Multi‐Species Multi‐Channel (MSMC): An Ab Initio‐based Parallel Thermodynamic and Kinetic Code for Complex Chemical Systems

Multi‐Species Multi‐Channel (MSMC) is an ab initio parallel program to calculate thermodynamic quantities (e.g., , , , and , time‐dependent species profiles, and rate coefficients as functions of temperature and pressure for complex chemical reaction systems, which consist of multiple stable species and multiple reaction channels interconnecting them. Thermodynamic properties of the species involved are calculated using statistical mechanics with molecular information from electronic structure calculations. Temperature‐ and pressure‐dependent behaviors are rigorously characterized within the eigenpair master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) framework. Corrections, e.g., for hindered internal rotation and tunneling treatment, are included. With the implementation of an ultra‐high precision package and rigorous matrix setup, MSMC is able to correctly mimic real behaviors of different types of chemical systems. Different eigenpair‐based approaches to extract phenomenological/macroscopic rate coefficients are implemented for different applications. Moreover, a friendly and platform‐independent graphical‐user‐interface (GUI) is provided to facilitate the use of MSMC and the pre‐/postcalculation data visualization/analysis on the fly. The program can be freely downloaded at https://sites.google.com/site/msmccode/ .     

Impulsive problems on the half-line with infinite impulse moments<Superscript>*</Superscript>

We present a two-point impulsive boundary value problem on the half-line with infinite impulsive effects on the unknown function and its derivative given by generalized functions.In this way, this problem can be applied to phenomena where the occurrence of infinite jumps depends not only on the instant, but also on their amplitude and frequency. The arguments apply Green’s functions and Schauder’s fixed-point theorem. The concept of equiconvergence at +∞ and at each impulsive moment is a key point to have a compact operator.     

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.     

Difference Schemes on Nonuniform Grids for the Two-Dimensional Convection–Diffusion Equation

New second-order accurate monotone difference schemes on nonuniform spatial grids for two-dimensional stationary and nonstationary convection–diffusion equations are proposed. The monotonicity and stability of the solutions of the computational methods with respect to the boundary conditions, the initial condition, and the right-hand side are proved. Two-sided and corresponding a priori estimates are obtained in the grid norm of C. The convergence of the proposed algorithms to the solution of the original differential problem with the second order is proved.     

Nanopatterning of functional materials by gas phase pattern deposition of self-assembled molecular thin films in combination with electrodeposition

We present a general methodology to pattern functional materials on the nanometer scale using self-assembled molecular templates on conducting substrates. A soft lithographic gas phase edge patterning process using poly(dimethylsiloxane) molds was employed to form electrically isolating organosilane patterns of a few nanometer thickness and a line width that could be tuned by varying the time of deposition. Electrodeposition was employed to deposit patterns of Ni and ZnO on these prepatterned substrates. Deposition occurred only on patches of the substrate where no organosilane monolayer was present. The process is simple, inexpensive, and scalable to large areas. We achieved formation of metallic and oxide material patterns with a lateral resolution of 80 nm.     

Optimum conditions for the water extraction of L-theanine from green tea

Theanine is a unique non-protein amino acid found in tea (Camellia sinensis). It contributes to the favourable umami taste of tea and is linked to various beneficial effects in humans. There is an increasing interest in theanine as an important component of tea, as an ingredient for novel functional foods and as a dietary supplement. Therefore, optimal conditions for extracting theanine from tea are required for the accurate quantification of theanine in tea and as an efficient first step for its purification. This study examined the effects of four different extraction conditions on the yield of theanine from green tea using water and applied response surface methodology to further optimise the extraction conditions. The results showed that temperature, extraction time, ratio of water-to-tea and tea particle sizes had significant impacts on the extraction yield of theanine. The optimal conditions for extracting theanine from green tea using water were found to be extraction at 80 °C for 30 min with a water-to-tea ratio of 20:1 mL/g and a tea particle size of 0.5-1 mm.     

Oleanolic triterpene saponins from the roots of Panax bipinnatifidus

Ten oleanane-type saponins (1-10), including three new compounds, namely bifinosides A-C (1-3), were isolated from the roots of Panax bipinnatifidus SEEM. Their structures were elucidated on the basis of chemical and spectroscopic methods.     

Density-dependent analysis of nonequilibrium paths improves free energy estimates II. A Feynman-Kac formalism

The nonequilibrium fluctuation theorems have paved the way for estimating equilibrium thermodynamic properties, such as free energy differences, using trajectories from driven nonequilibrium processes. While many statistical estimators may be derived from these identities, some are more efficient than others. It has recently been suggested that trajectories sampled using a particular time-dependent protocol for perturbing the Hamiltonian may be analyzed with another one. Choosing an analysis protocol based on the nonequilibrium density was empirically demonstrated to reduce the variance and bias of free energy estimates. Here, we present an alternate mathematical formalism for protocol postprocessing based on the Feynmac-Kac theorem. The estimator that results from this formalism is demonstrated on a few low-dimensional model systems. It is found to have reduced bias compared to both the standard form of Jarzynski's equality and the previous protocol postprocessing formalism.     

Enhanced stability by three-dimensional aromaticity of endohedrally doped clusters X(10)M(0/-) with X = Ge, Sn, Pb and M = Cu, Ag, Au

The group 14 clusters encapsulated by coinage metals in neutral and anionic states X(10)M(0/-) (X = Ge, Sn, Pb and M = Cu, Ag, Au) are investigated using quantum chemical calculations with the DFT/B3LYP functional and coupled-cluster CCSD(T) theory. Addition of transition metals into the empty cages forms high symmetry endohedral structures, except for Ge(10)Ag(0/-). In agreement with experiments available for X(10)Cu, the D(4d) global minima of the anions are calculated to be magic clusters with large frontier orbital gaps, high vertical and adiabatic detachment energies, and large embedding energies and binding energies as compared to those of the empty cages X(10)(2-). The enhanced stability of these magic clusters can be rationalized by the three-dimensional aromaticity.     

Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.