Creating Basis Sets from Scratch

Creating completely new basis sets is best left to professionals because it requires a very large amount of technical expertise. To be more correct, anyone could 

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A basis set is a set of functions used to describe the shape of the orbitals in an atom. Molecular orbitals and entire wave functions are created by taking linear combinations of basis functions and angular functions. Most semiempirical methods use a predehned basis set. When ah initio or density functional theory calculations are done, a basis set must be specihed. Although it is possible to create a basis set from scratch, most calculations are done using existing basis sets. The type of calculation performed and basis set chosen are the two biggest factors in determining the accuracy of results. This chapter discusses these standard basis sets and how to choose an appropriate one. 

The framework, however, as introduced so far is of little help for our purpose since the shift from any subspace to its immediate in hierarchy would require to change entirely the set of basis functions. Although j x) are all created by the same function, they are different functions and, consequently, the approximation problem has to be solved from scratch with any change of subspace. The theory of wavelets and its relation to multiresolution analysis provides the ladder that allows the transition from one space to the other. 

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