Modified interfacial statistical associating fluid theory: a perturbation density functional theory for inhomogeneous complex fluids

A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.     

基于密度泛函理论的外电场下c-C4F8的结构及其特性

采用密度泛函理论CAM-B3LYP/DGDZVP2对c-C4F8进行优化计算,得到基态分子结构.在该结构基础上施加线性外电场(0~10.284 V·pm^-1),获得了c-C4F8的几何特性、能量、前线轨道能级、键能和红外光谱数据.结果表明:当电场沿x轴变大时,c-C4F8的点群从D2d变为C1,偶极矩和极化率不断增大,结构稳定性降低;分子总能量和能隙不断减小,且C(4)-F(10)键的键能降低速度最快,最有可能率先在外电场作用下断裂,导致c-C4F8结构和对称性被破坏.同时c-C4F8的绝热电子亲和能单调上升,分子吸收自由电子的能力增强;红外光谱中,吸收峰的个数增加,4个主要吸收峰发生了红移.     

Global and critical test of the perturbation density-functional theory based on extensive simulation of Lennard-Jones fluid near an interface and in confined systems

The structure of a Lennard-Jones (LJ) fluid subjected to diverse external fields maintaining the equilibrium with the bulk LJ fluid is studied on the basis of the third-order+second-order perturbation density-functional approximation (DFA). The chosen density and potential parameters for the bulk fluid correspond to the conditions situated at "dangerous" regions of the phase diagram, i.e., near the critical temperature or close to the gas-liquid coexistence curve. The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. It is found that the DFA theory presented in this work performs successfully for the nonuniform LJ fluid only on the condition of high accuracy of the required bulk second-order direct correlation function. The present report further indicates that the proposed perturbation DFA is efficient and suitable for both supercritical and subcritical temperatures.     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.     

Modeling fluid diffusion using the lattice density functional theory approach: counterdiffusion in an external field

The dependence of the diffusivity on temperature, pressure, and composition is not understood well; consequently, data is preferred significantly over correlations in most practical situations. Even in dilute gases, the contributions of attractions and repulsions to the diffusivity are difficult to understand on a molecular level without performing simulations. We have developed a Lattice Density Functional Theory (LDFT) approach for modeling diffusion to supplement existing methods that are very rigorous but computationally demanding. The LDFT approach is analogous to the van der Waals equation in how it accounts for molecular interactions in that it has first-order corrections to ideal behavior; it is an extension of the Equilibrium LDFT for adsorption and phase behavior. In this work, the LDFT approach is presented and demonstrated by modeling the problem of color counterdiffusion in an externally-applied potential field. This potential field, in combination with the intermolecular potential function, creates a diffusion regime in which repulsions cause oscillations in the density profile. Using the LDFT approach, the oscillations were described and attributed to nearest-neighbor and next nearest-neighbor interactions. The LDFT approach gives qualitative and quantitative agreement with dual control-volume Grand Canonical Molecular Dynamics simulations.     

A perturbation density functional theory for the competition between inter and intramolecular association

Using the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient.     

密度泛函理论模拟外电场对铁氧体电子结构的影响

通过密度泛函理论(DFT)模拟了3种典型的铁氧体(Fe₂O₃、Fe₃O₄和α-FeOOH)受外电场作用下的电子结构,研究了外电场对不同铁氧体电子结构的影响。DFT模拟结果显示：外电场的存在能够有效提高Fe₂O₃、Fe₃O₄和α-FeOOH晶体结构的价带位置,从而导致3种铁氧体的带隙出现明显的降低;当外电场强度为0.01 V·nm^-1时,Fe₂O₃、Fe₃O₄和α-FeOOH的带隙分别降低了0.36、0.12和0.34 eV;当电场增大至0.1 V·nm^-1时,Fe₂O₃晶体出现击穿现象,Fe—O化学键断裂导致Fe原子的电子沿外电场方向高度离域至相邻Fe原子,而Fe₃O₄和α-FeOOH则仅出现不同价带能级电子局域性增强且能量同质化,因而显示出相对稳定的物理化学结构。此外,外电场的存在可导致3种铁氧体价带电子均出现简并现象,且随电场强度增大而增强。3种铁氧体中,外电场的存在导致Fe₂O₃晶体中Fe原子的电荷密度增大而降低O原子的电荷密度; Fe₃O₄晶体结构中不同配位结构的Fe原子以及配位O原子的Hirshfeld电荷几乎不受外电场的影响; α-FeOOH晶体中共边FeO₆配位结构的Hirshfeld电荷受外电场影响较小,而共角FeO₆配位结构的Hirshfeld电荷受外电场影响较大,且H原子的电荷在强外电场作用下发生歧化响应。随着外电场强度逐渐增大,Fe₃O₄晶体的电子自旋态密度逐渐增大,而α-FeOOH晶体的电子自旋态密度则显示出降低的规律。     

密度泛函理论模拟外电场对铁氧体电子结构的影响

通过密度泛函理论(DFT)模拟了3种典型的铁氧体(Fe₂O₃、Fe₃O₄和α-FeOOH)受外电场作用下的电子结构,研究了外电场对不同铁氧体电子结构的影响。DFT模拟结果显示:外电场的存在能够有效提高Fe₂O₃、Fe₃O₄和α-FeOOH晶体结构的价带位置,从而导致3种铁氧体的带隙出现明显的降低;当外电场强度为0.01 V·nm^-1时,Fe₂O₃、Fe₃O₄和α-FeOOH的带隙分别降低了0.36、0.12和0.34 eV;当电场增大至0.1 V·nm^-1时,Fe₂O₃晶体出现击穿现象,Fe—O化学键断裂导致Fe原子的电子沿外电场方向高度离域至相邻Fe原子,而Fe₃O₄和α-FeOOH则仅出现不同...     

