Local orbitals as basis sets have been widely used in various communities, including condensed matter physics, materials science, quantum chemistry and biochemistry for several decades. Beyond electronic structure, atomistic simulations based on local-orbital techniques are now routinely used to compute a variety of other physical properties such as energetics, geometry, dynamics, thermodynamics, etc. It is also the class of bases of choice for simulations of large systems for reasons of efficiency. There is a wide spectrum of techniques that use these basis sets, from very accurate ab initio calculations (Density Functional Theory, Hartree Fock, Configuration Interaction), to greatly simplified semi-empirical schemes restricted to two-center integrals with fitted parameters.
During the last few years, a number of new ideas for attaining high efficiencies in the electronic structure problem have emerged. Based on localization ideas, these so-called linear-scaling methods have boosted the interest in the use and development of localized basis sets, since they provide a natural framework for their practical implementation. Besides the traditional atomic-like orbital basis sets, there are new proposals of localized bases which are currently being investigated, including wavelets, blips or spherical Bessel functions.
Efficiency in linear-scaling methods demands the confinement of basis orbitals to small ranges. There is a new challenge of finding basis sets of quality (flexibility and transferability) while confining the orbital range and keeping the size of the basis set small. Quantum chemists are exploring the possibilities offered by their technology based on Gaussian-type orbitals, but they face the difficulty of the long range of these functions. Other efforts coming from the limit of smallest confinement ranges (working in real space with grids, finite elements, B-splines) face the difficulty of the large number of degrees of freedom.
This new challenge was identified a few years ago, and a first and very fruitful workshop was dedicated to it by CECAM in 1998. Different schemes scattered across different communities were presented to and discussed by a mixed audience of physicists and chemists, establishing communication and encouraging collaboration which is so important for the definition of the line of research and its future. Since then, new ideas and developments have emerged and it is time to meet again.
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