Effective Core Potentials

Note: ECPs are used automatically for the core electrons of heavy elements when specifying certain basis sets such as the Ahlrichs def2-XVP basis sets (that were intended for use with an ECP). If an all-electron description is wanted for heavy elements then use of a scalar relativistic approximation (ZORA or DKH) is recommended as relativistic effects start to become so important that they can not be ignored. See Relativistic page

ORCA can use effective core potentials (also called pseudopotentials) that can be useful for efficient calculations on molecules containing heavy elements as the chemically irrelevant core electrons are not explicitly part of the electronic problem and are replaced by a core potential function instead. Note, however, that ECPs are not the most accurate way of calculating heavy elements, see Relativistic approximations for a discussion on the much more accurate scalar relativistic all-electron approach. While ECPs have often been parameterized to implicitly account for relativistic effects, the accuracy achieved is sometimes disappointing and often only small-core ECPs give satisfactory accuracy.

General recommendations

• If your molecule does not contain elements heavier than Kr, then you typically should not use an ECP. Stick with an all-electron approach so as not to not sacrifice accuracy for marginal speed-up. If you use the def2-XVP or cc-pVnZ basis sets for elements H-Kr then no ECP is assigned.

• LANL2DZ and SDD basis-set ECP combinations for 1st TM row atoms are NOT recommended due to their bad accuracy, non-relativistic/relativistic all-electron calculations are much better.

• If your molecule contains one heavy element (heavier than Kr), e.g. in a typical transition metal complex, there is probably not a big advantage to using an ECP. You may get more accurate results and almost as fast, using an all-electron relativistic approximation instead. Note, that if you are using the def2-XVP basis sets, the def2-ECP is automatically used for elements heavier than Kr. If you prefer an all-electron approach, see Relativistic approximations.

• If your molecule contains many heavy elements (heaver than Kr), then ECPs have their greatest advantage (although the gradient can become expensive). Single-point calculations using an all-electron scalar relativistic approach might then be a good idea for even more accurate energies or property calculations.

• There are cases where one is dealing with so heavy elements that one runs into numerical problems when using an all-electron scalar relativistic method (ZORA, DKH). Using an ECP might then be preferred, particularly for the geometry optimization step.

• Choose your ECP wisely. Evaluations of different ECPs have found that some popular ECPs are not very accurate. See e.g. Bühl2006, Bühl2007, Bühl2008, Truhlar2011 . Generally I (RB) would recommend the Stuttgart ECPs (e.g. the ones called ECPXXMWB in the Stuttgart library, also called SDD or def2-SD ; see note below) together with the def2 basis sets. Also you should always use recommended basis set-ECP combinations, do not mix and match unless you know what you are doing.

Note: The def2-ECPs as described by Ahlrichs et al. in the def2 basis set paper (and can be found in EMSL and Turbomole basis set library) are the Stuttgart ECPXXMWB potentials except that g- and higher projectors of the ECPs were skipped (as such projectors were not available in Turbomole). As ORCA does not have this limitation, the full Stuttgart ECPs were implemented and this is what you get when you ask for the def2-ECPs in ORCA. This should make no appreciable difference when comparing relative energies but absolute energies may thus differ between codes.

Selecting a basis set and ECP for Ahlrichs def2 basis sets

The following input will put the def2-SVP basis set on all atoms and the def2-ECP is automatically assigned to molybdenum (molybdenum being a heavy atom for which the def2 basis consists of a valence basis set and ECP). This is consistent with the definition of the def2-XVP basis set by Ahlrichs (elements heavier than Kr have a valence basis set and the def2-ECP).

The !printbasis keyword is useful to check whether the correct basis set and ECP was added to each element.

! B3LYP def2-SVP printbasis

* xyz 0 1
Mo 0 0 0
F 0 0 1
C 0 0 2
H 0 0 3
*

The ORCA output reveals that the ECP was assigned:

Your calculation utilizes the basis: def2-SVP
F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys. 7, 3297 (2005).
cite the ECPs for Mo [Def2-ECP] as follows:
Ce-Yb(ecp-28): M. Dolg, H. Stoll, H.Preuss, J. Chem. Phys., 1989, 90, 1730-1734.
Y-Cd(ecp-28), Hf-Hg(ecp-46): D. Andrae,U. Haeussermann, M. Dolg, H. Stoll, H. Preuss, Theor. Chim. Acta, 1990, 77, 123-141.
In-Sb(ecp-28), Tl-Bi(ecp-46): B. Metz, H. Stoll, M. Dolg, J. Chem. Phys., 2000, 113, 2563-2569.
Te-Xe(ecp-28), Po-Rn(ecp-46): K. A. Peterson, D. Figgen, E. Goll, H. Stoll, M. Dolg, J. Chem. Phys., 2003, 119, 11113-11123.
Rb(ecp-28), Cs(ecp-46): T. Leininger, A. Nicklass, W. Kuechle, H. Stoll, M. Dolg, A. Bergner, Chem. Phys. Lett., 1996, 255, 274-280.
Sr(ecp-28), Ba(ecp-46): M. Kaupp, P. V. Schleyer, H. Stoll and H. Preuss, J. Chem. Phys., 1991, 94, 1360-1366.
La(ecp-46): M. Dolg, H. Stoll, A. Savin, H. Preuss, Theor. Chim. Acta, 1989, 75, 173-194.
Lu(ecp-28): X. Cao, M. Dolg, J. Chem. Phys., 2001, 115, 7348-7355.
ECP parameters for Mo [Def2-ECP] have been obtained from:
TURBOMOLE (7.0.2)
...
-------------------------
ECP PARAMETER INFORMATION
-------------------------
Group 1, Type Mo ECP Def2-ECP (replacing 28 core electrons, lmax=3)
Atom 0Mo ECP group => 1

To specify a small def2-SVP on light atoms and the larger def2-TZVP basis set and ECP on the metal:

! BP def2-SVP def2/J printbasis
%basis
newgto Mo "def2-TZVP" end
end
* xyz 0 1
Mo 0 0 0
F 0 0 1
C 0 0 2
H 0 0 3
*

Specifying a specific ECP

See ORCA manual for a list of available ECPs in ORCA.

%basis
ECP "def2-ECP" # will assign the def2-ECP to all possible elements.
newECP Pt "def2-SD" end # assign a specific ECP to Platinum
end
* xyz 0 1
Pt 0 0 0
F 0 0 1
C 0 0 2
H 0 0 3
*

Specifying an ECP manually

TODO...