Effect of charge density gradient on characteristics of electric double layer for salt melts

The equilibrium conditions are analyzed for a spatially inhomogeneous ionic liquid using the density functional theory with allowance made for the second order gradient corrections. Solutions for the distribution of potential and charge density in the electric double layer at the ionic liquid/vapor interface are obtained using a parameterized total density profile normal to the surface. It is shown that taking into account the effects of the charge density gradient in the theory results in the appearance of damped oscillations of the charge density near the surface, while the double layer localized on the surface is reduced.     

Adsorption and diffusion on a phosphorene monolayer: a DFT study

A computational study of the adsorption and diffusion behavior of alkali and alkaline earth metal atoms on a phosphorene monolayer is reported. Our calculations were performed within the framework of density functional theory using the Perdew–Burke–Ernzerhof functional and projector augmented wave potentials, as derived from the generalized gradient approximation. Our binding energy calculations for various potential adsorption sites showed that the site located above the center of a triangle formed by three surface phosphorus atoms is the most attractive to all adatoms. In addition, simulation of the diffusion of adatoms across the surface of the phosphorene monolayer showed that the diffusion is anisotropic, with K having the lowest diffusion barrier (0.02 eV along the zigzag pathway). To the best of our knowledge, this is the lowest diffusion barrier of any metal adatom on a single layer of phosphorene. While phosphorene exhibited significantly better adatom adsorption and diffusion than graphene, it also showed a reduced storage capacity compared to graphene, most probably due to the structural distortion induced by the oversaturated phosphorene surface. This finding strongly suggests that a phosphorene–graphene hybrid system could be employed as a promising high-capacity ion anode.     

A van der Waals density functional study of ice Ih

Density functional theory with the van der Waals density functional (vdW-DF) is used to calculate equilibrium crystal structure, binding energy, and bulk modulus of ice Ih. It is found that although it overestimates the equilibrium volume, vdW-DF predicts accurate binding energy of ice Ih, as compared with high level quantum chemistry calculations and experiment. Inclusion of the nonlocal correlation, i.e., van der Waals interaction, leads to an overall improvement over the standard generalized gradient approximation in describing water ice.     

Density functional theory study on the structure and capillary phase transition of a polymer melt in a slitlike pore: effect of attraction

A density functional theory is proposed to investigate the effects of polymer monomer-monomer and monomer-wall attractions on the density profile, chain configuration, and equilibrium capillary phase transition of a freely jointed multi-Yukawa fluid confined in a slitlike pore. The excess Helmholtz energy functional is constructed by using the modified fundamental measure theory, Wertheim's first-order thermodynamic perturbation theory, and Rosenfeld's perturbative method, in which the bulk radial distribution function and direct correlation function of hard-core multi-Yukawa monomers are obtained from the first-order mean spherical approximation. Comparisons of density profiles and bond orientation correlation functions of inhomogeneous chain fluids predicted from the present theory with the simulation data show that the present theory is very accurate, superior to the previous theory. The present theory predicts that the polymer monomer-monomer attraction lowers the strength of oscillations for density profiles and bond orientation correlation functions and makes the excess adsorption more negative. It is interesting to find that the equilibrium capillary phase transition of the polymeric fluid in the hard slitlike pore occurs at a higher chemical potential than in bulk condition, but as the attraction of the pore wall is increased sufficiently, the chemical potential for equilibrium capillary phase transition becomes lower than that for bulk vapor-liquid equilibrium.     

Thermodynamic driving force for diffusion: comparison between theory and simulation

In previous work, lattice density functional theory equations have been recast into differential form to determine a property whose gradient is universally proportional to the diffusive flux. For color counter diffusion, this property appears as the impingement rate onto vacancies and molecules of a species whose density gradient can be influenced by diffusion. Therefore, the impingement rate of a diffusing molecule depends on the mobility of its surroundings. In order to determine the validity of this finding, molecular dynamics simulations of color counter diffusion were performed in which the mobility of the solvent was varied to determine if the flux of the diffusing species responded to the change when all other factors, such as density gradient, available volume, and temperature are held constant.     

Vibrational and thermodynamic properties of β-HMX: a first-principles investigation

Thermodynamic properties of β-HMX crystal are investigated using the quasi-harmonic approximation and density functional theory within the local density approximation (LDA), generalized gradient approximation (GGA), and GGA + empirical van der Waals (vdW) correction. It is found that GGA well describes the thermal expansion coefficient and heat capacity but fails to produce correct bulk modulus and equilibrium volume. The vdW correction improves the bulk modulus and volume, but worsens the thermal expansion coefficient and heat capacity. In contrast, LDA describes all thermodynamic properties with reasonable accuracy, and overall is a good exchange-correlation functional for β-HMX molecular crystal. The results also demonstrate significant contributions of phonons to the equation of state. The static calculation of equilibrium volume for β-HMX differs from the room-temperature value incorporating lattice vibrations by over 5%. Therefore, for molecular crystals, it is essential to include phonon contributions when calculated equation of state is compared with experimental data at ambient condition.     

