Magnetic-Field-Dependent Electronic Relaxation of Gd3+ in Aqueous Solutions of the Complexes [Gd(H2O)8]3+, [Gd(propane-1,3-diamine-N,N,N′,N′-tetraacetate)(H2O)2]−, and [Gd(N,N′-bis[(N-methylcarbamoyl)methyl]-3-azapentane-1,5-diamine-3,N,N′-triacetate)(H2O)] of interest in magnetic-resonance imaging

EPR Spectra have been measured for aqueous solutions of a series of Gd³⁺ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an ⁸S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ², and a correlation time, τ_v, with activation energy, E_v. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to ¹H-NMR relaxivity.     

On the second smallest distance between finitely many points on the sphere

In the following note we investigate the second smallest distance between finitely many points on the sphere. Actually we look for the smallest upper bound for the second smallest distance between n points on the unit sphere. We solve this problem for n=9 and also we give a general, non-trivial upper bound for the second smallest distance of n points with n9.Supported by the Hungarian National Foundation for Scientific Research, Number 1238.     

Entropy evaluation using the kinetic method: is it feasible?

The kinetic method is one of the most widely used experimental techniques for the measurement of thermochemical parameters by mass spectrometry. Recently it has been realized that it can also be used to determine reaction entropies, but the validity of this approach has not been established. This Perspective evaluates kinetic method plots in cases where there is a significant entropy difference between the competing fragmentation channels (i.e. between sample and reference compounds in the dissociating cluster ion). The concept underlying this study is to calculate mass spectra theoretically, based on known thermochemical parameters and as a function of experimental conditions. This can be done accurately using the RRKM-based MassKinetics software. The resulting mass spectra are then interpreted by the kinetic method, yielding DeltaH and DeltaS values. These values are, in turn, compared with the true values used to generate the calculated mass spectra. The results show that the reaction entropy difference between sample and reference has a very large influence on kinetic method plots. This should always be considered when studying energy-dependent mass spectra (using metastable ions or low- or high-energy collision-induced dissociation (CID)), even if only DeltaH is to be determined. Kinetic method plots are not strictly linear and this becomes a serious issue in the case of small molecules showing a large entropy effect. In such cases, results obtained at a low degree of excitation are more accurate. Energy and entropy effects can be evaluated in a relatively straightforward manner: first, the apparent Gibbs energy (DeltaG(app)) and effective temperature (T(eff)) are determined from kinetic method plots (intercept and slope, respectively), obtained from experiments using various degrees of excitation. Second, the resulting DeltaG(app) is plotted against T(eff), the slope yielding DeltaS while the intercept (extrapolation to zero temperature) yields DeltaH. This data evaluation yields more accurate results than alternative methods used in the literature. The resulting DeltaH values are fairly accurate, with errors, in most cases, <4 kJ mol(-1). On the other hand, DeltaS is systematically underestimated by 20-40%. Empirically scaling DeltaS values determined by the kinetic method by 1.35 results in a DeltaS value within 20% (or 10 J mol(-1) K(-1)) of the theoretical value.     

Preparation of new 2,3-diphenylpropenoic acid esters - good yields even for the more hindered Z isomers

The potassium salt of E- and Z-2,3-diphenylpropenoic acids prepared in situ could be esterified efficiently in DMSO with the appropriate alkyl halides at room temperature. In this way 10 previously undescribed esters of these acids were synthesised and characterised. Excellent yields were observed for most of the E isomers and the more hindered Z esters were also obtained in good yields, far better than those obtained applying the classical acid-catalysed esterification reaction.     

Smallest maximal snakes of translates of convex domains

LetK be a convex domain. A maximal snake of sizen is a set of non-overlapping translatesK ₁, ...,K _N ofK, whereK _i touchesK _j if and only if |i –j|=1 and no translate ofK can touchK ₁ orK _n without intersecting an additionalK _i ,i=1, ...,n. The size of the smallest maximal snake is proved to be 11 ifK is a parallelogram and to be 10 otherwise.     

An improved Menshov-Rademacher theorem

We study the a.e. convergence of orthogonal series defined over a general measure space. We give sufficient conditions which contain the Menshov-Rademacher theorem as an endpoint case. These conditions turn out to be necessary in the particular case where the measure space is the unit interval and the moduli of the coefficients form a nonincreasing sequence. We also prove a new version of the Menshov-Rademacher inequality.

     

Comparison of mass spectrometric methods for studying thermally labile compounds: Rifapentine

Results of 16 different mass spectrometric ionization and sample-introduction methods are compared for the case of a thermally very labile antibiotic, rifapentine. These suggest that extensive thermal decomposition occurs during evaporation when the sample can come into contact with hot metal parts, usually the source housing. The intensity of the molecular ion and the extent of fragmentation depend on various parameters, such as the ionization process, positive or negative-ion detection and the type of sample introduction. The most informative methods for rifapentine seem to be ‘in-beam’ electron impact, negative ionization with particle beam and direct liquid introduction interfaces and positive- and negative-ion fast atom bombardment.     

Chemical reactions in fast atom bombardment mass spectrometry

Examples of various chemical reactions occurring in the matrix or in the selvedge region in fast atom bombardment (FAB) mass spectrometry are discussed. These are categorized as oxidations and reductions; substitutions; clusterings and additions; and sample decomposition or transformation. Some reactions observed showed significant time behaviour and in one case it was possible to determine rate constants. These data suggest that chemical reactions can be accelerated significantly by fast atom bombardment.     

4H-3,1-Benzoxazinone-(4), 3.Mitt.: Über die Königsche “N,N′-Diphenyl-guanidin-o,o′-dicarbonsäure”. Eine Richtigstellung

Zusammenfassung Bei der Einwirkung von Bromcyan auf überschüssige Anthranilsäure wird nicht N,N-Diphenyl-guanidin-o,o-dicarbonsäure (II), sondern N-(2-Ureido-benzoyl)-anthranilsäure (V) gebildet. Diese läßt sich sowohl zu 1,2,3,4-Tetrahydro-chinazolindion-(2,4) (III), als auch zu ihrem 3-(2-Carboxy-phenyl)-Derivat (VI) cyclisieren.     

Studies on the conversions of diols and cyclic ethers—49: Stereochemistry of cyclodehydration of 1,4-diols on the action of brönsted and lewis acids: a comprehensive study

The stereochemistry of the cyclodehydration of (±)- and meso-2,5-hexanediol on the action of various dehydrating agents was investigated. The earlier assumed and confirmed intramolecular S_N2 mechanism for acid-catalysed ring-closure was found to hold in most cases. Various extents of racemisation can be observed on the action of certain Lewis acids, and the solvents concentrated H₂SO₄ and HMPT (hexamethyl phosporic acid triamide) under previously unexamined reaction conditions.