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DOE OSTI2015

Long-range corrected density functional theory with accelerated Hartree-Fock exchange integration using a two-Gaussian operator [LC-ωPBE(2Gau)]

Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange

In this report, electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact exchange or hybrid functionals are associated with large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Though orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use gradient expansion of the kinetic energy, nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C 4 H 2 , C 4 N 2 and C 3 O 2 . We show that by using data from model one-dimensional KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems as well as electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Extreme sensitivity of higher-order interatomic force constants and thermal conductivity to the energy surface roughness of exchange-correlation functionals

In this Letter, we report that the fourth-order interatomic force constants (4th-IFCs) are significantly sensitive to the energy surface roughness of exchange-correlation (XC) functionals in density functional theory calculations. This sensitivity, which is insignificant for the second- (2nd-) and third-order (3rd-) IFCs, varies for different functionals in different materials and can cause misprediction of thermal conductivity by several times of magnitude. As a result, when calculating the 4th-IFCs using the finite difference method, the atomic displacement needs to be taken large enough to overcome the energy surface roughness, in order to accurately predict phonon lifetime and thermal conductivity. We demonstrate this phenomenon on a benchmark material (Si), a high-thermal conductivity material (BAs), and a low thermal conductivity material (NaCl). For Si, we find that the LDA, PBE, and PBEsol XC functionals are all smooth to the 2nd- and 3rd-IFCs but all rough to the 4th-IFCs. This roughness can lead to a prediction of nearly one order of magnitude lower thermal conductivity. For BAs, all three functionals are smooth to the 2nd- and 3rd-IFCs, and only the PBEsol XC functional is rough for the 4th-IFCs, which leads to a 40% underestimation of thermal conductivity. For NaCl, all functionals are smooth to the 2nd- and 3rd-IFCs but rough to the 4th-IFCs, leading to a 70% underprediction of thermal conductivity at room temperature. In conclusion, with these observations, we provide general guidance on the calculation of 4th-IFCs for an accurate thermal conductivity prediction.

42 ENGINEERING↗

DOE OSTI2025

Noncollinear ground states of solids with a source-free exchange correlation functional

In this paper, we expand upon the source-free (SF) exchange correlation (XC) functional developed by Sangeeta Sharma and coworkers to plane-wave density functional theory (DFT) based on the projector augmented wave (PAW) method. This constraint is implemented by the current authors within the VASP source code, using a fast Poisson solver that capitalizes on the parallel three-dimensional fast Fourier transforms (FFTs) implemented in VASP. Using this modified XC functional, we explore the improved convergence behavior that results from applying this constraint to the GGA-PBE+U+J functional. In the process, we compare the noncollinear magnetic ground state computed by each functional and their SF counterpart for a select number of magnetic materials in order to provide a metric for comparing with experimentally determined magnetic orderings. We observe significantly improved agreement with experimentally measured magnetic ground-state structures after applying the source-free constraint. Furthermore, we explore the importance of considering probability current densities in spin-polarized systems, even under no applied field. We analyze the XC torque as well, in order to provide theoretical and computational analyses of the net XC magnetic torque induced by the source-free constraint. Along these lines, we highlight the importance of properly considering the real-space integral of the source-free local magnetic XC field. Our analyses on probability currents, net torque, and constant terms draw additional links to the rich body of previous research on spin-current density functional theory (SCDFT), and pave the way for future extensions and corrections to the SF corrected XC functional.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Microbial functional diversity covaries with permafrost thaw-induced environmental heterogeneity in tundra soil

