Combining the lattice-sum and reaction-field approaches for evaluating long-range electrostatic interactions in molecular simulations

A new scheme, the lattice-sum-emulated reaction-field (LSERF) method, is presented that combines the lattice-sum (LS) and reaction-field (RF) approaches for evaluating electrostatic interactions in molecular simulations. More precisely, the LSERF scheme emulates a RF calculation (based on an atomic cutoff) via the LS machinery. This is achieved by changing the form of the electrostatic interactions in a standard LS calculation (Coulombic) to the form corresponding to RF electrostatics (Coulombic plus quadratic reaction-field correction term, truncated at the cutoff distance). It is shown (both analytically and numerically) that in the limit of infinite reciprocal-space accuracy, (i) the LSERF scheme with a finite reaction-field cutoff and a given reaction-field permittivity is identical to the RF scheme with the same parameters (and an atomic cutoff), and (ii) the LSERF scheme is identical to the LS scheme in the limit of an infinite reaction-field cutoff, irrespective of the reaction-field permittivity. This new scheme offers two key advantages: (i) from a conceptual point of view, it shows that there is a continuity between the RF and LS schemes and unifies them into a common framework; (ii) from a practical point of view, it allows us to perform RF calculations with arbitrarily large reaction-field cutoff distances for the same computational costs as a corresponding LS calculation. The optimal choice for the cutoff will be the one that achieves the best compromise between artifacts arising from the dielectric heterogeneity of the system (short cutoff) and its artificial periodicity (long cutoff). The implementation of the LSERF method is extremely easy, requiring only very limited modifications of any standard LS code. For practical applications to biomolecular systems, the use of the LSERF scheme with large reaction-field cutoff distances is expected to represent a significant improvement over the current RF simulations involving comparatively much shorter cutoffs.     

Role of radicals in UV‐initiated postplasma grafting of poly‐ε‐caprolactone: An electron paramagnetic resonance study

Electron paramagnetic resonance (EPR) measurements were performed on poly‐ε‐caprolactone (PCL) films at different stages of the postplasma‐grafting process. PCL films prepared by solvent casting (SC) or electrospinning (ESP) yield very similar EPR spectra after Ar‐plasma treatment and subsequent exposure to air, but the EPR signal is much stronger in the PCL‐ESP films. The free radicals appear to be mainly, and possibly exclusively, oxygen centered. The radicals generated by UV irradiation in PCL‐ESP films were studied in situ with EPR, using a UV‐LED (λ = (285 ± 5) nm). Their EPR spectrum is distinctly different from the plasma‐induced signal, indicative of carbon‐centered radicals, and appears to be independent of the plasma pretreatment. UV‐induced homolytic splitting of (hydro)peroxide bonds was not observed. Both the plasma‐ and UV‐induced radicals decay at room temperature (RT), even in an inert atmosphere. This study demonstrates the potential of electrospun films and UV‐LEDs for the study of plasma‐ and UV‐generated free radicals with EPR in polyesters, and raises questions with respect to the validity of some generally accepted molecular mechanisms underpinning the postplasma grafting technique for polyesters. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of Benzopyran Derivatives,XIV: New Procedure for the Preparation of 2,2-Dimethyl-2H-chromenes

2,2-Dimethyl-4-methoxychromans (1–12) have been converted into 2,2-dimethyl-2H-chromenes (13–24) in acidic media.     

Radical Reactivity of the Biradical [⋅P(μ-NTer)2P⋅] and Isolation of a Persistent Phosphorus-Cantered Monoradical [⋅P(μ-NTer)2P-Et]

The activation of C−Br bonds in various bromoalkanes by the biradical [⋅P(μ-NTer)₂P⋅] ( 1 ) (Ter=2,6-bis-(2,4,6-trimethylphenyl)-phenyl) is reported, yielding trans-addition products of the type [Br−P(μ-NTer)₂P−R] ( 2 ), so-called 1,3-substituted cyclo-1,3-diphospha-2,4-diazanes. This addition reaction, which represents a new easy approach to asymmetrically substituted cyclo-1,3-diphospha-2,4-diazanes, was investigated mechanistically by different spectroscopic methods (NMR, EPR, IR, Raman); the results suggested a stepwise radical reaction mechanism, as evidenced by the in-situ detection of the phosphorus-centered monoradical [⋅P(μ-NTer)₂P-R].< To provide further evidence for the radical mechanism, [⋅P(μ-NTer)₂P-Et] ( 3Et ⋅) was synthesized directly by reduction of the bromoethane addition product [Br-P(μ-NTer)₂P-Et] ( 2 a ) with magnesium, resulting in the formation of the persistent phosphorus-centered monoradical [⋅P(μ-NTer)₂P-Et], which could be isolated and fully characterized, including single-crystal X-ray diffraction. Comparison of the EPR spectrum of the radical intermediate in the addition reaction with that of the synthesized new [⋅P(μ-NTer)₂P-Et] radical clearly proves the existence of radicals over the course of the reaction of biradical [⋅P(μ-NTer)₂P⋅] ( 1 ) with bromoethane. Extensive DFT and coupled cluster calculations corroborate the experimental data for a radical mechanism in the reaction of biradical [⋅P(μ-NTer)₂P⋅] with EtBr. In the field of hetero-cyclobutane-1,3-diyls, the demonstration of a stepwise radical reaction represents a new aspect and closes the gap between P-centered biradicals and P-centered monoradicals in terms of radical reactivity.     

Fermion family recurrences in the Dyson–Schwinger formalism

We study the multiple solutions of the truncated propagator Dyson–Schwinger equation for a simple fermion theory with Yukawa coupling to a scalar field. Upon increasing the coupling constant g, other parameters being fixed, more than one non-perturbative solution breaking chiral symmetry becomes possible and we find these numerically. These “recurrences” appear as a mechanism to generate different fermion generations as quanta of the same fundamental field in an interacting field theory, without assuming any composite structure. The number of recurrences or flavors is reduced to the question of the value of the Yukawa coupling, and it has no special profound significance in the standard model. The resulting mass function can have one or more nodes and the measurement that potentially detects them can be thought of as a collider-based test of the virtual dispersion relation for the charged lepton member of each family. This requires the three independent measurements of the charged lepton’s energy, three-momentum and off-shellness. We illustrate how this can be achieved for the (more difficult) case of the tau lepton. PACS 12.15.Ff; 11.30.Rd     

An analysis of cross-correlations in an emerging market

We apply random matrix theory to compare correlation matrix estimators C$C$ obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C$C$ against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agreement with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the leading eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors.     

Level 17 Ramanujan–Sato series

The Ramanujan Journal - Two level 17 modular functions $$\begin{aligned} r = q^2 \prod _{n=1}^{\infty } (1-q^{n})^{\left( \frac{n}{17} \right) },\qquad s = q^{2} \prod _{n=1}^{\infty } \frac{(1 -...