choose the basis function method for c-c atom
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There is not really a 'correct' answer to this. The choice of basis set depends on system, methodology, and properties of interest. For example, polarised triple-zeta basis functions are nowadays standard, and should be good enough for *most* things. However, if you are interested in excited states or anionic systems, where the electron density tends to be more diffuse, you may need to augment your basis set with diffuse functions. If you are working on very small systems, then you may be looking for extremely high accuracy and it's not uncommon to find quintuple-zeta or even larger basis sets used, usually in conjunction with some CC based method.
Also, bear in mind that MP2 and CI use virtual orbitals to include electron correlation. Therefore your virtual space has to be large enough to be able to describe this correlation well.
An example where a small basis set (such as split-valence) would be appropriate would be in the early stages of a geometry optimisation, for a structure well away from it's energetic minimum. Here, a large basis set would be overkill in terms of computational expense. You can use the smaller basis to get a reasonable geometry, then switch to the larger basis set to get an accurate final structure.
Also, bear in mind that MP2 and CI use virtual orbitals to include electron correlation. Therefore your virtual space has to be large enough to be able to describe this correlation well.
An example where a small basis set (such as split-valence) would be appropriate would be in the early stages of a geometry optimisation, for a structure well away from it's energetic minimum. Here, a large basis set would be overkill in terms of computational expense. You can use the smaller basis to get a reasonable geometry, then switch to the larger basis set to get an accurate final structure.
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