Asymptotic analysis of Gaussian integrals,II: Manifold of minimum points

This paper derives the asymptotic expansions of a wide class of Gaussian function space integrals under the assumption that the minimum points of the action form a nondegenerate manifold. Such integrals play an important role in recent physics. This paper also proves limit theorems for related probability measures, analogous to the classical law of large numbers and central limit theorem.Alfred P. Sloan Research Fellow. Research supported in part by NSF Grant MCS-80-02149Research supported in part by NSF Grant MCS-80-02140     

Carbon-13 NMR studies of quinolines and isoquinolines. II. Chlorine–nitrogen interactions and N-oxide effects

Carbon-13 chemical shift assignments are reported for four chloroquinolines, six chloroisoquinolines, one dichloroquinoline, four dichloroisoquinolines, four methylchloroquinolines, two methylchloroisoquinolines, quinoline N-oxide, isoquinoline N-oxide, five methylquinoline N-oxides, two methylisoquinoline N-oxides and three chloroisoquinoline N-oxides. Chlorine substituent chemical shift (SCS) effects are reported for the alpha, ortho, meta, para and peri positions. Consistent patterns are observed for the para and peri positions, a vinylogous ortho pattern is reported and the additivity of these SCS effects is demonstrated. Alpha SCS effects vary widely from 1.1 ppm upfield in 1-chloroisoquinoline to 6.7 ppm downfield in 4-chloroquinoline. These results, together with those in the literature, permit the definition of steric and nitrogen lone-pair contributions which modify the ‘normal’ chlorine SCS effect, and these modifying contributions are shown to be roughly additive. Large (6–16 ppm) upfield shifts are observed for the carbons ortho and para to the N-oxide group. The individual magnitudes of these shifts and their sum are constant and the effects are additive in substituted systems. A 9.5 ppm upfield shift is also observed for C-8 in quinoline N-oxides which is attributed to a space–charge interaction. Substituent chemical shift (SCS) effects for the chloro and methyl groups and the chemical shifts of the methyl carbons are essentially the same in the N-oxides as in the parent heterocycles and are additive, except for those molecules where the substituent is adjacent to the N-oxide moiety, in which cases substantial interactions are observed.     

Measurement of the hydride donor abilities of [HM(diphosphine)2]+ complexes (M = Ni, Pt) by heterolytic activation of hydrogen

[M(diphosphine)2]2+ complexes (where M = Ni and Pt) react with hydrogen in the presence of bases to form the corresponding hydrides, [HM(diphosphine)2]+. In seven cases, equilibria have been observed from which the hydride donor ability (DeltaGdegrees(H-)) of the hydrides can be calculated. For six of these complexes, the DeltaGdegrees(H-) values calculated using heterolytic activation of hydrogen are compared with those based on thermodynamic cycles using pK(a) measurements and electrochemical half-wave potentials. The agreement between these two methods is good (within 1 kcal/mol). The reactivity of the various [M(diphosphine)2]2+ complexes toward hydrogen parallels their measured hydride acceptor abilities.     

Iterative high-throughput polymorphism studies on acetaminophen and an experimentally derived structure for form III

Three crystal forms of acetaminophen were prepared and characterized using a newly developed high-throughput crystallization platform, CrystalMax. The platform consists of design software, robotic sample dispensing and handling, and high-throughput microanalytics and is capable of running thousands of crystallizations in parallel using several different methods to drive supersaturation and subsequent crystallization. Additionally, structural models of the elusive third form of acetaminophen will be discussed on the basis of powder X-ray diffraction data. One structure suggested has a bilayer motif, held together by O-H...O(H) hydrogen bonds, and helps explain the difficulty associated with preparing this form from solution.     

Causality in Inflationary Universes with Positive Spatial Curvature

We show that in the case of positively-curved Friedmann-Lemaître universes (k = +1), an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of , 1, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a k = +1 frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.