Contraction orbital/shell

In the 6-3IG basis, the inner shell of carbon is represented by 6 primitives and the 4 valence shell orbitals are represented by 2 contracted orbitals each consisting of 4 primitives, 3 contracted and 1 uncontracted (hence the designation 6-31). That gives... 

For semiquantitative work, double-zeta or triple-zeta basis sets (in which there are two or three shells of AOs for each fully or partially occupied atomic shell) are needed, at least for the valence shell. For first-row atoms, for example, the popular 6-31G basis has a minimal representation of the l.v core orbital and a double-zeta representation of the valence orbitals. Moreover, each AO is represented by a fixed linear combination of primitive GTOs the l.v core orbital contains six primitive AOs, and each 2s and 2p valence orbital is represented by two contracted orbitals, containing three and one primitive functions. 

Qualitatively speaking, effects of the core electrons on the valence orbitals due to relativistically contracted core shells must be exerted by the surrogate potential. If an appropriate analytical form for this potential has been chosen, its parameters can be adjusted in four-component atomic structure calculations. Hence, the most important step is the choice of the analytical representation of the ECP. Formally we replace the many-electron Hamiltonian Hg/ of... 

Another family of basis sets, commonly referred to as the Pople basis sets, are indicated by the notation 6—31G. This notation means that each core orbital is described by a single contraction of six GTO primitives and each valence shell orbital is described by two contractions, one with three primitives and the other with one primitive. These basis sets are very popular, particularly for organic molecules. Other Pople basis sets in this set are 3—21G, 4—31G, 4—22G, 6-21G, 6-31IG, and 7-41G. 

Note that the occurrence of a maximum oxidation state, corresponding to the removal of all the valence shell electrons and the adoption of a configuration, does not occur after manganese. In Chapter 9 we see how this reflects the contraction of the poorly penetrating 3d orbitals as the nuclear charge increases and it becomes progressively more difficult to remove electrons. 

The electron density i/ (0)p at the nucleus primarily originates from the ability of s-electrons to penetrate the nucleus. The core-shell Is and 2s electrons make by far the major contributions. Valence orbitals of p-, d-, or/-character, in contrast, have nodes at r = 0 and cannot contribute to iA(0)p except for minor relativistic contributions of p-electrons. Nevertheless, the isomer shift is found to depend on various chemical parameters, of which the oxidation state as given by the number of valence electrons in p-, or d-, or /-orbitals of the Mossbauer atom is most important. In general, the effect is explained by the contraction of inner 5-orbitals due to shielding of the nuclear potential by the electron charge in the valence shell. In addition to this indirect effect, a direct contribution to the isomer shift arises from valence 5-orbitals due to their participation in the formation of molecular orbitals (MOs). It will be shown in Chap. 5 that the latter issue plays a decisive role. In the following section, an overview of experimental observations will be presented. 

The conduction-electron tail is expected to move into the metal as the surface charge qM becomes more positive, and away from the metal as qM becomes more negative. It has been suggested18 that, for large positive qM, the tail could contract enough to deshield the inner-shell d orbitals at the surface, which would have a strong... 

The third category is the high coordination number lanthanides and actinides. The trivalent lanthanides show a decrease in with the progressive filling of the 4f orbitals, called the lanthanide contraction. Since the 4f orbitals are shielded by the filled 5s and 5p orbitals, the electronic configuration has no remarkable effect and therefore the variation in rM and an eventual change in coordination number and geometry determine the lability of the 1st coordination shell. 

It is not possible to use normal AO basis sets in relativistic calculations The relativistic contraction of the inner shells makes it necessary to design new basis sets to account for this effect. Specially designed basis sets have therefore been constructed using the DKH Flamiltonian. These basis sets are of the atomic natural orbital (ANO) type and are constructed such that semi-core electrons can also be correlated. They have been given the name ANO-RCC (relativistic with core correlation) and cover all atoms of the Periodic Table.36-38 They have been used in most applications presented in this review. ANO-RCC are all-electron basis sets. Deep core orbitals are described by a minimal basis set and are kept frozen in the wave function calculations. The extra cost compared with using effective core potentials (ECPs) is therefore limited. ECPs, however, have been used in some studies, and more details will be given in connection with the specific application. The ANO-RCC basis sets can be downloaded from the home page of the MOLCAS quantum chemistry software (http //www.teokem.lu.se/molcas). 

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