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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

The H i content of the universe over the past 10 GYR

We use the Hubble Space Telescope (HST) archive of ultraviolet (UV) quasar spectroscopy to conduct the first blind survey for damped Lyα absorbers (DLAs) at low redshift (z<1.6). Our statistical sample includes 463 quasars with spectral coverage spanning a total redshift path Δz=123.3 or an absorption path ΔX=229.7. Within this survey path, we identify 4 DLAs defined as absorbers with H i column density N{sub HI} ⩾ 10{sup 20.3} cm{sup −2}, which implies an incidence per absorption length ℓ{sub DLA}(X) = 0.017{sub −0.008}{sup +0.014} at a median survey path redshift of z = 0.623. While our estimate of ℓ{sub DLA}(X) is lower than earlier estimates at z≈0 from H i 21 cm emission studies, the results are consistent within the measurement uncertainties. Our data set is too small to properly sample the N{sub HI} frequency distribution function f(N{sub HI},X), but the observed distribution agrees with previous estimates at z>2. Adopting the z>2 shape of f(N{sub HI},X), we infer an H i mass density at z∼0.6 of ρ{sub H I}{sup DLA} = 0.25{sub −0.12}{sup +0.20}×10{sup 8}M{sub ⊙} Mpc{sup −3}. This is significantly lower than previous estimates from targeted DLA surveys with the HST, but consistent with results from low-z H i 21 cm observations, and suggests that the neutral gas density of the universe has been decreasing over the past 10 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Asymptotic Behavior of Memristive Circuits

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such a Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Improved estimates of the Milky Way’s stellar mass and star formation rate from hierarchical Bayesian meta-analysis

We present improved estimates of several global properties of the Milky Way, including its current star formation rate (SFR), the stellar mass contained in its disk and bulge+bar components, as well as its total stellar mass. We do so by combining previous measurements from the literature using a hierarchical Bayesian (HB) statistical method that allows us to account for the possibility that any value may be incorrect or have underestimated errors. We show that this method is robust to a wide variety of assumptions about the nature of problems in individual measurements or error estimates. Ultimately, our analysis yields an SFR for the Galaxy of M-dot {sub ⋆}=1.65±0.19 M{sub ⊙} yr{sup −1}, assuming a Kroupa initial mass function (IMF). By combining HB methods with Monte Carlo simulations that incorporate the latest estimates of the Galactocentric radius of the Sun, R{sub 0}, the exponential scale length of the disk, L{sub d}, and the local surface density of stellar mass, Σ{sub ⋆}(R{sub 0}), we show that the mass of the Galactic bulge+bar is M{sub ⋆}{sup B}=0.91±0.07×10{sup 10} M{sub ⊙}, the disk mass is M{sub ⋆}{sup D}=5.17±1.11×10{sup 10} M{sub ⊙}, and their combination yields a total stellar mass of M{sub ⋆}=6.08±1.14×10{sup 10} M{sub ⊙} (assuming a Kroupa IMF and an exponential disk profile). This analysis is based upon a new compilation of literature bulge mass estimates, normalized to common assumptions about the stellar IMF and Galactic disk properties, presented herein. We additionally find a bulge-to-total mass ratio for the Milky Way of B/T=0.150{sub −0.019}{sup +0.028} and a specific SFR of M-dot {sub ⋆}/M{sub ⋆}=2.71±0.59×10{sup −11} yr{sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

SCEC/USGS Community Stress-Drop Validation Study: How Spectral Fitting Approaches Influence Measured Source Parameters

