Contraction of orbitals

Breit-Pauli Hamiltonian contact term (p. 148) contraction of orbitals (p. 140)... 

As a result of the electronic give and take of chemical bonding, the net population of electrons around each nuclear center may increase or decrease, resulting in partial anionic or cationic character. In accordance with the breathing variations noted in Chapter 2, this leads to expansions or contractions of orbital size, relative to the free-atom neutral species. 

The smallest basis sets are called minimal basis sets. The most popular minimal basis set is the STO—3G set. This notation indicates that the basis set approximates the shape of a STO orbital by using a single contraction of three GTO orbitals. One such contraction would then be used for each orbital, which is the dehnition of a minimal basis. Minimal basis sets are used for very large molecules, qualitative results, and in certain cases quantitative results. There are STO—nG basis sets for n — 2—6. Another popular minimal basis set is the MINI set described below. 

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. 

MINI—i i = 1—4) These four sets have different numbers of primitives per contraction, mostly three or four. These are minimal basis sets with one contraction per orbital. Available for Li through Rn. 

The horizontal axis corresponds to an intemuclear separation running from 1.5 to 2.5 flo and the vertical axis corresponds to an orbital exponent running from 1,0 to 1.4. The potential energy minimum corresponds to an exponent of 1.238, and we note the contraction of the atomic Is orbital on molecule formation. 

IG 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. 

The obvious conclusion to be reached is that there are three kinds of spd orbitals hybrid bond orbitals, contracted d orbitals, and about 0.70 other orbitals. In 1938 I considered this 0.70 unstable orbital per atom to be unsuited for either bond formation or... 

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. 

Snijders, J.G. and Pyykko, P. (1980) Is the relativistic contraction of bond lengths an orbital contraction effect Chemical Physics Letters, 75, 5-8. 

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