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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Data-driven approach to parameterize SCAN + U for an accurate description of 3 d transition metal oxide thermochemistry

Semilocal density-functional theory (DFT) methods exhibit significant errors for the phase diagrams of transition-metal oxides that are caused by an incorrect description of molecular oxygen and the large self-interaction error in materials with strongly localized electronic orbitals. Empirical and semiempirical corrections based on the DFT + U method can reduce these errors, but the parameterization and validation of the correction terms remains an on-going challenge. Here we develop a systematic methodology to determine the parameters and to statistically assess the results by considering interlinked thermochemical data across a set of transition metal compounds. We consider three interconnected levels of correction terms: (1) a constant oxygen binding correction, (2) Hubbard-U correction, and (3) DFT/DFT + U compatibility correction. The parameterization is expressed as a unified optimization problem. We demonstrate this approach for 3d transition metal oxides, considering a target set of binary and ternary oxides. With a total of 37 measured formation enthalpies taken from the literature, the dataset is augmented by the reaction energies of 1710 unique reactions that were derived from the formation energies by systematic enumeration. To ensure a balanced dataset across the available data, the reactions were grouped by their similarity using clustering and suitably weighted. The parameterization is validated using leave-one-out cross validation (CV), a standard technique for the validation of statistical models. We apply the methodology to the strongly constrained and appropriately normed (SCAN) density functional. Based on the CV score, the error of binary (ternary) oxide formation energies is reduced by 40% (75%) to 0.10 (0.03) eV/atom. A simplified correction scheme that does not involve SCAN/SCAN + U compatibility terms still achieves an error reduction of 30% (25%). The method and tools demonstrated here can be applied to other classes of materials or to parameterize the corrections to optimize DFT + U performance for other target physical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. Here, we select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

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

On the applicability of one- and many-electron quantum chemistry models for hydrated electron clusters

We evaluate the applicability of a hierarchy of quantum models in characterizing the binding energy of excess electrons to water clusters. In particular, we calculate the vertical detachment energy of an excess electron from water cluster anions with methods that include one-electron pseudopotential calculations, density functional theory (DFT) based calculations, and ab initio quantum chemistry using MP2 and eom-EA-CCSD levels of theory. The examined clusters range from the smallest cluster size (n = 2) up to nearly nanosize clusters with n = 1000 molecules. The examined cluster configurations are extracted from mixed quantum-classical molecular dynamics trajectories of cluster anions with n = 1000 water molecules using two different one-electron pseudopotenial models. We find that while MP2 calculations with large diffuse basis set provide a reasonable description for the hydrated electron system, DFT methods should be used with precaution and only after careful benchmarking. Strictly tested one-electron psudopotentials can still be considered as reasonable alternatives to DFT methods, especially in large systems. The results of quantum chemistry calculations performed on configurations, that represent possible excess electron binding motifs in the clusters, appear to be consistent with the results using a cavity structure preferring one-electron pseudopotential for the hydrated electron, while they are in sharp disagreement with the structural predictions of a non-cavity model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Hydrogen Bond Benchmark: Focal‐Point Analysis and Assessment of DFT Functionals

We performed a hierarchical, convergent ab initio benchmark study and systematically analyzed the performance of density functional approximations for describing hydrogen bonds in small neutral, cationic, and anionic complexes, as well as in larger systems involving amide, urea, deltamide, and squaramide moieties. Focal point analyses (FPA), extrapolating to the ab initio limit, were carried out using correlated wave function methods up to CCSDT(Q) for the small complexes and CCSD(T) for the larger systems, together with correlation-consistent Gaussian basis sets up to the complete basis set limit. Optimized geometries and vibrational frequencies were obtained at the CCSD(T) level. The resulting FPA hydrogen-bond energies converge within a few tenths of a kcal mol −1 . These reference data were used to evaluate 60 density functionals (including 12 dispersion-corrected), spanning the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. Overall, the meta-hybrid M06-2X provides the best performance for both hydrogen bond energies and geometries, while the dispersion-corrected GGAs BLYP-D3(BJ) and BLYP-D4 also yield accurate hydrogen-bond data and can serve as cost-effective options for studying large and complex systems.

