A density functional study on dielectric properties of acrylic acid grafted polypropylene

Influence of acrylic acid grafting of isotactic polypropylene on the dielectric properties of the polymer is investigated using density functional theory (DFT) calculations, both in the molecular modeling and three-dimensional (3D) bulk periodic system frameworks. In our molecular modeling calculations, polarizability volume, and polarizability volume per mass which reflects the permittivity of the polymer, as well as the HOMO-LUMO gap, one of the important measures indicating the electrical breakdown voltage strength, were examined for oligomers with various chain lengths and carboxyl mixture ratios. When a polypropylene oligomer is grafted with carboxyl groups (cf. acrylic acid), our calculations show that the increase of the polarizability volume α' of the oligomer is proportional to the increase of its mass m, while the ratio α'/m decreases from the value of a pure polymer when increasing the mixture ratio. The decreasing ratio of α'/m under carboxyl grafting indicates that the material permittivity might also decrease if the mass density of the material remains constant. Furthermore, our calculations show that the HOMO-LUMO gap energy decreases by only about 15% in grafting, but this decrease seems to be independent on the mixture ratio of carboxyl. This indicates that by doping polymers with additives better dielectric properties can be tailored. Finally, using the first-principles molecular DFT results for polarizability volume per mass in connection with the classical Clausius-Mossotti relation, we have estimated static permittivity for acrylic acid grafted polypropylene, assuming the structural density keeping constant under grafting. The computed permittivity values are in a qualitative agreement with the recent experiments, showing increasing tendency of the permittivity as a function of the grafting composition. In order to validate our molecular DFT based approach, we have also carried out extensive three-dimensional bulk periodic first-principles total-energy calculations in the frameworks of the density functional theory and density functional perturbation theory (DFPT) for crystalline acrylic acid grafted polypropylene. Interestingly, the computed electronic and dielectric properties behave very similarly between the simplified molecular DFT modeling and the more realistic 3D bulk periodic DFPT method. In particular, the static permittivity values [ε(r)(0)] from the molecular DFT-Clausius-Mossotti modeling are in excellent agreement with the high-frequency dielectric constant values (ε(∞)) from the DFPT method. This obviously implies that the chain-to-chain interaction to dielectric and electronic properties of acrylic acid polypropylene, to a first approximation, can be neglected, therefore justifying the usage of molecular DFT modeling in our calculations.     

Suitability of density functional methods for calculation of electrostatic properties

A systematic analysis was performed on the suitability of the molecular electrostatic potential (MEP) and MEP-derived properties determined by means of density functional (DFT) methods. Attention was paid to the electrostatic potential (ESP) derived charges, the ESP and exact quantum mechanical dipole moments, the depth of MEP minima, and the MEP distribution in layers around the molecule for a large series of molecules. The electrostatic properties were determined at either local or nonlocal DFT levels using different functionals. The results were compared with the values estimated from quantum mechanical calculations performed at Hartree–Fock, Møller–Plesset up to fourth order, and CIPSI levels. The suitability of the MEP-derived properties estimated from DFT methods is discussed for application in different areas of chemical interest. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 980–991, 1997     

Combining density functional theory and cluster expansion methods to predict H2 permeance through Pd-based binary alloy membranes

First-principles calculations offer a useful complement to experimental approaches for characterizing hydrogen permeance through dense metal membranes. A challenge in applying these methods to disordered alloys is to make quantitative predictions for the net solubility and diffusivity of interstitial H based on the spatially local information that can be obtained from first-principles calculations. In this study, we used a combination of density functional theory calculations and a cluster expansion method to describe interstitial H in alloys of composition Pd96M4, where M=Ag, Cu, and Rh. The cluster expansion approach highlights the shortcomings of simple lattice models that have been used in the past to study similar systems. We use Sieverts' law to calculate H solubility and a kinetic Monte Carlo scheme to find the diffusivity of H in PdAg, PdCu, and PdRh alloys at a temperature range of 400相似文献   

