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For two Banach spaces X X and Y Y , we denote by K ( X , Y ) K(X,Y) (resp. B ( X , Y ) B(X,Y) ) the space of all compact (resp. bounded) linear operators from X X to Y Y . In this paper, we show that for 1 ≤ p , q > ∞ 1\leq p,q>\infty , K ( ℓ p , ℓ q ) K(\ell _{p},\ell _{q}) is an 8-Lipschitz retract of B ( ℓ p , ℓ q ) B(\ell _{p},\ell _{q}) .

In this paper, we first show that for a Banach space X there is a fully order-reversing mapping T from conv(X) (the cone of all extended real-valued lower semicontinuous proper convex functions defined on X) onto itself if and only if X is reflexive and linearly isomorphic to its dual X*. Then we further prove the following generalized Artstein-Avidan-Milman representation theorem: For every fully order-reversing mapping T: conv(X) → conv(X) there exist a linear isomorphism U: X → X*, x 0 * , φ0 ∈ X*, α > 0 and r0 ∈ ℝ so that $$(Tf)(x) = \alpha ({\cal F}f)(Ux + x_0^ *) + \left\langle {{\varphi _0},x} \right\rangle + {r_0},\;\;\;\;\;\forall x \in X,$$ where ${\cal F}$ : conv(X) → conv(X*) is the Fenchel transform. Hence, these resolve two open questions. We also show several representation theorems of fully order-preserving mappings defined on certain cones of convex functions. For example, for every fully order-preserving mapping S: semn(X) → semn(X) there is a linear isomorphism U: X → X so that $$(Sf)(x) = f(Ux),\;\;\;\;\;\forall f \in {\rm{semn}}(X),\;\;\;\;\;x \in X,$$ where semn(X) is the cone of all lower semicontinuous seminorms on X.

Energy security and climate change are critical concerns in the present era. The booming of the vehicle population has worsened the environment and has caused severe air pollution problems, especially in urban areas. The utilization of hydrogen-enriched compressed natural gas in internal combustion engines shows abundant prospects for improved performance and reduced on-road emissions of greenhouse gases and air pollutants. This study aims to provide an insight to well-to-wheels environmental implications of the 20%HCNG fuel mixture in terms of total energy use, and greenhouse gas emissions per megajoules (MJ) of thermal energy output. The well-to-tank (WTT) impacts were evaluated using GREET 1 (2017). GREET 1 is a fuel cycle modeling tool developed by ‘Argonne national laboratory.’ GREET® is extensively used by researchers worldwide to analytically simulate energy use and emission output of various vehicle and fuel combinations. This study uses 12 prospective pathways of gaseous hydrogen production for analysis purposes. In the tank-to-wheels (TTW) phase, the 20%HCNG@EEV reduces the brake specific energy consumption (BSEC) by approximately 5%, and also decreases GHG emissions by 14% compared with 0%HCNG@EURO3. For simplicity, EURO5 is entitled as ‘EEV’ and has been excluded in most of the discussion, only highlighting ‘EEV,’ which abbreviates as ‘Enhanced Environmentally friendly Vehicles.’ For the entire well-to-wheels phase, this research work shows that all of the 20%HCNG@EEV pathways have lower total energy use and GHG emissions than 0%HCNG@EURO3 except the two pathways, such as grid electricity-to-hydrogen (without CO2 sequestration) and coal gasification-to-hydrogen (without CO2 sequestration). The WTW total energy and GHG emissions reduced by approximately 14% and 13%, respectively, with 20%HCNG@EEV based on the coke oven gas pathway compared with 0%HCNG@EURO3. It is essential to note that the use of cleaner feedstock for hydrogen, such as power-to-gas (P2G), biomass, coke oven gas (by-product), and natural gas shows tremendous prospects for realizing and practicing sustainable ‘hydrogen economy’ in China. Further technological advancement and reduction in total costs of HCNG utilization in powertrains will increase the number of HCNG vehicles decreasing the burden of air pollution, climate change, and energy crisis threats.

