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At least 1,783 records · Page 99
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DOE OSTI2012

Curvature and Frontier Orbital Energies in Density Functional Theory

Perdew et al. [Phys. Rev. Lett 49, 1691 (1982)] discovered and proved two different properties that exact Kohn-Sham density functional theory (DFT) must obey: (i) The exact total energy versus particle number must be a series of linear segments between integer electron points; (ii) Across an integer number of electrons, the exchange-correlation potential may ``jump’’ by a constant, known as the derivative discontinuity (DD). Here, we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT, the two are in fact two sides of the same coin. Absence of a derivative discontinuity necessitates deviation from piecewise linearity, and the latter can be used to correct for the former, thereby restoring the physical meaning of the orbital energies. Using selected small molecules, we show that this results in a simple correction scheme for any underlying functional, including semi-local and hybrid functionals as well as Hartree-Fock theory, suggesting a practical correction for the infamous gap problem of density functional theory. Moreover, we show that optimally-tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and show that this can be used as a sound theoretical basis for novel tuning strategies.

density functional theory↗
DOE OSTI2021

Ultraconserved enhancer function does not require perfect sequence conservation

Ultraconserved enhancer sequences show perfect conservation between human and rodent genomes, suggesting that their functions are highly sensitive to mutation. However, current models of enhancer function do not sufficiently explain this extreme evolutionary constraint. We subjected 23 ultraconserved enhancers to different levels of mutagenesis, collectively introducing 1,547 mutations, and examined their activities in transgenic mouse reporter assays. Overall, we find that the regulatory properties of ultraconserved enhancers are robust to mutation. Upon mutagenesis, nearly all (19/23, 83%) still functioned as enhancers at one developmental stage, as did most of those tested again later in development (5/9, 56%). Replacement of endogenous enhancers with mutated alleles in mice corroborated results of transgenic assays, including the functional resilience of ultraconserved enhancers to mutation. Furthermore, our findings show that the currently known activities of ultraconserved enhancers do not necessarily require the perfect conservation observed in evolution and suggest that additional regulatory or other functions contribute to their sequence constraint.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2013

Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions

In a previous work [J. Louko and E. Martínez-Pascual, “Constraint rescaling in refined algebraic quantisation: Momentum constraint,” J. Math. Phys. 52, 123504 (2011)], refined algebraic quantisation (RAQ) within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling one momentum-type constraint was investigated. In the present work, the first steps to generalise this analysis to cases where more constraints occur are developed. The system under consideration contains two momentum-type constraints, originally abelian, where rescalings of these constraints by a non-vanishing function of the coordinates are allowed. These rescalings induce structure functions at the level of the gauge algebra. Providing a specific parametrised family of real-valued scaling functions, the implementation of the corresponding rescaled quantum momentum-type constraints is performed using RAQ when the gauge algebra: (i) remains abelian and (ii) undergoes into an algebra of a nonunimodular group with nonconstant gauge invariant structure functions. Case (ii) becomes the first example known to the author where an open algebra is handled in refined algebraic quantisation. Challenging issues that arise in the presence of non-gauge invariant structure functions are also addressed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Generalized plasma dispersion function: One-solve-all treatment, visualizations, and application to Landau damping

A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the δ, flat top, triangular, κ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion γ∝∂f{sub 0}/∂v is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful tool for rigorous calculations of the linear wave and instability properties of plasma for general distribution functions. The results are also verified via a linear initial value simulation approach. Intuitive visualizations of the generalized plasma dispersion function are also provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Revisiting density functionals for the primitive model of electric double layers

