Search NASA⌕ Search

SEARCH · Search NASA

Results for “Basis function”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Polar Magnetic Field Experiment

This grant covers the initial data reduction and analysis of the magnetic field measurements of the Polar spacecraft. At this writing data for the first three years of the mission have been processed and deposited in the key parameter database. These data are also available in a variety of time resolutions and coordinate systems via a webserver at UCLA that provides both plots and digital data. The flight software has twice been reprogrammed: once to remove a glitch in the data where there were rare collisions between commands in the central processing unit and once to provide burst mode data at 100 samples per second on a regular basis. The instrument continues to function as described in the instrument paper (1.1 in the bibliography attached below). The early observations were compared with observations on the same field lines at lower altitude. The polar magnetic measurements also proved to be most useful for testing the accuracy of MHD models. WE also made important contributions to study of waves and turbulence.

Russell, C. T.↗
NASA NTRS1999

Likelihood Analysis for Mega Pixel Maps

The derivation of cosmological parameters from astrophysical data sets routinely involves operations counts which scale as O(N(exp 3) where N is the number of data points. Currently planned missions, including MAP and Planck, will generate sky maps with N(sub d) = 10(exp 6) or more pixels. Simple "brute force" analysis, applied to such mega-pixel data, would require years of computing even on the fastest computers. We describe an algorithm which allows estimation of the likelihood function in the direct pixel basis. The algorithm uses a conjugate gradient approach to evaluate X2 and a geometric approximation to evaluate the determinant. Monte Carlo simulations provide a correction to the determinant, yielding an unbiased estimate of the likelihood surface in an arbitrary region surrounding the likelihood peak. The algorithm requires O(N(sub d)(exp 3/2) operations and O(Nd) storage for each likelihood evaluation, and allows for significant parallel computation.

Kogut, Alan J.↗
NASA NTRS1999

Alterations in Cardiovascular Regulation and Function During Long-Term Simulated Microgravity

The Cardiovascular Alterations Team is conducting studies of hemodynamic regulation and susceptibility to arrhythmias resulting from sixteen days of simulated microgravity exposure. In these studies very intensive measurements are made during a short duration of bed rest. In this collaborative effort are making many of the same measurements, however much less frequently, on subjects who are exposed to a much longer duration of simulated microgravity. Alterations in cardiovascular regulation and function that occur during and after space flight have been reported. These alterations are manifested, for example, by reduced orthostatic tolerance upon reentry to the earth's gravity from space. However, the precise physiologic mechanisms responsible for these alterations remain to be fully elucidated. Perhaps, as a result, effective countermeasures have yet to be developed. In addition, numerous reports from the past 30 years suggest that the incidence of ventricular arrhythmias among astronauts is increased during space flight. However, the effects of space flight and the associated physiologic stresses on cardiac conduction processes are not known, and an increase in cardiac susceptibility to arrhythmias has never been quantified. In this project we are applying the most powerful technologies available to determine, in a ground-based study of long duration space flight, the mechanisms by which space flight affects cardiovascular function, and then on the basis of an understanding of these mechanisms to develop rational and specific countermeasures. To this end we are conducting a collaborative project with the Bone Demineralization/Calcium Metabolism Team of the National Space Biomedical Research Institute (NSBRI). The Bone Team is conducting bed rest studies in human subjects lasting 17 weeks, which provides a unique opportunity to study the effects of long duration microgravity exposure on the human cardiovascular system. We are applying a number of powerful new methods to these long term bed rest subjects, including cardiovascular system identification (CSI), microvolt level T wave alternans analysis, and cardiac magnetic resonance imaging to assess non-invasively the effects of simulated long duration space flight on the cardiovascular system.

Cohen, Richard J.↗
NASA NTRS2003

Morphology of the Vestibular Utricule in Toadfish, Opsanus Tau

The uticle is an otolith organ in the vertebrate inner ear that provides gravitoinertial acceleration information into the vestibular reflex pathways. The aim of the present study was to provide an anatomical description of this structure in the adult oyster toadfish, and establish a morphological basis for interpretation of subsequent functional studies. Light, scanning electron and transmission electron microscopy were applied to visualize the sensory epithelium and its neural innervation. Electrophysiological techniques were used to identify utricular afferents by their response to translation stimuli. Similar to nerve afferents supplying the semicircular canals and lagena, utricular afferents commonly exhibit a short-latency increase of firing rate in response to electrical activation of the central efferent pathway. Afferents were labeled with biocytin either intraaxonally or with extracellular bulk deposits. Light microscope images of serial thick sections were used to make three-dimensional reconstructions of individual labeled afferents to identify the dendritic morphology with respect to epithelial location. Scanning electron microscopy was used to visualize the surface of the otolith mass facing the otolith membrane, and the hair cell polarization patterns of strioler and extrastriolar regions. Transmission electron micrographs of serial thin sections were compiled to create a three-dimensional reconstruction of the labeled afferent over a segment of its dendritic field and to examine the hair cell-afferent synaptic contacts.

