Pople style basis sets

6-31IG This is a triple split valence basis, where die core orbitals are a contraction of six PGTOs and the valence split into three functions, represented by three, one, and one PGTOs, respectively. 

If only one set of polarization functions is used, an alternative notation in terms of is also widely used. The 6-31G=i basis is identical to 6-31G(d), and b-SlG ts is identical to 6-31G(d,p). A special note should be made for the 3-21G basis. The 3-21G basis is basiciy too small to support polarization functions (it becomes unbalanced). However, the 3-21G basis by itself performs poorly for hypervalent molecules, such as sulfoxides and sulfones. This can be substantially improved by adding a set of d-functions. The 3-2IG basis has only d-functions on second row elements (it is sometimes denoted 3-21G(=f=) to indicate this), and should not be considered a polarized basis. Rather, the addition of a set of d-functions should be considered an ad hoc repair of a known flaw. 

To each of these basis sets can be Diffuse functions are normally s 

They are denoted by + or ++, with the first + indicating one set of diffuse s- and p-functions on heavy atoms, and the second + indicating that a diffuse s-function is also 

If only one set of polarization functions is used, an alternative notation in terms of is also widely used. The 6-31G basis is identical to 6-31G(d), and 6-31G is identical to 6-31G(d,p). A special note should be made for the 3-21G basis. The 3-21G 

Basis Hydrogen First row elements Second row elements  

6-311G(2df,2pd) 3s2pld 5s 4s3p2dlf llsSp 6s4p2dlP 13s9p  

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The Dunning-Huzinaga type basis sets do not have the restriction of the Pople style basis sets of equal exponents for the s- and p-functions, and they are tlierefore somewhat more flexible, but computationally also more expensive. The major determining factor. 

The generic symbol to represent a Pople-style basis set is of the form... 

Table 5.1 Composition in terms of contracted and primitive basis functions for some Pople style basis sets...

Kjffir and Sauer ° have reported the construction of new Pople style basis sets for the calculation of NMR spin-spin couplings, 6-31G-J and 6-31IG-J. New basis sets were optimized to the calculation of Fermi-contact (FC) term, and were not expected to provide correctly the values of the remaining contributions (SD, PSO, DSO). The authors performed benchmark calculations of J(C.H). J(N.H), J(N.C), J(C.C), J(O.C), J(O.H), J(H,H), and couplings dominated by the FC contribution, using... 

In the previous discussion of contracted basis functions, the general contraction scheme of Raffenetti, in which every primitive can contribute to every contracted function, was mentioned. The alternate approach produces functions that are sometimes referred to as segmented contractions since the primitives are partitioned into disjoint or almost disjoint sets. Because FORTRAN programs to efficiently implement the general contraction scheme were not very common in the 1960s and 1970s, most basis sets are of the segmented variety. For example, all of the Pople-style basis sets are of this type. 

The perturbation operator in the calculation of electric dipole moments, electric dipole polarizabilities and hyperpolarizabilities, i.e. the electric dipole moment operator Eq. (4.30), contains the position vector r of the electrons, which implies that the tail of the wavefunction becomes important. However, this is not well described in GTOs as discussed before and it is therefore essential to include additional valence functions with very small exponents C - so-called diffuse basis functions. In the Pople-style basis sets this is done in the 6-31G-I- and 6-31G- -- - basis sets, where in the -h basis set one diffuse function is added only for second- and third-row atoms, while in the - -+ basis set one diffuse function is also added for hydrogen (Clark et al., 1983). In the series of correlation consistent and polarization consistent basis sets one set of diffuse functions of each type present in the basis set is added in the aug-cc-pVXZ (Kendall et at, 1992 Woon and Dunning Jr., 1993, 1994 Balabanov and Peterson, 2005) and aug-pc-n (Jensen, 2002c) version of these basis sets. In the series of correlation consistent basis sets it is also possible to add two or more sets of diffuse functions in the d-aug , t-aug and so forth versions. 

The Pople style basis sets (Binkley etal. 1980 Dobbs and Hehrel986, 1987a,b Gordon etal. 1982 Hehre et al. 1969 Pietro et al. 1982) have received widespread use in the computational community. They may be described as X - 7Zg where X is the number of primitive Gaus-sians used to describe the core atomic orbitals. The valence orbitals are composed of a linear combination of Y and Z primitive Gaussian functions, respectively. Split-valence triple- and quadruple-zetabasis sets are also used, denoted as X - YZ Wg X- 7ZV7V, etc. 

For certain applications, special basis sets (property-optimized basis sets) have been developed. For instance, NMR spin-spin couphng constants require a proper description of the electron density in the vicinity of the nuclei. The polarization-consistent as well as the correlation-consistent basis sets have been modified for the calculation of NMR properties (shielding constants and spin-spin coupling constants pcS-w and pcj-n [90], ccJ-pVNZ [91] and uTZ-w [92]). For the calculation of NMR coupling constants by DFT procedures, recently a modification of Pople-style basis sets (6-31G-J) has been proposed [93]. The use of the resolution of identity approximation, either in DFT or correlated calculations, requires appropriate auxiliary basis sets [21]. Special basis sets are also required for explicitly correlated calculations. 

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