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I know that coupled cluster is considered to provide better accuracy than DFT, but I am not sure for which materials science applications or types of molecules that this higher accuracy is considered desirable. For example, which of the following materials science areas would require the accuracy that CC provides:
organic electronics polymers consumer packaged goods catalysts/reactive systems semi-conductors energy capture and storage metals alloys and ceramics complex formulations ?
Coupled cluster is theoretically more accurate that DFT, as it's limiting behaviour is an exact solution to the Schrödinger equation. By limiting behaviour, I mean including all possible excitations (singles, doubles, triples, etc.) and a complete orbital basis set. There is no such guarantee of limiting accuracy with any known DFT method today, as we do not yet know the exact exchange-correlation functional. However, in principle an exact XC functional does exist and some modern DFT functionals can get very impressive accuracy.
I think all domains of materials science would benefit from the accuracy available in coupled cluster theory. The problem with applying canonical coupled cluster theory is its computational cost scales unfavorably with system size. The computational cost of full coupled cluster scales combinatorically with the number of electrons and orbital basis functions included in the calculation. This unfavorable scaling can be mitigated by only including up to single, double, triple, etc excitations or limiting one's active space in some way, at the cost of reduced accuracy, but this approach can only be taken so far before the accuracy drops below that of DFT. I'd say about the largest molecule you could expect to calculate accurately using canonical CC theory is benzene, and even that would be very expensive. In recent years, much work had been done to decrease the computational cost of coupled cluster methods by applying approximations of various kinds, but it remains a relatively expensive method.
Most DFT methods scale much more favorably with system size, so they remain the most popular option available for quantum mechanical calculation of systems beyond the size of benzene or so. Local and semi-local exchange-correlation implementations of DFT scale with the cube of the number of basis functions, although hybrid and double-hybrid functionals have worse scaling.
As S R Maiti pointed out, coupled cluster is also difficult to implement and costly for periodic systems and remains an active area of research.
