Orbital-Free Density Functional Theory for Molecular Structure Calculations

We give here an overview of the orbital-free density functional theory that is used for modeling atoms and molecules.We review typical approximations to the kinetic energy,exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials.We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.

Density functional theory study of B- and Si-doped carbons and their adsorption interactions with sulfur compounds

Understanding the adsorption interactions between carbon materials and sulfur compounds has far-reaching impacts,in addition to their well-known important role in energy storage and conversion,such as lithium-ion batteries.In this paper,properties of intrinsic B or Si single-atom doped,and B-Si codoped graphene(GR)and graphdiyne(GDY)were investigated by using density functional theory-based calculations,in which the optimal doping configurations were explored for potential applications in adsorbing sulfur compounds.Results showed that both B or Si single-atom doping and B-Si codoping could substantially enhance the electron transport properties of GR and GDY,improving their surface activity.Notably,B and Si atoms displayed synergistic effects for the codoped configurations,where B-Si codoped GR/GDY exhibited much better performance in the adsorption of sulfurcontaining chemicals than single-atom doped systems.In addition,results demonstrated that,after B-Si codoping,the adsorption energy and charge transfer amounts of GDY with sulfur compounds were much larger than those of GR,indicating that B-Si codoped GDY might be a favorable material for more effectively interacting with sulfur reagents.

Local thermal conductivity of inhomogeneous nano-fluidic films:A density functional theory perspective

Combining the mean field Pozhar-Gubbins(PG)theory and the weighted density approximation,a novel method for local thermal conductivity of inhomogeneous fluids is proposed.The correlation effect that is beyond the mean field treatment is taken into account by the simulation-based empirical correlations.The application of this method to confined argon in slit pore shows that its prediction agrees well with the simulation results,and that it performs better than the original PG theory as well as the local averaged density model(LADM).In its further application to the nano-fluidic films,the influences of fluid parameters and pore parameters on the thermal conductivity are calculated and investigated.It is found that both the local thermal conductivity and the overall thermal conductivity can be significantly modulated by these parameters.Specifically,in the supercritical states,the thermal conductivity of the confined fluid shows positive correlation to the bulk density as well as the temperature.However,when the bulk density is small,the thermal conductivity exhibits a decrease-increase transition as the temperature is increased.This is also the case in which the temperature is low.In fact,the decrease-increase transition in both the small-bulk-density and low-temperature cases arises from the capillary condensation in the pore.Furthermore,smaller pore width and/or stronger adsorption potential can raise the critical temperature for condensation,and then are beneficial to the enhancement of the thermal conductivity.These modulation behaviors of the local thermal conductivity lead immediately to the significant difference of the overall thermal conductivity in different phase regions.

Sensitivity impacts owing to the variations in the type of zero-range pairing forces on the fission properties using the density functional theory

Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pairing forces,as well as a combination of these two forces,were used for the Hartree–Fock–Bogoliubov approximation.Variations in the least-energy fission path,fission barrier,pairing energy,total kinetic energy,scission line,and mass distribution of the fission fragments based on the different forms of the pairing forces were analyzed and discussed.The fission dynamics were studied based on the timedependent generator coordinate method plus the Gaussian overlap approximation.The results demonstrated a sensitivity of the mass and charge distributions of the fission fragments on the form of the pairing force.Based on the investigation of the neutron-induced fission of^(239)Pu,among the volume,mixed,and surface pairing forces,the mixed pairing force presented a good reproduction of the experimental data.

Calculation of microscopic nuclear level densities based on covariant density functional theory

In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.

Solvent effects on Diels-Alder reaction in ionic liquids:A reaction density functional study

Extensive experimental studies have been performed on the Diels-Alder(DA)reactions in ionic liquids(ILs),which demonstrate that the IL environment can significantly influence the reaction rates and selectivity.However,the underlying microscopic mechanism remains ambiguous.In this work,the multiscale reaction density functional theory is applied to explore the effect of 1-butyl-3-methylimidazolium hexafluorophosphate([BMIM][PF_(6)])solvent on the reaction of cyclopentadiene(CP)with acrolein,methyl acrylate,or acrylonitrile.By analyzing the free energy landscape during the reaction,it is found that the polarization effect has a relatively small influence,while the solvation effect makes both the activation free energy and reaction free energy decrease.In addition,the rearrangement of local solvent structure shows that the cation spatial distribution responds more evidently to the reaction than the anion,and this indicates that the cation plays a dominant role in the solvation effect and so as to affect the reaction rates and selectivity of the DA reactions.

