A generalized force measure of conditions at crack tips

A tentative measure of the forces tending to cause crack growth—the apparent crack extension force—is defined within the framework of continuum mechanics. By an associated fracture criterion initiation of growth may be predicted as well as the direction of preferred growth. The theory is specialized to elastic, viscoelastic and elastic-plastic materials. Under specified conditions the apparent crack extension force may be expressed by surface integrals over the boundary of an arbitrary part of the body for quasi-static deformation and for steady-state propagation of the crack. For plane deformation and for infinitesimal deformation under plane stress conditions these surface integrals reduce to path independent line integrals which include the J integral by Rice[1] and the G integral by Sih[2] as special cases.     

The effect of hydration on the photo-deactivation pathways of 4-aminopyrimidine

The influence of water on the photo-deactivation process of 4-aminopyrimidine has been investigated by means of microsolvation and continuum solvation models. Two- and four-water models were used for the former purpose. Vertical excitations, stationary points on the first excited singlet surface, conical intersections (minima on the crossing seam) and reaction paths have been investigated at the state-averaged complete active space self-consistent field (CASSCF) and multistate CAS perturbation theory to second order (MS-CASPT2) levels of theory. A destabilizing effect of 0.2–0.3 eV has been observed for nπ∗ states while the ππ∗ state is almost unaffected. The two-water model gives already a good representation of hydration effects, especially when combined with the continuum model. A small enhancement of energy barriers (∼0.1 eV) is observed leading to the conclusion that the photodynamics of 4-aminopyrimidine should be affected only little by these solvent effects.     

NMR spectral assignment of 2α- and 3β-methylhopanes and evidence for boat conformation in D ring of 17α(H),21α(H)-hopanes

The full (1)H and (13)C NMR chemical shift assignment of 2α-methyl-17α(H),21β(H)-hopane is presented. This compound is formed in mature sediments from biogenic sources of 2β-methyl-17β(H),21β(H)-hopanoids, which include several cyanobacteria. In addition, full (1)H and (13)C NMR chemical shift data of all four 17,21 isomers of 3β-methylhopane have been assigned. The thermodynamically most stable 3β-configuration corresponds to that found in bacterial sources. The data presented here suggest minor corrections to the (13)C chemical assignments reported earlier for 17α(H)-hopanes. Moreover, spectral evidence indicates an unexpected ring-D boat conformation of 17α(H),21α(H)-hopanes, which may serve to explain the steric strain reported for this isomer.     

Systematic Investigation of Photoinduced Electron Transfer Controlled by Internal Charge Transfer and Its Consequences for Selective PdCl2 Coordination

Fluoroionophores of fluorophore–spacer–receptor format were prepared for detection of PdCl₂ by fluorescence enhancement. The fluorescent probes 1 – 13 consist of a fluorophore group, an alkyl spacer and a dithiomaleonitrile PdCl₂ receptor. First, varying the length of the alkylene spacer (compounds 1 – 3 ) revealed a dominant through‐space pathway for oxidative photoinduced electron transfer (PET) in CH₂‐bridged dithiomaleonitrile fluoroionophores. Second, fluorescent probes 4 – 9 containing two anthracene or pyrene fragments connected through CH₂ bridges to the dithiomaleonitrile unit were synthesized. Modulation of the oxidation potential (E_Ox) through electron‐withdrawing or ‐donating groups on the anthracene moiety regulates the thermodynamic driving force for oxidative PET (ΔG_PET) in bis(anthrylmethylthio)maleonitriles and therefore the fluorescence quantum yields (Φ_f), too. The new concept was confirmed and transferred to pyrenyl ligands, and fluorescence enhancements (FE) greater than 3.2 in the presence of PdCl₂ were achieved by 7 and 8 (FE=5.4 and 5.2). Finally, for comparison, monofluorophore ligands 10 – 13 were synthesized.     

A Bayesian method for construction of Markov models to describe dynamics on various time-scales

The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time-scales.     

