Direct extraction of spatial correlation functions from limited x-ray tomography data for microstructural quantification
Abstract not provided
Li, Hechao↗
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Mechanisms and Reactivity of Tl(III) Main-Group-Metal–Alkyl Functionalization in Water
Metal-mediated C–H activation reactions generate metal–alkyl intermediates that can be converted into carbon–oxygen bonds through functionalization reactions. Although the mechanisms and reactivity of C–H activation reactions have been well studied for transition-metal complexes, much less is known about functionalization reactions, especially for main-group-metal–alkyl complexes. Here we report density functional theory calculations on the reaction thermodynamics and kinetic pathways for main-group, p-block-metal Tl III –methyl functionalization reactions in water using a combination of continuum and explicit/continuum solvent models. Particularly, we examined the oxygen functionalization of (OAc)Tl III (CH 3 ) 2 and (OAc) 2 Tl III (CH 3 ) in water where in both cases functionalization gives methyl acetate and methanol. Our calculations suggest that (OAc)Tl III (CH 3 ) 2 is thermodynamically and kinetically stable against bond homolysis, heterolysis, protonolysis, and all reductive functionalization pathways. Functionalization is only possible after methyl anion group transfer to Tl III (OAc) 3 to give (OAc) 2 Tl III (CH 3 ). Our calculations indicate that this monomethyl structure is functionalized by acetate dissociation to give a Tl monocation and then a one-step nucleophilic functionalization where water and acetate have competitive transition states.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The Biogeographic Pattern of Microbial Functional Genes along an Altitudinal Gradient of the Tibetan Pasture
As the highest place of the world, the Tibetan plateau is a fragile ecosystem. Given the importance of microbial communities in driving soil nutrient cycling, it is of interest to document the microbial biogeographic pattern here. We adopted a microarray-based tool named GeoChip 4.0 to investigate grassland microbial functional genes along an elevation gradient from 3200 to 3800 m above sea level open to free grazing by local herdsmen and wild animals. Interestingly, microbial functional diversities increase with elevation, so does the relative abundances of genes associated with carbon degradation, nitrogen cycling, methane production, cold shock and oxygen limitation. The range of Shannon diversities (10.27-10.58) showed considerably smaller variation than what was previously observed at ungrazed sites nearby (9.95-10.65), suggesting the important role of livestock grazing on microbial diversities. Closer examination showed that the dissimilarity of microbial community at our study sites increased with elevations, revealing an elevation-decay relationship of microbial functional genes. Both microbial functional diversity and the number of unique genes increased with elevations. Furthermore, we detected a tight linkage of greenhouse gas (CO 2 ) and relative abundances of carbon cycling genes. Our biogeographic study provides insights on microbial functional diversity and soil biogeochemical cycling in Tibetan pastures.
altitudinal gradient↗
Cosmic reionization on computers: the faint end of the galaxy luminosity function
Using numerical cosmological simulations completed under the “Cosmic Reionization On Computers” project, I explore theoretical predictions for the faint end of the galaxy UV luminosity functions at z≳6. A commonly used Schechter function approximation with the magnitude cut at M{sub cut}∼−13 provides a reasonable fit to the actual luminosity function of simulated galaxies. When the Schechter functional form is forced on the luminosity functions from the simulations, the magnitude cut M{sub cut} is found to vary between −12 and −14 with a mild redshift dependence. An analytical model of reionization from Madau et al., as used by Robertson et al., provides a good description of the simulated results, which can be improved even further by adding two physically motivated modifications to the original Madau et al. equation.
79 ASTRONOMY AND ASTROPHYSICS↗
Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3d Transition Metals?