Preconditioners and Electron Density Optimization in Orbital-Free Density Functional Theory

Orbital-free density functional theory(OFDFT)is a quantum mechanical method in which the energy of a material depends only on the electron density and ionic positions.We examine some popular algorithms for optimizing the electron density distribution in OFDFT,explaining their suitability,benchmarking their performance,and suggesting some improvements.We start by describing the constrained optimization problem that encompasses electron density optimization.Next,we discuss the line search(including Wolfe conditions)and the nonlinear conjugate gradient and truncated Newton algorithms,as implemented in our open source OFDFT code.We finally focus on preconditioners derived from OFDFT energy functionals.Newlyderived preconditioners are successful for simulation cells of all sizes without regions of low electron-density and for small simulation cells with such regions.

Investigation of the structural, electronic and mechanical properties of CaO–SiO_(2) compound particles in steel based on density functional theory

CaO–SiO_(2)compounds compromise one of the most common series of oxide particles in liquid steels, which could significantly affect the service performance of the steels as crack initiation sites. However, the structural, electronic, and mechanical properties of the compounds in CaO–SiO_(2)system are still not fully clarified due to the difficulties in the experiments. In this study, a thorough investigation of these properties of CaO–SiO_(2)compound particles in steels was conducted based on first-principles density functional theory. Corresponding phases were determined by thermodynamic calculation, including gamma dicalcium silicate(γ-C2S), alpha-prime(L) dicalcium silicate(αL′-C2S), alpha-prime(H) dicalcium silicate(αH′-C2S), alpha dicalcium silicate(α-C2S), rankinite(C3S2), hatrurite(C3S), wollastonite(CS), and pseudowollastonite(Ps-CS). The results showed that the calculated crystal structures of the eight phases agree well with the experimental results. All the eight phases are stable according to the calculated formation energies, and γ-C2S is the most stable. O atom contributes the most to the reactivity of these phases. The Young’s modulus of the eight phases is in the range of 100.63–132.04 GPa. Poisson’s ratio is in the range of0.249–0.281. This study provided further understanding concerning the CaO–SiO_(2)compound particles in steels and fulfilled the corresponding property database, paving the way for inclusion engineering and design in terms of fracture-resistant steels.

Ultra-deep Removal of Metal Ions from Coal Tar by Complexation:Experimental Studies and Density Functional Theory Simulations

As one of the important aspects of upgrading coal tar,the ultra-deep removal of metal ions via the complexation method was investigated by screening four complexing agents and performing density functional theory(DFT)simulations.Analysis of the compositions and contents of the metallic compounds in the coal tar revealed that the main components were iron and calcium naphthenates.Direct filtration reduced the mechanical impurity content from 0.24%to 0.0752%,indicating that most of the large particles could be easily removed.Among the four complexing agents,namely,acetic acid,oxalic acid,citric acid,and ethylenediaminetetraacetic acid,oxalic acid exhibited the best demetallization performance.The DFT simulations suggested that the high performance of oxalic acid originated from its 1:1 coordination mode,rigid dicarboxyl structure,and greater binding energy.

