Extended basis sets Other approaches

This approach can, in many instances, be extended even to cases where the basis is comprised of physicochemical, topological, or other such parameters. The similarity matrix is replaced in these cases by the correlation matrix computed with respect to the basis set of parameters (vide supra). 

Improvement of the crystal-field splitting calculation has been achieved by two different approaches. On one hand the basis set of wavefunctions was extended to include also excited configurations. This approach will be dealt with in sect. 4.4.6. On the other hand, the one-electron approximation has been relaxed to take into account electron correlation effects. The original formulation of the correlation crystal-field parameterization has been proposed by Bishton and Newman (1968). Judd (1977) and Reid (1987) redefined the operators to ensure their mutual orthogonality ... 

Sims and Hagstrom[39] utilized this approach in their HY-CI method, adding a single correlation factor to a Cl basis. In this way, the HY-CI basis retains some of the advantages of a pure Cl basis. From Table 2 we can see that their 150-term result matches the accuracy of Larsson s 100-term calculation. Other calculations of this type for lithium have extended the method to basis sets with over 1000 terms[41]. 

A wide range of theoretical methods has been applied to the study of the structure of small metal clusters. The extremes are represented on the one hand by semi-empirical molecular orbital (Extended Huckel) (8 ) and valence bond methods (Diatomics-In-Molecules) ( ) and on the other hand by rigorous initio calculations with large basis sets and extensive configuration interaction (Cl) (10). A number of approaches lying between these two extremes have been employed Including the X-a method (11), approximate molecular orbital methods such as CNDO (12) and PRDDO (13) and Hartree-Fock initio molecular orbital theory with moderate Cl. 

There are alternatives to the most commonly used Boys-Bemardi counterpoise scheme. One approach that shows promise, for example, is a chemical Hamiltonian approach (CHA), pioneered by Mayer " ", which attempts to isolate the superposition error directly in the Hamiltonian operator. The Schrodinger equation that is solved is hence a modified one, which yields a wave function that is hopefully free of superposition error. In the case of (HF)2, it was found that this approach mimics rather closely the results of the standard counterpoise scheme for a series of small to moderate sized basis sets ". Later calculations " extended these tests to other small H-bonded systems as well, again limiting their testing to basis sets no larger than 6-31G. A recent test " has extended the method s use-... 

In an earlier version of this approach, we exploited the transferability to provide results for the correlation energy and density matrix of diamond, without any treatment for the extended system [198]. Unlike most of the other attempts at linear scaling, which tend to only really be realized in small basis sets, the rate determining step in the CC calculation... 

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