Fraction Of Exchange Research Articles

Disruption of liquid/liquid phase separation in asymmetric GUVs prepared by hemifusion.

Model asymmetric bilayers are useful for studying the coupling between lateral and transverse lipid organization. Here, we used calcium-induced hemifusion to create asymmetric giant unilamellar vesicles (aGUVs) for exploring the phase behavior of 16:0-PC/16:1-PC/Cholesterol, a simplified model for the mammalian plasma membrane. Symmetric GUVs (sGUVs) were first prepared using a composition that produced coexisting liquid-disordered and liquid-ordered phases visible by confocal fluorescence microscopy. The sGUVs were then hemifused to a supported lipid bilayer (SLB) composed of uniformly mixed 16:1-PC/Cholesterol. The extent of outer leaflet exchange was quantified in aGUVs in two ways: (1) from the reduction in fluorescence intensity of a lipid probe initially in the sGUV ("probe exit"); or (2) from the gain in intensity of a probe initially in the SLB ("probe entry"). These measurements revealed a large variability in the extent of outer leaflet exchange in aGUVs within a given preparation, and two populations with respect to their phase behavior: a subset of vesicles that remained phase separated, and a second subset that appeared uniformly mixed. Moreover, a correlation between phase behavior and extent of asymmetry was observed, with more strongly asymmetric vesicles having a greater probability of being uniformly mixed. We also observed substantial overlap between these populations, an indication that the uncertainty in measured exchange fraction is high. We developed models to determine the position of the phase boundary (i.e., the fraction of outer leaflet exchange above which domain formation is suppressed) and found that the phase boundaries determined separately from probe-entry and probe-exit data are in good agreement. Our models also provide improved estimates of the compositional uncertainty of individual aGUVs. We discuss several potential sources of uncertainty in the determination of lipid exchange from fluorescence measurements.

How Much Electron Donation Is There In Transition Metal Complexes? A Computational Study.

The "dative" covalent interactions between metals and ligands in coordination compounds, i.e., metal-to-ligand and ligand-to-metal donation, are manifestations of electron delocalization and subject to errors in approximate calculations. This work addresses the extent of dative bonding/donation in a series of closed-shell transition metal complexes. Several Kohn-Sham density functionals, representing different "rungs" of approximations, along with post-Hartree-Fock methods are assessed in comparison to CCSD(T). Two widely used nonhybrid and global hybrid density functionals (B3LYP, PBE0) tend to produce notably too strong donation. Global hybrids with elevated fractions of exact exchange (40 to 50%) and the range-separated exchange functional CAM-B3LYP tend to perform better for the description of the donation. The performance of a double-hybrid functional is found to be quite satisfactory, correcting errors seen in MP2 calculations. A fast approximate coupled-cluster model (DLPNO-CCSD) also gives a reasonable description of the donation, with a tendency to underestimate its extent.

Investigation of local Nusselt number in a rarefied microchannel gas flow using Direct Simulation Monte Carlo method

Heat transfer in microscale and rarefied gaseous flows has been investigated for high Knudsen number (Kn) flows using the Direct Simulation Monte Carlo (DSMC) method. A wide range of Kn [0.05 – 5], pressure ratio [1.2 – 4] and wall temperature [323 K – 723 K] is studied. The heat flux and local Nusselt number (Nu) are found to exhibit three distinct sections along the length of the microchannel – heat transfer-dominated section, constant heat transfer section and exit section. The defining roles of different effects such as non-equilibrium conditions at the wall, viscous dissipation, axial conduction, pressure work, and shear work have been considered implicitly in the DSMC method. These parameters are seen to influence the heat transfer differently at lower and higher Kn. These results help to quantify the fraction of total heat exchange and reveals the complex interplay of various terms of the energy equation in gas flow in microchannels.

Delocalization error poisons the density-functional many-body expansion.