The effect of excess air ratio (λ) and ignition advance angle (θig) on the combustion and emission characteristics of hydrogen enriched compressed natural gas (HCNG) on a 6-cylinder compressed natural gas (CNG) engine has been experimental studied in an engine test bench, aiming at enriching the sophisticated calibration of HCNG fueled engine and increasing the prediction accuracy of the SVM method on automobile engines. Three different fuel blends were selected for the experiment: 0%, 20% and 40% volumetric hydrogen blend ratios. It is noted that combustion intensity varies with the excess air ratio and the ignition advance angle, so are the emissions. The optimal value of λ or θig has been explored in the specific engine condition. Results show that blending hydrogen can enhance and advance the combustion and stability of CNG engine, and it also has some benefic influence on the emissions such as reducing the CO and CH4. Meanwhile, a simulation research on forecasting the engine performance by using the support vector machine (SVM) method was conducted in detail. The torque, brake specific fuel consumption and NOx emission have been selected to characterize the power, economic and emissions of the engine with various HCNG fuels, respectively. It can be seen that the optimal model built by the SVM method can highly describe the relationship of the engine properties and condition parameters, since the value of the complex correlation coefficient is larger than 0.97. Secondly, the prediction performance of the optimal model for torque or BSFC is much better than the case of NOx. Besides, the optimal model built by the PSO optimization method has the best prediction accuracy, and the accuracy of the model obtained based on the training group with 20% hydrogen blend ratio is the best compared with those of others. The upshots in this article provide experimental support and theoretical basis for the adoption of HCNG fuel on internal combustion engines as well as the application of intelligent algorithmic in the engine calibration technology field.

In this paper, a surface-enhanced Raman scattering (SERS) sensor with a giant field enhancement factor based on the coupling of surface plasmon polaritons (SPPs) is designed and studied theoretically. The proposed sensor adopts a metal-dielectric layered hybrid slot waveguide structure, combining thin metal (gold) layers and silicon nitride strip waveguides. Unlike other similar sensors, the silicon nitride waveguide structure does not serve as an excitation signal channel, conventionally loaded with the guided modes, but as an auxiliary layer, making it easier to concentrate the light field in the slot. Therefore, the sensor has a higher enhancement factor compared to the pure metal or dielectric slot structure. The results exhibit that we can obtain a maximum enhancement factor exceeding 10^6 under the compact configuration of 510 × 300 × 225nm^3 at the wavelength of 785 nm. By analyzing the dependence of the sensor performance on the structural parameters, we show that the structure of such sensor can directly be applied to SERS spectroscopic analysis as well as integrated with micro-and nano-photonic platform to perform on-chip detection system.

Increasing urban air pollution, greenhouse gases, and declining fossil energy sources are the three major problems of transportation sector which drive the use of alternative vehicular fuels to prevent energy shortage, reduce oil dependency and decrease tailpipe emissions including air pollutants and greenhouse gas emissions. This research work focused on life cycle analysis of HCNG® heavy-duty vehicle in which 20% gaseous hydrogen blended with compressed natural gas has been investigated in terms of net energy ratio, GHG value, and cost-effectiveness over a scale of ‘per MJ energy output’ in two fuel options, i.e. 0%HCNG and 20%HCNG for an entire well-to-wheel cycle. An engineering economic approach has been used to evaluate cost-effectiveness ratio of CNG and 20%HCNG pathways derived from fuel economy improvement. It has been shown that at pump-to-wheel stage, 7% reduction in fuel consumption can be achieved together with 11% reduction in GHGs, 7% reduction in energy consumption at operation and 7% reduction in total costs (RMB/MJ) for 20%HCNG compared with CNG. Rank (1 means ‘best and 10 means ‘worst’) showed that renewable-based hydrogen pathways such as solar, wind and biomass showed dual benefits of lower energy consumption and lower GHG emissions whereas grid electricity-to-hydrogen displayed the worst case in both scenarios. Usually, biomass-based HCNG pathways may have higher net energy ratio, but the sources are cleaner, and renewable in nature. The energy efficiency of fossil-based pathways such as natural gas, coal, etc., is higher than biomass gasification pathway.