coupled cluster theory↗
DOE OSTI2026

Improving coastal water level estimation by merging nadir-only satellite altimetry data into a hydrodynamic model

Providing robust real time flood warnings is of paramount importance to coastal communities. Although state-of-the-art hydrodynamic models are capable of robustly predicting Coastal Water Levels (CWL), unresolved drivers affecting level fluctuations are often not represented by the model governing equations. This work evaluates a novel method to improve the performance of the ADvanced CIRCulation (ADCIRC) hydrodynamic model by assimilating observations from four nadir-only satellite altimetry missions against a set of National Oceanic and Atmospheric Administration (NOAA) gauge stations located across the entire U.S. East Coast. Two different types of simulations were performed – Open Loop (OL) and Data Assimilation (DA). Five different simulations were performed where four different satellite altimetry observations were assimilated individually and combined with two different scenarios – with and without considering the data quality flags. Results indicate that, despite their limited spatial coverage, merging nadir-only observations into ADCIRC from the newly launched Surface Water and Ocean Topography (SWOT)’s nadir altimeter can improve the model performance at 76% of the gauge locations, whereas Sentinel-6 improves 73% of the total locations, Jason-3 74%, and SARAL 21%. Furthermore, combining observations from SWOT-nadir, Jason-3, and Sentinel-6 can improve the ADCIRC performance at more than 80% of the gauge locations for 107-day simulation. Nadir-only satellite altimetry observations can be useful for improving the model performance even if flagged as “poor quality” near the coast. When the flagged data are disregarded, SWOT can improve ADCIRC at 78%, Sentinel-6 at 73%, Jason-3 at 53%, and SARAL at 21% of the gauge locations. The ability to improve the model simulations largely depends on the availability of a satellite overpass nearby. Therefore, model performance can be further enhanced if satellite observations are available during a storm surge event, stressing the importance of frequent satellite overpasses.

Aafnan Bhuiyan, Soelem↗
DOE OSTI2022

A machine learning photon detection algorithm for coherent x-ray ultrafast fluctuation analysis

X-ray free electron laser experiments have brought unique capabilities and opened new directions in research, such as creating new states of matter or directly measuring atomic motion. One such area is the ability to use finely spaced sets of coherent x-ray pulses to be compared after scattering from a dynamic system at different times. This enables the study of fluctuations in many-body quantum systems at the level of the ultrafast pulse durations, but this method has been limited to a select number of examples and required complex and advanced analytical tools. By applying a new methodology to this problem, we have made qualitative advances in three separate areas that will likely also find application to new fields. As compared to the “droplet-type” models, which typically are used to estimate the photon distributions on pixelated detectors to obtain the coherent x-ray speckle patterns, our algorithm achieves an order of magnitude speedup on CPU hardware and two orders of magnitude improvement on GPU hardware. We also find that it retains accuracy in low-contrast conditions, which is the typical regime for many experiments in structural dynamics. Finally, it can predict photon distributions in high average-intensity applications, a regime which up until now has not been accessible. Our artificial intelligence-assisted algorithm will enable a wider adoption of x-ray coherence spectroscopies, by both automating previously challenging analyses and enabling new experiments that were not otherwise feasible without the developments described in this work.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Bardeen-Cooper-Schrieffer pairing of composite fermions