Permafrost soil in high latitude tundra is one of the largest terrestrial carbon (C) stocks and is highly sensitive to climate warming. Understanding microbial responses to warming-induced environmental changes is critical to evaluating their influences on soil biogeochemical cycles. In this study, a functional gene array (i.e., geochip 4.2) was used to analyze the functional capacities of soil microbial communities collected from a naturally degrading permafrost region in Central Alaska. Varied thaw history was reported to be the main driver of soil and plant differences across a gradient of minimally, moderately, and extensively thawed sites. Compared with the minimally thawed site, the number of detected functional gene probes across the 15-65 cm depth profile at the moderately and extensively thawed sites decreased by 25% and 5%, while the community functional gene β-diversity increased by 34% and 45%, respectively, revealing decreased functional gene richness but increased community heterogeneity along the thaw progression. Particularly, the moderately thawed site contained microbial communities with the highest abundances of many genes involved in prokaryotic C degradation, ammonification, and nitrification processes, but lower abundances of fungal C decomposition and anaerobic-related genes. Significant correlations were observed between functional gene abundance and vascular plant primary productivity, suggesting that plant growth and species composition could be co-evolving traits together with microbial community composition. Finally, altogether, this study reveals the complex responses of microbial functional potentials to thaw-related soil and plant changes and provides information on potential microbially mediated biogeochemical cycles in tundra ecosystems.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Functional Traits Resolve Mechanisms Governing the Assembly and Distribution of Nitrogen-Cycling Microbial Communities in the Global Ocean

Microorganisms drive much of the marine nitrogen (N) cycle, which jointly controls the primary production in the global ocean. However, our understanding of the microbial communities driving the global ocean N cycle remains fragmented. Focusing on “who is doing what, where, and how?”, this study draws a clear picture describing the global biogeography of marine N-cycling microbial communities by utilizing the Tara Oceans shotgun metagenomes. The marine N-cycling communities are highly variable taxonomically but relatively even at the functional trait level, showing clear functional redundancy properties. The functional traits and taxonomic groups are shaped by the same set of geo-environmental factors, among which, depth is the major factor impacting marine N-cycling communities, differentiating mesopelagic from epipelagic communities. Latitudinal diversity gradients and distance-decay relationships are observed for taxonomic groups, but rarely or weakly for functional traits. The composition of functional traits is strongly deterministic as revealed by null model analysis, while a higher degree of stochasticity is observed for taxonomic composition. Integrating multiple lines of evidence, in addition to drawing a biogeographic picture of marine N-cycling communities, this study also demonstrated an essential microbial ecological theory—determinism governs the assembly of microbial communities performing essential biogeochemical processes; the environment selects functional traits rather than taxonomic groups; functional redundancy underlies stochastic taxonomic community assembly.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Calibration of energy density functionals with deformed nuclei

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Regression models using shapes of functions as predictors

Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the $\mathbb L^2$ inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable. One past solution has been to perform phase–amplitude separation (as a pre-processing step) and then use only the amplitudes in the regression model. In this paper, we propose a more integrated approach, termed elastic functional regression model (EFRM), where phase-separation is performed inside the regression model, rather than as a pre-processing step. This approach generalizes the notion of phase in functional data, and is based on the norm-preserving time warping of predictors. Due to its invariance properties, this representation provides robustness to predictor phase variability and results in improved predictions of the response variable over traditional models. We demonstrate this framework using a number of datasets involving gait signals, NMR data, and stock market prices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Does DFT+U mimic hybrid density functionals?

Here, this work examines the question of how a Hubbard U correction to a local exchange–correlation functional compares with adding Hartree–Fock exchange to a local functional for both solid-state and molecular properties. We compute a solid-state property, namely the band gap, and thermochemical molecular properties, in particular main-group bond energies, transition-metal–ligand bond energies, and barrier heights, to elucidate whether the DFT+U method mimics hybrid DFT. We find that a calculation with a Hubbard U correction may or may not mimic a hybrid functional – depending on the atom, the subshell, and the property to which it is applied. For band gaps, we find that adding a Hubbard U correction to the valence d orbitals of transition metals increases the band gap, which thereby gets closer to the experimental value, while adding a Hubbard U correction to valence s or p orbitals of main group elements need not always increase the band gap. For molecular thermochemistry, we find that adding a Hubbard U correction to a local density functional need not have the same effect as adding Hartree–Fock exchange to a local density functional. For example when compared to a local DFT, hybrid DFT increases the barrier height in all cases, but DFT+U does not always increase the barrier height. For the band gaps of transition metal monoxides, the Hubbard-corrected results lowered the mean errors significantly and were comparable to what could be achieved with a much more expensive hybrid functional, but for reaction barrier heights and bond energies the Hubbard correction can lower the mean error by approximately a kcal/mol. As part of the analysis, we also compare VASP and Gaussian 09 calculations for the same density functional.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Weak measurement and Bohmian conditional wave functions