Geometry optimization in density functional methods

The geometry optimization in delocalized internal coordinates is discussed within the framework of the density functional theory program deMon. A new algorithm for the selection of primitive coordinates according to their contribution to the nonredundant coordinate space is presented. With this new selection algorithm the excessive increase in computational time and the deterioration of the performance of the geometry optimization for floppy molecules and systems with high average coordination numbers is avoided. A new step selection based on the Cartesian geometry change is introduced. It combines the trust radius and line search method. The structure of the new geometry optimizer is described. The influence of the SCF convergence criteria and the grid accuracy on the geometry optimization are discussed. A performance analysis of the new geometry optimizer using different start Hessian matrices, basis sets and grid accuracies is given.     

Simple tests for density functional methods

The performance of the currently used generalized gradient approximation density functionals is analyzed using several simple, yet critical requirements. We analyze the effects of the self-interaction error, the inclusion of the exact exchange, and the parameter settings used in the popular three-parameter hybrid density functionals. The results show that the elimination of the self-interaction error from the current density functionals lead to very poor results for H₂. The inclusion of the exact exchange does not significantly influence the self-interaction corrected results. The variation of the A, B, and C parameters of a hybrid DFT method influences the H(SINGLE BOND)H equilibrium bond length through a very simple linear equation, and it is possible to reproduce the experimental H(SINGLE BOND)H distance with appropriate selection of these parameters, although an infinite number of solutions exists. Similar results were obtained for the total energy and the electron density along the internuclear axis. The analysis of the exact KS potential at the bond critical point of the dissociating H₂ molecule shows that, for this property, the second order Moller–Plesset perturbation theory yields a better potential than the density functionals studied in this article. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1534–1545, 1997     

Multigrid methods in density functional theory

A multigrid method for real-space solution of the Kohr-Sham equations is presented. By using this multiscale approach, the problem of critical slowing down typical of iterative real-space solvers is overcome. The method scales linearly in computer time with the number of electrons if the orbitals are localized. Here, we describe details of our multigrid method, present preliminary many-electron numerical results illustrating the efficiency of the solver, and discuss its strengths and limitations. © 1997 John Wiley & Sons, Inc.     

Functionalized polynorbornene dielectric polymers: Adhesion and mechanical properties

Within the microelectronics industry, there is an ongoing trend toward miniaturization coupled with higher performance. High glass-transition temperature polynorbornenes exhibit many of the key performance criteria necessary for these demanding applications. However, homopolynorbornene exhibits poor adhesion to common substrate materials, including silicon, silicon dioxide, aluminum, gold, and copper. In addition, this homopolymer is extremely brittle, yielding less than 1% elongation-to-break values. To address these issues, the homopolymer was functionalized to improve adhesive and mechanical properties. Attaching triethoxysilyl groups to the polymer backbone substantially improved the adhesion, but at the cost of increasing the dielectric constant because of the polarity of the functional group. Alkyl groups were also added to the backbone, which decreased the rigidity of the system, and resulted in significantly higher elongation-to-break values and a decrease in residual stress. The addition of an alkyl group slightly decreased the dielectric constant of the polymer as a result of an increase in molar volume. The coefficient of thermal expansion and modulus are also reported for the polynorbornene functionalized with triethoxysilyl groups using a multiple substrate approach. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3003–3010, 1999     

Performance of density functional theory methods to describe intramolecular hydrogen shifts

The performance of three exchange and correlation density functionals, LDA, BLYP and B3LYP, with four basis sets is tested in three intramolecular hydrogen shift reactions. The best reaction and activation energies come from the hybrid functional B3LYP with triple-ζ basis sets, when they are compared with high-level post-Hartree-Fock results from the literature. For a fixed molecular geometry, the electrophilic Fukui function is computed from a finite difference approximation. Fukui function shows a small dependence with both the exchange and correlation functional and the basis set. Evolution of the Fukui function along the reaction path describes important changes in the basic sites of the corresponding molecules. These results are in agreement with the chemical behavior of those species.     

Benchmarking the performance of time-dependent density functional methods

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.     