Density functional theory (DFT) calculations are typically based on approximate functionals that link the free energy of a multi-body system of interest with the underlying one-body density distributions. Whereas good performance is often proclaimed for new developments, it is difficult to vindicate the theoretical merits relative to alternative versions without extensive comparison with the numerical results from molecular simulations. Besides, approximate functionals may defy statistical-mechanical sum rules and result in thermodynamic inconsistency. Here we compare systematically several versions of density functionals for ionic distributions near a charged surface using the primitive model of electric double layers. We find that the theoretical performance is sensitive not only to the specific forms of the density functional but also to the range of parameter space and the precise properties under consideration. In general, incorporation of the thermodynamic sum rule into the DFT calculations shows significant improvements for both electrochemical properties and ionic distributions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Two dimensional symmetric correlation functions of the S-circumflex operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} − S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters’ two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Modeling and characterizing anisotropic inclusion orientation in heterogeneous material via directional cluster functions and stochastic microstructure reconstruction

We present a framework to model and characterize the microstructure of heterogeneous materials with anisotropic inclusions of secondary phases based on the directional correlation functions of the inclusions. Specifically, we have devised an efficient method to incorporate both directional two-point correlation functions S{sub 2} and directional two-point cluster functions C{sub 2} that contain non-trivial topological connectedness information into the simulated annealing microstructure reconstruction procedure. Our framework is applied to model an anisotropic aluminum alloy and the accuracy of the reconstructed structural models is assessed by quantitative comparison with the actual microstructure obtained via x-ray tomography. We show that incorporation of directional clustering information via C{sub 2} significantly improves the accuracy of the reconstruction. In addition, a set of analytical “basis” correlation functions are introduced to approximate the actual S{sub 2} and C{sub 2} of the material. With the proper choice of basis functions, the anisotropic microstructure can be represented by a handful of parameters including the effective linear sizes of the iron-rich and silicon-rich inclusions along three orthogonal directions. This provides a general and efficient means for heterogeneous material modeling that enables one to significantly reduce the data set required to characterize the anisotropic microstructure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Hierarchy of model Kohn–Sham potentials for orbital-dependent functionals: A practical alternative to the optimized effective potential method

We describe a method for constructing a hierarchy of model potentials approximating the functional derivative of a given orbital-dependent exchange-correlation functional with respect to electron density. Each model is derived by assuming a particular relationship between the self-consistent solutions of Kohn–Sham (KS) and generalized Kohn–Sham (GKS) equations for the same functional. In the KS scheme, the functional is differentiated with respect to density, in the GKS scheme—with respect to orbitals. The lowest-level approximation is the orbital-averaged effective potential (OAEP) built with the GKS orbitals. The second-level approximation, termed the orbital-consistent effective potential (OCEP), is based on the assumption that the KS and GKS orbitals are the same. It has the form of the OAEP plus a correction term. The highest-level approximation is the density-consistent effective potential (DCEP), derived under the assumption that the KS and GKS electron densities are equal. The analytic expression for a DCEP is the OCEP formula augmented with kinetic-energy-density-dependent terms. In the case of exact-exchange functional, the OAEP is the Slater potential, the OCEP is roughly equivalent to the localized Hartree–Fock approximation and related models, and the DCEP is practically indistinguishable from the true optimized effective potential for exact exchange. All three levels of the proposed hierarchy require solutions of the GKS equations as input and have the same affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Electronic and transport properties edge functionalized graphene nanoribbons-An ab initio approach

With the help of ab initio approach we have investigated the electronic and transport properties of edge functionalized zigzag graphene nanoribbons using density functional theory. We have studied the energetic stability and Fermi energy of ZGNRs. We have reported that the edge functionalization of zigzag graphene nanoribbons can break the degeneracy that can be used to promote the onset of a semiconducting to metal transition or a half metal to semiconducting state. The edge functionalization also promotes a metal-semimetal transition. It has also been observed that the transmission spectrum of the edge functionalized ZGNRs are different from those of pristine.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2014

Excitation energies of molecules within time-independent density functional theory

Recently proposed exchange energy functional for excited-states is tested for obtaining excitation energies of diatomic molecules. The functional is the ground-state counterpart of the local-density approximation, the modified local spin density (MLSD). The MLSD functional is tested for the N{sub 2} and CO diatomic molecules. The excitation energy obtained with the MLSD functional for the N{sub 2} molecule is in close vicinity to that obtained from the exact exchange orbital functional, Krieger, Li and Iafrate (KLI). For the CO molecule, the departure in excitation energy is observed and is due to the overcorrection of self-interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

