The spectroscopic signature of the "all-surface" to "internally solvated" structural transition in water clusters in the n = 17-21 size regime

The existence of a transitional size regime where preferential stabilization alternates between "all-surface" (all atoms on the surface of a cluster) and "internally solvated" (one water molecule at the center of the cluster, fully solvated) configurations with the addition or the removal of a single water molecule, predicted earlier with the flexible, polarizable (many-body) Thole-type model interaction potential (TTM2-F), has been confirmed from electronic structure calculations for (H2O)n, n = 17-21. The onset of the appearance of the first "interior" configuration in water clusters occurs for n = 17. The observed structural alternation between interior (n = 17, 19, 21) and all-surface (n = 18, 20) global minima in the n = 17-21 cluster regime is accompanied by a corresponding spectroscopic signature, namely, the undulation in the position of the most redshifted OH stretching vibrations according to the trend: interior configurations exhibit more redshifted OH stretching vibrations than all-surface ones. These most redshifted OH stretching vibrations form distinct groups in the intramolecular region of the spectra and correspond to localized vibrations of donor OH stretches that are connected to neighbors via "strong" (water dimer-like) hydrogen bonds and belong to a water molecule with a "free" OH stretch.     

High-resolution infrared spectroscopy in the 1,200-1,300 cm(-1) region and accurate theoretical estimates for the structure and ring-puckering barrier of perfluorocyclobutane

We present experimental infrared spectra and theoretical electronic structure results for the geometry, anharmonic vibrational frequencies, and accurate estimates of the magnitude and the origin of the ring-puckering barrier in C4F8. High-resolution (0.0015 cm-1) spectra of the nu12 and nu13 parallel bands of perfluorocyclobutane (c-C4F8) were recorded for the first time by expanding a 10% c-C4F8 in helium mixture in a supersonic jet. Both bands are observed to be rotationally resolved in a jet with a rotational temperature of 15 K. The nu12 mode has b2 symmetry under D2d that correlates to a2u symmetry under D4h and consequently has +/- <-- +/- ring-puckering selection rules. A rigid rotor fit of the nu12 band yields the origin at 1292.56031(2) cm-1 with B' = 0.0354137(3) cm-1 and B' ' = 0.0354363(3) cm-1. The nu13 mode is of b2 symmetry under D2d that correlates to b2g under D4h, and in this case, the ring-puckering selection rules are +/- <-- -/+ . Rotational transitions from the ground and first excited torsional states will be separated by the torsional splitting in the ground and excited vibrational states, and indeed, we observe a splitting of each transition into strong and weak intensity components with a separation of approximately 0.0018 cm-1. The strong and weak sets of transitions were fit separately again using a rigid rotor model to give nu13(strong) = 1240.34858(4) cm-1, B' = 0.0354192(7) cm-1, and B' ' = 0.0354355(7) cm-1 and nu13(weak) = 1240.34674(5) cm-1, B' = 0.0354188(9) cm-1, and B' ' = 0.0354360(7) cm-1. High-level electronic structure calculations at the MP2 and CCSD(T) levels of theory with the family of correlation consistent basis sets of quadruple-zeta quality, developed by Dunning and co-workers, yield best estimates for the vibrationally averaged structural parameters r(C-C) = 1.568 A, r(C-F)alpha = 1.340 A, r(C-F)beta = 1.329 A, alpha(F-C-F) = 110.3 degrees , thetaz(C-C-C) = 89.1 degrees , and delta(C-C-C-C) = 14.6 degrees and rotational constants of A = B = 0.03543 cm-1 and C = 0.02898 cm-1, the latter within 0.00002 cm-1 from the experimentally determined values. Anharmonic vibrational frequencies computed using higher energy derivatives at the MP2 level of theory are all within <27 cm-1 (in most cases <5 cm-1) from the experimentally measured fundamentals. Our best estimate for the ring-puckering barrier at the CCSD(T)/CBS (complete basis set) limit is 132 cm-1. Analysis of the C4F8 electron density suggests that the puckering barrier arises principally from the sigmaCC-->sigmaCF hyperconjugative interactions that are more strongly stabilizing in the puckered than in the planar form. These interactions are, however, somewhat weaker in C4F8 than in C4H8, a fact that is consistent with the smaller barrier in the former (132 cm-1) with respect to the latter (498 cm-1).     

The bend angle of water in ice Ih and liquid water: The significance of implementing the nonlinear monomer dipole moment surface in classical interaction potentials

The implementation of the physically accurate nonlinear dipole moment surface of the water monomer in the context of the Thole-type, polarizable, flexible interaction potential results in the only classical potential, which, starting from the gas phase value for the bend angle (104.52 degrees), reproduces its experimentally observed increase in the ice Ih lattice and in liquid water. This is in contrast to all other classical potentials to date, which predict a decrease of the monomer bend angle in ice Ih and in liquid water with respect to the gas phase monomer value. Simulations under periodic boundary conditions of several supercells consisting of up to 288 molecules of water used to sample the proton disorder in the ice Ih lattice yield an average value of vartheta(HOH)(I(h))=108.4 degrees +/-0.2 degrees for the minimized structures (T=0 K) and 108.1 degrees +/-2.8 degrees at T=100 K. Analogous simulations for liquid water predict an average value of vartheta(HOH)(liquid)=106.3 degrees +/-4.9 degrees at T=300 K. The increase of the monomer bend angle of water in condensed environments is attributed to the use of geometry-dependent charges that are used to describe the nonlinear character of the monomer's dipole moment surface. Our results suggest a new paradigm in the development of classical interaction potential models of water that can be used to describe condensed aqueous environments.     

