Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.     

Metal-catalyzed transesterification for healing and assembling of thermosets

Catalytic control of bond exchange reactions enables healing of cross-linked polymer materials under a wide range of conditions. The healing capability at high temperatures is demonstrated for epoxy-acid and epoxy-anhydride thermoset networks in the presence of transesterification catalysts. At lower temperatures, the exchange reactions are very sluggish, and the materials have properties of classical epoxy thermosets. Studies of model molecules confirmed that the healing kinetics is controlled by the transesterification reaction rate. The possibility of varying the catalyst concentration brings control and flexibility of welding and assembling of epoxy thermosets that do not exist for thermoplastics.     

Very accurate potential energy curve of the He2+ ion

A very accurate ground-state potential energy curve (PEC) of the He(2)(+) molecule is calculated with 1200 explicitly correlated Gaussian functions with shifted centers in the range between 0.9 and 100 a(0). The calculations include the adiabatic corrections determined for the (3)He(4)He(+), (3)He(2)(+), and (4)He(2)(+) isotopologues. The absolute accuracy of the PEC is better than 0.05 cm(-1) and that of the adiabatic corrections is around 0.01 cm(-1). The depths of the PECs augmented with the adiabatic corrections for the three isotopologues are: 19 956.708 cm(-1) for (4)He(2)(+), 19 957.054 cm(-1) for (3)He(4)He(+), and 19 957.401 cm(-1) for (3)He(2)(+). The rovibrational energies are also determined. For (3)He(4)He(+) the computed rovibrational transitions corresponding to the ν = 1-0 band differ from the experiment by less than 0.005 cm(-1). For the rovibrational transitions corresponding to the ν = 23-22 band the difference is around 0.012 cm(-1). Presently, this represents the best agreement between theory and experiment for He(2)(+).     

Polymer-population mapping and localization in the space of phenotypes

We present a mapping between the thermodynamics of an ideal heteropolymer in an external field and the dynamics of structured populations in fluctuating environments. We employ a population model in which individuals may adopt different phenotypes, each of which may be optimal in a different environment. Using this mapping, we develop a path integral formulation for populations and predict the existence of a biological counterpart for the well-known heteropolymer localization phase transition.     

IR spectra of photopolymerized C60 films. Experimental and density functional theory study

IR spectra of photopolymerized fullerene films obtained by simultaneous deposition and UV irradiation were measured in the range of 1500-450 cm(-1). The degree of the polymerization of the C60 films was estimated to be about 95%. To assist the assignment of the experimental IR spectra of the films, quantum chemical calculations of the equilibrium structures of the C60 dimers and trimers were performed at the DFT(B3LYP)/3-21G level of theory. Next, IR frequencies and intensities for those structures were calculated. For the five-trimer structures found in the calculations, the relative stabilities were determined at the B3LYP/4-31G and B3LYP/6-31G levels and used to select the lowest-energy trimers, which are Trimer A (angle between monomer centers is 90 degrees ) and Trimer B (angle between monomer centers is 120 degrees). Next, the IR spectra of the polymerized fullerene films were compared with the calculated frequencies of the lowest-energy dimer and the two lowest-energy trimers. On the basis of this analysis and on the comparison of the film spectra with the IR spectra of the C60 dimer and trimer spectra obtained by other methods, it was shown that the main components of the films are C60 dimers and the orthorhombic (O) polymer phase. The tetragonal (T) and rhombohedral (R) polymers, as well as small amounts of monomers, were also found. Although vibrational frequencies of different C60 phases are similar in most cases, we found several unique spectral features of the C60 dimer and other polymers that may be used to determine the composition of the polymerized C60 film.     

Chloromethane and dichloromethane decompositions inside nanotubes as models of reactions in confined space

A combination of ab initio MP2 and molecular mechanics UFF calculations have been employed to study chloromethane and dichloromethane decomposition reaction inside carbon nanotubes (CNTs). The results suggest that the impact of the nanotubes on the mechanism of the reaction depends on the diameter of the nanotube. Nanotubes with a large diameter affect the reaction in a negligible way. On the other hand, most of the reactions taking place inside small nanotubes are considerably altered. The presence of the CNT may affect the geometries of the reactants, the reaction energy barriers, as well as the energetic outcome of the reactions. All the reactions have been described by means of energetic, thermodynamic, and vibrational analyses, which allowed us to form general conclusions concerning the reaction taking place in a confined space.     

A new class of epoxy thermosets

The reinforcing strategies of epoxy thermosets rely on the control of the phase separation between the additive and the growing thermoset. With standard additives, such as reactive liquid rubbers, the length scale of the resulting domains is the micrometer. Here, we present a route that enable a control of the morphology down to the nanometer scale. This strategy is based upon the self-assembly process of blends of epoxy and SBM triblock copolymers, namely Poly(Styrene-b-1,4 Butadiene-b-Methyl methacrylate). It relies on the respective affinities between the epoxy precursors and each of the three blocks. Liquid epoxy has a strong affinity for PMMA, whilst it is not miscible with polystyrene nor polybutadiene at standard processing temperatures. Thus, within the reactive system, microphase separation leads to a regular network of S-B domains. This nanostructure is governed by thermodynamics. The size and geometry of the dispersed domains are controlled by the concentration and the ratio between blocks lengths. The domain size is of the order of magnitude of the chain length, ranging typically from 10 to 30 nanometers. What controls the blend's morphology throughout the curing process of the thermoset was one topic on which we focused our interest. Nanostructured thermosets have been obtained. These supramolecular architectures yield significant toughness improvements while preserving the transparency of the material. The reinforcing mechanisms are not yet fully understood : it is intriguing to induce significant toughening with elastomer domains smaller than 30 nanometers in diameter. Besides being efficient epoxy tougheners, SBM can broaden the scope of applications of thermosets due to specific rheological behaviors. Thanks to the self assembly process taking place in the blend of the SBM block copolymers with the epoxy thermosets precursors, the reactive solvent can be turned into a reactive gel or solid (before curing). This physical gelation is induced by the microphase separation and is thus thermoreversible. At relatively moderate loadings of block copolymers the reactive blend behaves like a thermoplastic material, with adjustable modulus and tackiness. These results evidence that SBM block copolymers open a broad area for designing new class of thermoset materials.