The laminar burning velocity of H2 and CO enriched natural gas (HyCONG) mixtures measured through spherically expanding flames method under three different fuel-air equivalence ratios (0.6, 0.8, and 1.0) at room temperature and atmospheric pressure. Experiments have been conducted into constant volume combustion chamber by using high-speed schlieren photography technique. The five different CO fraction (0%, 20%, 40%, 60%, and 80%) and three HCNG (0%, 20%, and 40%) blends combinations are selected for the experiments. The laminar burning velocity and Markstein length were obtained for 45 operational conditions. The results reveal that the laminar burning velocity increases drastically with an increase of hydrogen and carbon monoxide in HyCONG blends and increasing fuel-air equivalence ratio. The maximum laminar burning velocities are determined as 24.42 cm/s, 45.7 cm/s, and 62.78 cm/s for 20–80 HyCONG at ϕ = 0.6, 40–60 HyCONG at ϕ = 0.8, and 40–60 HyCONG at ϕ = 1.0 respectively. Additionally, the artificial neural network model (ANN) of combustion chamber has been constructed to predict the laminar burning velocity of HyCONG blends. The ANN’s well known backpropagation algorithm is applied in multilayered feedforward networks. The forecasting of laminar burning velocity has been evaluated using four-input and one-output network structure with two different learning algorithm namely: Levenberg-Marquardt (LM) algorithm and Scale Conjugate Gradient (SCG) algorithm. The four-input parameters considered as; fuel-air equivalence ratio, hydrogen fraction, methane fraction, and carbon monoxide fraction while output parameter is laminar burning velocity. The model training has been accomplished using hyperbolic tangent transfer activation function (tansig) and various number of neurons. The maximum and minimum value of correlation coefficient (R) and mean square error (MSE) for validation were obtained for laminar burning velocity. The values of R (max-min) and MSE (max-min) are 0.9987–0.9944 & 2.1305–1.0195 for Levenberg-Marquardt (LM) algorithm and 0.9990–0.9952 & 2.7965–0.9501 for Scale Conjugate Gradient (SCG) algorithm. Presented article not only provides the experimental study of LBV as well as explores the possibility of artificial neural network application in combustion research area.

As one of the largest Internet of Things systems in the world, China’s expressway electronic toll collection (ETC) generates nearly one billion pieces of transaction data every day, recording the traffic trajectories of almost all vehicles on the expressway, which has great potential application value. However, there are inevitable missed transactions and false transactions in the expressway ETC system, which leads to certain false and missing rates in ETC data. In this work, a dynamic search step SegrDTW algorithm based on an improved DTW algorithm is proposed according to the characteristics of expressway ETC data with origin–destination (OD) data constraints and coupling between the gantry path and the vehicle trajectory. Through constructing the spatial window of segment retrieval, the spatial complexity of the DTW algorithm is effectively reduced, and the efficiency of the abnormal ETC data detection is greatly improved. In real traffic data experiments, the SegrDTW algorithm only needs 3.36 s to measure the abnormal events of a single set of OD path data for 10 days. Compared with the mainstream algorithms, the SegrDTW performs best. Therefore, the proposal provides a feasible method for the abnormal event detection of expressway ETC data in a province and even the whole country.

Considering germanium (Ge) material with one of the highest refractive index and semi-metal properties, the light scattering properties of Ge trimer and its metasurface structure were studied in this paper. In contrast to other dielectric materials, for which the magnetic-type resonance is commonly dominant, Ge has a strong electric-type resonance due to its semi-metal properties, which can be seen in the visible and near-infrared spectral range. The influence of the unique feature on the Fano line shapes can be reflected in the scattering spectra. Simultaneously, taking into account the substrate effects, we show that the behavior of the light scattering anisotropic exhibits a big difference in the presence of the different substrates, which can be manipulated to some extent. The results can provide a feasible way to control the “hot spots” in the local light field. Our work in this paper shows that Ge trimers as an excellent candidate can be applied to enhanced spectroscopy, directional sources, and other nanometer photonic devices, as well as on metasurface structures.

