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DOE OSTI2015

Accuracy of Lagrange-sinc functions as a basis set for electronic structure calculations of atoms and molecules

We developed a self-consistent field program based on Kohn-Sham density functional theory using Lagrange-sinc functions as a basis set and examined its numerical accuracy for atoms and molecules through comparison with the results of Gaussian basis sets. The result of the Kohn-Sham inversion formula from the Lagrange-sinc basis set manifests that the pseudopotential method is essential for cost-effective calculations. The Lagrange-sinc basis set shows faster convergence of the kinetic and correlation energies of benzene as its size increases than the finite difference method does, though both share the same uniform grid. Using a scaling factor smaller than or equal to 0.226 bohr and pseudopotentials with nonlinear core correction, its accuracy for the atomization energies of the G2-1 set is comparable to all-electron complete basis set limits (mean absolute deviation ≤1 kcal/mol). The same basis set also shows small mean absolute deviations in the ionization energies, electron affinities, and static polarizabilities of atoms in the G2-1 set. In particular, the Lagrange-sinc basis set shows high accuracy with rapid convergence in describing density or orbital changes by an external electric field. Moreover, the Lagrange-sinc basis set can readily improve its accuracy toward a complete basis set limit by simply decreasing the scaling factor regardless of systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets

We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller–Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn–Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn–Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.

Morales, Miguel A. (ORCID:0000000263893067)↗

NASA NTRS1990

Multiple strike slip faults sets: A case study from the Dead Sea transform

In many strike slip tectonic settings, large rotations of crust blocks about vertical axes have been inferred from paleomagnetic data. These blocks are bounded by sets of parallel faults which presumably accommodate the relative motion between the blocks as regional deformation progress. A mechanical model by Nur et al., (1986) suggests that rotations greater than phi sub c equals 25 to 45 degrees must be accommodated by more than one set of faults, with angle phi sub c between their direction; consequently the sum of the angles between sets must be roughly equal to the total tectonic material rotation. To test this model, the authors investigated the fault geometry and field relation of fault sets in the Mt. Hermon area in northern Israel, where paleomagnetic declination implies data 69 degrees plus or minus 13 degrees counter-clockwise block rotation. The statistical and field relation analysis of over 315 faults shows that the faulting is predominantly right lateral strike slip consisting of three distinct sets. The oldest set strikes 253 degrees, the second oldest set strikes 293 degrees and the youngest strikes 339 degrees. This last direction is consistent also with the current north-south direction of the maximum principle stress axis. The angle phi sub c between the first and second sets is 39 degrees and between the second and third sets 46 degrees, in good agreement with the phi sub c angle predicted from mechanical considerations. The sum of the two angles is 85 degrees, in good agreement with the 69 degrees plus or minus 13 degrees CCW paleomagnetically derived rotation. The results suggest specifically that the sequential development of multiple intersecting fault sets is responsible for the faulting in the Mt. Hermon area; and generally that the model of block rotation with multiple faults provides very good simple rules for analyzing very complex fault patterns.

Ron, Hagai↗

NASA NTRS1997

Tests of a Semi-Analytical Case 1 and Gelbstoff Case 2 SeaWiFS Algorithm with a Global Data Set