Modelling relaxation processes for fluids in porous materials using dynamic mean field theory: application to pore networks

We present an application of a recently developed dynamic mean field theory to the study of relaxation dynamics in adsorption and desorption from pore networks. The theory predicts the evolution of density distribution in the system, based on an underlying free energy functional from static mean field theory and the system evolves to equilibrium or metastable equilibrium states consistent with the static theory. The theory makes it possible to follow the evolution of the density distribution with time in response to a change in the bulk pressure or chemical potential. We compare uptake dynamics for a 2D slit pore network with that in a single slit pore. We see more rapid uptake dynamics in the pore network in some cases, due to the greater access of the pore space to the bulk. We also observe that the formation of liquid bridges can slow down the mass transfer in the pore network in certain situations.     

Contribution of concentration-dependent surface diffusion in ternary adsorption kinetics of ethane, propane and n-butane in activated carbon

The role of concentration-dependent surface diffusion in the adsorption kinetics of a multicomponent system is investigated in this paper. Ethane, propane and n-butane are selected as the model adsorbates and Ajax activated carbon as the model adsorbent. Adsorption equilibrium isotherm and dynamic parameters extracted from single-component systems are used to predict the ternary adsorption equilibria and kinetics. The effect of concentration-dependent surface diffusion on the adsorption kinetics predictions is studied by comparing the results of two mathematical models with the experimental data. Three diffusion mechanisms, macropore, surface and micropore diffusions are incorporated in both models. The distinction between these two models is the use of the chemical potential gradient as the driving force for the diffusion of the adsorbed species in one model and the concentration gradient in the other. It was found that the model using the chemical potential gradient provides a better prediction of the ternary adsorption kinetics data, suggesting the importance of the concentration dependency of the surface diffusion, which is implicitly reflected in the chemical potential gradient. The kinetic model predictions are also affected by the way how single-component adsorption equilibrium isotherm data are fitted.     

Analytical theory for permeation of condensable gases in a nanopore

The permeation of a condensable gas mixture in a pressure gradient is examined within a dynamic density functional theory (DDFT). The non-equilibrium density and flux profiles of gas molecules trapped within a nanopore are calculated for each species as a function of feed gas density. Because of important fluid–fluid interaction close to condensation the flux and density gradients are not related by constant transport diffusivities with the thermodynamic correction of uniform density. For long narrow pores the relation of the selectivity to the equilibrium adsorption isotherms is validated. Improved separation is achieved by combining preferential wall interaction and advantageous attraction between gas molecules of different species and examples are discussed. Results from experiments and simulations of permeation in binary mixtures near condensation are still rare and the theory provides a simple basis to study qualitative trends using known parameters.     

Density functional investigation of high-spin XY (X = Cr, Mo, W and Y = C, N, O) molecules

The performance of a density functional theory approach in calculating the equilibrium bond length, dipole moment, and harmonic vibrational frequency in a series of group 6 (Cr, Mo, W) transition metal-containing diatomic molecules is evaluated. Using flexible basis sets comprised of Slater type functions, a wide range of exchange-correlation functionals is investigated. Comparing with known experimental values and published results from high-level theoretical calculations, the most suitable functional form is selected. The importance of relativistic effects is checked, and predictions are made for several unknown dipole moments. The best agreement with experimental parameters is obtained when using a general gradient approximation, while special and hybrid functional forms give less accurate results.     

Investigation of excess adsorption, solvation force, and plate-fluid interfacial tension for Lennard-Jones fluid confined in slit pores

The excess Helmholtz free energy functional is formulated in terms of a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)] for a short ranged repulsion and a first-order mean-spherical approximation theory [Y. P. Tang, J. Chem. Phys. 118, 4140 (2003)] for a long ranged attraction. Within the framework of the density functional theory, the density profile, excess adsorption, solvation force, and plate-fluid interfacial tension of a Lennard-Jones fluid confined in slit pores are predicted, and the results agree well with the simulation data. The phase equilibria inside the slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal, and the plate-fluid interfacial tensions at equilibrium states are predicted consequently.     

α-Al2O3阻氢微观机制研究

采用基于密度泛函理论广义梯度近似下的平面波赝势方法研究了刚玉(α-Al2O3)的阻氢微观机制, 对氢原子在α-Al2O3中的占据结构进行了计算, 发现氢原子占据空隙位置时能量最低, 寻找其过渡态得到活化能为1.59 eV, 利用动力学计算得到了氢原子在α-Al2O3中的扩散系数表达式为D(T)=(3.37×10-7)exp(-1.59/kT). 结果表明, 氢原子占据在α-Al2O3八面体空隙处的结构最稳定; 低温时扩散难以发生; 高温时扩散沿着空隙方向.     