In today's era, the computational capabilities of artificial neural network has endorsed to be a bedrock and inferences in many fields, including internal-combustion engines. The presented research in ANN has been germinated to anticipate the performance and emission characteristics of a turbocharged SI engine fueled with various HCNG mixtures. The experiments were accomplished at various excess air ratios (λ), ignition timings (θi) at MAP of 105 kPa and 140 kPa, while engine speed was kept constant at 1600 rpm to obtain data for testing and training ANN model. The test results show that with the increase in values of λ, MAP, and hydrogen addition, the torque output effectively decreases while BSFC first decreases and after attaining minimum value it further increases. The NOx, CO, THC, and CH4 emissions all declined with the hike of ignition advance angle, and inclined with increase of the load. ANN’s popular backpropagation algorithm is adopted in multilayered feedforward networks. In order to predict the performance and emission characteristics of HCNG engine, the four-input and one-output network structure are used. HCNG0, HCNG20 and HCNG40 blends has been studied in the presented ANN model in which the excess air ratio (λ), engine load, ignition timing, and HCNG blends has been taken as four-input parameters. The bestowed model has been trained using hyperbolic tangent transfer activation function (tansig) and Levenberg-Marquardt learning algorithm (LM) along with numerous neurons. The lowest and highest value of correlation coefficient (R) and mean square errors (MSE) for validation were dig-out for various parameters, which were BSFC, torque, NOx, CO, THC, CH4. The values of R (min–max) and MSE (min–max) were BSFC; 09519–0.9963 and 5.72–64.29, torque; 0.9948–0.9997 and 8.3935–95.8350, NOx; 0.9938–0.9992 and 0.5271–3.4340, CO; 0.8595–0.9960 and 0.0188–1.0154, and THC; 0.9644–0.9972 and 0.0714–1.1695, CH4; 0.7965–0.9973, 0.0351–1.1789 respectively for various number of neurons. This research work provides the gist of ANN as an attractive choice to researchers for classical modelling techniques. In this regard, the ANN modeling can be utilized to minutely predict the performance and emission characteristics of hydrogen added CNG engines.

In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C(K) , then it can be equivalently renormed so that the set of norm-attaining functionals contains an infinite dimensional closed subspace of X * if and only if X * contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.

Assume that X; Y are real Banach spaces, Y has uniform convexity of type p (≥ 1), and f : X → Y is a standard coarse isometry. In this paper, we show that if∫ ∞ εf(S) 1/P __________ ds

Threshold conditions to realize electric field enhancement and energy confinement in the low-refractive-index core of nanoscale waveguides are studied by solving the field function. When the incident lightwave meets the relation of special thresholds, we observe the enhanced electric field and a concentrated light energy in the core. The electric field enhancement and the confined light power are highly dependent on the light wavelength. When the core width is 30 nm, for a wavelength of 1.55 µm, we achieve a power confinement factor above 40%. As the basis for a growing number of potential applications, the threshold conditions discovered in this work will find significant applications in many fields, such as optical sensors and optical communication components.

In this paper, we will study concentration inequalities for Banach space-valued martingales. Firstly, we prove that a Banach space X is linearly isomorphic to a p-uniformly smooth space ( $$1

Hydrogen enriched compressed natural-gas has emerged to be an alternative vehicular fuel, due to its adaptability for the current CNG infrastructure. The various research laboratories of China, did a remarkable experimental/numerical research on the development of HCNG engines. A deep perusal of the performance and emission characteristic of the HCNG blends under specific conditions has been explored by these research facilities. This is proved by the series of research paper published by researchers of these laboratory. Hydrogen addition to natural gas increases the laminar burning velocity of the mixture, which will boost the combustion and reduces the brake specific fuel consumption. At an optimum excess air ratio and spark timing, the brake thermal efficiency increases while cycle-by-cycle variations significantly reduces. However, the presence of hydrogen increases the combustion temperature result in high NOx emission. However, at optimized ignition timing and excess air ratio, higher thermal efficiency at low NOx under the limit of emission regulation is possible. Other pollutant species in exhaust smoke like total hydrocarbon (THC), carbon monoxide (CO), and methane (CH4) emission impressively reduces after hydrogen enrichment. These advantages of HCNG engines over CNG engines are impressive and provides an option for the betterment of environment. Apart from the laboratory research, many HCNG fueled, heavy-duty city bus demonstration projects have been successfully accomplished in various provinces of China. Presented review article not only gleams the contribution of China in the research and demonstration projects of HCNG engines, also included the studies of other HCNG research facilities worldwide.