Topological pairing of composite fermions has led to remarkable ideas, such as excitations obeying non-Abelian braid statistics and topological quantum computation. Here, we construct a p-wave paired Bardeen-Cooper-Schrieffer (BCS) wave function for composite fermions in the torus geometry, which is a convenient geometry for formulating momentum space pairing as well as for revealing the underlying composite-fermion Fermi sea. Following the standard BCS approach, we minimize the Coulomb interaction energy at half filling in the lowest and the second Landau levels, which correspond to filling factors ν = 1/2 and ν = 5/2 in GaAs quantum wells, by optimizing two variational parameters that are analogous to the gap and the Debye cut-off energy of the BCS theory. Our results show no evidence for pairing at ν = 1/2 but a clear evidence for pairing at ν = 5/2. To a good approximation, the highest overlap between the exact Coulomb ground state at ν = 5/2 and the BCS state is obtained for parameters that minimize the energy of the latter, thereby providing support for the physics of composite-fermion pairing as the mechanism for the 5/2 fractional quantum Hall effect. We discuss the issue of modular covariance of the composite-fermion BCS wave function, and calculate its Hall viscosity and pair correlation function. By similar methods, we look for but do not find an instability to s-wave pairing for a spin-singlet composite-fermion Fermi sea at half-filled lowest Landau level in a system where the Zeeman splitting has been set to zero.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Heat-activated Plasmonic Chemical Sensors for Harsh Environments

A passive plasmonics based chemical sensing system to be used in harsh operating environments was investigated and developed within this program. The initial proposed technology was based on combining technologies developed at the SUNY Polytechnic Institute Colleges of Nanoscale Science and Engineering (CNSE) and at the University of Minnesota (UM). Specifically, a passive wireless technique developed at UM was to utilize a heat-activated plasmonic design to passively harvest the thermal energy from within a combustion emission stream and convert this into a narrowly focused light source. This plasmonic device was based on a bullseye design patterned into a gold film using focused ion beam methods (FIB). Critical to the design was the use of thermal stabilizing under and overlayers surrounding the gold film. These stabilizing layers were based on both atomic layer deposited films as well as metal laminate layers developed by United Technologies Aerospace Systems (UTAS). While the bullseye design was never able to be thermally stabilized for operating temperatures of 500oC or higher, an alternative energy harvesting design was developed by CNSE within this program. With this new development, plasmonic sensing results are presented where thermal energy is harvested using lithographically patterned Au nanorods, replacing the need for an external incident light source. Gas sensing results using the harvested thermal energy are in good agreement with sensing experiments, which used an external incident light source. Principal Component Analysis (PCA) was used to reduce the wavelength parameter space from 665 variables down to 4 variables with similar levels of demonstrated selectivity. The method was further improved by patterning rods which harvested energy in the near infrared, which led to a factor of 10 decrease in data acquisition times as well as demonstrated selectivity with a reduced wavelength data set. The combination of a plasmonic-based energy harvesting sensing paradigm with PCA analysis and wavelength down selection offers a novel path towards simplification and integration of plasmonic-based sensing methods using selected wavelengths rather than a full spectral analysis. Integration efforts were designed and modeled for thermal and mass transport considerations by UTAS which led to the 3D printing of scaled models that would serve as the housing for the alternative energy harvesting plasmonic chemical sensor design developed by CNSE.

47 OTHER INSTRUMENTATION↗
NASA NTRS1990

Effect of Blade Planform Variation on a Small-Scale Hovering Rotor

A hover test was conducted on a small-scale rotor model for three sets of tapered rotor blades and a baseline rectangular planform rotor blade. All configurations had the same airfoils, twist, and thrust-weighted solidity. The tapered blade planforms had taper initiating at 50, 75, and 94 percent of the blade radius with a taper ratio of 3 to 1 for each blade set. The experiment was conducted for a range of thrust coefficients, and the data were compared to the predictions of three hover analysis methods. The data show the 94 percent tapered blade was slightly more efficient at the higher rotor thrust levels. The other tapered planform rotors did not show the expected improvement over the baseline rotor, and all configurations had similar performance for low thrust coefficients. None of the analysis methods correlated well with the experimental data.

