Pick the right basis for your calculation

The development of basis sets suitable to use in relativistic calculations reflects the relatively lateness of the field’s development. Because the more consistent efforts in method development started at about the mid 1980’s, it wasn’t until well into the late 1990’s that the pioneering works of the early and mid 1990’s were substantially complemented and improved upon.

This situations has dramatically improved in recent years, notably with the work of K. G. Dyall, and Dirac users are strongly advised to use Dyall’s basis sets whenever they are available. These sets follow roughly the “correlation-consistent” philosophy introduced by Dunning and coworkers [Dunning1989], so they already contain polarization functions, but the SCF sets are designed for an adequate SCF representation rather than to match correlating sets for the valence shells.

Dyall basis sets

We recommend that you use the Dyall basis set repository whenever they are available for the elements of interest. In order to make that usage as convenient as possible, the following files, containing all sets currently available at the URL above (published or to be published), are made available:

quality valence core-valence all-electron DFT
double-zeta dyall.v2z dyall.cv2z dyall.ae2z dyall.2zp
triple-zeta dyall.v3z dyall.cv3z dyall.ae3z dyall.3zp
quadruple-zeta dyall.v4z dyall.cv4z dyall.ae4z dyall.2zp

While the division in “valence” and “core-valence” can be at times not so clear-cut as for lighter elements, the option was made to stick to the usual jargon of non-relativistic theory, particularly in relation to the “correlation-consistent” family of basis sets.

The valence basis sets are defined to include functions for correlation of the outer ns shell and the (n-1)s and p shells for the s elements, the outer ns and np shells for the p elements, the ns, np, nd, and (n+1)s for the d elements, and the ns, np, nd, nf, (n+1)s, (n+1)p, (n+1)d, and (n+2)s for the f elements. The choice for the f block of these is necessary to cover correlation of the open f shell, which becomes a semicore shell towards the end of the row.

The core-valence basis sets include the (n-2) shell for the s elements, the (n-1) shell for the p elements, the (n-1) shell for the d elements, and nothing extra for the f elements.

The all-electron basis sets include correlating functions for all shells, down to the 1s for all elements. These are intended for use when correlating all electrons.

The DFT basis sets do not contain the correlating functions as these are not necessary for DFT (or Hartree-Fock) calculations. With inclusion of all required polarization functions they are the most economical choice for DFT calculations.

Users are encouraged to look in these files and in the original archives published at Theor. Chem. Acc. (as, for instance, for the 5p TZ basis to get a feel for what is included in each case.

In the case of p-block elements, additional files containing the corresponding diffuse functions, in addition to the valence and core-valence basis sets mentioned above, are also provided.

quality valence core-valence
double-zeta dyall.av2z dyall.acv2z
triple-zeta dyall.av3z dyall.acv3z
quadruple-zeta dyall.av4z dyall.acv4z

With the recent addition of Dyall basis sets for the light elements, it is no longer necessary to use the standard non-relativistic basis sets, such as the correlation-consistent sets of Dunning and coworkers. However, because the Dyall basis sets are quite a bit larger, you might want to continue using these basis sets. It is advisable that, in order to have a balanced description when light and heavy elements are present, that one uses either contracted or uncontracted sets thoughout.

See the Dyall basis set repository for the latest updates by Ken Dyall and the appropriate basis set references. In case of errors or omissions on any of the files in this directory, users are kindly asked to contact the authors of DIRAC.

Other relativistic basis sets

Apart from Dyall’s sets, one can choose several different basis sets based upon geometric progressions of exponents. One such set is that of K. Faegri, also available in the basis set library, but with the drawback that the user needs to extend it by adding polarization functions.

Non-relativistic and scalar-relativistic basis sets

The DIRAC distribution shares a large library of standard non-relativistic and scalar-relativistic basis sets with the Dalton program. These basis sets can be found in the directory basis_dalton of the DIRAC distribution.

These basis sets are not all suitable for relativistic calculations, especially not for the heavier elements. Basis sets developed for full relativistic calculations (including spin-orbit coupling) can be found in the directory basis.