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I know that CCSD(T) with the aug-cc-pVTZ basis set for geometry optimization of omeprazole (5-methoxy-2-[(4-methoxy-3,5-dimethylpyridin-2-yl)methanesulfinyl]-1H-benzimidazole, the active substance in Losec) is not suitable using normal computers. The substance is:
(omeprazole)
Can someone explain to me what exactly makes these methods too expensive for this substance?
To transform the question into something simpler, let's assume CISD instead CCSD(T), which is cheaper and share the common expensive step.
The molecule has 182 electrons and 1545 basis functions in the basis you specified, that means approx. 1400 virtual orbitals.
Therefore, the number of double excitation $ij \rightarrow ab$ is approximately $180 \cdot 180 \cdot 1400 \cdot 1400 = 32400 \cdot 1960000 = 63504\cdot10^6$
Unfortunately, in each of this excitation you have to calculate integral of type $(ab|cd)$, and there are $1400^4$ of them.
Such a big problem is out of reach for traditional CCSD, but tractable with more approximate methods.
I'd also like to add to ssavec's response. In addition to the insane amount of flops that you have to carry out to run the computation, you also run into problems of storage for the computation. In a CCSD calculation you have to store single and doubly excited amplitudes. ssavec pointed out that there are ${6.3\cdot10^{10}}$ double excitations...assuming 8 bytes per double precision floating point, that would mean storing the doubles would require 450 GB of storage! (Not to mention the I/O between iterations...)
Both previous answers by ssavec and jjgoings accurately describe the problem for a single point calculation. Doing a geometry optimisation, you have to run the procedure multiple times until you find a minimum on the potential energy surfaces.
Since one point already requires insane resources to compute this, an optimisation at this level will take significantly longer. From experience and common usage of chemical calculations it is often not necessary to optimise a geometry at this level. Often much simpler and more approximate methods, like density functional approximations or perturbation theory yield good and reliable results.
