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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 415 records · Page 23
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DOE OSTI2016

Advanced Potential Energy Surfaces for Molecular Simulation

Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). Here in this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. Finally, we have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Multipolar condensates and multipolar Josephson effects

When single-particle dynamics are suppressed in certain strongly correlated systems, dipoles arise as elementary carriers of quantum kinetics. These dipoles can further condense, providing physicists with a rich realm to study fracton phases of matter. Whereas recent theoretical discoveries have shown that an unconventional lattice model may host a dipole condensate as the ground state, we show that dipole condensates prevail in bosonic systems due to a self-proximity effect. Our findings allow experimentalists to manipulate the phase of a dipole condensate and deliver dipolar Josephson effects, where supercurrents of dipoles arise in the absence of particle flows. The self-proximity effects can also be utilized to produce a generic multipolar condensate. The kinetics of the n -th order multipoles unavoidably creates a condensate of the ( n + 1)-th order multipoles, forming a hierarchy of multipolar condensates that will offer physicists a whole new class of macroscopic quantum phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A quantum liquid of magnetic octupoles on the pyrochlore lattice

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the ground state of a frustrated magnet. For example, the ‘2-in–2-out’ ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores. However, $f$-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and ‘hidden’ orders. In this paper we show that the correlated ground state of a Ce 3+ -based pyrochlore, Ce 2 Sn 2 O 7 , is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with a fluid-like state where degrees of freedom have a more complex magnetization density than that of magnetic dipoles. The nature and strength of the octupole–octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a ‘2-plus–2-minus’ rule. Our work identifies Ce 2 Sn 2 O 7 as a unique example of frustrated multipoles forming a ‘hidden’ topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Planck 2013 results. IV. Low Frequency Instrument beams and window functions

This paper presents the characterization of the in-flight beams, the beam window functions, and the associated uncertainties for the Planck Low Frequency Instrument (LFI). Knowledge of the beam profiles is necessary for determining the transfer function to go from the observed to the actual sky anisotropy power spectrum. The main beam distortions affect the beam window function, complicating the reconstruction of the anisotropy power spectrum at high multipoles, whereas the sidelobes affect the low and intermediate multipoles. The in-flight assessment of the LFI main beams relies on the measurements performed during Jupiter observations. By stacking the datafrom multiple Jupiter transits, the main beam profiles are measured down to-20 dB at 30 and 44 GHz, and down to-25 dB at 70 GHz. The main beam solid angles are determined to better than 0.2% at each LFI frequency band. The Planck pre-launch optical model is conveniently tuned to characterize the main beams independently of any noise effects. This approach provides an optical model whose beams fully reproduce the measurements in the main beam region, but also allows a description of the beams at power levels lower than can be achieved by the Jupiter measurements themselves. The agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band. The simulated beams are used for the computation of the window functions for the effective beams. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer bandshapes. The total uncertainties in the effective beam window functions are: 2% and 1.2% at 30 and 44 GHz, respectively (at ℓ ≈ 600), and 0.7% at 70 GHz (at ℓ ≈ 1000).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Planck 2013 results. XXII. Constraints on inflation

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be n s = 0.9603 ± 0.0073, ruling out exact scale invariance at over 5σ. Planck establishes an upper bound on the tensor-to-scalar ratio of r< 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V "< 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n = 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining d n s /dlnk =-0.0134 ± 0.0090. Here, we verify these conclusions through a numerical analysis, which makes no slow-roll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by Δχ 2 eff &approx; 10 ; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on f NL . Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the χ 2 eff by approximately 4 as a result of slightly lowering the theoretical prediction for the &ell; ≳ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Planck 2013 results. XV. CMB power spectra and likelihood

