Correlated basis functions for large molecules

And what about the future of CC theory With these developments, much more effort can be devoted to multi-reference CC, Fock space CC, XCC, UCC, variational CC, methods like those discussed below for large molecules, and perhaps the ultimate current method, R12-CC [102]—where besides the correlation problem, we have the best current solution to the basis set problem—or a wealth of other methods that do not fit into the basic structure of the CC functional, discussed next, as that is the basis for the automated generation. 

Performing CI calculations with the inclusion of all excitations (for the assumed value of M), i.e. ih full CI, is not possible in praetieal ealeulations due to the too long expansion. We are foreed to truncate the CI basis somewhere. It would be good to terminate it in sueh a way that all essential (the problem is what we mean by essential) terms are retained. The most significant terms for the correlation energy come from the double excitations since these are the first excitations coupled to the Hartree-Fock function. Fig. 10.6. Smaller, although important, eontributions come from other excitations (usually of low excitation rank). We certainly wish that it would be like this for large molecules. Nobody knows what the truth is. 

The disadvantage of ah initio methods is that they are expensive. These methods often take enormous amounts of computer CPU time, memory, and disk space. The HF method scales as N, where N is the number of basis functions. This means that a calculation twice as big takes 16 times as long (2" ) to complete. Correlated calculations often scale much worse than this. In practice, extremely accurate solutions are only obtainable when the molecule contains a dozen electrons or less. However, results with an accuracy rivaling that of many experimental techniques can be obtained for moderate-size organic molecules. The minimally correlated methods, such as MP2 and GVB, are often used when correlation is important to the description of large molecules. 

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