Present research study explores the flame propagation and combustion characteristics of premixed hydrogen enriched natural gas under a 100 Hz low-frequency alternating-current (AC) electric field with various hydrogen blend ratios (0–100%) and fuel–air equivalent ratios (1.0/0.8/0.6) in a constant volume combustion chamber. Results show that: (1) With the application of the electric field, although the maximum pressure increases slightly, the mean flame propagation speed increases and the initial/main duration shortens apparently. At a hydrogen blend ratio of 20% and an equivalent ratio of 0.8, the mean flame propagation speed increases by 10.06%, and the initial/main duration shortens by 13.46%/10.72%. (2) The promotion effect of the electric field on the flame propagation and combustion of the fuel decreases gradually as the hydrogen blend ratio increases. There exists a maximum value of hydrogen blend ratio that electric field makes no difference to the combustion process and the value increases with the excess air ratio. The electric field almost has no effect on the pure hydrogen fuel. (3) Adding the AC electric field can improve the combustion of lean burn conditions more effectively than that of higher equivalent ratio conditions. Meanwhile, the support vector machine is applied for the predication of the flame propagation and combustion characteristics under electric fields. The prediction performance of the optimal model obtained by the SVM method for the maximum pressure is very accurate, while that of the mean flame propagation speed is relatively limited.

In this work we use molecular dynamics (MD) simulations with the ReaxFFSiOGSI potential to model the structure of quartz and amorphous silica surfaces exposed to atomic oxygen. The ReaxFFSiOGSI pot...

We employ noncollinear density functional theory to show that the low-spin state of Mn3 in a model of the oxygen-evolving complex of photosystem II avoids frustrated spin coupling by adopting a noncollinear arrangement of spins, thereby lowering the energy by 7 kcal/mol. The high-spin state also has noncollinear spins. The optimum self-consistent field solutions for this multinuclear oxomanganese complex correspond to states that cannot be described by the unrestricted Slater determinants used in Kohn-Sham collinear density functional methods. This kind of spin coupling can be important in many open-shell systems, and the conventional collinear spin interpretation of chemical bonding in such systems should be viewed with caution. © 2011 American Chemical Society.

The ability of density functional theory to predict the relative energies of different spin states, especially for systems containing transition metal atoms, is of great importance for many applications. Here, in order to sort out the key factors determining accuracy, we compare the predictions of 60 density functional approximations of 10 different types [local spin density approximation, generalized gradient approximation (GGA), nonseparable gradient approximation (NGA), global-hybrid GGA, range-separated hybrid GGA, range-separated hybrid GGA plus molecular mechanics, meta-GGA, meta-NGA, global-hybrid meta-GGA, and range-separated hybrid meta-GGA] for their ability to represent the spin-flip transitions of all 4d transition metal atoms of groups 3-10 (Y through Pd) and their singly positive cations. We consider all 16 excitation energies connecting the ground states (of the neutral atoms and the cations) to their first excited states of different multiplicities, and we also consider all eight ionization potentials. We also test the Hartree-Fock method. All density functional and Hartree-Fock calculations are converged to a stable solution, in which the spatial symmetry is allowed to be completely broken to achieve the lowest possible energy solution. By analyzing the fractional subshell occupancies and spin contaminations, we are able to sort out the effects of s orbital vs d orbital bias and high-spin vs low-spin bias. A reliable functional should have little or no bias of either type rather than succeeding for a limited subset of cases by cancellation of errors. We find that the widely used correlations of spin splittings to percentage of Hartree-Fock exchange are not borne out by the data, and the correlation functionals also play a significant role. We eventually conclude that SOGGA11-X, B1LYP, B3V5LYP, and MPW3LYP are the most consistently reliable functionals for balanced treatments of 4d transition metal atoms and their cations.