This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations that accounts for all known relevant uncertainties, both instrumental and astrophysical in nature. We use this likelihood to derive our best estimate of the CMB angular power spectrum from Planck over three decades in multipole moment, &ell;, covering 2 &le; &ell; &le; 2500. The main source of uncertainty at &ell; &le; 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher &ell;s. For &ell; < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz, separating the cosmological CMB signal from diffuse Galactic foregrounds through a physically motivated Bayesian component separation technique. At &ell; &le; 50, we employ a correlated Gaussian likelihood approximation based on a fine-grained set of angular cross-spectra derived from multiple detector combinations between the 100, 143, and 217 GHz frequency channels, marginalising over power spectrum foreground templates. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on the final cosmological parameters. We find good internal agreement among the high-&ell; cross-spectra with residuals below a few &mu;K 2 at &ell; ≲ 1000, in agreement with estimated calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit CDM cosmology is in excellent agreement with preliminary Planck EE and TE polarisation spectra. We find that the standard ΛCDM cosmology is well constrained by Planck from the measurements at &ell; ≲ 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4σ deviation from scale invariance, n s = 1. Increasing the multipole range beyond &ell; ≃ 1500 does not increase our accuracy for the ΛCDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the ΛCDM framework. Finally, we report a tension between the Planck best-fit ΛCDM model and the low-&ell; spectrum in the form of a power deficit of 5&ndash;10% at &ell; ≲ 40, with a statistical significance of 2.5&ndash;3σ. Without a theoretically motivated model for this power deficit, we do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent data set.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Planck 2015 results: XX. Constraints on inflation

In this paper, we present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n s = 0.968 ± 0.006 and tightly constrain its scale dependence to dn s / dlnk = -0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-ℓ polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r 0.002 < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth P R (k)over the range of scales 0.008 Mpc -1 ≲ k ≲ 0.1 Mpc -1 . At large scales, each method finds deviations from a power law, connected to a deficit at multipoles ℓ ≈ 20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | α non - adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum finding that the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. Lastly, these results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Planck intermediate results: LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters

We present that the six parameters of the standard ΛCDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in Planck the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We have investigated these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium Τ, the baryon density ω b , the matter density ω m , the angular size of the sound horizon θ&lowast; the spectral index of the primordial power spectrum, n s , and A s e -2τ (where A s is the amplitude of the primordial power spectrum), we have examined the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment < 800 in the Planck temperature power spectrum) and an all angular-scale data set (< 2500 Planck temperature power spectrum), each with a prior on τ of 0.07 ± 0.02. We find that the shifts, in units of the 1σ expected dispersion for each parameter, are { Δτ,ΔA s e - 2τ ,Δn s ,Δω m ,Δω b ,Δθ&lowast; } = { -1.7,-2.2,1.2,-2.0,1.1,0.9 }, with a χ2 value of 8.0. We find that this χ2 value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2σ in 9% of simulated data sets, meaning that the shifts are not unusually large. Comparing &ell; < 800 instead to &ell; > 800, or splitting at a different multipole, yields similar results. We examined the &ell; < 800 model residuals in the &ell; > 800 power spectrum data and find that the features there that drive these shifts are a set of oscillations across a broad range of angular scales. Although they partly appear similar to the effects of enhanced gravitational lensing, the shifts in ΛCDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to non-lensing effects; the only exception is Τ, which, at fixed A s e -2τ , affects the &ell; > 800 temperature power spectrum solely through the associated change in A s and the impact of that on the lensing potential power spectrum. We also ask, "what is it about the power spectrum at &ell; < 800 that leads to somewhat different best-fit parameters than come from the full range?" We find that if we discard the data at &ell; < 30, where there is a roughly 2σ downward fluctuation in power relative to the model that best fits the full range, the &ell; < 800 best-fit parameters shift significantly towards the &ell; < 2500 best-fit parameters. In contrast, including &ell; < 30, this previously noted "low-deficit" drives n s up and impacts parameters correlated with n s , such as ω m and H 0 . As expected, the &ell; < 30 data have a much greater impact on the &ell; < 800 best fit than on the &ell; < 2500 best fit. So although the shifts are not very significant, we find that they can be understood through the combined effects of an oscillatory-like set of high-residuals and the deficit in low-power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between PlanckTT data and two other CMB data sets, namely the Planck lensing reconstruction and the TT power spectrum measured by the South Pole Telescope, again finding a lack of convincing evidence of any significant deviations in parameters, suggesting that current CMB data sets give an internally consistent picture of the ΛCDM model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

BeyondPlanck: XII. Cosmological parameter constraints with end-to-end error propagation