The many-body expansion is a fragment-based approach to large-scale quantum chemistry that partitions a single monolithic calculation into manageable subsystems. This technique is increasingly being used as a basis for fitting classical force fields to electronic structure data, especially for water and aqueous ions, and for machine learning. Here, we show that the many-body expansion based on semilocal density functional theory affords wild oscillations and runaway error accumulation for ion-water interactions, typified by F-(H2O) N with N ≳ 15. We attribute these oscillations to self-interaction error in the density-functional approximation. The effect is minor or negligible in small water clusters, explaining why it has not been noticed previously, but grows to catastrophic proportion in clusters that are only moderately larger. This behavior can be counteracted with hybrid functionals but only if the fraction of exact exchange is ≳50%, whereas modern meta-generalized gradient approximations including ωB97X-V, SCAN, and SCAN0 are insufficient to eliminate divergent behavior. Other mitigation strategies including counterpoise correction, density correction (i.e., exchange-correlation functionals evaluated atop Hartree-Fock densities), and dielectric continuum boundary conditions do little to curtail the problematic oscillations. In contrast, energy-based screening to cull unimportant subsystems can successfully forestall divergent behavior. These results suggest that extreme caution is warranted when the many-body expansion is combined with density functional theory.

Constructing Mixed Density Functionals for Describing Dissociative Chemisorption on Metal Surfaces: Basic Principles.

The production of a majority of chemicals involves heterogeneous catalysis at some stage, and the rates of many heterogeneously catalyzed processes are governed by transition states for dissociative chemisorption on metals. Accurate values of barrier heights for dissociative chemisorption on metals are therefore important to benchmarking electronic structure theory in general and density functionals in particular. Such accurate barriers can be obtained using the semiempirical specific reaction parameter (SRP) approach to density functional theory. However, this approach has thus far been rather ad hoc in its choice of the generic expression of the SRP functional to be used, and there is a need for better heuristic approaches to determining the mixing parameters contained in such expressions. Here we address these two issues. We investigate the ability of several mixed, parametrized density functional expressions combining exchange at the generalized gradient approximation (GGA) level with either GGA or nonlocal correlation to reproduce barrier heights for dissociative chemisorption on metal surfaces. For this, seven expressions of such mixed density functionals are tested on a database consisting of results for 16 systems taken from a recently published slightly larger database called SBH17. Three expressions are derived that exhibit high tunability and use correlation functionals that are either of the PBE GGA form or of one of two limiting nonlocal forms also describing the attractive van der Waals interaction in an approximate way. We also find that, for mixed density functionals incorporating GGA correlation, the optimum fraction of repulsive RPBE GGA exchange obtained with a specific GGA density functional is correlated with the charge-transfer parameter, which is equal to the difference in the work function of the metal surface and the electron affinity of the molecule. However, the correlation is generally not large and not large enough to obtain accurate guesses of the mixing parameter for the systems considered, suggesting that it does not give rise to a very effective search strategy.

Spin state and magnetic coupling in polynuclear Ni(II) complexes from density functional theory: is there an optimal amount of Fock exchange?

Reliable prediction of the ground-state spin and magnetic coupling constants in transition-metal complexes is a well-known challenge for density functional theory (DFT). One popular strategy for addressing this long-standing issue involves the modification of the fraction of Fock exchange in a hybrid functional. Here we explore the viability of this approach using three polynuclear metal-organic complexes based on a Ni4O4 cubane motif, having different ground state spin values (S = 0, 2, 4) owing to the use of different ligands. We systematically search for an optimum fraction of Fock exchange, across various global, range-separated, and double hybrid functionals. We find that for all functionals tested, at best there only exists a very narrow range of Fock exchange fractions which results in a correct prediction of the ground-state spin for all three complexes. The useful range is functional dependent, but general trends can be identified. Typically, at least two similar systems must be used in order to determine both an upper and lower limit of the optimal range. This is likely owing to conflicting demands of minimizing delocalization errors, which typically requires a higher percentage of Fock exchange, and addressing static correlation, which typically requires a lower one. Furthermore, we find that within the optimal range of Fock exchange, the signand relative magnitude of Ni-Ni magnetic coupling constants are reasonably well reproduced, but there is still room for quantitative improvement in the prediction. Thus, the prediction of spin state and magnetic coupling in polynuclear complexes remains an ongoing challenge for DFT.

Nonempirical Range-Separated Hybrid Functional with Spatially Dependent Screened Exchange.

