Improved diffusion Monte Carlo for bosonic systems using time-step extrapolation "on the fly"

A diffusion Monte Carlo algorithm employing "on the fly" extrapolation with respect to the time step is implemented and demonstrated simulating realistic systems. Significant advantages are obtained when using on the fly extrapolation, leading to reduced systematic and statistical errors. The sound theoretical basis of extrapolation on the fly is discussed and compared to justifications for the a posteriori extrapolation.     

Novel naphthalene diimides as activatable precursors of bisalkylating agents, by reduction and base catalysis

Mild activation of water-soluble naphthalene diimides (NDIs) as bisalkylating agents has been achieved by base catalysis and by chemical and electrochemical reductions. NDI activation by a single electron reduction represents a novelty in the field of activatable electrophiles. Under mild reduction, induced by S2O4(2-) in aqueous solution, the resulting NDI radical anion (NDI*-) undergoes a monomolecular fragmentation to yield a new transient species, where the NDI radical anion is tethered to a quinone methide moiety. The latter still retains electrophilic properties, reacting with amines, thiols, and ethyl vinyl ether. Owing to the NDI recognition properties, these results represent the first step toward selective and bioactivatable cross-linking agents.     

Equivalency for Disconjugate Operators

The solutions of the dfferential equation L_nx + a₀(t)x = 0, where L_n is a disconjugate operator and a₀ is of one sign, are studied according to their behavior as t → ∞. We prove equivalence theorems between solutions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.     

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with It? calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Ito; calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.     

Efficient calculation of low energy statistical rates for gas phase dissociation using umbrella sampling

Monte Carlo (MC) simulations can be used to compute microcanonical statistical rates of gas phase dissociation reactions. Unfortunately, the MC approach may suffer from a slow convergence and large statistical errors for energies just above the dissociation threshold. In this work, umbrella sampling is proposed as a device to reduce the statistical error of MC rate constants. The method is tested by computing the classical dissociation rate for the reaction [H5O2+]* --> H2O + H3O(+) over the range of internal energy 38 < E < or = 100 kcal/mol. Comparing with other literature methods, it is found that umbrella sampling reduces the computational effort by up to two orders of magnitude when used in conjunction with a careful choice of sampling distributions. The comparison between MC rate constants and classical Rice-Ramsperberg-Kassel harmonic theory shows that anharmonicity plays an important role in the dissociation process of the Zundel cation (H5O2+) at all energies.     

Synthesis of monoprotected 1,4-diketones by photoinduced alkylation of enones with 2-substituted-1,3-dioxolanes

Photosensitized hydrogen abstraction from 2-alkyl-1,3-dioxolanes by triplet benzophenone gives the corresponding 1,3-dioxolan-2-yl radicals and these are trapped by ,β-unsatured ketones yielding monoprotected 1,4-diketones. With open chain ketones (3-buten-2-one and 4-penten-3-one) the yields are low and competitive pathways in part consume the radicals. With cyclic enones however, yields are good as tested with cyclopentenone, cyclohexenone and 4-hydroxy-cyclopentenone. More generally, this is a viable alternative for the synthesis of 1,4-diketones via radicals while the thermal initiation gives only low yield. The reaction cannot be extended to strongly stabilized radicals, such as the 2-phenyl-1,3-dioxolanyl radical.     

Contractions on a manifold polarized by an ample vector bundle

A complex manifold of dimension together with an ample vector bundle on it will be called a generalized polarized variety. The adjoint bundle of the pair is the line bundle . We study the positivity (the nefness or ampleness) of the adjoint bundle in the case . If this was previously done in a series of papers by Ye and Zhang, by Fujita, and by Andreatta, Ballico and Wisniewski.

If is nef then, by the Kawamata-Shokurov base point free theorem, it supports a contraction; i.e. a map from onto a normal projective variety with connected fiber and such that , for some ample line bundle on . We describe those contractions for which . We extend this result to the case in which has log terminal singularities. In particular this gives Mukai's conjecture 1 for singular varieties. We consider also the case in which for every fiber and is birational.

     

Generation and reactivity of the 4-aminophenyl cation by photolysis of 4-chloroaniline

4-Chloroaniline and its N,N-dimethyl derivative are photostable in cyclohexane but undergo efficient photoheterolysis in polar media via the triplet state and give the corresponding triplet phenyl cations. CASSCF and UB3LYP calculations show that the 4-aminophenyl triplet cation has a planar geometry and is stabilized by >10 kcal mol(-1) with respect to the slightly bent singlet. The triplet has a mixed carbene-diradical character at the divalent carbon. This species either adds to the starting substrate forming 5-chloro-2,4'-diaminodiphenyls (via an intermediate cyclohexadienyl cation) or is reduced to the aniline (via the aniline radical cation) in a ratio depending on the hydrogen-donating properties of the solvent. Transients attributable to the triplet aminophenyl cation as well as to the ensuing intermediates are detected. Chemical evidence for the generation of the phenyl cation is given by trapping via electrophilic substitution with benzene, mesitylene, and hexamethylbenzene (in the last case the main product is a 6-aryl-3-methylene-1,4-cyclohexadiene). Relative rates of electrophilic attack to benzene and to some alkenes and five-membered heterocycles are measured and span over a factor of 15 or 30 for the two cations. The triplet cation formed under these conditions is trapped by iodide more efficiently than by the best pi nucleophiles. However, in contrast to the singlet cation, it does not form ethers with alcohols, by which it is rather reduced.     

Bis (trimethylsilyl) thioketone

Tris (trimethylsilyl) methylsulphenylbromide undergoes facile Me₃ SiBr elimination to give bis (trimethylsilyl) thioketone.     

Photoinduced, ionic Meerwein arylation of olefins

Irradiation of 4-chloroaniline or of its N,N-dimethyl derivative in polar solvents generates the corresponding triplet phenyl cations. These are trapped by alkenes yielding arylated products in medium to good yields. B3LYP calculations show that the triplet cation slides with negligible activation energy to a bonded adduct with ethylene, whereas it forms only a marginally stabilized CT complex with water (chosen as a representative sigma nucleophile). The structure of the final products depends on the preferred path from the adduct cation with the alkene. In the case of aryl olefins, this deprotonates to stilbene derivatives, while, from 2,3-dimethyl-2-butene and allytrimethylsilane, allylanilines are obtained by elimination of an electrofugal group in gamma. In the case of mono- and disubstituted alkenes the cation adds chloride rather than eliminating and beta-chloroalkylanilines are obtained. The regio- and sterochemistry of the addition across the alkene are best understood with a phenonium ion structure for the adduct. The nucleophile entering in beta can be varied under conditions in which the adduct cation is trapped more efficiently than the starting phenyl cation. Thus, beta-methoxyalkylanilines are formed when the irradiation is carried out in methanol. beta-Iodoalkylanilines are obtained in acetonitrile containing iodide and unsubstituted alkylanilines in the presence of sodium borohydride. A case of intramolecular nucleophilic trapping is found with 4-pentenoic acid. The reaction is a wide-scope ionic analogue of the radicalic Meerwin arylation of olefins.