Classical density functional theory of orientational order at interfaces: application to water

A classical density functional formalism has been developed to predict the position-orientation number density of structured fluids. It is applied to the liquid-vapor interface of pure water, where it consists of a classical term, a gradient correction, and an anisotropic term that yields order through density gradients. The model is calibrated to predict that water molecules have their dipole moments almost parallel to a planar interface, while the molecular plane is parallel to it on the liquid side and perpendicular to it on the vapor side. For a planar interface, the surface tension obtained is twice its experimental value, while the surface potential is in qualitative agreement with that calculated by others. The model is also used to predict the orientation of water molecules near the surface of droplets, as well as the dependence of equilibrium vapor pressure around them on their size.     

Statistical mechanical theory for the structure of steady state systems: application to a Lennard-Jones fluid with applied temperature gradient

The constrained entropy and probability distribution are given for the structure that develops in response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory is linear but is applicable to gradients with arbitrary spatial variation. The phase space probability distribution is also given, and it is surprisingly simple with a straightforward physical interpretation. With it, all of the known methods of equilibrium statistical mechanics for inhomogeneous systems may now be applied to determining the structure of nonequilibrium steady state systems. The theory is illustrated by performing Monte Carlo simulations on a Lennard-Jones fluid with externally imposed temperature and chemical potential gradients. The induced energy and density moments are obtained, as well as the moment susceptibilities that give the rate of change of these with imposed gradient and which also give the fluctuations in the moments. It is shown that these moment susceptibilities can be written in terms of bulk susceptibilities and also that the Soret coefficient can be expressed in terms of them.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

Ab initio studies of properties of small potassium clusters

We have studied the properties of various isomers of potassium clusters containing even number of atoms ranging from 2 to 20 at the ab initio level. The geometry optimization calculations of the isomers of each cluster are performed by using all-electron density functional theory with gradient corrected exchange-correlation functional. Using the optimized geometries of different isomers we investigate the evolution of binding energy, ionization potential, and static polarizability with the increasing size of the clusters. The polarizabilities are calculated by employing M?ller-Plesset perturbation theory and time-dependent density functional theory. The polarizabilities of dimer and tetramer are also calculated by employing large basis set coupled cluster theory with single and double excitations and perturbative triple excitations. The time-dependent density functional theory calculations of polarizabilities are carried out with two different exchange-correlation potentials: (i) an asymptotically correct model potential and (ii) within the local density approximation. A systematic comparison with the other available theoretical and experimental data for various properties of small potassium clusters mentioned above has been performed. These comparisons reveal that both the binding energy and the ionization potential obtained with gradient-corrected potential match quite well with the already published data. Similarly, the polarizabilities obtained with M?ller-Plesset perturbation theory and with model potential are quite close to each other and also close to experimental data.     

A challenge for density functional theory: the XONO and XNO2 (X=F, Cl, and Br) molecules

The equilibrium geometries, harmonic frequencies, dipole moments, infrared intensities, and relative energies of the cis-XONO, trans-XONO, and XNO₂ (X=F, Cl, and Br) have been investigated using four functionals in common use in Kohn-Sham density functional theory (DFT) calculations. Two of the functionals include non-local or gradient correction terms, while the other two also incorporate some exact Hartree-Fock exchange and are labeled hybrid functionals. The quality of the results obtained from the functionals is determined by comparison to previously published high-level coupled-cluster calculations. The hybrid functionals perform better for prediction of the equilibrium geometries, where the two gradient corrected functionals yield qualitatively incorrect molecular structures for cis-FONO and cis-ClONO. None of the functionals perform well in predicting all six harmonic frequencies, showing that the correlation between equilibrium geometries and harmonic frequencies is not as strong for these DFT methods as it is for conventional wavefunction ab initio methods, such as coupled-cluster theory. Results from the various functionals generally come into better agreement with each other and also with the coupled-cluster results moving down the periodic table. Received: 12 February 1997 / Accepted: 25 March 1997     

Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree-Fock and density functional theory

An efficient and accurate analytic gradient method is presented for Hartree-Fock and density functional calculations using multiresolution analysis in multiwavelet bases. The derivative is efficiently computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann-Feynman theorem. A smoothed nuclear potential is directly differentiated, and the smoothing parameter required for a given accuracy is empirically determined from calculations on six homonuclear diatomic molecules. The derivatives of N2 molecule are shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussian-type basis sets. The optimized geometries of several molecules are presented using Hartree-Fock and density functional theory. A highly precise Hartree-Fock optimization for the H2O molecule produced six digits for the geometric parameters.