Basis Set Overview

In quantum mechanical calculations, basis sets are collections of mathematical functions used to represent the atomic orbitals in a system. The quality of these functions directly affects the accuracy of the calculation: a larger, more flexible basis set generally yields more accurate results at a higher computational cost. The choice of basis set is a tradeoff between accuracy and computational cost.

Many basis sets are described by the number of independent functions used per valence orbital — for example, def2-SVP is double-zeta (DZ) and def2-TZVP is triple-zeta (TZ). Polarization functions add higher angular momentum to improve the description of chemical bonding, and diffuse functions add slowly decaying functions to better describe electrons far from the nucleus (important for anions and excited states).

Basis Set Families in Jaguar

Jaguar supports basis sets from several widely used families. The tables in Basis Sets list all available basis sets along with the atoms they cover.

  • Pople basis sets — use the naming convention X-YZG, where X is the number of primitive Gaussian functions for the core orbitals and YZ describes a split valence (making 6-31G a DZ valence basis). A triple-zeta variant is X-YZWG (e.g., 6-311G). The symbols + and ++ indicate diffuse functions on non-hydrogen or all atoms, respectively. The symbols * and ** indicate polarization functions on non-hydrogen or all atoms, respectively. Examples: 6-31G**, 6-31+G*, 6-311++G**.

  • Ahlrichs/Karlsruhe (def2) basis sets — provide a consistent set of basis sets across a wide range of elements with systematic naming: def2-SVP (DZ), def2-TZVP (TZ), def2-QZVP (QZ). The suffix P indicates polarization, PP indicates additional polarization, and D indicates diffuse functions. The prefix m (as in def2-mTZVP) denotes a modified version used by 3c composite methods. The def2 basis sets are recommended for DFT calculations by recent best-practice literature because they are efficient, consistently available across the periodic table, and are less prone to basis set superposition error than comparably sized Pople basis sets.

  • LACVP basis sets — combine the 6-31G basis for light atoms (H-Ar) with the LANL2DZ effective core potential for heavier atoms. Effective core potentials replace the inner electrons with a pseudopotential, which reduces the number of electrons that must be modeled explicitly and implicitly accounts for scalar relativistic effects. LACVP** is the default basis set for calculations involving transition metals in Jaguar.

  • Dunning (cc-pVXZ) basis sets — the correlation-consistent basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ) are designed to systematically converge toward the complete basis set limit as the cardinal number increases. Diffuse-augmented variants (aug-cc-pVXZ, written as cc-pVXZ++ in Jaguar) are available. These basis sets are useful for studying convergence with respect to basis set size and for correlated methods.

Choosing a Basis Set

The appropriate basis set depends on the property being calculated and the required accuracy. Molecular structures are generally less sensitive to basis set size than energies, so a double-zeta basis set with polarization functions is often sufficient for geometry optimizations, while a triple-zeta or larger basis set is recommended for energy calculations. Including diffuse functions is important when modeling anions, excited states, intermolecular interactions, and other situations where the electron density extends far from the nuclei. For systems containing heavy elements (Z > 36), effective core potentials or the ZORA relativistic Hamiltonian with appropriate basis sets should be used. To check basis set convergence, compare results obtained with successively larger basis sets from the same family (e.g., the cc-pVXZ or def2 series).

See Recommended Settings for Jaguar for specific basis set recommendations by calculation type.

Basis Set Errors

Two common sources of error related to basis set size are the basis set superposition error (BSSE) and the basis set incompleteness error (BSIE). BSSE occurs when atoms in a complex "borrow" basis functions from neighboring atoms, artificially lowering the interaction energy. BSIE arises when the basis set is too small to adequately describe the electron density. Both errors decrease with increasing basis set size. The counterpoise correction can be used to estimate BSSE for intermolecular interactions (see Counterpoise Panel). The 3c Composite Methods for Geometry Optimization include built-in geometric counterpoise (gCP) corrections to mitigate BSSE while using small, efficient basis sets.

Using External Basis Sets from the Basis Set Exchange

The Basis Set Exchange (BSE) provides a wide variety of basis sets in many formats, including Jaguar format. You can use it to obtain basis sets that are not included in the Jaguar distribution.

To use an external basis set from BSE:

  1. Go to the BSE website, select the desired basis set, choose Jaguar as the output format, and download the file.

  2. Place the downloaded .basis file in the same directory as your Jaguar input file.

  3. Add the following line to your Jaguar input file:

    BASISFILE: filename

    where filename is the name of the basis set file (without a path).

External basis sets are only available for analytic (non-pseudospectral) calculations. See Customizing Basis Sets for details on the basis set file format and additional considerations.