Spectral source parameters used to estimate an earthquake’s stress drop (⁠Δσ⁠) can vary significantly across measurement approaches. The Statewide California Earthquake Center/U.S. Geological Survey Community Stress‐Drop Validation Study was initiated to compare source parameter estimates, focusing initially on a dataset from the 2019 Ridgecrest earthquake sequence. As part of that validation effort, here we focus on one potential source of uncertainty: whether spectral fitting approaches alone, applied to a common set of spectra from the 2019 Ridgecrest sequence result in different source parameter estimates. By using a common set of benchmark spectra analyzed across a consistent frequency band of 1–40 Hz, we eliminate many sources of variability. A subgroup of validation study participants volunteered to estimate the low‐frequency displacement (⁠Ω 0 ⁠) and corner frequency (⁠ƒ c ⁠) by fitting a smooth function to benchmark displacement spectra. Participants used linear‐ or log‐sampled spectra, assumed a Brune or Boatwright spectral model, and applied different misfit criteria. We compare 17 approaches used to estimate ⁠Ω 0 ⁠, ƒ c ⁠, and Δσ for 54 earthquake spectra. Our results reveal that 35% of events have Δσ estimates within a factor of two, whereas others exhibit variations exceeding an order of magnitude. The variability in and can largely be attributed to whether a spectrum is consistent with the smooth function of an idealized simple crack model. The trade‐off between Ω 0 and ƒ c may be more pronounced when using linearly sampled spectra, as higher frequency spectral bumps control the fits. As expected, methods that assumed a Boatwright model tended to have lower Ω 0 and somewhat higher ƒ c compared to those assuming a Brune model, although resulting Δσ estimates are similar. Finally, when compared to the overall validation study results, the fitting approach alone may account for between 5% and 90% (25% on average) of the total variability in spectral Δσ⁠.

58 GEOSCIENCES↗
DOE OSTI2022

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.

A-posterior estimates↗
DOE OSTI2016

On interfacial properties of tetrahydrofuran: Atomistic and coarse-grained models from molecular dynamics simulation

We have determined the interfacial properties of tetrahydrofuran (THF) from direct simulation of the vapor-liquid interface. The molecules are modeled using six different molecular models, three of them based on the united-atom approach and the other three based on a coarse-grained (CG) approach. In the first case, THF is modeled using the transferable parameters potential functions approach proposed by Chandrasekhar and Jorgensen [J. Chem. Phys. 77, 5073 (1982)] and a new parametrization of the TraPPE force fields for cyclic alkanes and ethers [S. J. Keasler et al., J. Phys. Chem. B 115, 11234 (2012)]. In both cases, dispersive and coulombic intermolecular interactions are explicitly taken into account. In the second case, THF is modeled as a single sphere, a diatomic molecule, and a ring formed from three Mie monomers according to the SAFT-γ Mie top-down approach [V. Papaioannou et al., J. Chem. Phys. 140, 054107 (2014)]. Simulations were performed in the molecular dynamics canonical ensemble and the vapor-liquid surface tension is evaluated from the normal and tangential components of the pressure tensor along the simulation box. In addition to the surface tension, we have also obtained density profiles, coexistence densities, critical temperature, density, and pressure, and interfacial thickness as functions of temperature, paying special attention to the comparison between the estimations obtained from different models and literature experimental data. The simulation results obtained from the three CG models as described by the SAFT-γ Mie approach are able to predict accurately the vapor-liquid phase envelope of THF, in excellent agreement with estimations obtained from TraPPE model and experimental data in the whole range of coexistence. However, Chandrasekhar and Jorgensen model presents significant deviations from experimental results. We also compare the predictions for surface tension as obtained from simulation results for all the models with experimental data. The three CG models predict reasonably well (but only qualitatively) the surface tension of THF, as a function of temperature, from the triple point to the critical temperature. On the other hand, only the TraPPE united-atoms models are able to predict accurately the experimental surface tension of the system in the whole temperature range.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The stellar mass assembly of low-redshift, massive, central galaxies in SDSS and the TNG300 simulation

