Is there a formula for analytical gradients (for geometry optimization) for the DLPNO-CCSD method? I ask because I know that it is not implemented in ORCA. Maybe PNO-CCSD is implemented in MRCC or MOLPRO.

  • $\begingroup$ I guess the answer is that geometry optimization can be done with DFT or DLPNO-MP2, so why do it with DLPNO-CCSD? I'm sure it can be implemented if someone really wants it, but it might not give better geometries than DFT or DLPNO-MP2. Sure CCSD can be more accurate than MP2, but the optimized geometry will involve so many approximations (e.g. DLPNO approximation, and small basis set since DLPNO would never be used with a big basis set) that there may be no value in using CCSD. $\endgroup$ Commented Sep 10, 2020 at 16:16
  • $\begingroup$ @NikeDattani - there are already several papers using DLPNO-CCSD(T) with basis set extrapolations. Sure, probably not 5Z or 6Z basis sets, but for medium-sized molecules, DLPNO-CCSD(T) with basis set extrapolation is tractable, so why not do a 2Z / 3Z or 2, 3, 4 extrapolation and remove basis set effects? $\endgroup$ Commented Sep 11, 2020 at 0:02
  • $\begingroup$ As to using DLPNO-CCSD(T) for geometry optimization or frequencies, it's clearly interesting, but it's not trivial. Neese is still a bit unsure about implementing polarizabilities. $\endgroup$ Commented Sep 11, 2020 at 0:04
  • $\begingroup$ @GeoffHutchison There's no doubt that DLPNO-CCSD(T) can be done with 3Z/4Z then extrapolated to the CBS limit. I can see the use in that for single-point energies; but for geometry optimization it seems like overkill! It would mean quite a lot of DLPNO-CCSD calculations with at least 3Z, and the resulting geometry is not guaranteed to be any closer to the "true" geometry than a good MP2 or DFT geometry. To get the "true" geometry we'd need to also properly account for things like Born-Oppenheimer breakdown and relativity: Doing FCI without fixing the rest isn't guaranteed to be more accurate. $\endgroup$ Commented Sep 11, 2020 at 0:18
  • $\begingroup$ @NikeDattani geometry optimization is available for canonical CCSD method in Gaussian. Thus, there is obvious motivation to do DLPNO-CCSD geometry opt if people do use canonical CCSD for geometry opt. $\endgroup$
    – Paulie Bao
    Commented Sep 11, 2020 at 4:27

2 Answers 2


Note that the DLPNO method is only implemented in ORCA. There are indeed analogous and similarly efficient and accurate methods, the PNO-LCCSD method in Molpro [doi.org/10.1021/acs.jctc.7b00799] and the LNO-CCSD method in MRCC [doi.org/10.1021/acs.jctc.9b00511].

To my knowledge exact analytical gradients are not implemented for either of them. There is an impressive implementation for analytical DLPNO-MP2 gradient in ORCA [https://doi.org/10.1063/1.5086544] and a first derivative for DLPNO-CCSD with respect to electric field components [http://dx.doi.org/10.1063/1.4962369].

So far it is not completely clear what kind of applications would benefit from the significantly higher cost of local CCSD or CCSD(T) gradients compared to, e.g., DFT, we will see.


As far as I know, analytic gradients for DLPNO-CCSD are not available in ORCA. Analytic first derivatives are available for both closed-shell and high-spin open-shell cases, which could be used for computing other first-order properties.

As the first exercise to implement analytic gradients within the DLPNO setup, the DLPNO-MP2 method was considered and the additional steps to implement gradients, especially those related to orbital response contributions, were carefully analysed.

It is indeed not clear whether or not it is worthwhile to use DLPNO-CC for geometry optimization, while there are cheaper and more efficient DFT methods for this purpose.

  • $\begingroup$ Welcome to our site! $\endgroup$
    – Camps
    Commented Sep 10, 2020 at 12:54
  • $\begingroup$ I tag geometry optimization in this question but the question itself is not limited to geometry optimization. Before the development of linear scaling DLPNO, coupled clusters is extremely expensive and single point calculations is only feasible in most cases. However, since we have linear scaling CC method and single point calculations are not satisfactory for many applications, if analytical gradient of DLPNO method is implemented, we could do ab initio MD which is really powerful. Consider if we could have dynamic simulations of bio-systems with CC level accuracy, it is going to be seminal . $\endgroup$
    – Paulie Bao
    Commented Sep 10, 2020 at 18:04
  • $\begingroup$ Another important aspect is simulation of high resolution spectra, once analytical gradient is available, one could evaluate numerical hessian which is associated with frequencies. And I don’t think DFT level frequency calculation is accurate enough in many cases. $\endgroup$
    – Paulie Bao
    Commented Sep 10, 2020 at 18:07
  • $\begingroup$ @PaulieBao Analytic gradients exist for DLPNO-MP2, but has anyone done AIMD with it? $\endgroup$ Commented Sep 11, 2020 at 0:21
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    $\begingroup$ I wouldn't say that MP2 is comparable to DFT, because DFT can be more accurate or less accurate. CCSD(T) is less and less often called the "gold standard". CCSD(T) is great for single-point energies of single-reference systems, but I wouldn't call it the "gold standard" for geometry optimization. I most often see geometries obtained at DFT or MP2 level. DLPNO-CC is a lot older than 4 years, and there's also PNO-LCC and LNO-CCSD which can be the same or better. The PNO idea has been around for decades. DFT can be better than CC, e.g. transition metal complexes where Frank Neese chooses B3LYP. $\endgroup$ Commented Sep 11, 2020 at 19:42

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