Primitive set

The optimization of HF primitive sets then proceeded much like the Y case, i.e., a (14j13/>1 d) ExtET base set was used in HF optimizations on the d ° state of Hg to generate s sets from (7i) - (14 ), p sets from (4p - 12p), and d sets... 

HF molecule we use the Dunning s contraction [As2pl2s [24] of Huzinaga s 9s5p As) [25] primitive set, augmented with a d polarization function with exponent 1.6 for F, and a set of p functions for H with exponent 0.75. We run different calculations for the equilibrium distance Re = 1.733 bohr), 1.5 Re, 2.0 Re and 3.0 Re. In this case, Cartesian Gaussians with 6fil-functions are used. Comparison is made with nearFCI (nFCI, up to sextuple excitation, i.e. CISDTQQS) [26]. 

Expert systems can also be used off-line as advisory systems. If some leeway is left in the process specifications, operators can even be instructed to make simple variations in the process. Hajicek developed an expert system for troubleshooting injection molding, which was designed to be used by operators to adjust controls as needed whenever part quality suffered [20], These expert systems do not necessarily plan an entire cycle. As we will see in the section on in-process control, however, they can be used to do so. There are even specifications that include rules for altering the cure cycle in response to the results of quality acceptance tests such as flow and volatiles, a primitive set of heuristics. 

Dunning-type contractions are characterized by considerable flexibility in the valence part of the primitive space. Typically, the outermost primitive functions are not contracted at all, contraction being reserved for the inner parts of the valence orbitals and the core orbitals. The commonest contracted set of this type is probably the [4s 2p] contraction of the (9s 5p) set. Unfortunately, there are at least two such double zeta contraction schemes in use, as well as an erroneous one. Some care may be required to reproduce results asserted to be obtained with a Huzinaga-Dunning [4s 2p] basis . Because of the relatively flexible contraction scheme these basis sets usually perform well, especially when large primitive sets such as van Duijneveldt s (13s 8p) sets are used. However, it should be noted that such primitive sets are difficult to contract this way without significant loss of accuracy at the atomic SCF level, unless very large contracted sets are used. 

Pople-type basis sets are generally characterized by heavier contraction (that is, fewer contracted functions for a given primitive set) and consequently somewhat lower accuracy. The earliest set was a minimal basis contraction (STO-3G) of a... 

In most calculations, improvement of the basis set involves an increase in both the primitive set and the contracted set. It is not generally obvious how one basis set is related to another (other than that larger basis sets are expected to perform better than smaller sets), and consequently it is not always clear how to extrapolate from a set of calculations to the basis set limit. It is preferable to use sequences of basis sets that form a well-defined chain of subspaces. 

In the case with NH, the contraction of the (7s3p/3s) primitive set to the minimum basis set was unequivocal. Unfortunately such a situation occurs rather rarely. Typically, there is some arbitrariness in the choice of the linear combinations. This holds particularly for larger basis sets where some primitives contribute significantly to both Is and 2s orbitals of the first-row atoms. For second-row and further atoms the situation with s-type functions is even more complex, Ambiguity is also encountered with p-sets. 

Up to now we have assumed that each primitive function is used in the contraction only once, i.e. each primitive function is only involved in one particular contracted function. The contractions of this type are referred to as segmented. In some cases it may occur that for a given primitive set the Dunning s rules suggest a higher number of CGTF s than we intended for a molecular calculation. Con-aider for example the (9s) and (lOs) basis sets of Huzinaga for the first-row atoms. The former contracts satisfactorily to a C4s] set,... 

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