Techniques for Basis Set Construction and Analysis

Regardless of the trial that is being performed, one would typically perform an analysis of energy contributions using intermediate normalization [46] and RCI coefficients of individual basis members and make decisions on how much to trim the new basis set before moving on to the next step. For a particular J calculation this requires careful removal of basis members with little contribution in all levels of interest. When considering more than a few levels, the effectiveness of simple removal of basis functions can lose much of its usefiil-ness as the set of fimctions small in all levels of interest is much smaller than the set of small contributors for any particular level. If one is concerned about using the wavefunction to compute some other property, impact on that calculation needs to be considered as well, e.g., transition probabilities to several potential initial or final states of other J-parity calculations. 

Although useful, even on a simple system, this approach can only trim an RCI basis size by a factor of 2-3 at most. For the lanthanide and actinide survey we are discussing here, we needed an order of magnitude or more for the mid-row anions to make the calculations feasible. 

At the time our RCI program [12] had two optional approaches to generate basis functions within the program. The first was a full-configuration option that was typically applied 

The first option happened to be more limited in terms of the complexity of the size of the configuration it could handle. The second could handle a ten fold larger set of basis 

Our solution to this issue was to allow mixed 1-electron radial bases with outer DFp radials each taken from a computation optimized to a corresponding attachment, avoiding either of the diffuse orbitals that had drifted away. This works because as the RCI program reads in the 1-electron radial functions it performs an additional Gram-Schmidt orthogonalization 

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