Factorization of involutions in characteristic two orthogonal groups: An application of the Jordan form to group theory

This paper uses the theory of the Jordan canonical form for a matrix and the theory of orthogonal sums of isometries in metric vector spaces (quadratic spaces) in order to prove a theorem on the factorization of involutions in the orthogonal groups of metric vector spaces over fields of characteristic two. Using this theorem, a classification scheme for such involutions is devised. This scheme is similar to the scheme for involutions when the field is of characteristic not equal of two.     

Comparison of various density functional methods for distinguishing stereoisomers based on computed (1)H or (13)C NMR chemical shifts using diastereomeric penam beta-lactams as a test set

Full (1)H and (13)C NMR chemical shift assignments were made for two sets of penam beta-lactams: namely, the diastereomeric (2S, 5S, 6S)-, (2S, 5R, 6R)-, (2S, 5S, 6R)-, and (2S, 5R, 6S)-methyl 6-(1,3-dioxoisoindolin-2-yl)-3,3-dimethyl-7-oxo-4-thia-1-aza-bicyclo[3.2.0]heptane-2-carboxylates (1-4) and (2S, 5R, 6R)-, (2S, 5S, 6R)-, and (2S, 5R, 6S)-6-(1,3-dioxoisoindolin-2-yl)-3,3-dimethyl-7-oxo-4-thia-1-aza-bicyclo[3.2.0]heptane-2-carboxylic acids (6-8). Each penam was then modeled as a family of conformers obtained from Monte Carlo searches using the AMBER* force field followed by IEFPCM/B3LYP/6-31G(d) geometry optimization of each conformer using chloroform solvation. (1)H and (13)C chemical shifts for each conformer were computed at the WP04, WC04, B3LYP, and PBE1 density functional levels as Boltzmann averages of IEFPCM/B3LYP/6-311 + G(2d,p) energies over each family. Comparisons between experimental and theoretical chemical shift data were made using the total absolute error (|Deltadelta| (T)) criterion. For the (1)H shift data, all methods were sufficiently accurate to identify the proper stereoisomers. Computed (13)C shifts were not always successful in identifying the correct stereoisomer, regardless of which DFT method was used. The relative ability of each theoretical approach to discriminate among stereoisomers on the basis of proton shifts was also evaluated.     

The onset of coulomb explosions in polyatomic molecules

With the development of high intensity femtosecond lasers, the ionisation and dissociation dynamics of molecules has become an area of considerable interest. Using the technique of femtosecond laser mass spectrometry (FLMS), the molecules carbon disulphide, pyrimidine, toluene, cyclohexanone and benzaldehyde are studied with pulse widths of 50 fs in the near infrared (IR) wavelength region (790 nm). Results are presented and contrasted for laser beam intensities around 10(15) and 10(16) W cm(-2). For the lower intensities, the mass spectra yield dominant singly charged parent ions. Additionally, the appearance of doubly charged parent ions is evident for carbon disulphide, toluene and benzaldehyde with envelopes of doubly charged satellite species existing in these local regions. Carbon disulphide also reveals a small triply charged component. Such atomic-like features are thought to be a strong fingerprint of FLMS at these intensities. However, upon increasing the laser intensity to approximately 10(16) W cm(-2), parent ion dominance decreases and the appearance of multiply charged atomic species occurs, particularly carbon. This phenomenon has been attributed to Coulomb explosions in which the fast absorption of many photons may produce transient highly ionised parent species which can subsequently blow apart. Copyright 1999 John Wiley & Sons, Ltd.     

Uniform molecular analysis using femtosecond laser mass spectrometry

The potential of femtosecond laser time-of-flight mass spectrometry (FLMS) for uniform quantitative analysis of molecules has been investigated. Various samples of molecular gases and vapours have been studied, using ultra-fast ( approximately 50 fs) laser pulses with very high intensity (up to 1.6 x 10(16) Wcm(-2)) for non-resonant multiphoton ionisation/tunnel ionisation. Some of these molecules have high ionisation potentials, requiring up to ten photons for non-resonant ionisation. The relative sensitivity factors (RSF) have been determined as a function of the laser intensity and it has been demonstrated that for molecules with very different masses and ionisation potentials, uniform ionisation has been achieved at the highest laser intensities. Quantitative laser mass spectrometry of molecules is therefore a distinct possibility. Copyright 1999 John Wiley & Sons, Ltd.     

A thermal decarbonylation of penam beta-lactams

Penam acids 6-8 [i.e., (2S,5R,6R)-, (2S,5S,6R)-, and (2S,5R,6S)-isomers of 6-(1,3-dihydro-1,3-dioxo-2H-isoindol-2-yl)-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylic acid] were prepared by deesterification of the corresponding methyl esters 2-4. The same methodology applied to ester 1 did not lead to the (2S,5S,6S)-isomer 5 but rather a 72% yield of the thiazoline derivative 9. High-resolution mass spectrometry analysis of the reaction headspace gases indicated that a stoichiometric amount of carbon monoxide is produced during the deesterification of 1. A mechanism for this decarbonylation reaction is proposed. This appears to represent a new type of fragmentation reaction for a penam carboxylic acid. The free energies of various reaction species along viable decarbonylation reaction coordinates for acids 5 and 7 were computed by using the density functional theory method IEFPCM/M06/6-31+G(d). Anionic and zwitterionic (neutral) variants of the proposed mechanism were considered, but each produced computed activation free energies deemed to be too high (>45 kcal/mol) to be experimentally relevant. The computed activation free energies for the protonated (cationic) variant of the mechanism were 17.3 kcal/mol for 7 vs 8.8 kcal/mol for 5. The value of this difference in energies of activation (DeltaDeltaG++) is quite consistent with experimental observations and supports the proposed mechanism. For a portion of the computed reaction coordinate that involves ring opening of the lactam ring by an internal carboxylic acid group to form a cyclic anhydride, the expected tetrahedral intermediate was circumvented by a direct (concerted) and facile N- to O-acyl migration event. Additional thermal gas-phase reaction products produced during gas chromatographic analysis of the penams 1-8 were characterized with high-resolution mass spectrometry, and possible mechanisms for their formation are presented.     

Evaluation of various DFT protocols for computing 1H and 13C chemical shifts to distinguish stereoisomers: diastereomeric 2‐, 3‐, and 4‐methylcyclohexanols as a test set

¹H and ¹³C NMR chemical shifts were measured for a set of six isomers—the cis and trans 2‐, 3‐, and 4‐methylcyclohexanols. ¹H and ¹³C NMR chemical shifts were computed at the B3LYP, WP04, WC04, and PBE1 density functional levels for the same compounds, taking into account the Boltzmann distribution among conformational isomers (chair–chair forms and hydroxyl rotamers). The experimental versus computed chemical shift values for proton and carbon were compared and evaluated (using linear correlation (r²), total absolute error (|Δδ|_T), and mean unsigned error (MUE) criteria) with respect to the relative ability of each method to distinguish between cis and trans stereoisomers for each of the three constitutional isomers. For ¹³C shift data, results from the B3LYP and PBE1 density functionals were not sufficiently accurate to distinguish all three pairs of stereoisomers, while results using the WC04 functional did do so. For ¹H shift data, each of the WP04, B3LYP, and PBE1 methods was sufficiently accurate to make the proper stereochemical distinction for each of the three pairs. Applying a linear correction to the computed data improved both the absolute accuracy and the degree of discrimination for most of the methods. The nature of the cavity definition used for continuum solvation had little effect. Overall, use of proton chemical shift data was more discriminating than use of carbon data. Copyright © 2007 John Wiley & Sons, Ltd.