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My experience with different theoretical methods in computational chemistry primarily comes from use and reading papers. My experience is that people almost always use CCSD instead of CISD if they wish to do calculations with single and double excitations.

My understanding is that truncated CI expansions suffer from not being size-extensive and also do not converge very quickly. I do not think coupled-cluster theories suffer in the same way.

Why, however, do people seem to prefer CCSD over CISD? What are the big advantages it has? Is any of it just a habit because CCSD(T) is the preferred method when possible, and so it's easier to make comparisons if these calculations come around in the future and can't be done in some current study?

Also, are there any systems for which it would definitely make more sense to choose a truncated configuration interaction calculation over a coupled-cluster method? Probably systems with some kind of low-lying excited state I would guess...


I'm not looking for a huge amount of math here, although that's totally fine. I would just be fine with the facts and any useful references.

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    $\begingroup$ Personally, I'd always prefer CC before CI... Good thing in CC2 (and other CC response models) for example is that you have a lucky error cancellation in the ground state and excited state dynamical correlation contributions (That's why F12 is so horrible for excited states, it eliminates the error cancellation because it only corrects the ground state contribution btw) which leads to mostly rather good excitation energies. And yes, due to the exponential ansatz CC is size extensive which truncated CI is not. $\endgroup$ – Fl.pf. Jul 3 '17 at 7:17
  • $\begingroup$ so, I thought about it a little bit more. I couldn't find/think of a case where the CISD excitation energies would be better suited than the CCSD energies. The "advantage" you ask for is probably just that CC exc. are generally better than CISD ones... $\endgroup$ – Fl.pf. Jul 3 '17 at 11:15
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    $\begingroup$ The main drawback of CC is not being variational (and maybe computational scaling). But since CC is usually more accurate, one does not really care. Or is there any property that benefits from a variational approach? $\endgroup$ – Feodoran Jul 3 '17 at 16:20
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CCSD is preferred in nearly all cases because size-extensivity/size-consistency is a critical property to have for practical chemistry, and on top of that, more of the correlation energy (the part of the energy missing from Hartree-Fock) is captured by CCSD. CISD only accounts correlation energy for up to double excitations and not at all for higher excitations. CCSD accounts for correlation up to double excitations and then approximates all higher excitations as combinations of the single and double excitations it has already calculated. This gives much more accurate numbers for pretty much all systems and provides for size-extensivity/size-consistency. The only time you would really be better off doing CISD than CCSD is if you wanted to do full CI on a 2-electron system, in which case CCSD is not as efficient.

So in short, CCSD is preferred because it almost always gives better, more usable numbers than CISD for similar or better costs (they both scale as ~$n^6$).

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Yes, to re-iterate the above answer, CI in its standard truncation schemes (CISD, CISDT, etc.) are nowadays out of use in favor of CC for 3 main reasons:

(1) CC's size extensivity, and if the reference is separable, size-consitency

(2) CC exhibits the most rapid convergence to full CI

(3) CC's insensitivity to choice and quality reference due to inclusion of singly-excited clusters

CIS is a special exception since it is an uncorrelated approach. It is actually size-extensive (it's basically HF for excited states). It's a crude method no doubt, but quite useful as a starting point for more sophisticated calculations or for other supplemental purposes (such as helping to pick active orbitals in excited-state calculations).

The other instance in which CI is preferred is when you're actually shooting at full CI. This is actually a popular strategy nowadays. There is full CI Quantum Monte Carlo which mathematically converges to the exact ground state using imaginary time propagation - it is CI in that the wavefunction is expressed using a linear wave operator, but implementation-wise, it's pretty different. Then there are selected CI approaches which are based on iteratively building the wavefunction only out Slater determinants that are deemed to be important based on perturbative thresholds and diagonalization. In the field of exact quantum chemistry, these methods are serious contenders (with open-source implementations) because they are amenable to large-scale parallel computing.

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