ABSTRACT The stellar mass assembly of galaxies can be affected by both secular and environmental processes. In this study, for the first time, we investigate the stellar mass assembly of $\sim 90\, 000$ low-redshift, central galaxies selected from SDSS group catalogues ($M_{\rm Stellar}\gtrsim 10^{9.5}\, \mathrm{M}_{\odot }$, $M_{\rm Halo}\gtrsim 10^{12}\, \mathrm{M}_{\odot }$) as a function of both stellar mass and halo mass. We use estimates of the times at which 10, 50, and 90 per cent of the stellar mass were assembled from photometric spectral energy distribution fitting, allowing a more complete investigation than single stellar ages alone. We consider trends in both stellar mass and halo mass simultaneously, finding dependences of all assembly times on both. We find that galaxies with higher stellar masses (at constant halo mass) have on average older lookback times, similar to previous studies of galaxy assembly. We also find that galaxies at higher halo mass (at constant stellar mass) have younger lookback times, possibly due to a larger reservoir of gas for star formation. An exception to this is a subsample with high stellar-to-halo mass ratios, which are likely massive, field spirals. We compare these observed trends to those predicted by the TNG300 simulation, finding good agreement overall as a function of either stellar mass or halo mass. However, some differences in the assembly times (of up to ∼3 Gyr) appear when considering both stellar mass and halo mass simultaneously, noticeably at intermediate stellar masses (MStellar ∼ 1011 M⊙). These discrepancies are possibly linked to the quenched fraction of galaxies and the kinetic mode active galactic nucleus feedback implemented in TNG300.

Jackson, Thomas M.↗
DOE OSTI2022

Sensitivity Analysis of Fluid–Fluid Interfacial Area, Phase Saturation and Phase Connectivity on Relative Permeability Estimation Using Machine Learning Algorithms

Recent studies have shown that relative permeability can be modeled as a state function which is independent of flow direction and dependent upon phase saturation (S), phase connectivity (X), and fluid–fluid interfacial area (A). This study evaluates the impact of each of the three state parameters (S, X, and A) in the estimation of relative permeability. The relative importance of the three state parameters in four separate quadrants of S-X-A space was evaluated using a machine learning algorithm (out-of-bag predictor importance method). The results show that relative permeability is sensitive to all the three parameters, S, X, and A, with varying magnitudes in each of the four quadrants at a constant value of wettability. We observe that the wetting-phase relative permeability is most sensitive to saturation, while the non-wetting phase is most sensitive to phase connectivity. Although the least important, fluid–fluid interfacial area is still important to make the relative permeability a more exact state function.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Constitutive law↗
DOE OSTI2020

Future projections and uncertainty assessment of precipitation extremes in the Korean peninsula from the CMIP5 ensemble

Abstract Projections of changes in extreme climate are sometimes predicted by multimodel ensemble methods that combine forecasts from individual simulation models using weighted averaging. One method to assign weight to each model is the Bayesian model averaging (BMA) in which posterior probability is used. For the cases of extreme climate, the generalized extreme value distribution (GEVD) is typically used. We applied the approach of GEV‐embedded BMA to a series of 35 years of the annual maximum daily precipitation data (both historical data and data gathered from simulation experiments for future periods) over the Korean peninsula as simulated by the models in the Coupled Model Intercomparison Project Phase 5 (CMIP5). Simulation data under two Representative Concentration Pathway (RCP) scenarios, namely RCP4.5 and RCP8.5, were used. Observed data and 17 CMIP5 models for 12 gird cells in Korea have been examined to predict future changes in precipitation extremes. A simple regional frequency analysis of pooling observations from three stations in each cell was employed to reduce the estimation variance and local fluctuations. A bias correction technique using the regression‐type transfer function was applied to these simulation data. Return levels spanning over 20 and 50 years, as well as the return periods relative to the reference years (1971–2005), were estimated for two future periods, namely Period 1 (2021–2050) and Period 2 (2066–2095). From these analyses, relative increase observed in the spatially averaged 20‐year (50‐year) return level was approximately 23% (16%) and 45% (36%) in the RCP4.5 and RCP8.5 experiments, respectively, by the end of the 21st century. We concluded that extreme rainfalls will likely occur two times and four times more frequently in the RCP4.5 and RCP8.5 scenarios, respectively, as compared to in the reference years by the end of the 21st century.

