A family of Numerov-type exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation

A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrödinger equation. The formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions. The new methods are very simple and integrate more exponential functions than both the well-known fourth-order Numerov-type exponentially fitted methods and the sixth algebraic order Runge-Kutta-type methods. Numerical results also indicate that the new methods are much more accurate than the other exponentially fitted methods mentioned above.     

What Is Bohmian Mechanics

Bohmian mechanics is a quantum theory with a clear ontology. To make clear what we mean by this, we shall proceed by recalling first what are the problems of quantum mechanics. We shall then briefly sketch the basics of Bohmian mechanics and indicate how Bohmian mechanics solves these problems and clarifies the status and the role of the quantum formalism.     

Fragmentation of 13C Labelled methylcyclohexanes under electron-impact

The methylcyclohexanes labelled with carbon-13 in the five possible positions have been synthesised and their mass spectra recorded. By comparison of these spectra with those of the corresponding deuterated molecules, it was possible to accurately determine the nature and the contribution of the various fragmentation paths. More than ninety percent of the fragment ions formed from methylcyclohexane result from the rupture, at one stage or another, of one of the C? C bonds attached to the tertiary carbon atoms. Besides the elemination of a polymethylene group from the ring, in either one or two steps, the two major fragmentation pathways involve the prior formation of a cyclohexyl or a cyclopentyl ion.     

Origin of the SN2 benzylic effect

The S N2 identity exchange reactions of the fluoride ion with benzyl fluoride and 10 para-substituted derivatives (RC6H 4CH 2F, R = CH3, OH, OCH 3, NH2, F, Cl, CCH, CN, COF, and NO2) have been investigated by both rigorous ab initio methods and carefully calibrated density functional theory. Groundbreaking focal-point computations were executed for the C6H5CH 2F + F (-) and C 6H 5CH2Cl + Cl (-) SN2 reactions at the highest possible levels of electronic structure theory, employing complete basis set (CBS) extrapolations of aug-cc-pV XZ (X = 2-5) Hartree-Fock and MP2 energies, and including higher-order electron correlation via CCSD/aug-cc-pVQZ and CCSD(T)/aug-cc-pVTZ coupled cluster wave functions. Strong linear dependences are found between the computed electrostatic potential at the reaction-center carbon atom and the effective SN2 activation energies within the series of para-substituted benzyl fluorides. An activation strain energy decomposition indicates that the SN2 reactivity of these benzylic compounds is governed by the intrinsic electrostatic interaction between the reacting fragments. The delocalization of nucleophilic charge into the aromatic ring in the SN2 transition states is quite limited and should not be considered the origin of benzylic acceleration of SN2 reactions. Our rigorous focal-point computations validate the benzylic effect by establishing SN2 barriers for (F (-), Cl (-)) identity exchange in (C6H5CH2F, C6H 5CH2Cl) that are lower than those of (CH3F, CH3Cl) by (3.8, 1.6) kcal mol (-1), in order.     

On the Classical Limit of Quantum Mechanics

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms of an adimensional parameter ε. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own structure the possibility of describing real objects in an observer-independent way.