Existence Results for Semilinear Perturbed Functional Differential Equations of Neutral Type with Infinite Delay

In this paper, by using semigroup theory and a nonlinear alternative for the sum of a completely continuous and a contraction operator, we establish sufficient conditions for the existence of solutions for perturbed semilinear neutral functional differential equations with infinite delay.     

Monitoring the Dynamics of Concentrated Suspensions by Enhanced Backward Light Scattering

The shear-induced flocculation of kaolin-polymer flocs in a stirred tank is investigated at medium to high solids concentrations (ϕ=1−10% w/w). The evolution of the average floc size is monitored by the change in intensity of laser light scattered in the 180° direction. The measurements reflect the change in particle number concentration as flocculation proceeds. As flocculation begins, coagulation dominates and the floc size increases (total particle number decreases) and then levels off at a steady state value as fragmentation becomes significant and balances coagulation. At steady state, the measurements indicate the extent of flocculation. Increasing the shear rate increases the coagulation and fragmentation rates, resulting in smaller floc sizes at steady state. Increasing the flocculant concentration increases the steady state floc size by strengthening the bonds between primary particles to resist fragmentation. At constant shear rate and flocculant concentration, increasing the solids fraction decreases the steady state floc size indicating formation of weakly bonded flocs. Flocculant mixing was the most important factor for flocculation efficiency at high solids concentrations.     

On the importance of zero-point effects in molecular level classical simulations of water

We discuss the fundamental difficulties involved in comparing energetic results obtained via classical simulations of bulk water with the observed values. Emphasis is placed on the difference between quantum and classical dynamics, and correction techniques, which can be used to emulate quantum effects in a classical system, are investigated. We present molecular dynamics simulation results for liquid water using the ‘Thole-type’ all atom polarizable water model, which has previously been shown to give reasonable results for both ice Ih and small water clusters. We employ expressions for the density of states power spectrum in the liquid in either atomic or rigid-body coordinates that are appropriate for rigid molecule simulations. It is demonstrated that the atomic power spectra can be written as a linear combination of the center of mass and rotational power spectra via the use of the ‘coupling matrix’ of linear coefficients. This approach allows us to introduce the concept of ‘fractional degrees of freedom’ (DOF) for nuclei in rigid molecule simulation. Within this framework, it is illustrated that in a rigid water molecule the oxygen and hydrogen atoms have 2.82 and 1.59 DOF, respectively (for the TIP4P geometry). Within our suggested approach, we finally demonstrate that Debye–Waller factors can be obtained from the coupling matrix and show that quantum corrections to the structure can be accounted for by raising the temperature of the system in a classical simulation by approximately 50°, a result consistent with previous suggestions.     

Differential evolution for sequencing and scheduling optimization

This paper presents a stochastic method based on the differential evolution (DE) algorithm to address a wide range of sequencing and scheduling optimization problems. DE is a simple yet effective adaptive scheme developed for global optimization over continuous spaces. In spite of its simplicity and effectiveness the application of DE on combinatorial optimization problems with discrete decision variables is still unusual. A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems. Extended comparisons with the well-known random-keys encoding scheme showed a substantially higher performance for the proposed. Furthermore, a simple slight modification in the acceptance rule of the original DE algorithm is introduced resulting to a more robust optimizer over discrete spaces than the original DE.     

Interaction of Fe(III) with herbicide-carboxylato ligands – Di-, tri- and tetra-nuclear compounds: Structure and magnetic behavior

The iron complexes with the phenoxyalkanoic acids 3,4-D, 2,3-D and 2,4,5-T in the presence or not of a nitrogen donor heterocyclic ligand, phen, were prepared and characterized. Interaction of Fe(III) with phenoxyalkanoic acids and phen leads to dinuclear neutral complexes while the absence of phen favours trinuclear cationic or tetranuclear neutral forms. The crystal structure of hexakis(2,3-dichlorophenoxyacetato)tris(methanol)oxotri-iron(III) chloride–methanol(1/3), [Fe₃O(2,3-D)₆(MeOH)₃]Cl · 3MeOH (2), and tetrakis(dimethyl-sulfoxide)octakis(2,4,5-trichlorophenoxyacetato)dioxotetra-iron(III) methanol(1/2)–water(1/1)–dimethylsulfoxide(1/0.8), {[Fe₄O₂(2,4,5-T)₈(dmso)₄] · 2MeOH · H₂O · 0.8dmso} (3), have been determined and refined by least-squares methods using three-dimensional Mo Kα data.     

Monotonic solutions of a perturbed quadratic fractional integral equation

We present an existence theorem for monotonic solutions of a perturbed quadratic fractional integral equation in C[0,1]. The concept of a measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. Finally, we give an example for indicating the natural realizations of our abstract result presented in the paper.