Bass, L.↗
NASA NTRS2011

NASA Occupant Protection Standards Development

Current National Aeronautics and Space Administration (NASA) occupant protection standards and requirements are based on extrapolations of biodynamic models, which were based on human tests performed under pre-Space Shuttle human flight programs where the occupants were in different suit and seat configurations than is expected for the Multi Purpose Crew Vehicle (MPCV) and Commercial Crew programs. As a result, there is limited statistical validity to the occupant protection standards. Furthermore, the current standards and requirements have not been validated in relevant spaceflight suit, seat configurations or loading conditions. The objectives of this study were to develop new standards and requirements for occupant protection and rigorously validate these new standards with sub-injurious human testing. To accomplish these objectives we began by determining which critical injuries NASA would like to protect for. We then defined the anthropomorphic test device (ATD) and the associated injury metrics of interest. Finally, we conducted a literature review of available data for the Test Device for Human Occupant Restraint New Technology (THOR-NT) ATD to determine injury assessment reference values (IARV) to serve as a baseline for further development. To better understand NASA s environment, we propose conducting sub-injurious human testing in spaceflight seat and suit configurations with spaceflight dynamic loads, with a sufficiently high number of subjects to validate no injury during nominal landing loads. In addition to validate nominal loads, the THOR-NT ATD will be tested in the same conditions as the human volunteers, allowing correlation between human and ATD responses covering the Orion nominal landing environment and commercial vehicle expected nominal environments. All testing will be conducted without the suit and with the suit to ascertain the contribution of the suit to human and ATD responses. In addition to the testing campaign proposed, additional data analysis is proposed to mine existing human injury and response data from other sources, including military volunteer testing, automotive Crash Injury Research Engineering Network (CIREN), and IndyCar impact and injury data. These data sources can allow a better extrapolation of the ATD responses to off-nominal conditions above the nominal range that can safely be tested. These elements will be used to develop injury risk functions for each of the injury metrics measured from the ATD. These risk functions would serve as the basis for the NASA standards. Finally, we propose defining standard test methodology for evaluating future spacecraft designs against the IARVs, including developing a star-rating system to allow crew safety comparisons between vehicles.

Somers, Jeffrey T.↗
NASA NTRS2018

Recommendations Emerging from an Analysis of NASA's Deep Space Communications Capacity

During 2016-2017, NASA’s Space Communications and Navigation (SCaN) Office chartered a study of Deep Space Network (DSN) communications capacity relative to projected future-mission demand over the next 30 years. In this paper, we briefly describe the methodology used to analyze capacity vs. demand over such a broad timeframe, summarize key findings emerging from the analysis, and discuss the associated recommendations. Performing the analysis entailed: identifying key factors shaping the anticipated future mission set, identifying several alternative future mission set scenarios consistent with these factors, and then analyzing each mission set scenario in terms of required antenna capacity, downlink and uplink capabilities, and spectrum as a function of time. On the basis of these aggregate requirements, DSN loading simulations were then conducted that examined how well each of the postulated mission sets could load up onto the the DSN’s “in-plan” architecture. To the extent that capacity shortfalls emerged during these baseline simulations, architectural solutions to the shortfalls were then postulated and tested via additional simulations. In general, the trend analyses and baseline loading simulations indicated a significant progression in challenges over the next three decades. In the current decade, the DSN appeared to be operating very close to capacity. The first human exploration mission and its secondary payload launch opportunities for cubesats traveling beyond GEO contributed to this loading. As a consequence, the main challenge appeared to be managing peak assetcontention periods. In the next decade, the DSN continued to operate close to capacity but also began transitioning to more frequent human mission support. Upgrading for, and operating, a human-rated system while continuing to meet robotic mission customer requirements emerged as the key challenge. In the 2030’s and beyond, simulations suggested a need for fundamentally new capability and capacity. The high data rates and long link distances characteristic of human Mars exploration drove requirements far beyond what is currently “in plan.” The key challenge then became determining the most cost-effective combination of RF and optical assets for communicating with the postulated human Mars assets while still providing for the needs of all the other missions across the solar system. Various link budget, visibility, and loading analyses ultimately suggested that the human Mars exploration demands of the 2030’s could best be addressed with two cross-linked RF-optical areostationary relays (or an areostationary relay and deep space habitat) providing a dual “trunk link” to an array of 2-to-3 additional 34m beam waveguide antennas and an ~8.5m optical antenna at each DSN Complex. The dual “trunk link” would enable the same amount of total data return to Earth as a single trunk link at twice the data rate, but with only half the required array size on the ground, assuming use of Multiple Spacecraft Per Antenna (MSPA) techniques. MSPA techniques, including a Multiple Uplink Per Antenna (MUPA) technique currently under investigation, also showed promise for reducing asset contention in the decades prior to human Mars exploration.

