Meta-generalized gradient approximation: explanation of a realistic nonempirical density functional

Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.     

Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.     

Structure of inhomogeneous polymer solutions: a density functional approach

The structure of polymer solutions confined between surfaces is studied using a density functional theory where the polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres. The present theory uses the concept of universality of the free energy density functional to obtain the first-order direct correlation function of the nonuniform system from that of the corresponding uniform system, calculated through the Verlet-modified type bridge function. The uniform bulk fluid direct correlation function required as input has been calculated from the reference interaction site model integral equation theory using the Percus-Yevick closure relation. The calculated results on the density profiles of the polymer as well as the solvent are shown to compare well with computer simulation results.     

The capture of carbonyl sulfide by N-methyldiethanolamine: A systematic density functional theory investigation

In this contribution, the mechanism of carbonyl sulfide (COS) absorption by N-methyldiethanolamine (MDEA) aqueous solution was explored via theoretical computations. Detailed reaction mechanisms were analyzed using density functional theory (DFT) calculations at the B3LYP-D3 level of theory. In total, four different pathways for COS absorption by MDEA have been considered. The most favorable pathway for the removal of COS is a three-step mechanism including the hydrolysis, proton transfer, and dissociation of CO₂, and hydrolysis is the rate-determining step. The mechanisms of the COS absorption by different amines were investigated, and the calculated results suggest that the total energy barrier for the COS absorption by MDEA is comparable to that by monoethanolamine (MEA), diethanolamine (DEA), and diisopropylamine (DIPA), indicating the COS absorption by all the four amines are feasible, while MDEA gives a better performance in terms of thermodynamics.     

Small fullerenes with BN belts: a density functional theory investigation

Density functional calculations have been carried out on a series of BCN hybrid fullerenes with certain substitution patterns in comparison with their parent compounds Cn (n = 30, 32, 36, 38, 40, 44, 48, 50, 52). The substitutional structures, energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, ionization potentials, electron affinities, as well as molecular electrostatic potentials have been systematically investigated. The following important points of BCN hybrid fullerenes are stressed: The present studied fullerenes, comprising tubular "belt" and polar "cap", could be divided into three types of structure; each has different indexes of tubular structure and terminal caps. The properties of BCN hybrid fullerenes depend on the type of "tubular belt + polar cap" structures, especially, the HOMO and LUMO characters and MEPs of BCN fullerene are strongly governed by their structure types.     

Theoretical investigation of hole mobility in 9,10-diphenylanthracene by density functional calculations

The charge transfer property of the 9,10-diphenylanthracene (DPA) single-crystal system was investigated by density functional calculations. The hole mobility of DPA was predicted according to a hopping mechanism and compared with that of two standard organic single-crystal systems, namely, naphthalene and anthracene. The reorganization energy was calculated by the adiabatic potential energy surface method. The electronic coupling matrix elements were calculated by two methods, namely, the energy splitting in dimer (ESD) method and charge transfer integral (CTI) method. Using the coupling matrix calculated by the CTI method, we predicted a hole mobility of 2.15?cm²/(Vs) for DPA, whereas the CTI method gives the values of 0.35 and 1.39?cm²/(Vs) for naphthalene and anthracene, respectively. It is shown that the electronic coupling calculated by the CTI method gives the qualitatively satisfactory result for the hole mobilities of the three single-crystal systems.     

A free-space density functional theory for polymer adsorption: influence of packing effect on conformations of polymer

We propose a free-space density functional theory for polymer adsorption. The derivation within the framework of density functional theory leads to the splitting of the intrinsic free energy into an ideal-gas term and a residual term responsible for the intrinsic energy and the nonbonded interactions between monomers, respectively. A more reasonable treatment is adopted for the residual free energy to count for the monomer-monomer correlation underestimated by the local density approximation. An approach using propagators is proposed to calculate the single-chain partition function and the segment-density distributions, the three adsorption conformations as trains, loops, and tails are further described by propagators. Dirac's bra-ket notation used makes the derivation simpler and provides clearer physical meanings. The theoretical calculations for the adsorption of hard-sphere chains onto a nonadsorbing and an adsorbing hard wall show that the structure of the adsorption layer is strongly affected by the packing effect which has been underestimated by the previous lattice adsorption theory.     