A semi-analytical algorithm was tested with a total of 733 points of either unpackaged or packaged-pigment data, with corresponding algorithm parameters for each data type. The 'unpackaged' type consisted of data sets that were generally consistent with the Case 1 CZCS algorithm and other well calibrated data sets. The 'packaged' type consisted of data sets apparently containing somewhat more packaged pigments, requiring modification of the absorption parameters of the model consistent with the CalCOFI study area. This resulted in two equally divided data sets. A more thorough scrutiny of these and other data sets using a semianalytical model requires improved knowledge of the phytoplankton and gelbstoff of the specific environment studied. Since the semi-analytical algorithm is dependent upon 4 spectral channels including the 412 nm channel, while most other algorithms are not, a means of testing data sets for consistency was sought. A numerical filter was developed to classify data sets into the above classes. The filter uses reflectance ratios, which can be determined from space. The sensitivity of such numerical filters to measurement resulting from atmospheric correction and sensor noise errors requires further study. The semi-analytical algorithm performed superbly on each of the data sets after classification, resulting in RMS1 errors of 0.107 and 0.121, respectively, for the unpackaged and packaged data-set classes, with little bias and slopes near 1.0. In combination, the RMS1 performance was 0.114. While these numbers appear rather sterling, one must bear in mind what mis-classification does to the results. Using an average or compromise parameterization on the modified global data set yielded an RMS1 error of 0.171, while using the unpackaged parameterization on the global evaluation data set yielded an RMS1 error of 0.284. So, without classification, the algorithm performs better globally using the average parameters than it does using the unpackaged parameters. Finally, the effects of even more extreme pigment packaging must be examined in order to improve algorithm performance at high latitudes. Note, however, that the North Sea and Mississippi River plume studies contributed data to the packaged and unpackaged classess, respectively, with little effect on algorithm performance. This suggests that gelbstoff-rich Case 2 waters do not seriously degrade performance of the semi-analytical algorithm.

Carder, Kendall L.↗

NASA NTRS1999

Time-dependent influence of sensorimotor set on automatic responses in perturbed stance

These experiments tested the hypothesis that the ability to change sensorimotor set quickly for automatic responses depends on the time interval between successive surface perturbations. Sensorimotor set refers to the influence of prior experience or context on the state of the sensorimotor system. Sensorimotor set for postural responses was influenced by first giving subjects a block of identical backward translations of the support surface, causing forward sway and automatic gastrocnemius responses. The ability to change set quickly was inferred by measuring the suppression of the stretched antagonist gastrocnemius responses to toes-up rotations causing backward sway, following the translations. Responses were examined under short (10-14 s) and long (19-24 s) inter-trial intervals in young healthy subjects. The results showed that subjects in the long-interval group changed set immediately by suppressing gastrocnemius to 51% of translation responses within the first rotation and continued to suppress them over succeeding rotations. In contrast, subjects in the short-interval group did not change set immediately, but required two or more rotations to suppress gastrocnemius responses. By the last rotation, the short-interval group suppressed gastrocnemius responses to 33%, similar to the long-interval group of 29%. Associated surface plantarflexor torque resulting from these responses showed similar results. When rotation and translation perturbations alternated, however, the short-interval group was not able to suppress gastrocnemius responses to rotations as much as the long-interval group, although they did suppress more than in the first rotation trial after a series of translations. Set for automatic responses appears to linger, from one trial to the next. Specifically, sensorimotor set is more difficult to change when surface perturbations are given in close succession, making it appear as if set has become progressively stronger. A strong set does not mean that responses become larger over consecutive trials. Rather, it is inferred by the extent of difficulty in changing a response when it is appropriate to do so. These results suggest that the ability to change sensorimotor set quickly is sensitive to whether the change is required after a long or a short series of a prior different response, which in turn depends on the time interval between successive trials. Different rate of gastrocnemius suppression to toes-up rotation of the support surface have been reported in previous studies. This may be partially explained by different inter-trial time intervals demonstrated in this study.

NASA Discipline Neuroscience↗

DOE OSTI2013

The role of Health Impact Assessment in the setting of air quality standards: An Australian perspective

The approaches used for setting or reviewing air quality standards vary from country to country. The purpose of this research was to consider the potential to improve decision-making through integration of HIA into the processes to review and set air quality standards used in Australia. To assess the value of HIA in this policy process, its strengths and weaknesses were evaluated aligned with review of international processes for setting air quality standards. Air quality standard setting programmes elsewhere have either used HIA or have amalgamated and incorporated factors normally found within HIA frameworks. They clearly demonstrate the value of a formalised HIA process for setting air quality standards in Australia. The following elements should be taken into consideration when using HIA in standard setting. (a) The adequacy of a mainly technical approach in current standard setting procedures to consider social determinants of health. (b) The importance of risk assessment criteria and information within the HIA process. The assessment of risk should consider equity, the distribution of variations in air quality in different locations and the potential impacts on health. (c) The uncertainties in extrapolating evidence from one population to another or to subpopulations, especially the more vulnerable, due to differing environmental factors and population variables. (d) The significance of communication with all potential stakeholders on issues associated with the management of air quality. In Australia there is also an opportunity for HIA to be used in conjunction with the NEPM to develop local air quality standard measures. The outcomes of this research indicated that the use of HIA for air quality standard setting at the national and local levels would prove advantageous. -- Highlights: • Health Impact Assessment framework has been applied to a policy development process. • HIA process was evaluated for application in air quality standard setting. • Advantages of HIA in the air quality standard setting process are demonstrated.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Improving the Accuracy of Nearest-Neighbor Classification Using Principled Construction and Stochastic Sampling of Training-Set Centroids