Lee, Carlyn-Ann↗
NASA NTRS1991

Dissociative recombination of the ground state of N2(+)

Large-scale calculations of the dissociative recombination cross sections and rates for the v = 0 level of the N2(+) ground state are reported, and the important role played by vibrationally excited Rydberg states lying both below and above the v = 0 level of the ion is demonstrated. The large-scale electronic wave function calculations were done using triple zeta plus polarization nuclear-centered-valence Gaussian basis sets. The electronic widths were obtained using smaller wave functions, and the cross sections were calculated on the basis of the multichannel quantum defect theory. The DR rate is calculated at 1.6 x 10 to the -7th x (Te/300) to the -0.37 cu cm/sec for Te in the range of 100 to 1000 K, and is found to be in excellent agreement with prior microwave afterglow experiments but in disagreement with recent merged beam results. It is inferred that the dominant mechanism for DR imparts sufficient energy to the product atoms to allow for escape from the Martian atmosphere.

Guberman, Steven L.↗
NASA NTRS1998

Empirical Mode Decomposition and Hilbert Spectral Analysis

The difficult facing data analysis is the lack of method to handle nonlinear and nonstationary time series. Traditional Fourier-based analyses simply could not be applied here. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data. This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. The classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.

Huang, Norden E.↗
NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗
DOE OSTI2015

Extended hierarchy equation of motion for the spin-boson model

An extended hierarchy equation of motion (HEOM) is proposed and applied to study the dynamics of the spin-boson model. In this approach, a complete set of orthonormal functions are used to expand an arbitrary bath correlation function. As a result, a complete dynamic basis set is constructed by including the system reduced density matrix and auxiliary fields composed of these expansion functions, where the extended HEOM is derived for the time derivative of each element. The reliability of the extended HEOM is demonstrated by comparison with the stochastic Hamiltonian approach under room-temperature classical ohmic and sub-ohmic noises and the multilayer multiconfiguration time-dependent Hartree theory under zero-temperature quantum ohmic noise. Upon increasing the order in the hierarchical expansion, the result obtained from the extended HOEM systematically converges to the numerically exact answer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems

In this paper, we study the relation between the well-posedness of the inverse problem of the recovering the source in an abstract differential equation and the basis property of a certain class of function systems in a Hilbert space. As a consequence, based on the results concerning the well-posedness of inverse problems, we obtain the Riesz basis property and—under certain additional conditions—the Bari basis property of such systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Transverse momentum structure of proton within the basis light-front quantization framework

We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extensive treatments of QCD. Furthermore, we obtain a non-trivial x-dependence of the <(p ⊥ ) 2 > and some consistency with the Gaussian ansatz but only in the small <(p ⊥ ) 2 > region. Those features suggest our results may be a useful alternative in future experimental extractions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Periodic density functional theory study of structural and electronic properties of single-walled zinc oxide and carbon nanotubes

Periodic density functional theory calculations with the B3LYP hybrid functional and all-electron Gaussian basis set were performed to simulate the structural and electronic properties as well as the strain and formation energies of single-walled ZnO nanotubes (SWZnONTs) and Carbon nanotubes (SWCNTs) with different chiralities as functions of their diameters. For all SWZnONTs, the band gap, strain energy, and formation energy converge to ~4.5 eV, 0.0 eV/atom, and 0.40 eV/atom, respectively. This result suggests that the nanotubes are formed more easily from the surface than from the bulk. For SWCNTs, the strain energy is always positive, while the formation energy is negative for armchair and zigzag nanotubes, therefore suggesting that these types of nanotubes can be preferentially formed from the bulk. The electronic properties of SWCNTs depend on the chirality; all armchair nanotubes are metallic, while zigzag and chiral nanotubes can be metallic or semiconducting, depending on the n and m vectors. - Graphical abstract: DFT/B3LYP were performed to simulate the structural and electronic properties as well as the strain and formation energies of SWZnONTs and SWCNTs with different chiralities as functions of their diameters. - Highlights: • The energies of SWZnONTs converge for chirality with diameters up 20 Å. • SWCNTs electronic properties depend on the chirality. • The properties of SWZnONTs are very similar to those of monolayer surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale twodimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. In conclusion, employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Search for the Standard Model Higgs boson produced in association with a W Boson in the isolated-track charged-lepton channel using the Collider Detector at Fermilab