Althoff, Susan L.↗
NASA NTRS1990

Efficient design of CMOS TSC checkers

This paper considers the design of an efficient, robustly testable, CMOS Totally Self-Checking (TSC) Checker for k-out-of-2k codes. Most existing implementations use primitive gates and assume the single stuck-at fault model. The self-testing property has been found to fail for CMOS TSC checkers under the stuck-open fault model due to timing skews and arbitrary delays in the circuit. A new four level design using CMOS primitive gates (NAND, NOR, INVERTERS) is presented. This design retains its properties under the stuck-open fault model. Additionally, this method offers an impressive reduction (greater than 70 percent) in gate count, gate inputs, and test set size when compared to the existing method. This implementation is easily realizable and is based on Anderson's technique. A thorough comparative study has been made on the proposed implementation and Kundu's implementation and the results indicate that the proposed one is better than Kundu's in all respects for k-out-of-2k codes.

Biddappa, Anita↗
DOE OSTI2020

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of H2 and Li2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quantum computing, variational quantum solver, cou↗
DOE OSTI2021

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: II. Fully vibrationally-resolved electronic excitation of the isotopologues of H 2 (X 1 $Σ^{+}_{g}$)

Here, we present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of the isotopologues of molecular hydrogen (D 2 , T 2 , HD, HT, and DT) initially in the ground electronic state. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 500 eV for excitation of all bound vibrational levels and dissociative excitation of the B 1 $Σ^{+}_{g}$, C 1 Π u , EF 1 $Σ^{+}_{g}$, B' 1 $Σ^{+}_{g}$, GK 1 $Σ^{+}_{g}$, I 1 Π g , J 1 Δ g , D 1 Π u , H 1 $Σ^{+}_{g}$, b 1 $Σ^{+}_{g}$, c 3 Π u , a 3 $Σ^{+}_{g}$, e 3 $Σ^{+}_{u}$, d 3 Π u , h 3 $Σ^{+}_{g}$, g 3 $Σ^{+}_{g}$, i 3 Π g , and j 3 Δ g electronic states from all bound vibrational levels of the ground electronic (X 1 $Σ^{+}_{g}$) state. Including the previously-published MCCC e-H2 cross sections the data set contains cross sections for over 60,000 electronic and vibrational transitions. The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at mccc-db.org.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

An angle-dependent estimation of CT x-ray spectrum from rotational transmission measurements

Purpose: Computed tomography (CT) performance as well as dose and image quality is directly affected by the x-ray spectrum. However, the current assessment approaches of the CT x-ray spectrum require costly measurement equipment and complicated operational procedures, and are often limited to the spectrum corresponding to the center of rotation. In order to address these limitations, the authors propose an angle-dependent estimation technique, where the incident spectra across a wide range of angular trajectories can be estimated accurately with only a single phantom and a single axial scan in the absence of the knowledge of the bowtie filter. Methods: The proposed technique uses a uniform cylindrical phantom, made of ultra-high-molecular-weight polyethylene and positioned in an off-centered geometry. The projection data acquired with an axial scan have a twofold purpose. First, they serve as a reflection of the transmission measurements across different angular trajectories. Second, they are used to reconstruct the cross sectional image of the phantom, which is then utilized to compute the intersection length of each transmission measurement. With each CT detector element recording a range of transmission measurements for a single angular trajectory, the spectrum is estimated for that trajectory. A data conditioning procedure is used to combine information from hundreds of collected transmission measurements to accelerate the estimation speed, to reduce noise, and to improve estimation stability. The proposed spectral estimation technique was validated experimentally using a clinical scanner (Somatom Definition Flash, Siemens Healthcare, Germany) with spectra provided by the manufacturer serving as the comparison standard. Results obtained with the proposed technique were compared against those obtained from a second conventional transmission measurement technique with two materials (i.e., Cu and Al). After validation, the proposed technique was applied to measure spectra from the clinical system across a range of angular trajectories [−15°, 15°] and spectrum settings (80, 100, 120, 140 kVp). Results: At 140 kVp, the proposed technique was comparable to the conventional technique in terms of the mean energy difference (MED, −0.29 keV) and the normalized root mean square difference (NRMSD, 0.84%) from the comparison standard compared to 0.64 keV and 1.56%, respectively, with the conventional technique. The average absolute MEDs and NRMSDs across kVp settings and angular trajectories were less than 0.61 keV and 3.41%, respectively, which indicates a high level of estimation accuracy and stability. Conclusions: An angle-dependent estimation technique of CT x-ray spectra from rotational transmission measurements was proposed. Compared with the conventional technique, the proposed method simplifies the measurement procedures and enables incident spectral estimation for a wide range of angular trajectories. The proposed technique is suitable for rigorous research objectives as well as routine clinical quality control procedures.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2015