Cyanide adsorbed on coinage metal electrodes: A relativistic density functional investigation

The adsorptive properties of cyanide (CN⁻) on coinage metal (M) electrodes (M=Cu, Ag, Au) have been investigated using a relativistic density functional method. The way to model the electrochemical potential applied to the electrodes is to consider the systems in the presence of a perturbative external field F. The field-perturbative approach is proven to be a suitable method in interpreting the observed spectral shifts with electrode potential. The calculated potential-dependent shifts of ω_{M(SINGLE BOND)CN} and ω_{C(SINGLE BOND)M} are similar for the three metals, in agreement with experiment observations. The relativistic effects are required to account for the similarity in the frequency shifts of ω_{M(SINGLE BOND)CN}. The calculated vibrational tuning rates dω_{C(SINGLE BOND)N}/dF are 6.61×10⁻⁷, 6.61×10⁻⁷, and 5.64×10⁻⁷ cm⁻¹/(V/cm) for M=Cu, Ag, and Au, respectively. The coupling of the M(SINGLE BOND)CN and C(SINGLE BOND)N internal modes contributes significantly (about 25%) to the size of the frequency shifts Δω_{C(SINGLE BOND)N} of the ligand. The effect of electric fields on the metal(SINGLE BOND)CN⁻ bonding is also investigated. It is shown that changes in the magnitude of CN⁻ to the metal donation and M(SINGLE BOND)CN bond strength occur under the influence of the electric field. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 175–185, 1998     

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in good agreement with simulation. We compute the colloid-colloid potential of mean force and the second virial coefficient, and analyze the behavior of these quantities as a function of the polymer solution density, the polymer chain length, and the colloid/polymer bead size ratio.     

Octacoordinate carbons encaged inside carborane clusters: a density functional theory investigation

This work focuses on the computational design and characterization of a novel series of endohedral carborane clusters containing octacoordinate carbon centers. The structural and bonding features and the thermodynamic and kinetic stabilities are discussed extensively based on density functional theory calculations. These nonclassical carboranes are fascinating in structure not only for the octacoordinate carbon center but also for the surrounding carbon and boron ligands with inverted bonding configuration. These endohedral carboranes are higher in energy than the corresponding exohedral isomers due to the high strain in the system. A new stability rule based on the donor-acceptor model is proposed to predict the stability ordering for these carborane isomers. In addition, some of these octacoordinate carboranes might have relatively high kinetic stabilities, which is rather hopeful for the experimental syntheses.     

Addition of hydrazine to natural terpene-based isothiocyanates derivatives: density functional theory investigation

The hydrazine addition to isothiocyanoterpenes to produce thiosemicarbazides occurs with excellent yields. The reaction rate to conversion of the camphene-based (NCS1), R-(+)-limonene-based (NCS2), and (−)-α-bisabolol-based (NCS3) isothiocyanoterpene derivatives in the respective thiosemicarbazides was experimentally studied. It was observed that NCS3 reacts two times faster than NCS2 and 3.5 times faster than NCS1. A complete theoretical investigation of the transition states of these reactions was accomplished, showing that the difference in the reaction rates can be explained by the differences in the electrophilic character of the -NCS group and the relative stability of the proposed transition states.     

Surface forces in polymer fluids: a comparison between simulations and density functional theory

A polymer density functional theory is evaluated in terms of its ability to predict interactions between large surfaces in a polymer fluid. Comparisons are made with results from simulations in an expanded isotension ensemble. The variation of the net surface-surface interaction with adsorption strength is examined. Cases where the monomers interact via a pure hard sphere potential are investigated, but we have also studied the effect of attractions between the monomers. In all cases, we obtain an almost quantitative agreement between the simulated results and the predictions from the polymer density functional theory.     

Tuning nonlinear optical and optoelectronic properties of vinyl coupled triazene chromophores: a density functional theory and time-dependent density functional theory investigation

Triazenes are a unique class of polyazo compounds containing three consecutive nitrogen atoms in an acyclic arrangement and are promising NLO candidates. In the present work, a series of 15 donor-π-acceptor type vinyl coupled triazene derivatives (VCTDs) with different acceptors (-NO(2), -CN, and -COOH) have been designed, and their structure, nonlinear response, and optoelectronic properties have been studied using density functional theory and time-dependent density functional theory methods. B3LYP/6-311g(d,p) optimized geometries of the designed candidates show delocalization from the acceptor to donor through a π-bridge. Molecular orbital composition analysis reveals that HOMO is stabilized by the π-bridge, whereas acceptors play a major role in the stabilization of LUMO. Among the three acceptors, nitro derivatives are found to be efficient NLO candidates, and tri- and di-substituted cyano and carboxylic acid derivatives also show reasonably good NLO response. The effect of solvation on these properties has been studied using PCM calculations. From TDDFT calculations, the computed absorption spectra of these candidates lie in the range of 350-480 nm in the gas phase and have positive solvatochromism. The ground-state stabilization interactions are accounted from NBO calculations. In an effort to substantiate the thermal stability of the designed candidates, computations have been done to identify the weak interactions in the systems through NCI and AIM analysis. In summary, 10 out of 15 designed candidates are found to have excellent NLO and optoelectronic properties.     

