Subregion-Adaptive Integration of Functions Having a Dominant Peak

Abstract

Many statistical multiple integration problems involve integrands that have a dominant peak. In applying numerical methods to solve these problems, statisticians have paid relatively little attention to existing quadrature methods and available software developed in the numerical analysis literature. One reason these methods have been largely overlooked, even though they are known to be more efficient than Monte Carlo for well-behaved problems of low dimensionality, may be that when applied naively they are poorly suited for peaked-integrand problems. In this article we use transformations based on “split t” distributions to allow the integrals to be efficiently computed using a subregion-adaptive numerical integration algorithm. Our split t distributions are modifications of those suggested by Geweke and may also be used to define Monte Carlo importance functions. We then compare our approach to Monte Carlo. In the several examples we examine here, we find subregion-adaptive integration to be substantially more efficient than importance sampling.     

The thiomethyl anion: Formation,reactivity, and thermodynamic properties

The thiomethyl anion (1) has been generated by fluorodesilylation of trimethylsilylmethanethiol in a variable-temperature flowing afterglow device. The proton affinity (1649 ± 12 kJ mol^?1) and electron affinity (0.67 ± .13 eV) were determined and compared to a previously reported molecular orbital calculation. Isomerization via a 1,2-proton shift does not take place between ?40° and 100°C despite a 156 kJ mol^?1 driving force. Ion-molecule reactions of 1 were examined with a number of reagents including N₂0, O₂, CS₂, COS, and CO₂, Hydride ion transfer was observed in every case, along with other products, and thermodynamic information has been derived.     

A search for precursors to extensive air showers

No evidence for precursors to cosmic ray air showers was found ($\text{“}\text{flux}\text{”?10}{}^{\mathrm{?8}}\text{cm}{}^{\mathrm{?2}}\text{sr}{}^{\mathrm{?1}}\text{s}{}^{\mathrm{?1}}$) in a sample 2.8 times that of Clay and Crouch and a system noise level several times lower. A simple model leads to a cross leation for production ?60 times the total proton-nucleus cross section.     

Photodetachment of zwitterions: probing intramolecular Coulomb repulsion and attraction in the gas phase using mono-decarboxylated pyridinium dicarboxylates. Implications on the mechanism of orotidine 5'-monophosphate decarboxylase

Negative ion photoelectron spectra resulting from the decarboxylation of nine zwitterionic pyridinium dicarboxylates (D(x,y)) are reported. Structural assignments are made on the basis of analogy to the spectra of related species, labeling experiments with (13)C- or (2)H-containing substrates, independent syntheses, and comparison to density functional theory and ab initio (B3LYP and CCSD(T), respectively) results. In some cases, an acid-catalyzed isomerization of the D(x,y)-CO(2) ions was found to take place. Adiabatic detachment energies of the resulting zwitterionic ions were measured and are well reproduced by theory. The relative stabilities of the D(x,y)-CO(2) decarboxylation products are largely determined by their intramolecular electrostatic interactions, which are directly probed by the photoelectron spectra and were analyzed in terms of the resulting Coulombic forces. Expulsion of carbon dioxide from the D(x,y) ions was also used as an electrostatic model to probe the mechanism of the enzyme-catalyzed conversion of orotidine 5'-monophosphate (OMP) to uridine 5'-monophosphate (UMP). It was found that the loss of CO(2) from these zwitterions and from oxygen-protonated OMP is retarded by the presence of an additional anionic group. This suggests that the formation of a zwitterion intermediate in the enzyme-catalyzed transformation of OMP to UMP may have less of an energetic impact than commonly thought and could be a "red herring". If so, the electrostatic stress mechanism proposed by Larsen et al. and Pai, Guo, and co-workers maybe followed.     

Formation of a 1-bicyclo[1.1.1]pentyl anion and an experimental determination of the acidity and C-H bond dissociation energy of 3-tert-butylbicyclo[1.1.1]pentane

Decarboxylation of 1-bicyclo[1.1.1]pentanecarboxylate anion does not afford 1-bicyclo[1.1.1]pentyl anion as previously assumed. Instead, a ring-opening isomerization which ultimately leads to 1,4-pentadien-2-yl anion takes place. A 1-bicyclo[1.1.1]pentyl anion was prepared nevertheless via the fluoride-induced desilylation of 1-tert-butyl-3-(trimethylsilyl)bicyclo[1.1.1]pentane. The electron affinity of 3-tert-butyl-1-bicyclo[1.1.1]pentyl radical (14.8 plus minus 3.2 kcal/mol) was measured by bracketing, and the acidity of 1-tert-butylbicyclo[1.1.1]pentane (408.5 +/- 0.9) was determined by the DePuy kinetic method. These values are well-reproduced by G2 and G3 calculations and can be combined in a thermodynamic cycle to provide a bridgehead C-H bond dissociation energy (BDE) of 109.7 +/- 3.3 kcal/mol for 1-tert-butylbicyclo[1.1.1]pentane. This bond energy is the strongest tertiary C-H bond to be measured, is much larger than the corresponding bond in isobutane (96.5 +/- 0.4 kcal/mol), and is more typical of an alkene or aromatic compound. The large BDE can be explained in terms of hybridization.     

Reactions of strong bases with vinyl fluoride formation and characterization of 1-fluorovinyl anion and the fluoride-acetylene hydrogen-bonded complex

Vinyl fluoride reacts with strong bases to afford I-fluorovinyl anion (1a) and a fluoride-acetylene cluster (1b). The former ion can be prepared independently, and cleanly, by the fluorodesilylation of 1-(trimethylsilyl) fluoroethylene. Reactions of 1a are reported, and its proton affinity is assigned (387 ± 3 kcal mol^?1). Vinyl fluoride is 22 kcal mol^?1 more acidic than ethylene. This unusually large substituent effect is reproduced by ab initio calculations, and can be accounted for by geometric changes which minimize the electron-electron repulsion in 1a. Computations on 2-fluorovinyl anions (1c and 1d) have also been carried out, and both ions are only slightly less stable than 1a. The cis isomer (1c) has a larger barrier for fluoride elimination and is a reasonable target for preparation.     

Lithiated hydrocarbons, their conjugate bases, and corresponding radicals: a computational study of RLi (R = CH3, CH3CH2, CH2=CH, and HC triple bond C)

Organolithium compounds RLi (R = CH(3), CH(3)CH(2), CH(2)=CH, and HC(triple bond)C) and their corresponding hydrocarbons were fully optimized at the MP2/6-311+G(2df,2pd) level. Single-point energy calculations also were carried out at the CCSD(T) and B3LYP levels with the same triple split-valence basis set. Acidities, electron affinities, and bond dissociation energies are reported, and the following general results were found: (1) Alpha-lithio anions are ground-state triplet molecules. (2) Lithium is an acid-enhancing substituent. (3) Conjugate bases of organolithiums are stable with respect to electron loss and therefore are attractive targets for mass spectrometry investigations. (4) Lithium weakens alpha- and beta-C-H bonds, the latter by approximately 25 kcal mol(-1). Consequently, radical chemistry of lithiated compounds at remote sites is a promising area for exploration.