General coalescence conditions for the exact wave functions. II. Higher-order relations for many-particle systems

We derived the necessary conditions that must be satisfied by the non-relativistic time-independent exact wave functions for many-particle systems at a two-particle coalescence (or cusp) point. Some simple conditions are known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In a previous study, we derived an infinite number of necessary conditions that two-particle wave functions must satisfy at a coalescence point. In the present study, we extend these conditions to many-particle systems. They are called general coalescence conditions (GCCs), and Kato's CC and Rassolov and Chipman's CC are included as special conditions. GCCs can be applied not only to Coulombic systems but also to any system in which the interaction between two particles is represented in a power series of inter-particle distances. We confirmed the correctness of our derivation of the GCCs by applying the exact wave function of a harmonium in electron-electron and electron-nucleus coalescence situations. In addition, we applied the free complement (FC) wave functions of a helium atom to the GCCs to examine the accuracy of the FC wave function in the context of a coalescence situation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Density functional theory based generalized effective fragment potential method

We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Single or functionalized fullerenes interacting with heme group

The heme group is responsible for iron transportation through the bloodstream, where iron participates in redox reactions, electron transfer, gases detection etc. The efficiency of such processes can be reduced if the whole heme molecule or even the iron is somehow altered from its original oxidation state, which can be caused by interactions with nanoparticles as fullerenes. To verify how such particles alter the geometry and electronic structure of heme molecule, here we report first principles calculations based on density functional theory of heme group interacting with single C{sub 60} fullerene or with C{sub 60} functionalized with small functional groups (−CH{sub 3}, −COOH, −NH{sub 2}, −OH). The calculations shown that the system heme + nanoparticle has a different spin state in comparison with heme group if the fullerene is functionalized. Also a functional group can provide a stronger binding between nanoparticle and heme molecule or inhibit the chemical bonding in comparison with single fullerene results. In addition heme molecule loses electrons to the nanoparticles and some systems exhibited a geometry distortion in heme group, depending on the binding energy. Furthermore, one find that such nanoparticles induce a formation of spin up states in heme group. Moreover, there exist modifications in density of states near the Fermi energy. Although of such changes in heme electronic structure and geometry, the iron atom remains in the heme group with the same oxidation state, so that processes that involve the iron might not be affected, only those that depend on the whole heme molecule.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Triplet correlation functions in liquid water

Triplet correlations have been shown to play a crucial role in the transformation of simple liquids to anomalous tetrahedral fluids [M. Singh, D. Dhabal, A. H. Nguyen, V. Molinero, and C. Chakravarty, Phys. Rev. Lett. 112, 147801 (2014)]. Here we examine triplet correlation functions for water, arguably the most important tetrahedral liquid, under ambient conditions, using configurational ensembles derived from molecular dynamics (MD) simulations and reverse Monte Carlo (RMC) datasets fitted to experimental scattering data. Four different RMC data sets with widely varying hydrogen-bond topologies fitted to neutron and x-ray scattering data are considered [K. T. Wikfeldt, M. Leetmaa, M. P. Ljungberg, A. Nilsson, and L. G. M. Pettersson, J. Phys. Chem. B 113, 6246 (2009)]. Molecular dynamics simulations are performed for two rigid-body effective pair potentials (SPC/E and TIP4P/2005) and the monatomic water (mW) model. Triplet correlation functions are compared with other structural measures for tetrahedrality, such as the O–O–O angular distribution function and the local tetrahedral order distributions. In contrast to the pair correlation functions, which are identical for all the RMC ensembles, the O–O–O triplet correlation function can discriminate between ensembles with different degrees of tetrahedral network formation with the maximally symmetric, tetrahedral SYM dataset displaying distinct signatures of tetrahedrality similar to those obtained from atomistic simulations of the SPC/E model. Triplet correlations from the RMC datasets conform closely to the Kirkwood superposition approximation, while those from MD simulations show deviations within the first two neighbour shells. The possibilities for experimental estimation of triplet correlations of water and other tetrahedral liquids are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Self-interaction corrected density functional calculations of Rydberg states of molecular clusters: N,N-dimethylisopropylamine

