The standard solution is to run a new ORCA calculation with a larger grid, and read your current wavefunction (from the GBW files that you got) as initial guess:
! (level of theory etc...)
! DefGrid3 (if you are using ORCA 4.x, use something like Grid6 instead)
This performs the SCF using the large grid until convergence, which may take a few cycles, hopefully no more than 10.
If you want to "reintegrate" the XC energy without changing the wavefunction, you can set the number of SCF cycles to 1 via:
Or alternatively, set the SCF convergence threshold to extremely loose values. This way the calculation is much faster. It still wastes some time on evaluating the Coulomb and exact exchange contributions, but the evaluation happens only once (or maybe twice?) per calculation, and AFAIK it's impossible to avoid.
However, XC integration error is probably not the dominant reason for the discrepancy. Since XC integration is usually not the rate-limiting step of a SCF single point calculation, in most programs the default grid is large enough so that the SCF energy error is negligible. You can also see this from the integrated number of electrons, printed after the SCF section of the ORCA output file, which is usually on the same order of magnitude as the error of the XC energy. Usually it is only necessary to increase the grid during e.g. geometry optimization (where small numerical noise may prevent convergence), frequency analysis (where small numerical noise can turn a small real frequency into an imaginary one), and the calculation of certain properties that involve the wavefunction near nuclei (EPR hyperfine couplings, Mössbauer spectroscopy, etc.).
The following differences of the ORCA and Turbomole default settings may have greater contributions to the observed energy discrepancies than the grid differences:
- For hybrid functionals, ORCA (except for older versions) uses the RIJCOSX approximation by default (that is, RI for the Coulomb term and COSX for the exchange term), while Turbomole by default evaluates the Coulomb term by RI but the exchange term exactly. To reproduce the latter behavior, one should use the keyword "! RIJONX" in the ORCA input file. Turbomole also supports COSX, but it is called SENEX in Turbomole terminology and is turned off by default.
- The default RI auxiliary basis set of Turbomole is different for every orbital basis set, but the default auxiliary basis set of ORCA is mostly independent of the orbital basis set (def2/J for non-relativistic and ECP calculations, SARC/J for scalar relativistic calculations, with very few exceptions). Therefore, the RI auxiliary basis set that you used is probably different from the one used in Turbomole. In particular, the def2/J auxiliary basis set is designed for the def2 series of basis sets, and may or may not be suitable for aug-cc-pVDZ and aug-cc-pVDZ-PP.