Electronic structure calculations based on density functional theory (DFT) have successfully predicted numerous ground-state properties of a variety of molecules and materials. However, exchange and correlation functionals currently used in the literature, including semilocal and hybrid functionals, are often inaccurate to describe the electronic properties of heterogeneous solids, especially systems composed of building blocks with large dielectric mismatch. Here, we present a dielectric-dependent range-separated hybrid functional, screened-exchange range-separated hybrid (SE-RSH), for the investigation of heterogeneous materials. We define a spatially dependent fraction of exact exchange inspired by the static Coulomb-hole and screened-exchange (COHSEX) approximation used in many-body perturbation theory, and we show that the proposed functional accurately predicts the electronic structure of several nonmetallic interfaces, three- and two-dimensional, pristine, and defective solids and nanoparticles.

Rutile, anatase, brookite and titania thin film from Hubbard corrected and hybrid DFT

As a benchmark, the structural, electronic and optical properties of the three main phases of TiO2 crystals have been calculated using Hubbard U correction and hybrid functional methods in density-functional theory. These calculations are compared concerning the available experimental observations on pristine TiO2 crystals. Modified hybrid functionals, particularly the PBE0 functional with 11.4% fraction of exact exchange, are shown to provide highly accurate atomic structures and also accurate electronic structure data, including optical excitation energies. With DFT + U, accurate optical spectra are also possible, but only if the Hubbard U is applied on the O 2p electrons exclusively. Furthermore, both methods, the 11.4%-PBE0 hybrid functional and the DFT + U p scheme have been used to study TiO2 amorphous ultra-thin films, confirming the agreement of the two methods even with respect to small details of the optical spectra. Our results show that the proposed DFT + U p methodology is computationally efficient, but still accurate. It can be applied to well-ordered TiO2 polymorphs as well as to amorphous TiO2 and will allow for the calculations of complex titania-based structures.

High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeA Approach.

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank operator), and (iii) adaptively compressed exchange (ACE, a low-rank approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H2O)64 configurations (with densities spanning 0.4-1.7 g/cm3), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H2O)64 configurations. Using an out-of-sample set of (H2O)512 configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

Computational study of defect complexes in β-LiGaO2 and their relation to the donor–acceptor-pair recombination

Hybrid functional calculations are presented for defects in LiGaO2 with the fraction of non-local exchange adjusted to reproduce the recently reported exciton gap of 6.0 eV. We study how the defect transition levels of the main native defects change with respect to the band edges compared to earlier calculations which assumed a smaller bandgap near 5.1 eV. In addition, we consider defect complexes formed by combining the main native donor GaLi with the main acceptors, VLi and LiGa antisites as a function of their relative position. These results are used to tentatively identify the photoluminescence bands previously assigned to donor–acceptor-pair recombination.

Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization.

This work introduces a new class of hybrid density functional theory (DFT) approximations, which incorporate different fractions of nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are related to range-separated hybrid functionals, which incorporate different fractions of nonlocal exchange at different electron-electron separations. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, introduces the projected operator into the noninteracting Kohn-Sham reference system, and employs a formally exact density functional to model the remaining electron-electron interactions. Projected hybrids, like range-separated hybrids, approximate the partially interacting reference system's ground-state wave function as a single Slater determinant. Projected hybrids are readily implemented into existing density functional codes, requiring only a projection of the one-particle density matrices and exchange operators entering existing routines. This work also presents an application to core electron ionization. Projecting onto core atomic orbitals allows us to introduce additional nonlocal exchange into atomic core regions. This reduces the impact of self-interaction error on computed core electron properties. Benchmark studies are reported for PBE0c70, a core-projected variant of the Perdew-Burke-Ernzerhof global hybrid PBE0, in which the fraction of nonlocal exchange is increased from 25% to 70% in atomic core regions. PBE0c70-predicted core orbital energies accurately recover nonrelativistic core-electron binding energies of second-period elements Li-Ne and third-period elements Na-Ar, without degrading the good performance of PBE0 for atomization energies and valence ionization potentials.

CRYSTAL23: A Program for Computational Solid State Physics and Chemistry.

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Faster Exact Exchange for Solids via occ-RI-K: Application to Combinatorially Optimized Range-Separated Hybrid Functionals for Simple Solids with Pseudopotentials Near the Basis Set Limit.

