D-orbital participation

FIGURE 22. Partial CS d) Wiberg indexes characterizing d-orbital participation plotted against the experimentally determined S—C bond lengths in some sulfonyl derivatives70. ... 

Attempts to account for this bending have emphasized two physical effects, (1) d-orbital participation,18 and (2) core polarization,19 but no clear theoretical consensus has been achieved. The calculated bending in BaH2, for example, is found to disappear with removal of either d-orbitals or a polarizable-core, suggesting that both aspects are operative. The adequacy of the core-polarization rationale was questioned, and an alternative rationalization based on differences in atomic softness between metal and ligand was proposed by Szentpaly and Schwerdtfeger.20... 

Two general conceptual models of hypervalency have been proposed. The first, d-orbital participation, is represented in practically every general-chemistry... 

It is noteworthy that Rydberg orbital occupancies on the central atom (rY, final column of Table 3.29) are relatively negligible (0.01-0.03e), showing that d-orbital participation or other expansion of the valence shell is a relatively insignificant feature of hyperbonded species. However, the case of HLiH- is somewhat paradoxical in this respect. The cationic central Li is found to use conventional sp linear hybrids to form the hydride bonds, and thus seems to represent a genuine case of expansion of the valence shell (i.e., to the 2p subshell) to form two bonding hybrids. However, the two hydride bonds are both so strongly polarized toward H (93%) as to have practically no contribution from Li orbitals, so the actual occupancy of extra-valent 2pu orbitals ( 0.03< ) remains quite small in this case. 

Structure (3.226c), for example, depicts a central heptavalent Cl atom (Fa = 7), exceeding the normal valence octet by six electrons (These excess electrons are assumed to be accommodated in chlorine 3d orbitals, whereas d-orbital participation is prevented in first-row compounds.) Hypervalent structures such as (3.226a)-(3.226c) are claimed to be justified by the electroneutrality principle, which stipulates that second-row central atoms have zero formal charge (whereas first-row oxyanion Lewis structures commonly violate this principle).148... 

For symmetry-based qualitative molecular-orbital analyses of molecular shapes in the limit of strong metal s- and d-orbital participation in bonding, see R. B. King, Inorg. Chem. 37 (1998), 3057 and C. A. Bayse and M. B. Hall, J. Am. Chem. Soc. 121 (1999), 1348. 

A larger covalent radius such as of sulfur, selenium, or tellurium reduces the ring strain d-orbital participation in thiophene is not significant in the ground state, and thiophene exhibits a pronounced aromatic character that is substantiated by its physical and chemical properties.103... 

X-Ray.—The crystal and molecular structure of tri-o-tolylphosphine, its oxide, sulphide, and selenide (125) have been compared. The mean P—C bond lengths appear to be determined by the n-electron density along the P—C bond and intramolecular steric interactions, d-Orbital participation was considered to be of little importance.152 X-Ray diffraction established the structure of diphosphinofumarate (126)153 and showed that the phospholanium iodide (127) has an envelope ring with the methyl group at the point of the flap.154 The bicyclic phosphonium bromide (128) has a distorted half-chair phosphorus-containing ring, one of the P—C bonds in the... 

Structure C is usually written with a pentavalent phosphorus this description, however, should merely denote that the phosphorus lone pair is delocalized and no allenic bond with two perpendicular jr-systems has been formed. H2C=P(H)=CH2, a typical representative of structure C phosphorus, can be described by an allyl-like r-system, ° with the p -type lone pair of a planar tricoordinate phosphorus participating in the 4-electron-3-center jT-bonding, without invoking d-orbital participation. " Thus, the C -type bonding of phosphorus involves tricoordination, with a planar bonding environment, whereby the lone pair is available for jT-bonding. 

While 4bp/-type structures can be considered as resonance structures, 4cp/is also an alternative. The importance of structure 4cp/is supported by the fact that the negative charge at the carbon atoms in the 2 and 5 positions is indeed larger than at the 3 and 4 positions. ° The common feature in all 4ap/-, 4bp7-, and 4cp/-type structures is that the lone pair of the planar tricoordinate phosphorus is fully delocalized, resulting in an enhanced bond order about the tricoordinate planar phosphorus. The d-orbital participation at phosphorus is insignificant in 4, either in the planar or nonplanar form. °... 

These unusual shifts may be an indication of a significant d orbital participation, especially in phosphiran which probably has a nearly planar geometry and may possess some aromatic character as in the parent cyclopropanes [the P-H coupling in 3 of 155 Hz is between that found in PH2s (138 Hz) and PH3 (182 Hz)]. The same conclusions would to some extent apply to organogermyl-, organostannyl- and organosilyl-phosphines recently discussed by Schumann/1969,14)... 

One of the simplest molecules in which it is customary to invoke outer d-orbital participation in a bonding is the triiodide ion. This ion has been observed with a large number of different cations and X-ray crystal studies have revealed both symmetrical and unsymmetrical species, although in both forms it is essentially linear. If the bonding involves only the valence p-orbitals then the Hiickel orbitals for the symmetric species are those shown in Fig. 12. This description is exactly equivalent to the covalent-ionic resonance formulation VII. 

There are no doubt a number of studies of this problem which have been overlooked in this review and for this the author asks your indulgence. However in very few of the examples presented has it been possible to provide clear evidence of outer d-orbital participation in bonding and particularly in the case of d-tr bonding what evidence there is seems definitely against it. It is important to remember however that we are forced to use approximate methods to analyse the experimental data and... 

From a strictly quantum-mechanical point of view, the question of valence-shell expansion and d-orbital participation has two different aspects. One may either look for d-character in Lowdin s natural spin-orbitals of the complete, but unknown, total wave-function or one may ask the question whether the agreement with experimental results is ameliorated significantly when d-orbitals are included in the basis functions of approximate M. 0. calculations. It is a well known tendency for approximate calculations always to ameliorate in certain aspects when the basis is expanded, but also that the extent of this amelioration does not always bear a direct relation to the final results of far more sophisticated calculations. 

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