A study of basis set imbalance effects on the calculation of intramolecular potentials for van der Waals systems

The effects of using different basis sets have been investigated in the study of the intermolecular potential (IMP) of Ne₂, a prototypical van der Waals system. A balancing effect on the strength of the IMP was observed, whereby basis set inclusion of diffuse atom centred polarization functions (ACPFs) in conjunction with bond functions, at the expense of compact ACPFs, resulted in an overestimated IMP, while the opposite situation resulted in an underestimated IMP. Recent proposals made for monitoring the saturation of the SCF total atomic energy [10] and SCF interaction energy [11] are shown to be insufficient criteria with which to judge whether a basis set predicts an underestimated repulsive contribution to the interaction energy at the MP4(SDTQ) level, and hence whether a basis set predicts an overestimate in the IMP. The observations result in an unresolved ambiguity in choosing an appropriate basis set for larger van der Waals systems, where one is forced to make major concessions in basis set quality and where one does not have the experimental results with which to ‘guide’ the competing balance between the above basis functions.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.