Coupled-cluster (CC) methods have been extensively used as the high-level approach in quantum electronic structure theory to predict various properties of molecules when experimental results are unavailable. It is often assumed that CC methods, if they include at least up to connected-triple-excitation quasiperturbative corrections to a full treatment of single and double excitations (in particular, CCSD(T)), and a very large basis set, are more accurate than Kohn–Sham (KS) density functional theory (DFT). In the present work, we tested and compared the performance of standard CC and KS methods on bond energy calculations of 20 3d transition metal-containing diatomic molecules against the most reliable experimental data available, as collected in a database called 3dMLBE20. It is found that, although the CCSD(T) and higher levels CC methods have mean unsigned deviations from experiment that are smaller than most exchange-correlation functionals for metal–ligand bond energies of transition metals, the improvement is less than one standard deviation of the mean unsigned deviation. Furthermore, on average, almost half of the 42 exchange-correlation functionals that we tested are closer to experiment than CCSD(T) with the same extended basis set for the same molecule. The results show that, when both relativistic and core–valence correlation effects are considered, even the very high-level (expensive) CC method with single, double, triple, and perturbative quadruple cluster operators, namely, CCSDT(2)Q, averaged over 20 bond energies, gives a mean unsigned deviation (MUD(20) = 4.7 kcal/mol when one correlates only valence, 3p, and 3s electrons of transition metals and only valence electrons of ligands, or 4.6 kcal/mol when one correlates all core electrons except for 1s shells of transition metals, S, and Cl); and that is similar to some good xc functionals (e.g., B97-1 (MUD(20) = 4.5 kcal/mol) and PW6B95 (MUD(20) = 4.9 kcal/mol)) when the same basis set is used. We found that, for both coupled cluster calculations and KS calculations, the T1 diagnostics correlate the errors better than either the M diagnostics or the B1 DFT-based diagnostics. The potential use of practical standard CC methods as a benchmark theory is further confounded by the finding that CC and DFT methods usually have different signs of the error. We conclude that the available experimental data do not provide a justification for using conventional single-reference CC theory calculations to validate or test xc functionals for systems involving 3d transition metals.
Environmental Molecular Sciences Laboratory↗
Quantum Monte Carlo benchmark of exchange-correlation functionals for bulk water
Abstract not provided
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Structure-Assisted Functional Anchor Implantation in Robust Metal-Organic Frameworks with Ultra large Pores
A facile functionalization assisted by the structural attributes of PCN-333 has been studied while maintaining the integrity of the parent MOF including ultralarge pores, chemical robustness, and crystallinity. Herein we thoroughly analyzed ligand exchange phenomena in PCN-333 and demonstrate that the extent of exchange can be tailored by varying the exchange conditions as potential applications may require. Through this method a variety of functional groups are incorporated into PCN-333. To further show the capabilities of this system introduction of a BODIPY fluorophore as a secondary functionality was performed to the functionalized framework via a click reaction. We anticipate the PCN-333 with functional anchor can serve as a stable platform for further chemistry to be explored in future applications
Park, J↗
Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory
Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Electron energy distributions and electron impact source functions in Ar/N{sub 2} inductively coupled plasmas using pulsed power
In plasma materials processing, such as plasma etching, control of the time-averaged electron energy distributions (EEDs) in the plasma allows for control of the time-averaged electron impact source functions of reactive species in the plasma and their fluxes to surfaces. One potential method for refining the control of EEDs is through the use of pulsed power. Inductively coupled plasmas (ICPs) are attractive for using pulsed power in this manner because the EEDs are dominantly controlled by the ICP power as opposed to the bias power applied to the substrate. In this paper, we discuss results from a computational investigation of EEDs and electron impact source functions in low pressure (5–50 mTorr) ICPs sustained in Ar/N{sub 2} for various duty cycles. We find there is an ability to control EEDs, and thus source functions, by pulsing the ICP power, with the greatest variability of the EEDs located within the skin depth of the electromagnetic field. The transit time of hot electrons produced in the skin depth at the onset of pulse power produces a delay in the response of the EEDs as a function of distance from the coils. The choice of ICP pressure has a large impact on the dynamics of the EEDs, whereas duty cycle has a small influence on time-averaged EEDs and source functions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Dark Energy Survey year 1 results: Joint analysis of galaxy clustering, galaxy lensing, and CMB lensing two-point functions
We perform a joint analysis of the auto and cross-correlations between three cosmic fields: the galaxy density field, the galaxy weak lensing shear field, and the cosmic microwave background (CMB) weak lensing convergence field. These three fields are measured using roughly 1300 sq. deg. of overlapping optical imaging data from first year observations of the Dark Energy Survey (DES) and millimeter-wave observations of the CMB from both the South Pole Telescope Sunyaev-Zel’dovich survey and Planck. We present cosmological constraints from the joint analysis of the two-point correlation functions between galaxy density and galaxy shear with CMB lensing. We test for consistency between these measurements and the DES-only two-point function measurements, finding no evidence for inconsistency in the context of flat Λ CDM cosmological models. Performing a joint analysis of five of the possible correlation functions between these fields (excluding only the CMB lensing autospectrum) yields S 8 ≡ σ 8 $\sqrt{Ω_{m}}/0.3$ = 0.782$^{+0.019}_{-0.025}$ and Ω m = 0.260$^{+0.029}_{-0.019}$. We test for consistency between these five correlation function measurements and the Planck -only measurement of the CMB lensing autospectrum, again finding no evidence for inconsistency in the context of flat Λ CDM models. Combining constraints from all six two-point functions yields S 8 = 0.776$^{+0.014}_{-0.021}$ and Ω m = 0.271$^{+0.022}_{-0.016}$. These results provide a powerful test and confirmation of the results from the first year DES joint-probes analysis.