Enhancing atlas based segmentation with multiclass linear classifiers

Purpose: To present a method to enrich atlases for atlas based segmentation. Such enriched atlases can then be used as a single atlas or within a multiatlas framework. Methods: In this paper, machine learning techniques have been used to enhance the atlas based segmentation approach. The enhanced atlas defined in this work is a pair composed of a gray level image alongside an image of multiclass classifiers with one classifier per voxel. Each classifier embeds local information from the whole training dataset that allows for the correction of some systematic errors in the segmentation and accounts for the possible local registration errors. The authors also propose to use these images of classifiers within a multiatlas framework: results produced by a set of such local classifier atlases can be combined using a label fusion method. Results: Experiments have been made on the in vivo images of the IBSR dataset and a comparison has been made with several state-of-the-art methods such as FreeSurfer and the multiatlas nonlocal patch based method of Coupé or Rousseau. These experiments show that their method is competitive with state-of-the-art methods while having a low computational cost. Further enhancement has also been obtained with a multiatlas version of their method. It is also shown that, in this case, nonlocal fusion is unnecessary. The multiatlas fusion can therefore be done efficiently. Conclusions: The single atlas version has similar quality as state-of-the-arts multiatlas methods but with the computational cost of a naive single atlas segmentation. The multiatlas version offers a improvement in quality and can be done efficiently without a nonlocal strategy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2011

Auto-segmentation of normal and target structures in head and neck CT images: A feature-driven model-based approach

Purpose: Intensity modulated radiation therapy (IMRT) allows greater control over dose distribution, which leads to a decrease in radiation related toxicity. IMRT, however, requires precise and accurate delineation of the organs at risk and target volumes. Manual delineation is tedious and suffers from both interobserver and intraobserver variability. State of the art auto-segmentation methods are either atlas-based, model-based or hybrid however, robust fully automated segmentation is often difficult due to the insufficient discriminative information provided by standard medical imaging modalities for certain tissue types. In this paper, the authors present a fully automated hybrid approach which combines deformable registration with the model-based approach to accurately segment normal and target tissues from head and neck CT images. Methods: The segmentation process starts by using an average atlas to reliably identify salient landmarks in the patient image. The relationship between these landmarks and the reference dataset serves to guide a deformable registration algorithm, which allows for a close initialization of a set of organ-specific deformable models in the patient image, ensuring their robust adaptation to the boundaries of the structures. Finally, the models are automatically fine adjusted by our boundary refinement approach which attempts to model the uncertainty in model adaptation using a probabilistic mask. This uncertainty is subsequently resolved by voxel classification based on local low-level organ-specific features. Results: To quantitatively evaluate the method, they auto-segment several organs at risk and target tissues from 10 head and neck CT images. They compare the segmentations to the manual delineations outlined by the expert. The evaluation is carried out by estimating two common quantitative measures on 10 datasets: volume overlap fraction or the Dice similarity coefficient (DSC), and a geometrical metric, the median symmetric Hausdorff distance (HD), which is evaluated slice-wise. They achieve an average overlap of 93% for the mandible, 91% for the brainstem, 83% for the parotids, 83% for the submandibular glands, and 74% for the lymph node levels. Conclusions: Our automated segmentation framework is able to segment anatomy in the head and neck region with high accuracy within a clinically-acceptable segmentation time.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1991