In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the Gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The largest calculation performed in this work involves 16 electrons and 350 basis functions in the unit cell utilizing a 6 × 6 × 6 k-mesh. With 20-27% exact exchange, global hybrid functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly with a root-mean-square deviation (RMSD) of 0.61-0.77 eV, while other global hybrid functionals such as M06-2X (2.02 eV) and MN15 (1.05 eV) show higher RMSD due to their increased fraction of exact exchange. A short-range hybrid functional, HSE achieves a similar RMSD (0.76 eV) but shows a notable underestimation of band gaps due to the complete lack of long-range exchange. We found that two combinatorially optimized range-separated hybrid functionals, ωB97X-rV (3.94 eV) and ωB97M-rV (3.40 eV), and the two other range-separated hybrid functionals, CAM-B3LYP (2.41 eV) and CAM-QTP01 (4.16 eV), significantly overestimate the band gap because of their high fraction of long-range exact exchange. Given the failure of ωB97X-rV and ωB97M-rV, we have yet to find a density functional that offers consistent performance for both molecules and solids. Our algorithm development and density functional assessment will serve as a stepping stone toward developing more accurate hybrid functionals and applying them to practical applications.

Role of spin currents on electron-electron interaction in the quantum spin Hall phase

The spin current density functional theory (SCDFT) is the generalization of the standard DFT to treat a fermionic system embedded in the effective external field produced by the spin-orbit coupling interaction. Even in the absence of a spin polarization, the SCDFT requires the electron-electron potential to depend on the spin currents ${\mathbf{J}}^{x}, {\mathbf{J}}^{y}$, and ${\mathbf{J}}^{z}$, which only recently was made possible for practical relativistic quantum-mechanical simulations, through the inclusion of a fraction of nonlocal Fock exchange into local-density or generalized-gradient density functional approximations [J. K. Desmarais, J.-P. Flament, and A. Erba, Phys. Rev. B 102, 235118 (2020)]. Here, we apply the SCDFT to the quantum spin Hall phase and show how it improves (even qualitatively) the description of its electronic features relative to the DFT. We study the Bi (001) 2D bilayer and its band insulator to topological insulator phase transition (via $s+{p}_{z}\ensuremath{\leftrightarrow}{p}_{x}+i{p}_{y}$ band inversion) as a function of mechanical strain. We show that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone at the $\mathrm{\ensuremath{\Gamma}}$ point in the valence band structure at the onset of the topological phase transition. Finally, the valence band structure of this system is rationalized using a simple first-order $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ quasidegenerate perturbation theory model.

Computational modeling of redox enzymes.

A computational methodology is briefly described, which appears to be able to accurately describe the mechanisms of redox active enzymes. The method is built on hybrid density functional theory where the inclusion of a fraction of exact exchange is critical. Two examples of where the methodology has been applied are described. The first example is the mechanism for water oxidation in photosystem II, and the second one is the mechanism for N2 activation by nitrogenase. The mechanism for PSII has obtained very strong support from subsequent experiments. For nitrogenase, the calculations suggest that there should be an activation process prior to catalysis, which is still strongly debated.

Nonunique fraction of Fock exchange for defects in two-dimensional materials

By investigating the vacancy and substitutional defects in monolayer ${\mathrm{WS}}_{2}$ with hybrid functionals, we find that there is no unique amount of Fock exchange that concurrently satisfies the generalized Koopmans' condition and reproduces the band-gap and band-edge positions. Fixing the mixing parameter of Fock exchange based on the band gap can lead to qualitatively incorrect defect physics in two-dimensional materials. Instead, excellent agreement is achieved with both experiment and many-body perturbation theory within the $GW$ approximation once the mixing parameters are tuned individually for the defect species and the band edges. We show the departure from a unique optimized mixing parameter is inherent to two-dimensional systems as the band edges experience a reduced screening while the localized defects are subject to bulklike screening.

Role of exact exchange in the structural and electronic properties of the α and γ phases of cerium: a density functional theory study

Modeling the α–γ isostructural phase transition of cerium (Ce) within the framework of density functional theory is challenging because the 4f electron in Ce is difficult to characterize. The use of a fraction of exact exchange in the hybrid functional (2012 Phys. Rev. Lett. 109 146402) predicts the existence of the α and γ phases but their relative energy is inconsistent with the experiments. In fact, the role of exact exchange in affecting properties of the α and γ phases has not been well investigated. In this regard, we choose a variable amount of exact exchange (0.05–0.4) and systematically explore the properties of the α and γ phases of Ce including cohesive energies, lattice constants, bulk moduli, magnetic moments, and 4f electron numbers. Notably, a small portion of exact exchange close to 0.1 yields an accurate description of these properties, in particular the predicted relative energy between the α and γ phases agrees with the experiment. We further analyze the density of states, partial density of states, band structures and electron densities of the two phases. We observe that the exact exchange substantially affects the γ phase by localizing the 4f electrons, while it tends to delocalize the electrons in the α phase. Our work provides deep insights into the structural and electronic properties of the α and γ phases of Ce by elucidating the role of exact exchange in hybrid functional calculations.

