Gaussian basis sets notation

There is one other detail about the contracted basis set notation. For hydrogen, there is only the valence Is orbital and this is true too for helium. But for lithium, and any other atom in the Periodic Table, we divide the electron configuration into component core and valence orbitals and leave the core representation uncontracted. Thus, for lithium the 4-31 basis is the one linear combination of four primitive Gaussians of Table 1.8 scaled by the Slater exponent for Is and then the two linear combinations of equations 1.21 and 1.22 scaled by the Slater exponent for lithium 2s and then the two linear combinations defined... 

The types of (Gaussian) basis sets used in ab initio MO SCF theory have been described elsewhere. It may be helpful to list a few references as examples.The basis set designation in quantiam chemistry appears to be mysterious for non-specialists. However, it frequently has been explained,e.g. recently in a succinct form on current levels of theory. In order to characterize the theoretical level which has been employed for the PES calculation, a double-slash notation is used, introduced by Pople. It characterizes the method and basis set which are used for calculating stationary points of PES ("geometry optimization ) by the information found after the double slashes. The more sophisticated level for subsequent single point calculations of the PES is designated by the information preceding the double slashes. 

Quantum chemists have devised efficient short-hand notation schemes to denote the basis set aseti in an ab initio calculation, although this does mean that a proliferation of abbrevia-liijii.s and acronyms are introduced. However, the codes are usually quite simple to under-sland. We shall concentrate on the notation used by Pople and co-workers in their Gaussian aerie-, of programs (see also the appendix to this chapter). 

Sometimes it turns out that we need to include a number of polarization functions, not just one of each type. The notation 4-31G(3d, 2p) indicates a standard 4-31G basis set augmented with three d-type primitive Cartesian Gaussians per centre and two p-type primitives on every hydrogen atom. Again, details of the... 

The notation STO-nG means a minimal basis set of Slater Type Orbitals is used each of which is expanded into n simple Gaussians, l2-113). 

According to Pople s nomenclature the polarized basis sets are denoted by adding a superscript asterisk to the basis set, e.g. the popular 6-31G 34 [other authors prefer the notation 6-31G(d)]. When p-orbitals are added to H as well, a second asterisk is added (e.g. 6-31G )34. The first basis set developed in this series for third-row elements, STO-3G 35, was only partially polarized, i.e., it included polarization functions (5 pure d-type Gaussians) only on third-row elements, e.g. Si, but not on second-row elements. This basis set was later replaced by the 3-21G( basis set (parentheses around the asterisk indicate that only third-row elements are augmented by d-functions)36. Both STO-3G and 3-21G(, t) should not be viewed as full polarized basis sets. The philosophy in using these half-polarized basis sets is similar to that used in going from a dz to a sv basis set. Thus, polarization functions are added only on the atoms for which it is believed that they play a larger role. This tactic may be helpful in cases where calculations with a fully polarized basis set are not feasible. 

An alternative to the double zeta basis approach is to double the number of functions used to describe the valence electrons but to keep a single fxmction for the iimer shells. The rationale for this approach is that the core orbitals, unlike the valence orbitals, do not affect chemical properties very much and vary only slightly from one molecule to another. The notation used for such split valence double zeta basis sets is exemplified by 3-21G. In this basis set three Gaussian functions are used to describe the core orbitals. The valence electrons are also represented by three Gaussians the contracted part by two Gaussians and the diffuse part by one Gaussian. The most commonly used split valence basis sets are 3-21G, 4-31G and 6-31G. 

Au(l) has a 5d ( S) electronic state configuration. The RCEPs used here were generated from Dirac-Fock (DF) aU-electron (AE) relativistic atomic orbitals, and therefore implicitly include the major radial scahng effects of the core electron on the valence electrons. In the closed-sheU metal-ion system these indirect relativistic effects are dominant. In the smaU-core RCEP used here the 5s 5p subsheUs are included in the valence orbital space together with 5d, 6s and 6p atomic orbitals, and aU must be adequately represented by basis functions. The gaussian function basis set on each metal atom consists of the pubUshed [4 P3 ] distribution which is double-zeta each for the 5sp and 6sp orbitals, and triple-zeta for the 5d electrons. The standard notation for this basis set is RCEP-4111/31 IG to show exphcitly the gaussian primitive distribution in each basis function. 

Another subtlety concerns the set of higher L Cartesian Gaussians, i.e., d, f, and g functions. There are six Cartesian d s with / -I- w + = 2. The dxx + dyy + da combination of these corresponds to a function of atomic s symmetry. Sometimes this combination is included in calculations and sometimes it is omitted. When one compares literature results from various sources, it is important to know whether the s component of the d s was present. With many commonly used basis sets the effect, even with only one d set, is not negligible. When adding a set of d functions to the 6-3IG basis, ° for example, the difference in the SCF energy between keeping or omitting the s component of the d set is on the order of 1 millihartree (0.6 kcal/mol) for each first-row atom present in the molecule. Unfortunately, there is no standard notation that tells whether the s component of the d s has been kept. For... 

For molecular basis sets of Gaussian-type functions (GTF) general acronyms and notations are used that are well known in molecular quantum chemistry. 

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