Applicability of hybrid density functional theory methods to calculation of molecular hyperpolarizability

The donor/acceptor (D/A) substituted pi-conjugated organic molecules possess extremely fast nonlinear optical (NLO) response time that is purely electronic in origin. This makes them promising candidates for optoelectronic applications. In the present study, we utilized four hybrid density functionals (B3LYP, B97-2, PBE0, BMK), Hartree-Fock, and second order Moller-Plesset correlation energy correction, truncated at second-order (MP2) methods with different basis sets to estimate molecular first hyperpolarizability (beta) of D/A-substituted benzenes and stilbenes (D=OMe, OH, NMe(2), NH(2); A=NO(2), CN). The results of density functional theory (DFT) calculations are compared to those of MP2 method and to the experimental data. We addressed the following questions: (1) the accurate techniques to compare calculated results to each other and to experiment, (2) the choice of the basis set, (3) the effect of molecular planarity, and (4) the choice of the method. Comparison of the absolute values of hyperpolarizabilities obtained computationally and experimentally is complicated by the ambiguities in conventions and reference values used by different experimental groups. A much more tangible way is to compare the ratios of beta's for two (or more) given molecules of interest that were calculated at the same level of theory and measured at the same laboratory using the same conventions and reference values. Coincidentally, it is the relative hyperpolarizabilities rather than absolute ones that are of importance in the rational molecular design of effective NLO materials. This design includes prediction of the most promising candidates from particular homologous series, which are to be synthesized and used for further investigation. In order to accomplish this goal, semiquantitative level of accuracy is usually sufficient. Augmentation of the basis set with polarization and diffuse functions changes beta by 20%; however, further extension of the basis set does not have significant effect. Thus, we recommend 6-31+G(*) basis set. We also show that the use of planar geometry constraints for the molecules, which can somewhat deviate from planarity in the gas phase, leads to sufficient accuracy (with an error less than 10%) of predicted values. For all the molecules studied, MP2 values are in better agreement with experiment, while DFT hybrid methods overestimate beta values. BMK functional gives the best agreement with experiment, with systematic overestimation close to the factor of 1.4. We propose to use the scaled BMK results for prediction of molecular hyperpolarizability at semiquantitative level of accuracy.     

Combination of MOMM and VEH methods to calculate electronic properties of polymers

A Molecular-Orbital-Based Molecular Mechanics method (MOMM) has been employed to calculate the structures of cyclopentadiene, pyrrole, furan, thiophene, dibenzocyclopentadiene (fluorene), dibenzopyrrole, dibenzofuran, and dibenzothiophene. The dimer structures of the above compounds have also been calculated using the same method to derive the unit cells of polycyclopentadiene, polypyrrole, polyfuran, polythiophene, polydibenzocyclopentadiene, polydibenzopyrrole, polydibenzofuran, and polydibenzothiophene. The band structures, densities of states, ionization potentials, band gaps, reduction potentials, and oxidation potentials of these polymers then have been calculated by using the Valence Effective Hamiltonian method (VEH). The structural effects on electronic properties are discussed.     

Synthesis,structures, luminescent and dielectric properties of lanthanide coordination polymers

Under hydrothermal conditions, four lanthanide coordination polymers were synthesized based on 4-(4,5-dicarboxy-1H-imidazol-2-yl)pyridine 1-oxide (H₃DCImPyO), with the molecular forumulas [Eu(HDCImPyO)·(H₂O)₂·(CHO₂)]_n (1), [Sm(HDCImPyO)·(H₂O)₂·(HCO₂)]_n (2), {[La(HDCImPyO)·(H₂O)·(HCO₂)]·O₂}_n (3) and {[Y(HDCImPyO)·(C₂O₄)·(H₂O)₂]·H₂O}_n (4). With diverse coordination modes, they were further characterized by elemental analysis, infrared spectroscopy, dielectric measurement, and single-crystal X-ray structural analysis. Complexes 1 and 2 were isostructural and had similar structures with {4⁴, 6²} topology. Complex 1 exhibited strong fluorescent emission in the solid state at room temperature. In 3, HDCImPyO^2? adopted μ₄-kO, O′: kO′, O′′: O′′′: O′′′′ coordination to bridge four La(III) ions to form a 3-D framework with {4. 5²}₂{4². 5¹⁰. 6¹². 7. 8³} topology. In 4, both HDCImPyO^2? ligands and Y³⁺ cations were simplified as linkers to form an interpenetrating 3-D framework with {4¹³. 6²}₂{4²². 6⁶} topology.     