Single Excitation Energies Obtained from the Ensemble “HOMO–LUMO Gap”: Exact Results and Approximations

In calculations based on density functional theory, the "HOMO-LUMO gap" (difference between the highest occupied and lowest unoccupied molecular orbital energies) is often used as a low-cost, ad hoc approximation for the lowest excitation energy. Here we show that a simple correction based on rigorous ensemble density functional theory makes the HOMO-LUMO gap exact in principle and significantly more accurate in practice. The introduced perturbative ensemble density functional theory approach predicts different and useful values for singlet-singlet and singlet-triplet excitations, using semilocal and hybrid approximations. Excitation energies are similar in quality to time-dependent density functional theory, especially at high fractions of exact exchange. The approach therefore offers an easy-to-implement and low-cost route to robust prediction of molecular excitation energies.

Extracellular Vesicles Mediate the Intercellular Exchange of Nanoparticles.

To exert their therapeutic effects, nanoparticles (NPs) often need to travel into the tissues composed of multilayered cells. Accumulative evidence has revealed the crucial role of transcellular transport route (entry into one cell, exocytosis, and re‐entry into another) in this process. While NP endocytosis and subcellular transport are intensively characterized, the exocytosis and re‐entry steps are poorly understood, which becomes a barrier for NP delivery into complex tissues. Here, the authors term the exocytosis and re‐entry steps together as intercellular exchange. A collagen‐based three‐dimension assay is developed to specifically quantify the intercellular exchange of NPs, and distinguish the contributions of several potential mechanisms. The authors show that NPs can be exocytosed freely or enclosed inside extracellular vesicles (EVs) for re‐entry, while direct cell–cell contact is hardly involved. EVs account for a significant fraction of NP intercellular exchange, and its importance in NP transport is demonstrated in vitro and in vivo. While freely released NPs engage with the same receptors for re‐entry, EV‐enclosed ones bypass this dependence. These studies provide an easy and precise system to investigate the intercellular exchange stage of NP delivery, and shed the first light in the importance of EVs in NP transport between cells and into complex tissues.

Canopy Solar-Induced Chlorophyll Fluorescence and Its Link to Transpiration in a Temperate Evergreen Needleleaf Forest during the Fall Transition

Northern hemisphere evergreen needleleaf forest (ENF) contributes a significant fraction of global water exchange but regional transpiration (T) observation in ENF ecosystems is still challenging. Traditional remote sensing techniques and terrestrial biosphere models reproduce the transpiration seasonality with difficulty, and with large uncertainties. Solar-induced chlorophyll fluorescence (SIF) emission from vegetation correlates to photosynthesis at multiple spatial and temporal scales. However, how SIF links to transpiration of evergreen forest during seasonal transition is unclear. Here, we explored the relationship between canopy SIF and T retrieved from ground observation towers in ENF. We also examined the role of meteorological and soil factors on the relationship between SIF and T. A slow decrease of SIF and T with a fast reduction in photosynthetically active radiation (PAR), air temperature, vapor pressure deficit (VPD), soil temperature and soil water content (SWC) were found in the ENF during the fall transition. The correlation between SIF and T at hourly and daily scales varied significantly among different months (Pearson correlation coefficient = 0.29–0.68, p < 0.01). SIF and T were significantly linearly correlated at hourly (R2 = 0.53, p < 0.001) and daily (R2 = 0.67, p < 0.001) timescales in the October. Air temperature and PAR were the major moderating factors for the relationship between SIF and T in the fall transition. Soil water content (SWC) influenced the SIF-T relationship at an hourly scale. Soil temperature and VPD’s effect on the SIF-T relationship was evident at a daily scale. This study can help extend the possibility of constraining ecosystem T by SIF at an unprecedented spatiotemporal resolution during season transitions.