We present cosmological parameter constraints estimated using the Bayesian BEYONDPLANCK analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data onto final cosmological parameters. As a first demonstration of the method, we analyzed time-ordered Planck LFI observations, combined with selected external data (WMAP 33–61 GHz, Planck HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps that are used to break critical astrophysical degeneracies. Overall, all the results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter amounting about 1σ when considering only temperature multipoles between 30 ≤ ℓ ≤ 600. In cases where there are differences, we note that the BEYONDPLANCK results are generally slightly closer to the high-ℓ HFI-dominated Planck 2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low-ℓ polarization information from LFI and WMAP, we find a best-fit value of τ = 0.066 ± 0.013, which is higher than the low value of τ = 0.052 ± 0.008 derived from Planck 2018 and slightly lower than the value of 0.069 ± 0.011 derived from the joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the BEYONDPLANCK processing is about 30 % greater than when analyzing the official products, after taking into account the different sky coverage. We argue that this uncertainty is due to a marginalization over a more complete model of instrumental and astrophysical parameters, which results in more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve a robust convergence for a low-resolution cosmic microwave background (CMB) covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

BEYONDPLANCK XI. Bayesian CMB analysis with sample-based end-to-end error propagation

We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations as derived through global end-to-end Bayesian processing within the BeyondPlanck framework. We first use these samples to study correlations between CMB, foreground, and instrumental parameters, and we identify a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), which is mitigated through model reduction, masking, and resampling. We compare our posterior-based CMB results with previous Planck products, and find generally good agreement, although with notably higher noise due to our exclusion of HFI data. We find a best-fit CMB dipole amplitude of 3362.7 ± 1.4 µK, in excellent agreement with previous Planck results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution, and does not involve any ad hoc contributions for Planck instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of ${σ}_{2}^{TT}$ = 229 ± 97 µK 2 , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is an order of magnitude larger than the naive diagonal Fisher uncertainty. Relatedly, we find lower evidence for a possible alignment between the quadrupole and octopole than previously reported due to a much larger scatter in the individual quadrupole coefficients, caused both by marginalizing over a more complete set of systematic effects, but also by our more conservative analysis mask required to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. At the same time, we note that this is the first time the sample-based asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ ≤ 600, and it now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation, and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Communication: The origin of rotational enhancement effect for the reaction of H{sub 2}O{sup +} + H{sub 2} (D{sub 2})

We have measured the absolute integral cross sections (σ’s) for H{sub 3}O{sup +} formed by the reaction of rovibrationally selected H{sub 2}O{sup +}(X{sup 2}B{sub 1}; v{sub 1}{sup +}v{sub 2}{sup +}v{sub 3}{sup +} = 000; N{sup +}{sub Ka}{sup +}{sub Kc}{sup +} = 0{sub 00}, 1{sub 11}, and 2{sub 11}) ion with H{sub 2} at the center-of-mass collision energy (E{sub cm}) range of 0.03–10.00 eV. The σ(0{sub 00}), σ(1{sub 11}), and σ(2{sub 11}) values thus obtained reveal rotational enhancements at low E{sub cm} < 0.50 eV, in agreement with the observation of the previous study of the H{sub 2}O{sup +}(X{sup 2}B{sub 1}) + D{sub 2} reaction. This Communication presents important progress concerning the high-level ab initio quantum calculation of the potential energy surface for the H{sub 2}O{sup +}(X{sup 2}B{sub 1}) + H{sub 2} (D{sub 2}) reactions, which has provided valuable insight into the origin of the rotational enhancement effect. Governed by the charge and dipole-induced-multipole interactions, the calculation shows that H{sub 2} (D{sub 2}) approaches the H end of H{sub 2}O{sup +}(X{sup 2}B{sub 1}) in the long range, whereas chemical force in the short range favors the orientation of H{sub 2} (D{sub 2}) toward the O side of H{sub 2}O{sup +}. The reorientation of H{sub 2}O{sup +} reactant ion facilitated by rotational excitation thus promotes the H{sub 2}O{sup +} + H{sub 2} (D{sub 2}) reaction along the minimum energy pathway, rendering the observed rotational enhancement effects. The occurrence of this effect at low E{sub cm} indicates that the long range charge and dipole-induced-multipole interactions of the colliding pair play a significant role in the dynamics of the exothermic H{sub 2}O{sup +} + H{sub 2} (D{sub 2}) reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Physical origins of weak H{sub 2} binding on carbon nanostructures: Insight from ab initio studies of chemically functionalized graphene nanoribbons

