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When molecular calculations are performed, it is common to use basis composed of a finite number of Atomic Orbital s, centered at each atomic nucleus within the molecule ( Linear Combination Of Atomic Orbitals Ansatz ). Initially, these atomic orbitals were typically Slater Orbitals , which corresponded to a set of functions which decayed exponentially with distance from the nuclei. Later, it was realized that these Slater-type orbitals could in turn be approximated as linear combinations of Gaussian Orbital s instead. Because it is easier to calculate overlap and other integrals with Gaussian basis functions, this led to huge computational savings. (See John Pople ) Today, there are hundreds of basis sets composed of Gaussian-type orbitals, (GTOs). The smallest of these are called ''minimal basis sets'', and they are typically composed of the minimum number of basis functions required to represent all of the electrons on each atom. The largest of these can contain literally dozens to hundreds of basis functions on each atom.
Another common addition to basis sets is the addition of ''diffuse functions'', denoted by a plus sign, ''+''. Two plus signs indicate that diffuse functions are also added to light atoms (hydrogen and helium). These are very shallow Gaussian basis functions, which more accurately represent the "tail" portion of the atomic orbitals, which are distant from the atomic nuclei. These additional basis functions can be important when considering anions and other large, "soft" molecular systems. MINIMAL BASIS SETS A common naming convention for minimal basis sets is ''STO-XG'', where X is an integer. This ''X'' value represents the number of Gaussian primitive functions comprising a single basis function. In these basis sets, the same number of Gaussian primitives comprise core and valence orbitals. Minimal basis sets typically give rough results that are insufficient for research-quality publication, but are much cheaper than their larger counterparts. Here is a list of commonly used minimal basis sets:
SPLIT-VALENCE BASIS SETS During most molecular bonding, it is the valence electrons which principally take part in the bonding. In recognition of this fact, it is common to represent valence orbitals by more than one basis function, (each of which can in turn be composed of a fixed linear combination of primitive Gaussian functions). The notation for these ''split-valence'' basis sets is typically ''X-YZg''. In this case, ''X'' represents the number primitive Gaussians comprising each core atomic orbital basis function. The ''Y'' and ''Z'' indicate that the valence orbitals are composed of two basis functions each, the first one composed of a linear combination of ''Y'' primitive Gaussian functions, the other composed of a linear combination of ''Z'' primitive Gaussian functions. In this case, the presence of two numbers after the hyphens implies that this basis set is a ''split-valence double-zeta'' basis set. Split-valence triple- and quadruple-zeta basis sets are also used, denoted as ''X-YZWg'', ''X-YZWVg'', etc. Here is a list of commonly used split-valence basis sets:
DOUBLE, TRIPLE, QUADRUPLE ZETA BASIS SETS Basis sets in which there are multiple basis functions corresponding to each atomic orbital, including both valence orbitals and core orbitals or just the valence orbitals, are called double, triple, or quadruple-zeta basis sets. Here is a list of commonly used multiple zeta basis sets:
The 'cc-p' at the beginning of some of the above basis sets stands for 'correlation consistent polarized' basis sets. They are double/triple/quadruple/quintuple-zeta for the valence orbitals only {the 'V' stands for valence) and include successively larger shells of polarization (correlating) functions (d, f, g, etc.) that can yield convergence of the electronic energy to the complete basis set limit. These basis sets are the current state of the art for correlated or Post Hartree-Fock calculations. SEE ALSO
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