Geometries and stabilities of l-ascorbic acid dimer and its derivatives: a computational investigation by density functional methods

Geometries, relative stabilities, and hydrogen bonds of l-ascorbic acid (LAA) and d-Erythroascorbate (DEAA) dimers as well as their S- and Se-substituted isomers in gas phase and water solvent are studied using density functional method. Furthermore, the hydrogen bond lengths in LAA and DEAA dimers are generally increased along with the binding dissociation energy of the dimers being decreased as apex O atoms in the five-membered C5 rings of LAA and DEAA dimers are substituted by S and Se atoms in gas phase and water solvent. Interestingly, one LAA dimer and its S- or Se-substituted isomer with four hydrogen bonds in gas and water solvent are the three-centers structures. In addition, the chemical bonding and charge distributions of all the dimers are discussed. A good agreement with available experimental results is reached.     

Self-bonding in an amorphous polymer below the glass transition: A T-peel test investigation

Films of amorphous polystyrene (PS) with a weight-average molecular weight (M_w) of 225 × 10³ g/mol were bonded in a T-peel test geometry, and the fracture energy (G) of a PS/PS interface was measured at the ambient temperature as a function of the healing time (t_h) and healing temperature (T_h). G was found to develop with (t_h)^1/2 at T_h = T_g-bulk − 33 °C (where T_g-bulk is the glass-transition temperature of the bulk sample), and log G was found to develop with 1/T_h at T_g-bulk − 43 °C ≤ T_h ≤ T_g-bulk − 23 °C. The smallest measured value of G = 1.4 J/m² was at least one order of magnitude larger than the work of adhesion required to reversibly separate the PS surfaces. These three observations indicated that the development of G at the PS/PS interface in the temperature range investigated (<T_g-bulk) was controlled by the diffusion of chain segments feasible above the glass-transition temperature of the interfacial layer, in agreement with our previous findings for fracture stress development at several polymer/polymer interfaces well below T_g-bulk. Close values of G = 8–9 J/m² were measured for the symmetric interfaces of polydisperse PS [M_w = 225 × 10³, weight-average molecular weight/number-average molecular weight (M_w/M_n) = 3] and monodisperse PS (M_w = 200 × 10³, M_w/M_n = 1.04) after healing at T_h = T_g-bulk − 33 °C for 24 h. This implies that the self-bonding of high-molecular-weight PS at such relatively low temperatures is not governed by polydispersity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1861–1867, 2004     

Rheological investigation of swollen gluten polymer networks: effects of process parameters on cross-link density

Wheat gluten samples were subjected to different thermo-mechanical treatments. Kinetics of protein aggregation and changes in network structure were investigated through biochemical and rheological measurements. Temperature induced protein aggregation through disulphide cross-links. Shear treatment alters the aggregation mechanism since a lower energy of activation was observed. Accumulation of aggregated protein enhances the elastic behaviour of the material. The strong correlation found between the extent of protein aggregation and the molecular weight between cross-links reveals the important role of covalent bonds in the network connectivity.     

Theoretical investigation on electronic structure and stability of some inverted cucurbiturils by density functional theory

Structure and stability of diastereoisomers of cucurbit[n]urils (CB[n = 5–10]), the inverted CB[n]s, were investigated by density functional theory (DFT) computations. All the inverted CB[n]s were less stable than their normal CB[n]s and the mono-inverted ones with one inverted glycoluril unit in their structures were more stable than their doubly-inverted isomers. Relative change in dipole moments and molecular electrostatic potentials (MEP) were discussed with the deformation in geometric structure and charge distribution of the normal and inverted CB[n]s.     

Interactions between polymer brushes in solvents of variable quality: a density functional theory study

We present a density functional theory study of interactions between sterically stabilized colloidal particles in solvents of variable quality. Both flat and spherical polymer brushes are considered, as well as both monatomic and polymeric solvents. It is shown that the interaction between sterically stabilized particles can be tuned from repulsive to attractive by varying the solvent quality, the relative length of free and grafted chains, and by employing a mixed brush consisting of both well and poorly solvated chains.     

Theoretical investigation of novel silsesquioxane-supported Phillips-type catalyst by density functional theory (DFT) method

In spite of great commercial importance of the Phillips CrO_x/SiO₂ catalyst and long term research efforts, the precise physicochemical nature of active sites and polymerization mechanisms still remains unclear. The difficulties in a clear mechanistic understanding of this catalyst mainly come from the complexity of the surface chemistry of the amorphous silica gel support. In this work, novel silsesquioxane-supported Phillips Cr catalysts are utilized as realistic models of the industrial catalyst for theoretical investigation using the density functional theory (DFT) method in order to elucidate the effects of surface chemistry of silica gel in terms of supporting of chromium compounds and fluorination of the silica surface on the catalytic properties of the Phillips catalyst. Both qualitative and quantitative aspects with respect to various electronic properties and thermodynamic characteristics of the model catalysts were achieved. The future prospects of a state-of-the-art catalyst design and mechanistic approaches for the heterogeneous SiO₂-supported Phillips catalyst has been demonstrated. The text was submitted by the authors in English.