When the spins of molecular orbitals are allowed to be aligned with different directions in space rather than being aligned collinearly, the resulting noncollinear spin orbitals add extra flexibility to variational optimization of the orbitals, and solutions obtained with collinear spin orbitals may be unstable with respect to becoming noncollinear in the expanded variational space. The goal of the present work is to explore whether and in what way the molecular orbitals of the Kohn-Sham density functional theory become noncollinear when fully optimized for multi-reference molecules, transition states, and reaction paths. (We note that a noncollinear determinant has intermediate flexibility between a collinear determinant and a linear combination of many collinear determinants with completely independent coefficients. However, the Kohn-Sham method is defined to involve the variational optimization of a single determinant, and a noncollinear determinant represents the limit of complete optimization in the Kohn-Sham scheme.) We compare the results obtained with the noncollinear Kohn-Sham (NKS) scheme to those obtained with the widely used unrestricted Kohn-Sham (UKS) scheme for two types of multi-reference systems. For the dissociation of the MnO and NiO transition metal oxides, we find UKS fails to dissociate to the ground states of neutral atoms, while NKS dissociates to the correct limit and predicts potential energy curves that vary smoothly at intermediate bond lengths. This is due to the instability of UKS solutions at large bond distances. For barrier heights of O3, BeH2, and H4, NKS is shown to stabilize the multi-reference transition states by expanding the variational space. Although the errors vary because they are closely coupled with the capability of the employed exchange-correlation functionals in treating the multi-configurational states, these findings demonstrate that results with collinear spin orbitals should be further scrutinized, and future development of exchange-correlation functionals for multi-reference systems should incorporate the flexibilities of NKS.

We present a new theoretical framework, called Multiconfiguration Pair-Density Functional Theory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of density functional theory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of density functionals by translating conventional density functionals of the spin densities using a simple prescription, and we perform post-SCF density functional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of density functionals, that is comparable to much more expensive multireference perturbation theory methods.

The 3d-series transition metals (also called the fourth-period transition metals), Sc to Zn, are very important in industry and biology, but they provide unique challenges to computing the electronic structure of their compounds. In order to successfully describe the compounds by theory, one must be able to describe their components, in particular the constituent atoms and cations. In order to understand the ingredients required for successful computations with density functional theory, it is useful to examine the performance of various exchange-correlation functionals; we do this here for 4s(N)3d(N') transition-metal atoms and their cations. We analyze the results using three ways to compute the energy of the open-shell states: the direct variational method, the weighted-averaged broken symmetry (WABS) method, and a new broken-symmetry method called the reinterpreted broken symmetry (RBS) method. We find the RBS method to be comparable in accuracy with the WABS method. By examining the overall accuracy in treating 18 multiplicity-changing excitations and 10 ionization potentials with the RBS method, 10 functionals are found to have a mean-unsigned error of5 kcal/mol, with ωB97X-D topping the list. For local density functionals, which are more practical for extended systems, the M06-L functional is the most accurate. And by combining the results with our previous studies of p-block and 4d-series elements as well as databases for alkyl bond dissociation, main-group atomization energies, and π-π noncovalent interactions, we find five functionals, namely, PW6B95, MPW1B95, M08-SO, SOGGA11-X, and MPWB1K, to be highly recommended. We also studied the performance of PW86 and C09 exchange functionals, which have drawn wide interest in recent studies due to their claimed ability to reproduce Hartree-Fock exchange at long distance. By combining them with four correlation functionals, we find the performance of the resulting functionals disappointing both for 3d transition-metal chemistry and in broader tests, and thus we do not recommend PW86 and C09 as components of generalized gradient approximations for general application.

A notorious failing of approximate exchange-correlation functionals when applied to problems involving catalysis has been the inability of most local functionals to predict the correct adsorption site for CO on metal surfaces or to simultaneously predict accurate surface formation energies and adsorption energies for transition metals. By adding the kinetic energy density τ to the density functional, the revTPSS density functional was shown recently to achieve a balanced description of surface energies and adsorption energies. Here, we show that the older M06-L density functional, also containing τ, provides improved surface formation energies and CO adsorption energies over revTPSS for five transition metals and correctly predicted the on-top/hollow site adsorption preferences for four of the five metals, which was not achieved by most other local functionals. Because M06-L was entirely designed on the basis of atomic and molecular energies, its very good performance is a confirmation of the reasonableness of its functional form. Two GGA functionals with an expansion in the reduced gradient that is correct through second order, namely, SOGGA and SOGGA11, were also tested and found to produce the best surface formation energies of all tested GGA functionals, although they significantly overestimate the adsorption energies.