Surface wind convergence as a short-term predictor of cloud-to-ground lightning at Kennedy Space Center

Cloud-to-ground lightning is a significant forecast problem at the Kennedy Space Center (KSC) in Florida. In this study, cloud-to-ground lightning is related in time and space to surface convergence for 244 days during the convective seasons of 1985 and 1986 over a 790 sq-km network at KSC. The method uses surface convergence, particularly the average over the area, to identify the potential for new, local thunderstorm growth, and it can be used to specify the likely time and location of lightning during the life cycle of the convection. A threshold of 75 x 10 to the -6th/s change in divergence is the main criterion used to define a convergence event, and a set of flashes less than 30 min apart defines a lightning event. Time intervals are found from the study to be approximately 1 h from beginning convergence to first flash, and another hour to the end of lightning. The influences of low-level winds and midlevel moisture in determining the location and intensity of convection are discussed. This is the first known dynamically-based forecast method for lightning prediction. The technique, currently in use at KSC, has been shown to be a systematic, quantitative tool for predicting lightning onset in situations where conventional analysis tools such as radar and satellite are limited.

Watson, Andrew I.↗
DOE OSTI2014

Concepts, Challenges, and Successes in Modeling Thermodynamics of Metabolism

The modeling of the chemical reactions involved in metabolism is a daunting task. Ideally, the modeling of metabolism would use kinetic simulations, but these simulations require knowledge of the thousands of rate constants involved in the reactions. The measurement of rate constants is very labor intensive, and hence rate constants for most enzymatic reactions are not available. Consequently, constraint-based flux modeling has been the method of choice because it does not require the use of the rate constants of the law of mass action. However, this convenience also limits the predictive power of constraint-based approaches in that the law of mass action is used only as a constraint, making it difficult to predict metabolite levels or energy requirements of pathways. An alternative to both of these approaches is to model metabolism using simulations of states rather than simulations of reactions, in which the state is defined as the set of all metabolite counts or concentrations. While kinetic simulations model reactions based on the likelihood of the reaction derived from the law of mass action, states are modeled based on likelihood ratios of mass action. Both approaches provide information on the energy requirements of metabolic reactions and pathways. However, modeling states rather than reactions has the advantage that the parameters needed to model states (chemical potentials) are much easier to determine than the parameters needed to model reactions (rate constants). Herein, we discuss recent results, assumptions, and issues in using simulations of state to model metabolism.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Self-interaction corrected density functional calculations of molecular Rydberg states

A method is presented for calculating the wave function and energy of Rydberg excited states of molecules. A good estimate of the Rydberg state orbital is obtained using ground state density functional theory including Perdew-Zunger self-interaction correction and an optimized effective potential. The total energy of the excited molecule is obtained using the Delta Self-Consistent Field method where an electron is removed from the highest occupied orbital and placed in the Rydberg orbital. Results are presented for the first few Rydberg states of NH{sub 3}, H{sub 2}O, H{sub 2}CO, C{sub 2}H{sub 4}, and N(CH{sub 3}){sub 3}. The mean absolute error in the energy of the 33 molecular Rydberg states presented here is 0.18 eV. The orbitals are represented on a real space grid, avoiding the dependence on diffuse atomic basis sets. As in standard density functional theory calculations, the computational effort scales as NM{sup 2} where N is the number of orbitals and M is the number of grid points included in the calculation. Due to the slow scaling of the computational effort with system size and the high level of parallelism in the real space grid approach, the method presented here makes it possible to estimate Rydberg electron binding energy in large molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