Basis Sets

Table 1 lists the available basis sets in Jaguar that do not use effective core potentials. The table indicates the atoms these basis sets can describe and shows which sets include the options of polarization and diffuse functions. The sarc-zora and dyall basis sets are contracted for relativistic calculations with the (scalar) ZORA Hamiltonian. Basis sets with the suffix (-f) indicate that the f and higher functions have been removed from the original basis set; the suffix (-g) indicates that g and higher functions have been removed.

^aThis basis is referred to in the literature as 6‑311G(3df-3pd).

^bThis basis set is the same as 6-31G, except that the basis sets for K and Ca are taken from Ref.134 rather than Ref. 135.

Table 1 also gives the method used for integral evaluation: the fast pseudospectral method or the slower analytic method, in which all integrals are computed explicitly. The analytic method is used only when pseudospectral grids and dealiasing function sets for any atom in the molecule are not available. For molecules containing only atoms H–Ar, we recommend the 6‑31G** basis set, which permits pseudospectral calculations (and is the default).

The column headed “# of d fns.” indicates whether d shells include the five real spherical functions d_x²−y², d_{2z²−x²−y²}, d_xy, d_xz, and d_yz, all with the same angular momentum (l = 2), or whether d shells include the six Cartesian d functions d_x², d_y², d_z², d_xy, d_xz, and d_yz. This choice also affects the dimension of the Fock matrix for diagonalization. To override this selection, set the keyword numd in the gen section of the input file, as described in Basis Set Keywords in the Jaguar Input File. The orbital coefficients are always printed out in terms of the six Cartesian functions. For basis sets with f functions, the real spherical set of 7 f functions is always used.

For RI-MP2 calculations, the use of an additional auxiliary basis set is required. The available auxiliary basis sets are listed in RI-MP2 Keywords in the Jaguar Input File.

The references describing the basis sets are in the Jaguar References.

The other available basis sets, which are listed in Table 2, include effective core potentials (ECPs). The names of eight of these basis sets begin with “LA” to indicate they were developed at Los Alamos National Laboratory. If the next character in the name is a “V”, the basis set is valence-only, containing only the highest s and p shells for main group atoms and the highest s, p, and d shells for transition metals. For example, 5s and 5p would be included for tellurium, and 6s, 5d, and 6p for tungsten. “LAV1” indicates that the basis set has been fully contracted to form a minimal basis set, “LAV2” that the last Gaussian has been uncontracted to form a double zeta basis, and “LAV3” that all of the s functions and the last p and d Gaussian have been uncontracted.

Names starting with “LACV” indicate that the basis set also includes the outermost core orbitals (e.g., 5s5p6s5d6p for W). The last letter in each LA basis set name refers to the basis set used for atoms not described by ECPs: S indicates the STO‑3G basis set, D indicates the D95V basis set, and P indicates the 6‑31G set developed by Pople and coworkers. (Note that in addition, for some atoms, the LACVD and LACVP basis sets use the same basis functions as the LAV3D and LAV3P basis sets, respectively.)

The Los Alamos effective core potentials, which were developed by Hay and Wadt, include one-electron mass-velocity and Darwin relativistic corrections for elements beyond Kr.

The Cundari-Stevens ECP basis set [173], named CSDZ, has been provided to cover the lanthanides. This basis set uses a relativistic effective core potential for the inner core electrons and treats the outer core and valence electrons with a 4s/4p/2d/2f basis set.

The ECP basis set developed by Ermler and coworkers [[174]-[179]], named ERMLER2, is also available. The basis set provided is the “small core” set that includes the outer core orbitals in the valence space, in the same way as the LACV basis sets. The basis set is a double-zeta contraction in which the outermost primitive function in each symmetry has been uncontracted. The core is treated by a relativistic effective core potential for all elements. For Tl-Rn the refitted ECPs have been taken from Wildman et al. [180], but the basis set from the original ECPs has been retained, because the new basis sets are much larger, and do not match the basis sets for the other elements. Polarization and diffuse functions for the 4p, 5p, and 6p elements and polarization functions for the 3d, 4d, and 5d elements have been added from the relativistic all-electron double-zeta basis sets of Dyall [181].

In Table 2, the atoms described by the effective core potential are listed first, followed by the atoms described by the alternate basis set or sets. The other table entries provide the same information as that given in the previous table, except that the polarization functions are only applied to atoms obtained from the non-ECP basis sets, with the exception of the ERMLER2 basis sets. All ECP basis sets use five d functions, as described earlier in this section.

Currently, the LACVP, LAV3P, LACV3P, and CSDZ basis sets use the pseudospectral method, while all other ECP basis sets use the analytic method, with the exception of Br and I in the cc-pVTZ-pp and cc-pVTZ-pp(-f) basis sets. We strongly recommend using either the LACVP or the LACV3P basis set for non-lanthanide molecules containing atoms beyond Ar in the periodic table, especially for studies involving charge transfer, d⁰ metals, or correlated wave functions. The LACV3P basis set seems to give substantial improvements over the LACVP basis set for HF, LDA, and B3LYP atomic state splittings. The LACV3P++ basis set, which includes a diffuse d function on any metal atoms, is useful for calculations on anions or low-spin M(0) complexes of the late first row metals.

Note: You should not use ECP basis sets to calculate NMR shieldings on the ECP atom, as the ECP orbitals do not have the necessary density at the nucleus for the shielding calculation.

Note: You should not use ECP basis sets with the ZORA Hamiltonian as the basis sets for ZORA require the core to be present in the basis set. ECP basis sets for heavy atoms already include the relativistic effects described by the ZORA Hamiltonian.