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased using coarse-graining (replacing groups of images by their centroids) and stochastic sampling (using distinct sets of centroids in combination). We use the MNIST and Fashion-MNIST data sets to show that a principled coarse-graining algorithm can convert training images into fewer image centroids without loss of accuracy of classification of test-set images by nearest-neighbor classification. Distinct batches of centroids can be used in combination as a means of stochastically sampling configuration space, and can classify test-set data more accurately than can the unaltered training set. On the MNIST and Fashion-MNIST data sets this approach converts nearest-neighbor classification from a mid-ranking- to an upper-ranking member of the set of classical machine-learning techniques.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Global temperature response to the major volcanic eruptions in multiple reanalysis data sets

Abstract. The global temperature responses to the eruptions of Mount Agung in 1963, El Chichón in 1982, and Mount Pinatubo in 1991 are investigated using nine currently available reanalysis data sets (JRA-55, MERRA, ERA-Interim, NCEP-CFSR, JRA-25, ERA-40, NCEP-1, NCEP-2, and 20CR). Multiple linear regression is applied to the zonal and monthly mean time series of temperature for two periods, 1979–2009 (for eight reanalysis data sets) and 1958–2001 (for four reanalysis data sets), by considering explanatory factors of seasonal harmonics, linear trends, Quasi-Biennial Oscillation, solar cycle, and El Niño Southern Oscillation. The residuals are used to define the volcanic signals for the three eruptions separately, and common and different responses among the older and newer reanalysis data sets are highlighted for each eruption. In response to the Mount Pinatubo eruption, most reanalysis data sets show strong warming signals (up to 2–3 K for 1-year average) in the tropical lower stratosphere and weak cooling signals (down to -1 K) in the subtropical upper troposphere. For the El Chichón eruption, warming signals in the tropical lower stratosphere are somewhat smaller than those for the Mount Pinatubo eruption. The response to the Mount Agung eruption is asymmetric about the equator with strong warming in the Southern Hemisphere midlatitude upper troposphere to lower stratosphere. Comparison of the results from several different reanalysis data sets confirms the atmospheric temperature response to these major eruptions qualitatively, but also shows quantitative differences even among the most recent reanalysis data sets. The consistencies and differences among different reanalysis data sets provide a measure of the confidence and uncertainty in our current understanding of the volcanic response. The results of this intercomparison study may be useful for validation of climate model responses to volcanic forcing and for assessing proposed geoengineering by stratospheric aerosol injection, as well as to link studies using only a single reanalysis data set to other studies using a different reanalysis data set.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

Weight, center of gravity and modal test report for NTF fan blade set no. 3

A complete set of fan blades for the National Transonic Facility (NTF) at the NASA Langley Research Center was recently fabricated by Dynamic Engineering Inc. (DEI). These blades were the third complete set of blades fabricated by the NTF. The first set of blades was fabricated by NASA and installed in the tunnel in December 1981. This original set was destroyed in a mishap in January 1989. The second set of blades is currently in use in the NTF. The third set of blades recently fabricated by DEI is a spare set. In order to ensure that the blades met the requirements, DEI performed a series of tests on each of the completed blades. In addition, a model survey was conducted on each blade to define the dynamic characteristics. Discussed here are the blade tests conducted by DEI and the test results. The test set-ups and procedures are discussed in detail. The results obtained for each of the 27 blades are documented and comparisons are made between this set of blades and similar data for two previous sets of NTF fan blades.