Theoretical calculations of Rydberg excited states of molecular clusters consisting of N,N-dimethylisopropylamine molecules using a Perdew-Zunger self-interaction corrected energy functional are presented and compared with results of resonant multiphoton ionization measurements. The binding energy of the Rydberg electron in the monomer is calculated to be 2.79 eV and 2.27 eV in the 3s and 3p state, respectively, which compares well with measured values of 2.88 eV and 2.21 eV. Three different stable configurations of the dimer in the ground state were found using an energy functional that includes van der Waals interaction. The lowest ground state energy conformation has the two N-atoms widely separated, by 6.2 Å, while the Rydberg state energy is lowest for a configuration where the N-atoms of the two molecules come close together, separated by 3.7 Å. This conformational change is found to lower the Rydberg electron binding energy by 0.2 eV. The self-interaction corrected functional gives a highly localized hole on one of the two molecules, unlike results obtained using the PBE functional or the hybrid B3LYP functional which give a delocalized hole. For the trimer, the self-interaction corrected calculation gives a Rydberg electron binding energy lowered further by 0.13 eV as compared with the dimer. The calculated results compare well with trends observed in experimental measurements. The reduction of the Rydberg electron binding energy with cluster size can be ascribed to an effective delocalization of the positive charge of the hole by the induced and permanent dipole moments of the neighboring molecules. A further decrease observed to occur on a time scale of tens of ps can be ascribed to a structural rearrangement of the clusters in the Rydberg state where molecules rotate to orient their dipoles in response to the formation of the localized hole.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The ground state and electronic structure of Gd@C{sub 82}: A systematic theoretical investigation of first principle density functionals

As a representative lanthanide endohedral metallofullerene, Gd@C{sub 82} has attracted a widespread attention among theorists and experimentalists ever since its first synthesis. Through comprehensive comparisons and discussions, as well as references to the latest high precision experiments, we evaluated the performance of different computational methods. Our results showed that the appropriate choice of the exchange-correlation functionals is the decisive factor to accurately predict both geometric and electronic structures for Gd@C{sub 82}. The electronic structure of the ground state and energy gap between the septet ground state and the nonet low-lying state obtained from pure density functional methods, such as PBE and PW91, are in good agreement with current experiment. Unlike pure functionals, the popularly used hybrid functionals in previous studies, such as B3LYP, could infer the qualitative correct ground state only when small basis set for C atoms is employed. Furthermore, we also highlighted that other geometric structures of Gd@C{sub 82} with the Gd staying at different positions are either not stable or with higher energies. This work should provide some useful references for various theoretical methodologies in further density functional studies on Gd@C{sub 82} and its derivatives in the future.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Nested sampling of isobaric phase space for the direct evaluation of the isothermal-isobaric partition function of atomic systems

Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions.

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

Influence of the exchange and correlation functional on the structure of amorphous InSb and In{sub 3}SbTe{sub 2} compounds

We have investigated the structural, vibrational, and electronic properties of the amorphous phase of InSb and In{sub 3}SbTe{sub 2} compounds of interest for applications in phase change non-volatile memories. Models of the amorphous phase have been generated by quenching from the melt by molecular dynamics simulations based on density functional theory. In particular, we have studied the dependence of the structural properties on the choice of the exchange-correlation functional. It turns out that the use of the Becke-Lee-Yang-Parr functional provides models with a much larger fraction of In atoms in a tetrahedral bonding geometry with respect to previous results obtained with the most commonly used Perdew-Becke-Ernzerhof functional. This outcome is at odd with the properties of Ge{sub 2}Sb{sub 2}Te{sub 5} phase change compound for which the two exchange-correlation functionals yield very similar results on the structure of the amorphous phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