It was recently pointed out and demonstrated experimentally by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be “directly measured” using weak measurement. Here it is shown that if this same technique is applied, with appropriate post-selection, to one particle from a perhaps entangled multi-particle system, the result is precisely the so-called “conditional wave function” of Bohmian mechanics. Thus, a plausibly operationalist method for defining the wave function of a quantum mechanical sub-system corresponds to the natural definition of a sub-system wave function which Bohmian mechanics uniquely makes possible. Similarly, a weak-measurement-based procedure for directly measuring a sub-system’s density matrix should yield, under appropriate circumstances, the Bohmian “conditional density matrix” as opposed to the standard reduced density matrix. Experimental arrangements to demonstrate this behavior–and also thereby reveal the non-local dependence of sub-system state functions on distant interventions–are suggested and discussed. - Highlights: • We study a “direct measurement” protocol for wave functions and density matrices. • Weakly measured states of entangled particles correspond to Bohmian conditional states. • Novel method of observing quantum non-locality is proposed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Determination of many-electron basis functions for a quantum Hall ground state using Schur polynomials

A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the (5/2) quantum Hall state with a few particles. We find that one of the basis functions is precisely the Moore–Read Pfaffian wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Functional Data Analysis Applied to Modeling of Severe Acute Mucositis and Dysphagia Resulting From Head and Neck Radiation Therapy

Purpose: Current normal tissue complication probability modeling using logistic regression suffers from bias and high uncertainty in the presence of highly correlated radiation therapy (RT) dose data. This hinders robust estimates of dose-response associations and, hence, optimal normal tissue–sparing strategies from being elucidated. Using functional data analysis (FDA) to reduce the dimensionality of the dose data could overcome this limitation. Methods and Materials: FDA was applied to modeling of severe acute mucositis and dysphagia resulting from head and neck RT. Functional partial least squares regression (FPLS) and functional principal component analysis were used for dimensionality reduction of the dose-volume histogram data. The reduced dose data were input into functional logistic regression models (functional partial least squares–logistic regression [FPLS-LR] and functional principal component–logistic regression [FPC-LR]) along with clinical data. This approach was compared with penalized logistic regression (PLR) in terms of predictive performance and the significance of treatment covariate–response associations, assessed using bootstrapping. Results: The area under the receiver operating characteristic curve for the PLR, FPC-LR, and FPLS-LR models was 0.65, 0.69, and 0.67, respectively, for mucositis (internal validation) and 0.81, 0.83, and 0.83, respectively, for dysphagia (external validation). The calibration slopes/intercepts for the PLR, FPC-LR, and FPLS-LR models were 1.6/−0.67, 0.45/0.47, and 0.40/0.49, respectively, for mucositis (internal validation) and 2.5/−0.96, 0.79/−0.04, and 0.79/0.00, respectively, for dysphagia (external validation). The bootstrapped odds ratios indicated significant associations between RT dose and severe toxicity in the mucositis and dysphagia FDA models. Cisplatin was significantly associated with severe dysphagia in the FDA models. None of the covariates was significantly associated with severe toxicity in the PLR models. Dose levels greater than approximately 1.0 Gy/fraction were most strongly associated with severe acute mucositis and dysphagia in the FDA models. Conclusions: FPLS and functional principal component analysis marginally improved predictive performance compared with PLR and provided robust dose-response associations. FDA is recommended for use in normal tissue complication probability modeling.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2022

Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green’s function

Computing the numerical solution of the Kadanoff–Baym equations, a set of nonlinear integral differential equations satisfied by the two-time Green's functions derived from many-body perturbation theory for a quantum many-body system away from equilibrium, is a challenging task. Recently, we have successfully applied dynamic mode decomposition (DMD) to construct a data driven reduced order model that can be used to extrapolate the time-diagonal of a two-time Green's function from numerical solutions of the KBE within a small time window. In this paper, we extend the previous work and use DMD to predict off-diagonal elements of the two-time Green's function. We partition the two-time Green's function into a number of one-time functions along the diagonal and subdiagonals of the two-time window as well as in horizontal and vertical directions. We use DMD to construct separate reduced order models to predict the dynamics of these one-time functions in a two-step procedure. We extrapolate along diagonal and several subdiagonals within a subdiagonal band of a two-time window in the first step. In the second step, we use DMD to extrapolate the Green's function outside of the sub-diagonal band. In conclusion, we demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Quantum partition functions of composite particles in a hydrogen-helium plasma via path integral Monte Carlo