Lee, Youngsaeng↗
DOE OSTI2018

Global land model development: time to shift from a plant functional type to a plant functional trait approach (Final Report)

This project advanced global land models by shifting from the current plant functional type approach to one that better utilizes what is known about the importance and variability of plant traits, within a framework of simultaneously improving fundamental physiological relations that are at the core of model carbon cycling algorithms. A primary goal for Earth system modeling is to make accurate predictions of the future trajectory of the climate system, based on a mechanistic understanding of processes regulating fluxes of mass and energy among system components. Land plays an important role in modifying the Earth’s mass and energy balance, as a critical link in the global cycling of carbon, among others. Land surface models have developed to include mechanistic representations of vegetation physiology, carbon and nutrient dynamics in plants and soils, how they might respond to changing climate and chemistry, and how those changes might feedback to influence changes in atmospheric greenhouse gases themselves. Existing models represent the global distribution of vegetation types using the Plant Functional Type concept. Plant Functional Types are classes of plant species with similar evolutionary and life history with presumably similar responses to environmental conditions like CO 2 , water and nutrient availability. Fixed properties for each Plant Functional Type are specified through a collection of physiological parameters, or traits. These traits, mostly physiological in nature (e.g., leaf nitrogen and longevity) are used in model algorithms to estimate ecosystem properties and/or drive calculated process rates. In most models, 5 to 15 functional types represent terrestrial vegetation; in essence, they assume there are a total of only 5 to 15 different kinds of plants on the entire globe. This assumption of constant plant traits captured within the functional type concept has serious limitations, as a single set of traits does not reflect trait variation observed within and between species and communities. While this simplification was necessary decades past, substantial improvement is now possible. Rather than assigning a small number of constant parameter values to all grid cells in a model, we developed procedures that predict a frequency distribution of values for any given grid cell. Thus, by incorporating the mean and variance model fidelity has been improved. The trait-based approach has improved land modeling by (1) incorporating patterns and heterogeneity of traits into model parameterization, thus evolving away from a framework that considers large areas of vegetation to have near identical trait values and (2) allowing for improved treatment of physiological responses to environmental drivers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Electron Cloud Trapping in Recycler Combined Function Dipole Magnets

Electron cloud can lead to a fast instability in intense proton and positron beams in circular accelerators. In the Fermilab Recycler the electron cloud is confined within its combined function magnets. We show that the field of combined function magnets traps the electron cloud, present the results of analytical estimates of trapping, and compare them to numerical simulations of electron cloud formation. The electron cloud is located at the beam center and up to 1% of the particles can be trapped by the magnetic field. Since the process of electron cloud build-up is exponential, once trapped this amount of electrons significantly increases the density of the cloud on the next revolution. In a Recycler combined function dipole this multiturn accumulation allows the electron cloud reaching final intensities orders of magnitude greater than in a pure dipole. The multi-turn build-up can be stopped by injection of a clearing bunch of 1010 p at any position in the ring.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

A Method for Estimation and Suppression of Quasi-Periodic Noise

Electromagnetic interference, particularly from sources such as light fixtures and power supplies, negatively affects the function and performance of electronic systems. This noise, often quasi-periodic in nature, contains harmonic structure that can be used for noise estimation and suppression. This work proposes a novel method for tracking and filtering such noise signals that reduces the comb filter bandwidth required for noise estimation and suppression by tracking the instantaneous frequency of the fundamental component.

