Nucleophilic identity substitution reactions. The reaction between water and protonated alcohols

The potential energy surfaces for the reaction between H2O and the protonated alcohols MeOH2+, EtOH2+, PriOH2+, and Bu(t)OH2+ have been explored by means of high level ab initio theoretical methods. Both nucleophilic substitution (SN2) and elimination (E2) pathways have been investigated. Front side (SNF) and the familiar back side (SNB) Walden inversion attack of the nucleophile have been found to be competing for the H2O Bu(t)OH2+ system. In contradiction with the customary relationship between so-called "steric effects" and barrier heights--more alkyl-substituted SN2 reaction centres have higher SN2 reaction barriers--the SN2 reaction barriers are found to be Et > Me > Pri > Bui. This result is in excellent agreement with available experimental data.     

A combined theoretical and experimental approach to the unimolecular loss of molecular hydrogen from protonated formaldehyde: Determination of the average internal energy of metastable [CH2OH]+ ions

Ab initio quantum chemical calculations (MP2/4–31G**) were performed for the dihydrogen elimination reaction from protonated formaldehyde. The energy difference between reactants and products and the activation energies were found to be in good agreement with the corresponding experimental quantities. Theoretical rate vs. energy curves were computed for a series of isotopic variants of the reaction using the Rice–Ramsperger–Kassel–Marcus (RRKM) method. The vibrational frequencies used in these calculations were taken from the 4–31G** geometry-optimized transition state and reactant structures. Quantum mechanical tunnelling was introduced to explain the existence of metastable CH₂OH ions, and a negative kinetic shift of about 0.1 eV was found. The intramolecular kinetic isotope effect for loss of HH/HD and DH/DD was calculated and compared with the experimental data. The result is consistent with the assumption that the average internal energy of metastable [CH₂OH]⁺ ions is very close to the critical energy for H₂ loss.     

Decomposition of protonated formic acid: One transition state—Two product channels

The unimolecular chemistry of protonated formic acid, [HCOOH]H(+), has been investigated by analyzing the fragmentation of metastable ions (MI) during flight in a sector mass spectrometer, and by proton transfer to formic acid in a Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometer. High level ab initio calculations have been used to model the relevant parts of the potential energy surface (PES). In addition, ab initio direct dynamics calculations have been conducted, tracing out 60 different reaction trajectories. The only stable isomer in the mass spectrometric experiments is HC(OH)(2)(+), which is the precursor to both observed ionic products, HCO(+) and H(3)O(+), via the same saddle point of the potential energy surface. The detailed motion of the dissociating molecule during passage of the post-transition state region of the PES therefore determines which product ion is formed. After passing the TS a transient HC(O)OH(2)(+) molecule is first formed. High total energy increases the probability that the nascent water molecule will have sufficient speed to escape the HCO(+) moiety. Otherwise, typically at low energies, the two units recombine, upon which intra-complex proton transfer is very likely. Eventually, this will give the more stable H(3)O(+).     

Isolated rational curves on K3-fibered Calabi–Yau threefolds

In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙ ^{n 1}}×ℙ¹. These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d,0) for every positive integer d on a general Calabi–Yau variety of these types. The proof depends heavily on existence theorems for curves on K3-surfaces proved by S. Mori and K. Oguiso. Some of these varieties are related to Calabi–Yau varieties in projective space by a determinantal contraction, and we use this to prove existence of rational curves of every degree for a general Calabi–Yau variety in projective space. Received: 14 October 1997 / Revised version: 18 January 1998     

Multidimensional analyses of voicing offsets and onsets in female speakers

This study investigates cross-speaker differences in the factors that predict voicing thresholds during abduction-adduction gestures in six normal women. Measures of baseline airflow, pulse amplitude, subglottal pressure, and fundamental frequency were made at voicing offset and onset during intervocalic /h/, produced in varying vowel environments and at different loudness levels, and subjected to relational analyses to determine which factors were most strongly related to the timing of voicing cessation or initiation. The data indicate that (a) all speakers showed differences between voicing offsets and onsets, but the degree of this effect varied across speakers; (b) loudness and vowel environment have speaker-specific effects on the likelihood of devoicing during /h/; and (c) baseline flow measures significantly predicted times of voicing offset and onset in all participants, but other variables contributing to voice timing differed across speakers. Overall, the results suggest that individual speakers have unique methods of achieving phonatory goals during running speech. These data contribute to the literature on individual differences in laryngeal function, and serve as a means of evaluating how well laryngeal models can reproduce the range of voicing behavior used by speakers during running speech tasks.     

The Pfaffian Calabi–Yau, its Mirror, and their Link to the Grassmannian G(2,7)

The rank 4 locus of a general skew-symmetric 7 × 7 matrix gives the Pfaffian variety in P ²⁰ which is not defined as a complete intersection. Intersecting this with a general P ⁶ gives a Calabi–Yau manifold. An orbifold construction seems to give the 1-parameter mirror-family of this. However, corresponding to two points in the 1-parameter family of complex structures, both with maximally unipotent monodromy, are two different mirror-maps: one corresponding to the general Pfaffian section, the other to a general intersection of G(2,7) P ²⁰ with a P ¹³. Apparently, the Pfaffian and G(2,7) sections constitute different parts of the A-model (Kähler structure related) moduli space, and, thus, represent different parts of the same conformal field theory moduli space.