We have performed ab initio density functional theory calculations, incorporating London dispersion corrections, to study the absorption of molecular hydrogen on zigzag graphene nanoribbons whose edges have been functionalized by OH, NH{sub 2}, COOH, NO{sub 2}, or H{sub 2}PO{sub 3}. We find that hydrogen molecules always preferentially bind at or near the functionalized edge, and display induced dipole moments. Binding is generally enhanced by the presence of polar functional groups. The largest gains are observed for groups with oxygen lone pairs that can facilitate local charge reorganization, with the biggest single enhancement in adsorption energy found for “strong functionalization” by H{sub 2}PO{sub 3} (115 meV/H{sub 2} versus 52 meV/H{sub 2} on bare graphene). We show that for binding on the “outer edge” near the functional group, the presence of the group can introduce appreciable contributions from Debye interactions and higher-order multipole electrostatic terms, in addition to the dominant London dispersion interactions. For those functional groups that contain the OH moiety, the adsorption energy is linearly proportional to the number of lone pairs on oxygen atoms. Mixed functionalization with two different functional groups on a graphene edge can also have a synergistic effect, particularly when electron-donating and electron-withdrawing groups are combined. For binding on the “inner edge” somewhat farther from the functional group, most of the binding again arises from London interactions; however, there is also significant charge redistribution in the π manifold, which directly reflects the electron donating or withdrawing capacity of the functional group. Our results offer insight into the specific origins of weak binding of gas molecules on graphene, and suggest that edge functionalization could perhaps be used in combination with other strategies to increase the uptake of hydrogen in graphene. They also have relevance for the storage of hydrogen in porous carbon materials, such as activated carbons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Efficient implementation of the three-dimensional reference interaction site model method in the fragment molecular orbital method

The three-dimensional reference interaction site model (3D-RISM) method was efficiently implemented in the fragment molecular orbital (FMO) method. The method is referred to as the FMO/3D-RISM method, and allows us to treat electronic structure of the whole of a macromolecule, such as a protein, as well as the solvent distribution around a solute macromolecule. The formalism of the FMO/3D-RISM method, for the computationally available form and variational expressions, are proposed in detail. A major concern leading to the implementation of the method was decreasing the computational costs involved in calculating the electrostatic potential, because the electrostatic potential is calculated on numerous grid points in three-dimensional real space in the 3D-RISM method. In this article, we propose a procedure for decreasing the computational costs involved in calculating the electrostatic potential in the FMO method framework. The strategy involved in this procedure is to evaluate the electrostatic potential and the solvated Fock matrix in different manners, depending on the distance between the solute and the solvent. The electrostatic potential is evaluated directly in the vicinity of the solute molecule by integrating the molecular orbitals of monomer fragments of the solute molecule, whereas the electrostatic potential is described as the sum of multipole interactions when an analog of the fast multipole method is used. The efficiency of our method was demonstrated by applying it to a water trimer system and three biomolecular systems. The FMO/3D-RISM calculation can be performed within a reasonable computational time, retaining the accuracy of some physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Electrostatics on the sphere with applications to Monte Carlo simulations of two dimensional polar fluids

We present two methods for solving the electrostatics of point charges and multipoles on the surface of a sphere, i.e., in the space S{sub 2}, with applications to numerical simulations of two-dimensional (2D) polar fluids. In the first approach, point charges are associated with uniform neutralizing backgrounds to form neutral pseudo-charges, while in the second, one instead considers bi-charges, i.e., dumbells of antipodal point charges of opposite signs. We establish the expressions of the electric potentials of pseudo- and bi-charges as isotropic solutions of the Laplace-Beltrami equation in S{sub 2}. A multipolar expansion of pseudo- and bi-charge potentials leads to the electric potentials of mono- and bi-multipoles, respectively. These potentials constitute non-isotropic solutions of the Laplace-Beltrami equation, the general solution of which in spherical coordinates is recast under a new appealing form. We then focus on the case of mono- and bi-dipoles and build the theory of dielectric media in S{sub 2}. We notably obtain the expression of the static dielectric constant of a uniform isotropic polar fluid living in S{sub 2} in terms of the polarization fluctuations of subdomains of S{sub 2}. We also derive the long range behavior of the equilibrium pair correlation function under the assumption that it is governed by macroscopic electrostatics. These theoretical developments find their application in Monte Carlo simulations of the 2D fluid of dipolar hard spheres. Some preliminary numerical experiments are discussed with a special emphasis on finite size effects, a careful study of the thermodynamic limit, and a check of the theoretical predictions for the asymptotic behavior of the pair correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Computationally efficient dielectric calculations of molecular crystals

