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WIREs Comput Mol Sci
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Atomic orbital basis sets

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Electronic structure methods for molecular systems rely heavily on using basis sets composed of Gaussian functions for representing the molecular orbitals. A number of hierarchical basis sets have been proposed over the last two decades, and they have enabled systematic approaches to assessing and controlling the errors due to incomplete basis sets. We outline some of the principles for constructing basis sets, and compare the compositions of eight families of basis sets that are available in several different qualities and for a reasonable number of elements in the periodic table. © 2012 John Wiley & Sons, Ltd.

This article is categorized under:

  • Electronic Structure Theory > Ab Initio Electronic Structure Methods
Figure 1.

Hartree–Fock optimized s‐exponent values for the neon atom for basis sets of increasing size.

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Figure 2.

Hartree–Fock energy contribution of basis functions for the neon atom, using either a full optimization, a fourth‐order Legendre [Eq. (7)] or an even‐tempered [Eq. (4)] parameterization for determining the basis function exponents.

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Figure 3.

Hartree–Fock energy contribution of basis functions for the krypton atom, using either a full optimization, a fourth‐order Legendre [Eq. (7)] or an even‐tempered [Eq. (4)] parameterization for determining the basis function exponents.

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Figure 4.

Number of primitive (blue dots) and contracted (black squares) functions for a first‐row s‐block atom as a function of basis set quality for the basis sets in Table 1.

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Figure 5.

Number of primitive (blue dots) and contracted (black squares) functions for a first‐row p‐block atom as a function of basis set quality for the basis sets in Table 1.

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Figure 6.

Number of primitive (blue dots) and contracted (black squares) functions for a second‐row s‐block atom as a function of basis set quality for the basis sets in Table 2.

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Figure 7.

Number of primitive (blue dots) and contracted (black squares) functions for a second‐row p‐block atom as a function of basis set quality for the basis sets in Table 2.

[ Normal View | Magnified View ]
Figure 8.

Number of primitive (blue dots) and contracted (black squares) functions for a third‐row s‐block atom as a function of basis set quality for the basis sets in Table 3.

[ Normal View | Magnified View ]
Figure 9.

Number of primitive (blue dots) and contracted (black squares) functions for a third‐row p‐block atom as a function of basis set quality for the basis sets in Table 3.

[ Normal View | Magnified View ]
Figure 10.

Number of primitive (blue dots) and contracted (black squares) functions for a third‐row d‐block atom as a function of basis set quality for the basis sets in Table 4.

[ Normal View | Magnified View ]

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