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.
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.