42 ENGINEERING↗
DOE OSTI2016

WE-AB-202-06: Correlating Lung CT HU with Transformation-Based and Xe-CT Derived Ventilation

Purpose: Regional lung ventilation is useful to reduce radiation-induced function damage during lung cancer radiation therapy. Recently a new direct HU (Hounsfield unit)-based method was proposed to estimate the ventilation potential without image registration. The purpose of this study is to examine if there is a functional dependence between HU values and transformation-based or Xe-CT derived ventilation. Methods: 4DCT images acquired from 13 patients prior to radiation therapy and 4 mechanically ventilated sheep subjects which also have associated Xe-CT images were used for this analysis. Transformation-based ventilation was computed using Jacobian determinant of the transformation field between peak-exhale and peak-inhale 4DCT images. Both transformation and Xe-CT derived ventilation was computed for each HU bin. Color scatter plot and cumulative histogram were used to compare and validate the direct HU-based method. Results: There was little change of the center and shape of the HU histograms between free breathing CT and 4DCT average, with or without smoothing, and between the repeated 4DCT scans. HU of −750 and −630 were found to have the greatest transformation-based ventilation for human and sheep subjects, respectively. Maximum Xe-CT derived ventilation was found to locate at HU of −600 in sheep subjects. The curve between Xe-CT ventilation and HU was noisy for tissue above HU −400, possibly due to less intensity change of Xe gas during wash-out and wash-in phases. Conclusion: Both transformation-based and Xe-CT ventilation demonstrated that lung tissues with HU values in the range of (-750, −600) HU have the maximum ventilation potential. The correlation between HU and ventilation suggests that HU might be used to help guide the ventilation calculation and make it more robust to noise and image registration errors. Research support from NIH grants CA166703 and CA166119 and a gift from Roger Koch.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Mobile sensing of point-source gas emissions using Bayesian inference: An empirical examination of the likelihood function

This paper evaluates likelihood function forms for Bayesian inference of point-source gas emissions using a mobile sensor. Whereas Bayesian inference has been successfully used to estimate emission rates from time-averaged concentration data measured by stationary sensors, data collected by mobile sensors do not represent ensemble or time-averaged conditions. To examine the potential impact of this contrast, controlled release experiments were conducted with a mobile sensor measuring concentrations repeatedly along transverse cross sections of the downwind plumes. Experiments were conducted with measurements made at different downwind distances, different sensor heights, and with different obstacle states. An examination is made between two commonly-used likelihood functions, the Gaussian and the log-normal. For experiments conducted in the absence of obstacles, the Bayesian estimates using the log-normal likelihood function yield a much smaller bias than those based on the Gaussian likelihood function. This finding is consistent with the non-Gaussian nature of concentration fluctuations near a point-source. For experiments conducted in the presence of obstacles, the Bayesian inference based on the Gaussian likelihood function exhibits a better performance. This can be explained by the enhanced turbulent mixing due to the obstacle-introduced wake eddies. Overall, we find that the selection of the likelihood function can be physically related to the underlying conditions, and the proper selection is critical to ensure the performance of the Bayesian inference for source characterization using mobile sensing data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Reachable set bounding for a class of bidirectional associative memory NNSs with Markov jump switching parameters

This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Density functional study of the electronic structure of dye-functionalized fullerenes and their model donor-acceptor complexes containing P3HT

We study the electronic structure of C{sub 60} fullerenes functionalized with a thiophene-diketo-pyrrolopyrrole-thiophene based chromophore using density functional theory combined with large polarized basis sets. As the attached chromophore has electron donor character, the functionalization of the fullerene leads to a donor-acceptor (DA) system. We examine in detail the effect of the linker and the addition site on the electronic structure of the functionalized fullerenes. We further study the electronic structure of these DA complexes with a focus on the charge transfer excitations. Finally, we examine the interface of the functionalized fullerenes with the widely used poly(3-hexylthiophene-2,5-diyl) (P3HT) donor. Our results show that all functionalized fullerenes with an exception of the C{sub 60}-pyrrolidine [6,6], where the pyrrolidine is attached at a [6,6] site, have larger electron affinities relative to the pristine C{sub 60} fullerene. We also estimate the quasi-particle gap, lowest charge transfer excitation energy, and the exciton binding energies of the functionalized fullerene-P3MT model systems. Results show that the exciton binding energies in these model complexes are slightly smaller compared to a similarly prepared phenyl-C{sub 61}-butyric acid methyl ester (PCBM)-P3MT complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