The Higgs boson is the only elementary particle predicted by the Standard Model (SM) that has not yet been observed experimentally. If it exists, it explains the spontaneous electroweak symmetry breaking and the origin of mass for gauge bosons and fermions. We test the validity of the SM by performing a search for the associated production of a Higgs boson and a W boson in the channel where the Higgs boson decays to a bottom-antibottom quark pair and the W boson decays to a charged lepton and a neutrino (the WH channel). We study a dataset of proton-antiproton collisions at a centre-of-mass energy √s = 1.96 TeV provided by the Tevatron accelerator, corresponding to an integrated luminosity of 5.7 fb -1 , and recorded using the Collider Detector at Fermilab (CDF).We select events consistent with the signature of exactly one charged lepton (electron or muon), missing transverse energy due to the undetected neutrino (MET) and two collimated streams of particles (jets), at least one of which is required to be identified as originating from a bottom quark. We improve the discrimination of Higgs signal from backgrounds through the use of an artificial neural network. Using a Bayesian statistical inference approach, we set for each hypothetical Higgs boson mass in the range 100-150 GeV/c 2 with 5 GeV/c 2 increments a 95% credibility level (CL) upper limit on the ratio between the Higgs production cross section times branching fraction and the SM prediction. Our main original contributions are the addition of a novel charged lepton reconstruction algorithm with looser requirements (ISOTRK) with respect the electron or muon tight criteria (TIGHT), as well as the introduction of a novel trigger-combination method that allows to maximize the event yield while avoiding trigger correlations and that is used for the ISOTRK category. The ISOTRK candidate is a high-transverse-momentum good-quality track isolated from other activity in the tracking system and not required to match a calorimeter cluster, as for a tight electron candidate, or an energy deposit in the muon detector, as for a tight muon candidate. The ISOTRK category recovers real charged leptons that otherwise would be lost in the non-instrumented regions of the detector. This allows the reconstruction of more W boson candidates, which in turn increases the number of reconstructed WH signal candidate events, and therefore improves the sensitivity of the WH search. For the TIGHT charged lepton categories, we employ charged-lepton-dedicated triggers to improve the rate of WH signal acceptance during data taking. Since there is no ISOTRK-dedicated trigger at CDF, for the ISOTRK charged lepton category we employ three MET-plus-jets-based triggers. For each trigger we first identify the jet selection where the trigger efficiency is flat with respect to jet information (transverse energy and direction of motion in the transverse plane for the two jets in the event) and then we parametrize the trigger efficiency as a function of trigger MET. On an event-by-event basis, for each trigger we compute a trigger efficiency as a function of trigger parametrization, trigger MET, jet information, trigger prescale and information about whether the trigger is defined or not. For the ISOTRK category we combine the three triggers using a novel method, which allows the combination of any number of triggers in order to maximize the event yield while avoiding trigger correlations. On an event-by-event basis, only the trigger with the largest efficiency is used. By avoiding a logical 'OR' between triggers, the loss in the yield of events accepted by the trigger combination is compensated by a smaller and easier-to-compute corresponding systematic uncertainty. The addition of the ISOTRK charged lepton category to the TIGHT category produces an increase of 33% in the WH signal yield and a decrease of 15.5% to 19.0% in the median expected 95% CL cross-section upper limits across the entire studied Higgs mass interval. The improvement in analysis sensitivity is smaller than the improvement in signal yield because the ISOTRK category has a smaller signal over background ratio than the TIGHT category, due to the looser ISOTRK reconstruction criteria. The observed (median expected) 95% CL SM Higgs upper limits on cross section times branching ratio vary between 2.39 x SM (2.73 x SM) for a Higgs mass of 100 GeV/c 2 to 31.1 x SM (31.2 x SM) for a Higgs mass of 150 GeV/c 2 , while the value for a 115 GeV/c 2 Higgs boson is that of 5.08 x SM (3.79 x SM). The novel trigger combination method is already in use by several CDF analyses. It is applicable to any analysis that uses triggers based on MET and jets, such as supersymmetry searches at the ATLAS and CMS experiments at the Large Hadron Collider. In its most general form, the method can be used by any analysis that combines any number of different triggers.