The microscopic dielectric response is a key quantity for electronic materials such as organic semiconductors. Calculations of this response for molecular crystals are currently either expensive or rely on extreme simplifications such as multipole expansions which lack microscopic detail. We present an alternate approach using a microscopic analogue of the Clausius-Mossotti equation, which constructs the dielectric response of a crystal from an eigenvalue decomposition of the dielectric response of individual molecules. This method can potentially be used to examine the effects of defects, disorder, and surfaces on the dielectric properties of molecular solids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

We previously developed an efficient screened hybrid functional called Gaussian-Perdew–Burke–Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A classical model for three-body interactions in aqueous ionic systems

We present a classical induction model to evaluate the three-body ion–water–water (I–W–W) and water–water–water (W–W–W) interactions in aqueous ionic systems. The classical description of the induction energy is based on electrostatic distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole–quadrupole on the O and H atoms of water. The monatomic ions were described by a point charge and a dipole–dipole polarizability, while for the polyatomic ions, distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole–quadrupole were used. The accuracy of the classical model is benchmarked against an accurate dataset of 936 (I–W–W) and 2184 (W–W–W) three-body terms for 13 different monatomic and polyatomic cation and anion systems. The classical model shows excellent agreement with the reference second order Moller–Plesset and coupled-cluster single double and perturbative triple [CCSD(T)] three-body energies. The Root-Mean-Square-Errors (RMSEs) for monatomic cations, monatomic anions, and polyatomic ions were 0.29, 0.25, and 0.12 kcal/mol, respectively. The corresponding RMSE for 1744 CCSD(T)/aVTZ three-body (W–W–W) energies, used to train MB-pol, was 0.12 kcal/mol. The accuracy of the proposed classical model demonstrates that the three-body term for aqueous ionic systems can be accurately modeled classically. This approach provides a fast, efficient, and as-accurate path toward modeling the three-body term in aqueous ionic systems that is fully transferable across systems with different ions without the need to fit to tens of thousands of ab initio calculations for each ion to extend existing many-body force fields to interactions between water and ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Cosmological implications of the CMB large-scale structure

The Wilkinson Microwave Anisotropy Probe (WMAP) and Planck may have uncovered several anomalies in the full cosmic microwave background (CMB) sky that could indicate possible new physics driving the growth of density fluctuations in the early universe. These include an unusually low power at the largest scales and an apparent alignment of the quadrupole and octopole moments. In a ΛCDM model where the CMB is described by a Gaussian Random Field, the quadrupole and octopole moments should be statistically independent. The emergence of these low probability features may simply be due to posterior selections from many such possible effects, whose occurrence would therefore not be as unlikely as one might naively infer. If this is not the case, however, and if these features are not due to effects such as foreground contamination, their combined statistical significance would be equal to the product of their individual significances. In the absence of such extraneous factors, and ignoring the biasing due to posterior selection, the missing large-angle correlations would have a probability as low as ∼0.1% and the low-l multipole alignment would be unlikely at the ∼4.9% level; under the least favorable conditions, their simultaneous observation in the context of the standard model could then be likely at only the ∼0.005% level. In this paper, we explore the possibility that these features are indeed anomalous, and show that the corresponding probability of CMB multipole alignment in the R{sub h}=ct universe would then be ∼7–10%, depending on the number of large-scale Sachs–Wolfe induced fluctuations. Since the low power at the largest spatial scales is reproduced in this cosmology without the need to invoke cosmic variance, the overall likelihood of observing both of these features in the CMB is ⩾7%, much more likely than in ΛCDM, if the anomalies are real. The key physical ingredient responsible for this difference is the existence in the former of a maximum fluctuation size at the time of recombination, which is absent in the latter because of inflation.

79 ASTRONOMY AND ASTROPHYSICS↗