Gerhard Binsch

Iterative computer analysis of complex exchange-broadened NMR bandshapes

Abstract Various known minimization algorithms have been scrutinized for their convergence behavior and speed in the least-squares fitting of computed to experimental NMR bandshapes arising from coupled multispin systems involved in intramolecular exchange. The computational experience gathered on synthetic and experimental test cases is summarized in general terms. The procedure finally adopted and incorporated in the computer program DNMR5 is based on an interpolation between the gradient and Gauss-Newton methods of minimization.

Automated analysis of high-resolution NMR spectra. I. Principles and computational strategy

Abstract A general iterative method for analyzing high-resolution NMR spectra for chemical shifts and isotropic coupling constants is presented that differs from conventional procedures in that it does not depend on the assignment of energy levels or transitions; makes use of the full information content of a spectrum; and is in principle, and in the great majority of cases also in practice, capable of arriving at the correct solution from starting parameters chosen randomly within liberally specified boundaries. The basic equations are derived from a generalized formulation of the least-squares problem. One is led to an ordered sequence of correlation matrices Wk in data space, whose off-diagonal elements provide a general mechanism for smoothing out the multitude of false local minima on the error hypersurface of the ordinary least-squares method. The conditions to be satisfied by the Wk matrices to establish a unique pathway to the global minimum are stated in a formally rigorous way. It is demonstrated that although specific information about the Wk matrices is not accessible in practice, and paradoxically only because of this, one may conclude that they must be symmetric band matrices with diagonal elements wii = 1 and off-diagonal elements wii decaying monotonically with absolute distance from the principal diagonal and satisfying the condition 0 ⩽ wij

Automated analysis of high-resolution NMR spectra. II. Illustrative applications of the computer program DAVINS

Abstract The formalism developed in a previous paper has been implemented in the computer program DAVINS. The theoretical insights gained from a variety of computer experiments are condensed into a few phenomenological rules characterizing the performance of DAVINS in practical applications. Specific experience is reported for 4 tightly coupled synthetic ABCD examples and for the experimental spectra of the aromatic proton [AB] 2 C spin systems in 12 monosubstituted benzenes. Flexible and efficient procedures for dealing with ubiquitous technical problems such as automated data acquisition, data format conversion, baseline artifacts, transient phenomena, noise, and impurity signals are described. It is concluded that with the availability of DAVINS the rigorous analyses of complicated high-resolution NMR spectra need in the future only rarely engage the attention of the spectroscopic specialist; in many if not most instances such tasks can now be entrusted to technicians to be performed as a routine service.

A liouville space formulation of wangsness-bloch-redfield theory of nuclear spin relaxation suitable for machine computation. I. fundamental aspects

Abstract This is the first of a projected series of papers whose ultimate aim is to construct a general computational framework for the analysis of relaxation effects in multispin systems. In the present paper we address ourselves to the fundamental aspects of the theory of nuclear spin relaxation developed by Wangsness, Bloch, and Redfield. It is shown that by starting from a consistent quantum-mechanical treatment of the combined system of spins and bath, thereby avoiding the ad hoc assumptions of the semiclassical approach, and by making systematic use of the Liouville representation of quantum mechanics, it is possible to arrive at a formulation which is simultaneously compact, coherent, and well adapted to computer implementation. The formalism presented covers the most general case, but is at the same time capable of accommodating the simplifications arising from the special situations commonly encountered in practice. The latter are subdivided into intrinsic symmetry properties inherent in the basic structure of the theory itself or attributable to special features of the spin system, such as nuclear permutation symmetry or the weak coupling approximation, and into extrinsic symmetry properties ensuing from special physical situations or associated with specific types of experiments. Each of these symmetries is subjected to a separate analysis by means of general operator techniques and group theory and it is demonstrated how the resulting invariance properties can be exploited in practice. In the final section we tie all this together and are thus led to the global symmetry groups that apply under particular sets of conditions.

Self-consistent perturbation theory for interacting electron systems: II. Semi-empirical treatment for two closed-shell molecules and an application to the Diels-Alder reaction

The self-consistent perturbation theory of the preceding paper is simplified for the use in semi-empirical valence-shell SCF calculations. The validity and limitations of the procedure are tested f...

The molecular structure of cyclopentene in solution as obtained from a nematic phase proton N.M.R. study

The novel technique of automated spectral analysis proposed in recent papers has been applied to the proton N.M.R. spectrum of cyclopentene partially oriented in a nematic solvent. The dipolar coupling constants thus extracted are used to obtain information about the structure of the molecule in solution and about the dynamic details of its large amplitude vibration. It is concluded that cyclopentene exists in an equilibrium conformation characterized by a puckering angle of 30·8°. The data favour a model in which the large amplitude internal motion and the overall reorientation of the molecule are correlated, thus requiring an infinite number of orientation tensors.

Aromaticity — An exercise in chemical futility?

The rap id ly proliferating at tempts of recent years to come to grips with the timehonored and vexed question concerning a purported molecular property called aromatic character have channeled current research efforts into a number of seemingly divergent directions. In this article aimed at the nonspecialist we shall t ry to take stock of what has been accomplished and to sift the unifying features from a bewildering mass of accumulated knowledge.

A dynamic proton magnetic resonance analysis of multiple rate processes in Di- and tri-N-nitroso compounds

Abstract The proton NMR spectra of 1,4-dinitrosopiperazine ( 1 ) and its cis -2,6-dimethyl ( 2 ) and trans -2,5-dimethyl ( 3 ) derivatives and of 1,3,5-trinitrosohexahydro- s -triazine ( 4 ) were recorded as a function of temperature. At and around room temperature two isomers could be identified in compounds 1 , 2 , and 4 and three in 3 . At elevated temperatures one observes the onset of internal rotations about the NN bonds of the N -nitroso groups. An iterative bandshape analysis of the exchange-broadened spectra revealed two independent rate processes in 3 and three in 4 , whereas only a single one could be detected in 1 and 2 . The possibility of correlated two-bond rotations could be rigorously excluded for 1 , and the spectra of 3 and 4 are also consistent with the exclusive operation of sequential rate processes.

A lionville space formulation of wangsness-bloch-redfield theory of nuclear spin relaxation. II. Scalar relaxation

Abstract The superoperator formalism of nuclear spin relaxation theory presented in part I of this series is extended to the case of scalar relaxation, where attention is focused on observables associated with only part of a spin system while the remainder, which may consist of a set of rapidly relaxing nuclei, is treated as a pseudobath whose indirect influence on the subsystem of interest is exerted through scalar spin coupling. The consequences of symmetry features present in the subsystem of interest and/or the pseudobath are analyzed. In particular, it is demonstrated that the situation which has entered the literature under the appellation of “non-fully dissipative case” is to be interpreted as a manifestation of microscopic symmetry invariance. A new, simpler version of a general theory of scalar relaxation of the first kind is presented.

Sterically crowded cyclohexanes-2 synthesis, structure and dynamics of hexaspiro[2.0.3.0.2.0.3.0.2.0.3.0]heneicosane

Abstract The synthesis, structure and dynamics of hexaspiro[2.0.3.0.2.0.3.0.- 2.0.3.0]heneicosane 3 are described. 3 adopts a chair conformation in the crystal state but prefers a chair-to-twistboat equilibrium in solution. The activation parameters of the chair-to-chair interconversion of 3 and the closely related hexaspiro[2.0.2.0.2.0.2.0.2.0.2.0]- octadecane ([6]rotane) 4 have been determined by DNMR. Some consequences appertaining to the conformation and dynamics of other fully (cyclo-)alkylated cyclohexanes are discussed.