43 PARTICLE ACCELERATORS↗
DOE OSTI2019

Molecular basis of synaptic specificity by immunoglobulin superfamily receptors in Drosophila

In stereotyped neuronal networks, synaptic connectivity is dictated by cell surface proteins, which assign unique identities to neurons, and physically mediate axon guidance and synapse targeting. We recently identified two groups of immunoglobulin superfamily proteins in Drosophila, Dprs and DIPs, as strong candidates for synapse targeting functions. Here, we uncover the molecular basis of specificity in Dpr–DIP mediated cellular adhesions and neuronal connectivity. First, we present five crystal structures of Dpr–DIP and DIP–DIP complexes, highlighting the evolutionary and structural origins of diversification in Dpr and DIP proteins and their interactions. We further show that structures can be used to rationally engineer receptors with novel specificities or modified affinities, which can be used to study specific circuits that require Dpr–DIP interactions to help establish connectivity. We investigate one pair, engineered Dpr10 and DIP-α, for function in the neuromuscular circuit in flies, and reveal roles for homophilic and heterophilic binding in wiring.

Life Sciences & Biomedicine - Other Topics↗
DOE OSTI2012

Predictive Capability for Strongly Correlated Systems

Diffusion Monte Carlo methods can give highly accurate results for correlated systems, provided that well optimized trial wave functions with accurate nodal surfaces are employed. The Cornell team developed powerful methods for optimizing all the parameters within a multi-determinant Slater-Jastrow form of the wave function. These include the Jastrow parameters within a flexible electron-electron-nucleus form of the Jastrow function, the parameters multiplying the configuration state functions, the orbital parameters and the basis exponents. The method optimizes a linear combination of the energy and the variance of the local energy. The optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. It is highly robust, has become the method of choice for correlated wave function optimization and has been adopted by other QMC groups. This optimization method was used on the first-row atoms and homonuclear diatomic molecules, demonstrating that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems. In addition the complete ground-state potential energy curve of the C 2 molecule up to the dissociation limit was obtained, and, size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations were studied. The method was used with a eight-electrons-in-eight-orbitals complete active space CAS(8,8) wave function to study the relative energies of the monocyclic and bicyclic forms of m-benzyne. The DMC calculations show that the monocyclic structure is lower in energy than the bicyclic structure by 1.92 kcal/ mole, which is in excellent agreement with the best coupled cluster results (CCSD(T)) and in disagreement with the CCSD results. QMC methods have for the most part been used only for ground states of a given symmetry. We developed a method for calculating low-lying excited states as well and tested it on the ground and lowest three adiabatic excited states of methylene with progressively larger JastrowSlater multideterminant complete active space CAS wave functions. The highest of these states has the same symmetry, 1 A 1 , as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment. In contrast, single-determinant wave functions do not yield accurate DMC energies, indicating that it is important to include in the wave function Slater determinants that describe static strong correlation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Triplet Tuning: A Novel Family of Non-Empirical Exchange–Correlation Functionals

In the framework of density functional theory (DFT), the lowest triplet excited state (T1) can be evaluated using multiple formulations, the most straightforward of which are unrestricted density functional theory (UDFT) and time-dependent density functional theory (TDDFT). Assuming the exact exchange-correlation (XC) functional is applied, UDFT and TDDFT provide identical energies for T1 ( ET), which is also a constraint that we require our XC functionals to obey. However, this condition is not satisfied by most of the popular XC functionals, leading to inaccurate predictions of low-lying, spectroscopically and photochemically important excited states, such as T1 and the lowest singlet excited state (S1). Inspired by the optimal tuning strategy for frontier orbital energies [T. Stein, L. Kronik, and R. Baer, J. Am. Chem. Soc. 2009, 131, 2818], we proposed a novel and nonempirical prescription of constructing an XC functional in which the agreement between UDFT and TDDFT in ET is strictly enforced. Referred to as "triplet tuning", our procedure allows us to formulate the XC functional on a case-by-case basis, using the molecular structure as the exclusive input, without fitting to any experimental data. The first triplet tuned XC functional, TT-ωPBEh, is formulated as a long-range-corrected (LRC) hybrid of Perdew-Burke-Ernzerhof (PBE) and Hartree-Fock (HF) functionals [M. A. Rohrdanz, K. M. Martins, and J. M. Herbert, J. Chem. Phys. 2009, 130, 054112] and tested on four sets of large organic molecules. Compared to existing functionals, TT-ωPBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to ET, the optical band gap ( ES), the singlet-triplet gap (Δ EST), and the vertical ionization potential ( I⊥), as it adjusts the effective electron-hole interactions to arrive at the correct excitation energies. This promising triplet tuning scheme can be applied to a broad range of systems that were notorious in DFT for being extremely challenging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