A density functional elongation method for the theoretical synthesis of aperiodic polymers

The elongation method, a theoretical tool to synthesize the electronic states of polymers, is applied within the framework of the density functional approach and using a linear combination of Gaussian-type orbitals. In this treatment, the wave function of a cluster is localized and the interaction with an attacking monomer is self-consistently calculated according to the Kohn–Sham equation. The reliability and the applicability of our treatment are examined by the application to a random hydrogen molecule cluster, comparing the results with those obtained by the usual diagonalization method for the whole system. The results show that this treatment efficiently provides the electronic states of the end part of aperiodic polymers. © 1994 John Wiley & Sons, Inc.     

Theoretical studies on nonlinear optical properties of formaldehyde oligomers by ab initio and density functional theory methods

The first and second hyperpolarizability beta and gamma are obtained for formaldehyde oligomers (H2CO)n (n = 1-7) using computational methods. We have used the finite field (FF) approach and hyperpolarizability density analysis (HDA) to predict the microscopic first and second nonlinear hyperpolarizability of the formaldehyde oligomers. The spatial contributions of electrons to the hyperpolarizability by using plots of HDA are presented. It has been found from the numerical stability checking of the hyperpolarizability calculations that the calculated values by FF method are more stable than those by HDA approach. The values of beta are zero when n is even as the molecule possesses centrosymmetry, and when n is odd, the differences among beta values are not clear. The gamma values are increased with increase in n.     

Electron density and related properties in stereoregular polymers and biopolymers

Formulas fully exploiting the periodicity symmetry of the electron density of polymers are deduced. They are shown to lead to efficient algorithms for the evaluation of Coulomb and exchange interactions in those systems.     

Structural and optical properties of a neutral Nickel bisdithiolene complex: density functional versus ab initio methods

Density functional theory (DFT) and ab initio computations are applied to examine different properties of diamagnetic, square planar neutral nickel complexes that contain two bidentate ligands derived from bis ((ethylene)-1,2-dithiolato) ligands. Geometry, vibrational spectra (IR and Raman) are well reproduced in the density functional framework whereas TD-DFT methods are clearly insufficient to reproduce absorption properties. Multiconfigurational perturbation theory based on a complete active space self-consistent field wave function, i.e. MRPT2 and MRPT4 methods, reveal the pronounced multiconfigurational character of the ground state wave function. The singlet–triplet energy gap, the energy gained from symmetry breaking and the singlet diradical character are discussed in the DFT and ab initio frameworks. The complex of interest does not display a strong singlet diradical character. This molecule having a peculiar electronic structure; strong delocalization as shown by a new electron pair localization function analysis (EPLF); exemplifies the fragility of the TD-DFT method and thus, caution should be taken in the determination of the energetic properties of such compounds.     

Polydisperse telechelic polymers at interfaces: analytic results and density functional theory

We use a recently developed continuum theory to expand on an exact treatment of the interfacial properties of telechelic polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. A new surface adsorption transition is identified for ideal telechelic chains, wherein the central block is an equilibrium polymer. This transition occurs in the limit of strong end adsorption. Additionally, closed expressions are derived for the ideal continuum telechelic chain in contact with two large spheres, using the Derjaguin approximation. We analyze the interactions between colloids as a function of polydispersity and molecular weight, and the results are compared with polymer density functional theory in the dilute limit. Significant variations in polymer mediated forces are observed as a function of polydispersity, molecuar weight, and chain stiffness.