Hydrogen evolution reaction between small-sized Zr_(n)(n=2–5)clusters and water based on density functional theory

Density functional theory(DFT)is used to calculate the most stable structures of Zr_(n)(n=2-5)clusters as well as the adsorption energy values of Zr_(n)(n=2-5)clusters after adsorbing single water molecule.The results reveal that there is a significant linear relationship between the adsorption energy values and the energy gaps of the Zr_(n)(n=2-5)clusters.Furthermore,the calculations of the reaction paths between Zr_(n)(n=2-5)and single water molecule show that water molecule can react with Zr_(n)(n=2-5)clusters to dissociate,producing hydrogen,and O atoms mix with the clusters to generate Zr_(n)O(n=2-5),all of which are exothermic reactions.According to the released energy,the Zr4 cluster is the most efficient in Zr_(n)(n=2-5)clusters reacting with single water molecule.The natural population analysis(NPA)and density of states(DOS)demonstrate the production of hydrogen and orbital properties in different energy ranges,respectively,jointly forecasting that Zr_(n)O(n=2-5)will probably continue to react with more water molecules.Our findings contribute to better understanding of Zr's chemical reactivity,which can conduce to the development of effective Zr-based catalysts and hydrogen-production methods.

Density Functional Theory Study of Marine Polybrominated Diphenyl Ethers in Anaerobic Degradation

Polybrominated diphenyl ethers(PBDEs)are a kind of serious pollutants in the ocean.Biodegradation is considered as an economical and safe way for PBDEs removal and reductive debromination dominates the initial pathway of anaerobic degradation.On the basis of experimental study,Octa-BDE 197,Hepta-BDE 183,Hexa-BDE 153,Penta-BDE 99 and Tetra-BDE 47 were selected as the initial degradation objects,and their debromination degradation were studied using density functional theory.The structures were optimized by Gaussian 09 program.Furthermore,the molecular orbitals and charge distribution were analyzed.All C-Br bond dissociation energies at different positions including ortho,meta and para bromine atoms were calculated and the sequence of debromination was obtained.There is a close relationship between molecular structure,charge,molecular orbital and C-Br bond.All PBDEs exhibited similar debromination pathways with preferential removal of meta and para bromines.

Direct atomic-level insight into oxygen reduction reaction on size-dependent Pt-based electrocatalysts from density functional theory calculations

Developing novel oxygen reduction reaction(ORR)catalysts with high activity is urgent for proton exchange membrane fuel cells.Herein,we investigated a group of size-dependent Pt-based catalysts as promising ORR catalysts by density functional theory calculations,ranging from single-atom,nanocluster to bulk Pt catalysts.The results showed that the ORR overpotential of these Pt-based catalysts increased when its size enlarged to the nanoparticle scale or reduced to the single-atom scale,and the Pt_(38)cluster had the lowest ORR overpotential(0.46 V)compared with that of Pt_(111)(0.57 V)and single atom Pt(0.7 V).Moreover,we established a volcano curve relationship between the ORR overpotential and binding energy of O*(ΔE_(O*),confirming the intermediate species anchored on Pt38cluster with suitable binding energy located at top of volcano curve.The interaction between intermediate species and Pt-based catalysts were also investigated by the charge distribution and projected density of state and which further confirmed the results of volcano curve.

Development of the Orbital-Free Density Functional Approach: The Problem of Angles between Covalent Bonds

The Paulie’s principle is used for development of the orbital-free (OF) version of the density functional theory. On the example of the three-atomic clusters, Al3, Si3, and C3, it is shown that the OF approach may lead to equilibrium configurations of atomic systems with both the metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found in good accordance with the known data. Results will be useful for developing of theoretical study of huge molecules and nanoparticles.

A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.

Effects of zinc on χ-Fe_(5)C_(2) for carbon dioxide hydrogenation to olefins:Insights from experimental and density function theory calculations

Production of light olefins from CO_(2), the primary greenhouse gases, is of great importance to mitigate the adverse effects of CO_(2) emission on environment and to supply the value-added products from nonpetroleum resource. However, development of robust catalyst with controllable selectivity and stability remains a challenge. Herein, we report that Zn-promoted Fe catalyst can boost the stable and selective production of light olefins from CO_(2). Specifically, the Zn-promoted Fe exhibits a highly stable activity and olefin selectivity over 200 h time-on-stream compared to the unpromoted Fe catalyst, primarily owing to the preservation of active χ-Fe_(5)C_(2) phase. Structural characterizations of the spent catalysts suggest that Zn substantially regulates the content of iron carbide on the surface and suppresses the reoxidation of bulk iron carbide during the reaction. DFT calculations confirm that adsorption of surface carbon atoms and graphene-like carbonaceous species are not thermochemically favored on Zn-promoted Fe catalyst. Carbon deposition by CAC coupling reactions of two surface carbon atoms and dehydrogenation of CH intermediate are also inhibited. Furthermore, the effects of Zn on antioxidation of iron carbide were also investigated. Zn favored the hydrogenation of surface adsorbed oxygen atoms to H_(2)O and the desorption of H_(2)O, which reduces the possibility of surface carbide being oxidized by the chemisorbed oxygen.