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.     

Resonance Raman spectra of uracil based on Kramers-Kronig relations using time-dependent density functional calculations and multireference perturbation theory

The use of time-dependent density functional calculations for the optimization of excited-state structures and the subsequent calculation of resonance Raman intensities within the transform-theory framework is compared to calculations of Hartree-Fock/configuration interaction singles-type (CIS). The transform theory of resonance Raman scattering is based on Kramers-Kronig relations between polarizability tensor components and the optical absorption. Stationary points for the two lowest excited singlet states of uracil are optimized and characterized by means of numerical differentiation of analytical excited-state gradients. It is shown that the effect of electron correlation leads to substantial modifications of the relative intensities. Calculations of vibrational frequencies for ground and excited states are carried out, which show that the neglect of Duschinsky mixing and the assumption of equal wave numbers for ground and excited state are not in all cases good approximations. We also compare the transform-theory resonance Raman intensities with those obtained within a simple approximation from excited-state gradients at the ground-state equilibrium position, and find that they are in qualitative agreement in the case of CIS, but show some important differences in calculations based on density functional theory. Since the results from CIS calculations are in better agreement with experiment, we also present approximate resonance Raman spectra obtained using excited-state gradients from multireference perturbation theory calculations, which confirm the CIS gradients.     

Ionization potentials of tantalum-carbide clusters: an experimental and density functional theory study

We have used photoionization efficiency spectroscopy to determine the ionization potentials (IP) of the tantalum-carbide clusters, Ta3Cn (n = 1-3) and Ta4Cn (n = 1-4). The ionization potentials follow an overall reduction as the number of carbon atoms increases; however, the trend is not steady as expected from a simple electrostatic argument. Instead, an oscillatory behavior is observed such that clusters with an odd number of carbon atoms have higher IPs and clusters with an even number of carbon atoms have lower IPs, with the Ta4C4 cluster exhibiting the lowest IP. Excellent agreement is found with relative IPs calculated using density functional theory for the lowest energy structures, which are consistent with the development of a 2 x 2 x 2 face-centered nanocrystal. This work shows that IPs may be used as a reliable validation for the geometries of metal-carbide clusters calculated by theory. The variation in IP can also be interpreted qualitatively with application of a simple model based upon isolobal frontier orbitals.     

Analysis of vibrational spectra of L-alanylglycine based on density functional theory calculations

FT Raman and IR spectra of the crystallized biologically active molecule, L-alanylglycine (L-Ala-Gly) have been recorded and analyzed. The equilibrium geometry, bonding features and harmonic vibrational frequencies of L-Ala-Gly have been investigated with the help of B3LYP density functional theory (DFT) method. The calculated molecular geometry has been compared with the experimental data. The assignments of the vibrational spectra have been carried out with the help of normal coordinate analysis (NCA) following the scaled quantum mechanical force field methodology (SQMFF). The optimized geometry shows the non-planarity of the peptide group of the molecule. Potential energy surface (PES) scan studies has also been carried out by ab initio calculations with B3LYP/6-311+G** basis set. The red shifting of NH3+ stretching wavenumber indicates the formation of N-H...O hydrogen bonding. The change in electron density (ED) in the sigma* antibonding orbitals and E2 energies have been calculated by natural bond orbital analysis (NBO) using DFT method. The NBO analysis confirms the occurrence of strong intermolecular hydrogen bonding in the molecule.     

Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.     

Studies on the encapsulation of various anions in different fullerenes using density functional theory calculations and Born-Oppenheimer molecular dynamics simulation

The density functional theory (DFT)-based Becke's three parameter hybrid exchange functional and Lee-Yang-Parr correlation functional (B3LYP) calculations and Born-Oppenheimer molecular dynamics (BOMD) simulations have been performed to understand the stability of different anions inside fullerenes of various sizes. As expected, the stability of anion inside the fullerene depends on its size as well as on the size of the fullerene. Results show that the encapsulation of anions in larger fullerenes (smaller fullerene) is energetically favorable (not favorable). The minimum size of the fullerene required to encapsulate F(-) is equal to C(32). It is found from the results that C(60) can accommodate F(-), Cl(-), Br(-), OH(-), and CN(-). The electron density topology analysis using atoms in molecule (AIM) approach vividly delineates the interaction between fullerene and anion. Although F(-)@C(30) is energetically not favorable, the BOMD results reveal that the anion fluctuates around the center of the cage. The anion does not exhibit any tendency to escape from the cage.     

Core-valence correlation potentials based on density functional theory. Applications to valence-electron-only calculations on Na and K diatomics

The core-valence correlation potential has been derived for Na and K employing atomic calculations which make use of the density functional formula worked out by Lee, Yang and Parr based on Colle-Salvetti approach. The numerical potential is fitted with a small number of Gaussians leading to a very simple expression for an one-electron corevalence correlation operator? _cv . The core-valence correlation corrections can be computed by applying? _cv on a quite general class of wavefunctions. Applications of the? _cv operator within the framework of valence-electron-only calculations using effective Hamiltonians are presented for Na and K atoms, for Na₂, K₂, NaK and their cations. Almost all the corrections calculated for the physical properties due to the core-valence correlation lead to results which are in good agreement with those obtained from much more sophisticated treatments and experimental data.     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999