Friedman, Inger P.↗

NASA NTRS1997

Intelligent System Development Using a Rough Sets Methodology

The purpose of this research was to examine the potential of the rough sets technique for developing intelligent models of complex systems from limited information. Rough sets a simple but promising technology to extract easily understood rules from data. The rough set methodology has been shown to perform well when used with a large set of exemplars, but its performance with sparse data sets is less certain. The difficulty is that rules will be developed based on just a few examples, each of which might have a large amount of noise associated with them. The question then becomes, what is the probability of a useful rule being developed from such limited information? One nice feature of rough sets is that in unusual situations, the technique can give an answer of 'I don't know'. That is, if a case arises that is different from the cases the rough set rules were developed on, the methodology can recognize this and alert human operators of it. It can also be trained to do this when the desired action is unknown because conflicting examples apply to the same set of inputs. This summer's project was to look at combining rough set theory with statistical theory to develop confidence limits in rules developed by rough sets. Often it is important not to make a certain type of mistake (e.g., false positives or false negatives), so the rules must be biased toward preventing a catastrophic error, rather than giving the most likely course of action. A method to determine the best course of action in the light of such constraints was examined. The resulting technique was tested with files containing electrical power line 'signatures' from the space shuttle and with decompression sickness data.

Anderson, Gray T.↗

NASA NTRS2010

Algorithms for Learning Preferences for Sets of Objects

A method is being developed that provides for an artificial-intelligence system to learn a user's preferences for sets of objects and to thereafter automatically select subsets of objects according to those preferences. The method was originally intended to enable automated selection, from among large sets of images acquired by instruments aboard spacecraft, of image subsets considered to be scientifically valuable enough to justify use of limited communication resources for transmission to Earth. The method is also applicable to other sets of objects: examples of sets of objects considered in the development of the method include food menus, radio-station music playlists, and assortments of colored blocks for creating mosaics. The method does not require the user to perform the often-difficult task of quantitatively specifying preferences; instead, the user provides examples of preferred sets of objects. This method goes beyond related prior artificial-intelligence methods for learning which individual items are preferred by the user: this method supports a concept of setbased preferences, which include not only preferences for individual items but also preferences regarding types and degrees of diversity of items in a set. Consideration of diversity in this method involves recognition that members of a set may interact with each other in the sense that when considered together, they may be regarded as being complementary, redundant, or incompatible to various degrees. The effects of such interactions are loosely summarized in the term portfolio effect. The learning method relies on a preference representation language, denoted DD-PREF, to express set-based preferences. In DD-PREF, a preference is represented by a tuple that includes quality (depth) functions to estimate how desired a specific value is, weights for each feature preference, the desired diversity of feature values, and the relative importance of diversity versus depth. The system applies statistical concepts to estimate quantitative measures of the user s preferences from training examples (preferred subsets) specified by the user. Once preferences have been learned, the system uses those preferences to select preferred subsets from new sets. The method was found to be viable when tested in computational experiments on menus, music playlists, and rover images. Contemplated future development efforts include further tests on more diverse sets and development of a sub-method for (a) estimating the parameter that represents the relative importance of diversity versus depth, and (b) incorporating background knowledge about the nature of quality functions, which are special functions that specify depth preferences for features.

Wagstaff, Kiri L.↗

NASA NTRS2013

A Validated Set of MIDAS V5 Task Network Model Scenarios to Evaluate Nextgen Closely Spaced Parallel Operations Concepts