Singlet and triplet potential surfaces for the O2+C2H4 reaction

Electronic structure calculations at the CASSCF and UB3LYP levels of theory with the aug-cc-pVDZ basis set were used to characterize structures, vibrational frequencies, and energies for stationary points on the ground state triplet and singlet O(2)+C(2)H(4) potential energy surfaces (PESs). Spin-orbit couplings between the PESs were calculated using state averaged CASSCF wave functions. More accurate energies were obtained for the CASSCF structures with the MRMP2/aug-cc-pVDZ method. An important and necessary aspect of the calculations was the need to use different CASSCF active spaces for the different reaction paths on the investigated PESs. The CASSCF calculations focused on O(2)+C(2)H(4) addition to form the C(2)H(4)O(2) biradical on the triplet and singlet surfaces, and isomerization reaction paths ensuing from this biradical. The triplet and singlet C(2)H(4)O(2) biradicals are very similar in structure, primarily differing in their C-C-O-O dihedral angles. The MRMP2 values for the O(2)+C(2)H(4)→C(2)H(4)O(2) barrier to form the biradical are 33.8 and 6.1 kcal/mol, respectively, for the triplet and singlet surfaces. On the singlet surface, C(2)H(4)O(2) isomerizes to dioxetane and ethane-peroxide with MRMP2 barriers of 7.8 and 21.3 kcal/mol. A more exhaustive search of reaction paths was made for the singlet surface using the UB3LYP/aug-cc-pVDZ theory. The triplet and singlet surfaces cross between the structures for the O(2)+C(2)H(4) addition transition states and the biradical intermediates. Trapping in the triplet biradical intermediate, following (3)O(2)+C(2)H(4) addition, is expected to enhance triplet→singlet intersystem crossing.     

Optical response of small closed-shell sodium clusters

Absorption spectra of closed-shell Na(2), Na(3) (+), Na(4), Na(5) (+), Na(6), Na(7) (+), and Na(8) clusters are calculated using a complex Bethe-Salpeter equation derived using a conserving linear response method. In the framework of a quasiparticle approach, we determine electron-hole correlations in the presence of an external field. The calculated results are in excellent agreement with experimental spectra, and some possible cluster geometries that occur in experiments are analyzed. The position and the broadening of the resonances in the spectra arise from a consistent treatment of the scattering and dephasing contributions in the linear response calculation. Comparison between the experimental and the theoretical results yields information about the cluster geometry, which is not accessible experimentally.     

Electronic effects on atom tunneling: conformational isomerization of monomeric para-substituted benzoic acid derivatives

We present the first generation and spectroscopic identification of the higher-lying E conformer of the simplest aromatic carboxylic acid, benzoic acid (1a), as its O-deuterated isotopologue (E)-d(1)-1a using matrix-isolation techniques; the parent (E)-1a could not be observed because of fast H-tunneling to the more stable conformer (Z)-1a. Even deuterated (E)-d(1)-1a converts quickly back to (Z)-d(1)-1a through D-tunneling with a half-life (τ) of ～12 min in Ar at 11 K. Tunneling computations using an Eckart barrier in conjunction with a CCSD(T)/cc-pVTZ//MP2/cc-pVDZ + ZPVE intrinsic reaction path revealed that τ of (E)-1a is only ～10(-5) min, in marked contrast to those of simple aliphatic acids, which are in the range of minutes. The electronic substituent effects on D-tunneling in para-substituted benzoic acid derivatives (p-X-PhCOOD, d(1)-1) were systematically studied in Ar matrices at 11 K to derive the first Hammett relationships for atom tunneling. σ-Electron donors (X = alkyl) increase the half-life of d(1)-1, while σ-acceptor/π-donor groups (X = OD, NH(2), halogen) and to an even greater extent a σ-/π-acceptor group (X = NO(2)) decrease τ. The latter finding is in line with the smaller E-to-Z reaction barriers and narrower reaction widths for the isomerization. Tunneling substituent constants (σ(t)) for this conformational isomerization were derived experimentally and computationally.     

Synthesis and Molecular Structures of Tetrasilyl Ethers of Calix[4]arenes

The tetrasilyl ethers calix[4]areneOSiMe₂R (R = Me, H, vinyl, allyl) were prepared by salt elimination; the calix[4]arene was deprotonated with sodium hydride and subsequently reacted with chlorosilanes ClSiMe₂R. In general, DMF was chosen as solvent in order to steer the reactions in terms of a preference for the cone‐conformation of the products. In the case of calix[4]areneOSiMe₃ both, partial‐cone‐ and cone‐conformers, were synthesised. All products were characterised by NMR (¹H, ¹³C, ²⁹Si) spectroscopy, mass spectrometry and single‐crystal X‐ray diffraction.