A density functional theory study on the decomposition of aliphatic hydrocarbons and cycloalkanes during coal pyrolysis in hydrogen plasma

To get deep understanding of the reaction mechanism of coal pyrolysis in hydrogen plasma, the decomposition reaction pathways of aliphatic hydrocarbons and cycloalkanes, which are two main components in volatiles from coal, were investigated. Methane and cyclohexane were chosen as the model compounds. Density functional theory was employed, and many reaction pathways were involved. Calculations were carried out in Gaussian 09 at the B3LYP/6-31G（d,p） level of the theory. The results indicate that the main pyrolysis products of methane and cyclohexane in hydrogen plasma are both hydrogen and acetylene, and the participation of active hydrogen atoms makes dehydrogenation reactions more favorable. H2 mainly comes from dehydrogenation process, while many reaction pathways are responsible for acetylene formation. During coal pyrolysis in hydrogen plasma, three main components in volatiles like aliphatic hydrocarbons, cycloalkanes and aromatic hydrocarbons lead to the formation of hydrogen and acetylene, but their contributions to products distribution are different.

Structure and electronic structure of S-doped graphitic C_3N_4 investigated by density functional theory

The structures of the heptazine-based graphitic C3N4 and the S-doped graphitic C3N4 are investigated by using the density functional theory with a semi-empirical dispersion correction for the weak long-range interaction between layers.The corrugated structure is found to be energetically favorable for both the pure and the S-doped graphitic C3N4.The S doptant is prone to substitute the N atom bonded with only two nearest C atoms.The band structure calculation reveals that this kind of S doping causes a favorable red shift of the light absorption threshold and can improve the electroconductibility and the photocatalytic activity of the graphitic C3N4.

Chemical Concepts from Density Functional Theory

Chemical concepts such as structure,bonding,reactivity,etc.have been widely used in the literature and text books to appreciate molecular properties and chemical transformations.Even though modern theoretical and computational chemistry is well established from the perspective of accuracy and complexity,how to quantify these concepts is a still unresolved task.Conceptual density functional theory and its related recent developments provide unique opportunities to tackle this problem.In this Special Issue,27 contributions from top investigators over the world are collected to highlight the state-of-art research on this topic,which not only showcases the status of where we are now but also unveils a number to possible future directions to be pursued.

Thermodynamics and density functional theory study of potassium dichromate interaction with galena

The adsorption heat and reaction rate constant of potassium dichromate on the surface of galena were studied. The results indicate that potassium dichromate tends to adsorption on the galena surface. The reaction order is only 0.08385, suggesting that the concentration of potassium dichromate has little influence on its adsorption on the galena surface. In addition, the simulation of CrO2 4- adsorption on the PbS （100） surface in the absence and presence of O2 was carried out by density functional theory （DFT）. The calculated results show that CrO2 4- species adsorb energetically at the Pb-S bond site, and the presence of O2 can enhance this adsorption.

Density Functional Theory Study on La Complex with Schiff-base as Building Block

Quantum density functional theory （DFT） results are reported for the building block [LaL^1（NO3）] of La complex [LaL^1（NO3）]NO3·5H2O （L^1 = （CH3）2CHCH2CH（NCHC4H3O）COO^-）. The structure was optimized and the calculation results show that the lanthanum ion is coordinated by one nitrogen atom and three oxygen atoms of L^1 and two oxygen atoms of nitrate ion. The bond length of La-N is 0.2637 nm and the average length of La-O is 0.2526 nm, which are consistent with the literatures. In addition, the stabilities, electronic structural characteristics and IR spectra of the complex have been analyzed, which describe the coordination of lanthanum ion with other atoms in detail.