Abbott, T. M. C.↗
Introducing constricted variational density functional theory in its relaxed self-consistent formulation (RSCF-CV-DFT) as an alternative to adiabatic time dependent density functional theory for studies of charge transfer transitions
We have applied the relaxed and self-consistent extension of constricted variational density functional theory (RSCF-CV-DFT) for the calculation of the lowest charge transfer transitions in the molecular complex X-TCNE between X = benzene and TCNE = tetracyanoethylene. Use was made of functionals with a fixed fraction (α) of Hartree-Fock exchange ranging from α = 0 to α = 0.5 as well as functionals with a long range correction (LC) that introduces Hartree-Fock exchange for longer inter-electronic distances. A detailed comparison and analysis is given for each functional between the performance of RSCF-CV-DFT and adiabatic time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation. It is shown that in this particular case, all functionals afford the same reasonable agreement with experiment for RSCF-CV-DFT whereas only the LC-functionals afford a fair agreement with experiment using TDDFT. We have in addition calculated the CT transition energy for X-TCNE with X = toluene, o-xylene, and naphthalene employing the same functionals as for X = benzene. It is shown that the calculated charge transfer excitation energies are in as good agreement with experiment as those obtained from highly optimized LC-functionals using adiabatic TDDFT. We finally discuss the relation between the optimization of length separation parameters and orbital relaxation in the RSCF-CV-DFT scheme.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Using the electron localization function to correct for confinement physics in semi-local density functional theory
We have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu–O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Discovery of Stable Surfaces with Extreme Work Functions by High‐Throughput Density Functional Theory and Machine Learning
Abstract The work function is the key surface property that determines the energy required to extract an electron from the surface of a material. This property is crucial for thermionic energy conversion, band alignment in heterostructures, and electron emission devices. This work presents a high‐throughput workflow using density functional theory (DFT) to calculate the work function and cleavage energy of 33,631 slabs (58,332 work functions) that are created from 3,716 bulk materials. The number of calculated surface properties surpasses the previously largest database by a factor of ≈27. Several surfaces with an ultra‐low (<2 eV) and ultra‐high (>7 eV) work function are identified. Specifically, the (100)‐Ba‐O surface of BaMoO 3 and the (001)‐F surface of Ag 2 F have record‐low (1.25 eV) and record‐high (9.06 eV) steady‐state work functions. Based on this database a physics‐based approach to featurize surfaces is utilized to predict the work function. The random forest model achieves a test mean absolute error (MAE) of 0.09 eV, comparable to the accuracy of DFT. This surrogate model enables rapid predictions of the work function (≈ 10 5 faster than DFT) across a vast chemical space and facilitates the discovery of material surfaces with extreme work functions for energy conversion and electronic device applications.
97 MATHEMATICS AND COMPUTING↗
Function space requirements for the single-electron functions within the multiparticle Schroedinger equation
Our previously described method to approximate the many-electron wavefunction in the multiparticle Schroedinger equation reduces this problem to operations on many single-electron functions. In this work, we analyze these operations to determine which function spaces are appropriate for various intermediate functions in order to bound the output. This knowledge then allows us to choose the function spaces in which to control the error of a numerical method for single-electron functions. We find that an efficient choice is to maintain the single-electron functions in L{sup 2} Intersection L{sup 4}, the product of these functions in L{sup 1} Intersection L{sup 2}, the Poisson kernel applied to the product in L{sup 4}, a function times the Poisson kernel applied to the product in L{sup 2}, and the nuclear potential times a function in L{sup 4/3}. Due to the integral operator formulation, we do not require differentiability.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Hexagon functions and the three-loop remainder function
We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.
extended supersymmetry↗
Examination of How Well Long-Range-Corrected Density Functionals Satisfy the Ionization Energy Theorem
For this work, we calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients (r 2 ) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee–Yang–Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee–Yang–Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Water on BN doped benzene: A hard test for exchange-correlation functionals and the impact of exact exchange on weak binding
Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces, whereas the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we show that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B{sub 3}N{sub 3}H{sub 6}) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential
A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