computed for the components of a solar-type, detached eclipsing binary (DEB) system, EF Aquarii, shown to exhibit large disagreements with stellar models. The addition of the magnetic perturbation corrects the radius and effective temperature discrepancies observed in EF Aquarii. Furthermore, the required magnetic field strength at the model photosphere is within a factor of two of the magnetic field strengths estimated from the stellar X-ray luminosities measured by ROSAT and those predicted from Ca II K line core emission. These models provide firm evidence that the suppression of thermal convection arising from the presence of a magnetic field is sufficient to significantly alter the structure of solar-type stars, producing noticeably inflated radii and cooler effective temperatures. The inclusion of magnetic effects within a stellar evolution model has a wide range of applications, from DEBs and exoplanet host stars to the donor stars of cataclysmic variables.

79 ASTRONOMY AND ASTROPHYSICS↗