Hybrid atomic states

Hybrid Atomic States.—For many atomic states the observed properties are not those corresponding closely to a single Russell-Saunders structure. For example, the four most stable states of the neutral tin atom are the following  

Configuration Symbol J Energy value Observed 9 Calculated 9 

This description of these two states, as resonance hybrids of the two states Pi and lD is arbitrary, but it is useful, inasmuch as the Russell-Saunders structures correspond closely to the actual properties for many atomic states, and it is convenient to continue to use these structures in the description of states for which no single Russell-Saunders structure provides a completely satisfactory representation of the observed properties. 

Even the electron configuration represents an idealization, which for some atomic states is not satisfactory. For example, the neutral osmium atom is conventionally described as having 5(2 6 as its most stable electron configuration. The lowest states to which this con- 

Hybrid states of this sort are to be formed from structures with the same value of J and also with the same parity. The parity of a configuration is even in case that it involves an even number of electrons in orbitals with odd value of l (p,/, etc.) and odd in case that it involves an odd number of electrons in orbitals with odd l. In tables of spectral terms the parity is often indicated by use of a superscript ° on the symbols of states with odd parity. In the above example of neutral osmium the two configurations considered have even parity. 

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The general understanding of the electronic structure and the bonding properties of transition-metal silicides is in terms of low-lying Si(3.s) and metal-d silicon-p hybridization. There are two dominant contributions to the bonding in transition-metal compounds, the decrease of the d band width and the covalent hybridization of atomic states. The former is caused by the increase in the distance between the transition-metal atoms due to the insertion of the silicon atoms, which decreases the d band broadening contribution to the stability of the lattice. 

To truly understand the geometry of bonds, we need to understand the geometry of these three different hybridization states. The hybridization state of an atom describes the type of hybridized atomic orbitals (ip, sp, or sp) that contain the valence electrons. Each hybridized orbital can be used either to form a bond with another atom or to hold a lone pair. 

The use of hybrid atomic orbitals in qualitative valence theory has, in the past, rested on two points (i) an empirical justification of their use involving the concept of the valence state of an atom and (ii) a simple linear transformation technique for the construction of the explicit forms of the orbitals. In this section we show that both of these points can be replaced. The justification can be replaced by a derivation and this derivation can be used to suggest variational forms which render the linear transformation technique redundant. 

Pauling showed that the quantum mechanical wave functions for s and p atomic orbitals derived from the Schrodinger wave equation (Section 5.7) can be mathematically combined to form a new set of equivalent wave functions called hybrid atomic orbitals. When one s orbital combines with three p orbitals, as occurs in an excited-state carbon atom, four equivalent hybrid orbitals, called sp3 hybrids, result. (The superscript 3 in the name sp3 tells how many p atomic orbitals are combined to construct the hybrid orbitals, not how many electrons occupy each orbital.)... 

Separating methods which use molecular parts into two categories, atom-based or fragment-based/ seems to make a distinction without a significant difference. In atom-based methods, each atom of the molecule is examined in respect to its connectivity index, and to the oxidation and hybridization state of all those atoms directly attached to it (Viswa-nadhan, 1989) or to some similar measure of atomic state (Broto, 1984). 

Hyperconjugation between sp3 hybridized atoms can have important implications for the ground-state conformation of organic compounds. It has, for example, been suggested that the energy difference between the staggered and the eclipsed conformations of ethane is due to both hyperconjugation and repulsion [2-5]. The fact that... 

The hybrids are then written in terms of atomic states, as in Eq. (3-1), and familiar properties of the angular momentum operators are used to evaluate the intra-atomic matrix elements. In terms of our notation in Eq. (3-1), (Py = ih, but... 

We have emphasized the importance of open d-orbitals and a proper atomic state if should dissociate with a low barrier on a transition metal surface. For clusters, however, the same type of dissociation puts up another requirement, which will turn out to be even more significant in the present context There must be at least one open shell valence orbital (of s-character) on the cluster, otherwise the sd-hybridization will not take place (8). For an infinite surface, this requirement can always be satisfied since states with open valence orbitals must at least be reachable by a low energy excitation. For clusters, the same type of excitation may be much more expensive. Since all nickel clusters dissociate it seems clear that a dissociative state is reachable in all cases for nickel. The question that has worried us for the past years is why the same type of states do not always seem reachable for iron and cobalt clusters. The answer to this question is discussed in section VI. 

Conformational effects also play an important role in determining IMDA diastereoselectivity. For example, trienes like (49) and (50) with two sp hybridized atoms within the connecting chain cyclize preferentially to ci s-fused rather than the trans-fuscd products that would be expected based tm the presence of the C(8)-methyl substituent (Figure 15). The benzo fusion forces the bridging chain to adopt boat-like conformations in the transition states, and the 1,3-diaxial interactions that the C(8)-methyl ordinarily experiences in the cif-fused, chair-like transition state are thus relieved (refer to Figure 12). The preferential formation of the cif-fused diastereomer may then be the consequence of a favored skew butene rotamer at C(6)—C(7) in (51) compared with a less favorable gauche butene rotamer at this position in the trans-fused transition state. This effect is discussed in more detail in Section 4.4.3.2 concerning relative diastereoselection in the IMDA reactions of substituted decatrienones. 

The triple bond in acetylene, like that in nitrogen, is composed of one a and two tt bonds and here also the tt bonds arc formed between electrons in non-hybridized p states. The a electrons, two to each carbon atom, are located in sp hybrid orbitals, formed by the linear combination of one s and one p wave function, as in beryllium, and the molecule is therefore linear. The arrangement of bonds is shown diagrammatically in Figure si. In a similar way the triple bond in the nitrile group G N is composed also of one n and two tt bonds. 

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