We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H{sup −}, H{sub 2}{sup +}, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Regarding the use and misuse of retinal protonated Schiff base photochemistry as a test case for time-dependent density-functional theory

The excited-state relaxation of retinal protonated Schiff bases (PSBs) is an important test case for biological applications of time-dependent (TD) density-functional theory (DFT). While well-known shortcomings of approximate TD-DFT might seem discouraging for application to PSB relaxation, progress continues to be made in the development of new functionals and of criteria allowing problematic excitations to be identified within the framework of TD-DFT itself. Furthermore, experimental and theoretical ab initio advances have recently lead to a revised understanding of retinal PSB photochemistry, calling for a reappraisal of the performance of TD-DFT in describing this prototypical photoactive system. Here, we re-investigate the performance of functionals in (TD-)DFT calculations in light of these new benchmark results, which we extend to larger PSB models. We focus on the ability of the functionals to describe primarily the early skeletal relaxation of the chromophore and investigate how far along the out-of-plane pathways these functionals are able to describe the subsequent rotation around formal single and double bonds. Conventional global hybrid and range-separated hybrid functionals are investigated as the presence of Hartree-Fock exchange reduces problems with charge-transfer excitations as determined by the Peach-Benfield-Helgaker-Tozer Λ criterion and by comparison with multi-reference perturbation theory results. While we confirm that most functionals cannot render the complex photobehavior of the retinal PSB, do we also observe that LC-BLYP gives the best description of the initial part of the photoreaction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Development on electromagnetic impedance function modeling and its estimation

Today the Electromagnetic methods such as magnetotellurics (MT) and controlled sources audio MT (CSAMT) is used in a broad variety of applications. Its usefulness in poor seismic areas and its negligible environmental impact are integral parts of effective exploration at minimum cost. As exploration was forced into more difficult areas, the importance of MT and CSAMT, in conjunction with other techniques, has tended to grow continuously. However, there are obviously important and difficult problems remaining to be solved concerning our ability to collect process and interpret MT as well as CSAMT in complex 3D structural environments. This talk aim at reviewing and discussing the recent development on MT as well as CSAMT impedance functions modeling, and also some improvements on estimation procedures for the corresponding impedance functions. In MT impedance modeling, research efforts focus on developing numerical method for computing the impedance functions of three dimensionally (3-D) earth resistivity models. On that reason, 3-D finite elements numerical modeling for the impedances is developed based on edge element method. Whereas, in the CSAMT case, the efforts were focused to accomplish the non-plane wave problem in the corresponding impedance functions. Concerning estimation of MT and CSAMT impedance functions, researches were focused on improving quality of the estimates. On that objective, non-linear regression approach based on the robust M-estimators and the Hilbert transform operating on the causal transfer functions, were used to dealing with outliers (abnormal data) which are frequently superimposed on a normal ambient MT as well as CSAMT noise fields. As validated, the proposed MT impedance modeling method gives acceptable results for standard three dimensional resistivity models. Whilst, the full solution based modeling that accommodate the non-plane wave effect for CSAMT impedances is applied for all measurement zones, including near-, transition-as well as the far-field zones, and consequently the plane wave correction is no longer needed for the impedances. In the resulting robust impedance estimates, outlier contamination is removed and the self consistency between the real and imaginary parts of the impedance estimates is guaranteed. Using synthetic and real MT data, it is shown that the proposed robust estimation methods always yield impedance estimates which are better than the conventional least square (LS) estimation, even under condition of severe noise contamination. A recent development on the constrained robust CSAMT impedance estimation is also discussed. By using synthetic CSAMT data it is demonstrated that the proposed methods can produce usable CSAMT transfer functions for all measurement zones.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Optimization of an exchange-correlation density functional for water

We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the “correct” parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