We studied the Co4O4 subnanocluster and its MeCN-coated species using density functional theory, and we found that the Co4O4 core presents distinctive structures in bare and ligand-coated species. We propose a possible ligand-mediated ring → cube transformation mechanism during the ligand-coating process of the Co4O4 core due to the stronger binding energies of the MeCN ligands to the 3D distorted cube structure than to the 2D ring and ladder structures; theory indicates that three ligands are sufficient to stabilize the cube structure. Both ring and cube structures are ferromagnetic. Our finding is potentially useful for understanding the catalysis mechanism of Co4O4 species, which have important applications in solar energy conversion and water splitting; these catalysis reactions usually involve frequent addition and subtraction of various ligands and thus possibly involve core rearrangement processes similar to our findings.

Theoretical studies on the electrode materials in lithium-ion batteries provide information on the structural changes during the charging and discharging processes. In the present study, we tested the M06-L and N12 exchange-correlation functionals on some well-studied lithium-containing materials. These functionals, which have already shown good performance for a variety of databases, outperform the widely used PBE functional for reproducing the experimental structures and averaged intercalation potentials. It is especially noteworthy that the M06-L functional gives voltages as accurate as those provided by the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional, but with less computational cost.

The metal-organic framework Fe2(dobdc) (dobdc(4-) = 2,5-dioxido-1,4-benzenedicarboxylate), often referred to as Fe-MOF-74, possesses many interesting properties such as a high selectivity in olefin/paraffin separations. This compound contains open-shell Fe(II) ions with open coordination sites which may have large single-ion magnetic anisotropies, as well as isotropic couplings between the nearest and next nearest neighbor magnetic sites. To complement a previous analysis of experimental data made by considering only isotropic couplings [Bloch et al. Science 2012, 335, 1606], the magnitude of the main magnetic interactions are here assessed with quantum chemical calculations performed on a finite size cluster. It is shown that the single-ion anisotropy is governed by same-spin spin-orbit interactions (i.e., weak crystal-field regime), and that this effect is not negligible compared to the nearest neighbor isotropic couplings. Additional magnetic data reveal a metamagnetic behavior at low temperature. This effect can be attributed to various microscopic interactions, and the most probable scenarios are discussed.

In this work the ISOL24 database of isomerization energies of large organic molecules presented by Huenerbein et al. [Phys. Chem. Chem. Phys., 2010, 12, 6940] is updated, resulting in the new benchmark database called ISOL24/11, and this database is used to test 50 electronic model chemistries. To accomplish the update, the very expensive and highly accurate CCSD(T)-F12a/aug-cc-pVDZ method is first exploited to investigate a six-reaction subset of the 24 reactions, and by comparison of various methods with the benchmark, MCQCISD-MPW is confirmed to be of high accuracy. The final ISOL24/11 database is composed of six reaction energies calculated by CCSD(T)-F12a/aug-cc-pVDZ and 18 calculated by MCQCISD-MPW. We then tested 40 single-component density functionals (both local and hybrid), eight doubly hybrid functionals, and two other methods against ISOL24/11. It is found that the SCS-MP3/CBS method, which is used as benchmark for the original ISOL24, has an MUE of 1.68 kcal mol(-1), which is close to or larger than some of the best tested DFT methods. Using the new benchmark, we find ωB97X-D and MC3MPWB to be the best single-component and doubly hybrid functionals respectively, with PBE0-D3 and MC3MPW performing almost as well. The best single-component density functionals without molecular mechanics dispersion-like terms are M08-SO, M08-HX, M05-2X, and M06-2X. The best single-component density functionals without Hartree-Fock exchange are M06-L-D3 when MM terms are included and M06-L when they are not.