The Closely Spaced Parallel Operations (CSPO) scenario is a complex, human performance model scenario that tested alternate operator roles and responsibilities to a series of off-nominal operations on approach and landing (see Gore, Hooey, Mahlstedt, Foyle, 2013). The model links together the procedures, equipment, crewstation, and external environment to produce predictions of operator performance in response to Next Generation system designs, like those expected in the National Airspaces NextGen concepts. The task analysis that is contained in the present report comes from the task analysis window in the MIDAS software. These tasks link definitions and states for equipment components, environmental features as well as operational contexts. The current task analysis culminated in 3300 tasks that included over 1000 Subject Matter Expert (SME)-vetted, re-usable procedural sets for three critical phases of flight; the Descent, Approach, and Land procedural sets (see Gore et al., 2011 for a description of the development of the tasks included in the model; Gore, Hooey, Mahlstedt, Foyle, 2013 for a description of the model, and its results; Hooey, Gore, Mahlstedt, Foyle, 2013 for a description of the guidelines that were generated from the models results; Gore, Hooey, Foyle, 2012 for a description of the models implementation and its settings). The rollout, after landing checks, taxi to gate and arrive at gate illustrated in Figure 1 were not used in the approach and divert scenarios exercised. The other networks in Figure 1 set up appropriate context settings for the flight deck.The current report presents the models task decomposition from the tophighest level and decomposes it to finer-grained levels. The first task that is completed by the model is to set all of the initial settings for the scenario runs included in the model (network 75 in Figure 1). This initialization process also resets the CAD graphic files contained with MIDAS, as well as the embedded operator models that comprise MIDAS. Following the initial settings, the model progresses to begin the first tasks required of the two flight deck operators, the Captain (CA) and the First Officer (FO). The task sets will initialize operator specific settings prior to loading all of the alerts, probes, and other events that occur in the scenario. As a note, the CA and FO were terms used in developing this model but the CA can also be thought of as the Pilot Flying (PF), while the FO can be considered the Pilot-Not-Flying (PNF)or Pilot Monitoring (PM). As such, the document refers to the operators as PFCA and PNFFO respectively.

task network model↗

DOE OSTI2023

Adaptive basis sets for practical quantum computing

Electronic structure calculations on small systems such as H 2 , H 2 O, LiH, and BeH 2 with chemical accuracy are still a challenge for the current generation of noisy intermediate-scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allows one to keep the number of qubits employed in the calculations at a minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provides an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H 2 molecule, in which exponents and contraction coefficients depend on the H—H distance, and apply it to the generation of H 2 potential energy surface on IBM-Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double-zeta basis sets, thus allowing one to perform double-zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

New Basis Set Exchange: An Open, Up-to-date Resource for the Molecular Sciences Community

In computational quantum chemistry, the basis set is a fundamental input to many types of simulations, and the choice of basis set can have dramatic effects on both the accuracy and performance of the simulation. Due to this fundamental nature, basis sets have been developed starting at the beginning of the computational chemistry field, and extending to the present day, with new basis sets taking into account new theories and methods now accessible due to increases in computing power. Practically, computations are most comparable when they use the same basis set. However, early distribution channels often led to differing incorporation of basis sets indifferent computational chemistry codes, harming reproducibility and introducing errors in calculations that can go unnoticed. Such errors can be due to many causes, including transcription errors, neglecting publication of the full precision of numerical values, updated values not being incorporated in a timely manner, or development of an ‘improved’ version by different developers that retains the same name as the original basis set. Therefore, there was a need to store basis sets in a central location and make them easily and freely accessible by any researcher. The Basis Set Exchange (BSE) is widely considered by the field to be such a resource.

basis set, ab initio, web application, web interfa↗

DOE OSTI2018

A remarkable case of basis set dependence: the false convergence patterns of the methyl anion

Here, the gas phase methyl anion, CH 3 ¯, has been difficult to study experimentally, and the extreme basis set dependence of its molecular properties has presented a comparable challenge to theoreticians. Reliable predictions for the electronic structure of CH 3 ¯ require the use of basis sets capable of describing both the diffuse and valence characteristics of the system. The present study examines the basis set dependence of the equilibrium geometry and harmonic vibrational frequencies of CH 3 ¯. Both Hartree–Fock and CCSD(T) levels of theories are used with cc-pVXZ (, T, Q, 5, 6) basis sets with up to triple augmentation to describe the diffuse nature of the electron distribution. We find that non-augmented basis sets systematically yield vibrational frequencies that are too high for the umbrella mode and too low for the C–H symmetric and antisymmetric stretch even when extrapolated to the complete basis set limit, displaying false convergence patterns. The inclusion of one set of augmented functions significantly improves the convergence of these properties, but again yields false convergence patterns. Only with the doubly augmented basis set do we approach the basis set limit for the CH 3 ¯ vibrational frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Correlation consistent basis sets for actinides. II. The atoms Ac and Np–Lr

New correlation consistent basis sets optimized using the all-electron third-order Douglas-Kroll-Hess (DKH3) scalar relativistic Hamiltonian are reported for the actinide elements Ac and Np through Lr. These complete the series of sets reported previously for Th–U [K. A. Peterson, J. Chem. Phys. 142, 074105 (2015); M. Vasiliu et al., J. Phys. Chem. A 119, 11422 (2015)]. The new sets range in size from double- to quadruple-zeta and encompass both those optimized for valence (6s6p5f7s6d) and outer-core electron correlations (valence + 5s5p5d). The final sets have been contracted for both the DKH3 and eXact 2-component (X2C) Hamiltonians, yielding cc-pVnZ-DK3/cc-pVnZ-X2C sets for valence correlation and cc-pwCVnZ-DK3/cc-pwCVnZ-X2C sets for outer-core correlation (n = D, T, Q in each case). In order to test the effectiveness of the new basis sets, both atomic and molecular benchmark calculations have been carried out. In the first case, the first three atomic ionization potentials (IPs) of all the actinide elements Ac–Lr have been calculated using the Feller-Peterson-Dixon (FPD) composite approach, primarily with the multireference configuration interaction (MRCI) method. Excellent convergence towards the respective complete basis set (CBS) limits is achieved with the new sets, leading to good agreement with experiment, where these exist, after accurately accounting for spin-orbit effects using the 4-component Dirac-Hartree-Fock method. For a molecular test, the IP and atomization energy (AE) of PuO 2 have been calculated also using the FPD method but using a coupled cluster approach with spin-orbit coupling accounted for using the 4-component MRCI. The present calculations yield an IP 0 for PuO 2 of 159.8 kcal/mol, which is in excellent agreement with the experimental electron transfer bracketing value of 162 ± 3 kcal/mol. Likewise, the calculated 0 K AE of 305.6 kcal/mol is in very good agreement with the currently accepted experimental value of 303.1 ± 5 kcal/mol. The ground state of PuO 2 is predicted to be the 5 Σ$+\atop{0g}$ state.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2017

Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

WE-G-207-02: Full Sequential Projection Onto Convex Sets (FS-POCS) for X-Ray CT Reconstruction

Purpose: To develop an iterative reconstruction method for X-ray CT, in which the reconstruction can quickly converge to the desired solution with much reduced projection views. Methods: The reconstruction is formulated as a convex feasibility problem, i.e. the solution is an intersection of three convex sets: 1) data fidelity (DF) set – the L2 norm of the difference of observed projections and those from the reconstructed image is no greater than an error bound; 2) non-negativity of image voxels (NN) set; and 3) piecewise constant (PC) set - the total variation (TV) of the reconstructed image is no greater than an upper bound. The solution can be found by applying projection onto convex sets (POCS) sequentially for these three convex sets. Specifically, the algebraic reconstruction technique and setting negative voxels as zero are used for projection onto the DF and NN sets, respectively, while the projection onto the PC set is achieved by solving a standard Rudin, Osher, and Fatemi (ROF) model. The proposed method is named as full sequential POCS (FS-POCS), which is tested using the Shepp-Logan phantom and the Catphan600 phantom and compared with two similar algorithms, TV-POCS and CP-TV. Results: Using the Shepp-Logan phantom, the root mean square error (RMSE) of reconstructed images changing along with the number of iterations is used as the convergence measurement. In general, FS- POCS converges faster than TV-POCS and CP-TV, especially with fewer projection views. FS-POCS can also achieve accurate reconstruction of cone-beam CT of the Catphan600 phantom using only 54 views, comparable to that of FDK using 364 views. Conclusion: We developed an efficient iterative reconstruction for sparse-view CT using full sequential POCS. The simulation and physical phantom data demonstrated the computational efficiency and effectiveness of FS-POCS.

60 APPLIED LIFE SCIENCES↗