Outer d-orbitals in bonding

The physical chemist of today has a wide variety of methods at his disposal for the experimental investigation of electronic structure and all of them have been used in attempts at obtaining evidence of the participation of outer d-orbitals in bonding. One such group of methods is constituted by the various techniques of radiofrequency spectroscopy, which have the advantage that they yield information about the molecule in its ground state. In this they have a distinct superiority over, say, electronic absorption spectra where it is necessary to consider both ground and excited states. Moreover much of the data derived from radiofrequency spectroscopic methods concerns essentially just one part of the molecule so that attention can be concentrated on those atoms of interest in whatever study happens to be under way. 

Expanded Valence Shells Many molecules and ions have more than eight valence electrons around the central atom. An atom expands its valence shell to form more bonds, a process that releases energy. A central atom can accommodate additional pairs by using empty outer d orbitals in addition to occupied s and p orbitals. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

In this discussion of the transition elements we have considered only the orbitals (n— )d ns np. It seems probable that in some metals use is made also of the nd orbitals in bond formation. In gray tin, with the diamond structure, the four orbitals 5s5p3 are used with four outer electrons in the formation of tetrahedral bonds, the 4d shell being filled with ten electrons. The structure of white tin, in which each atom has six nearest neighbors (four at 3.016A and two at 3.17.5A), becomes reasonable if it is assumed that one of the 4d electrons is promoted to the 5d shell, and that six bonds are formed with use of the orbitals 4dSs5p35d. 

These electronic interpretations of valency allow us to interpret the phenomenon of variable valency exhibited by many of the transition metal elements. As shown in Fig. 10.5 (Chapter 10), the transition metals exist because the energy of the outer d orbitals lies between the 5 and p energy levels of the next lowest orbitals, and thus are filled up in preference to the p orbitals. Copper, for example (1 s22s22p63s23p63dl04sl), has a single outer s electron available for bonding, giving rise to Cu(I) compounds, but it can also lose one of the 3d electrons, giving rise to Cu(II) compounds. 

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... 

In a complexes, the a ligand is side-on (rj2 mode) bonded to the metal (M) to form a 3c-2e bond. The electron donation in a complexes is analogous to that in it complexes. The transition metals can uniquely stabilize the a ligands and it ligands due to back donation from their d orbitals, as shown in Fig. 11.5.9. The main-group metals, lacking electrons in their outer d orbitals, do not form stable a complexes. 

Low-spin complexes in which the metal configuration is d3, d4, d5, or d6 would require either a ligand to leave before substitution could occur or the utilization of an outer d orbital to form a seven-bonded transition state. Such complexes frequently undergo substitution by a dissociative process because expanding the coordination number of the metal is made difficult by the lack of a vacant orbital of suitable energy. In either the SN1 or the SN2 case, the substitution should be much slower than it is for labile complexes. Accordingly, complexes of V2+, Cri+, Mn4+ (all of which are d3 ions), low-spin complexes of Co3+, Fe2+, Ru2+, Rh3+, Ir3+, Pd4+, and Pt4+ (all of which are dt ions) and low-spin complexes of Mn3+, Re3+, and Ru4+ are classified as inert. Inert does not mean that substitution does not occur, but rather that it occurs much more slowly than it does in labile complexes. 

Among the typically organic heterocycles of Fig. 1, the 1-methylphos-phole 12) 1 does not necessarily contribute dn orbitals to the rr-system besides its p lone pair13). The same holds for the phosphabenzene derivatives 2a 14> and 2b 1ST But in the phosphorine derivatives 3a 16>, 3b l7>, 3c 18> and 3d 19>, as well as in 1,1,3,3-tetraphenyl-l,3-diphosphabenzene 2°) 4 and 1-phenyl-1 H-phosphepine-l-oxide 21> 5 which contain tetrahedral phosphorous atoms, cyclic conjugation can only be achieved by the use of outer d orbitals. The resultant bonding situation has been treated theoretically by Mason 22> using HMO theory. 

This approach is a limited MO treatment, predicated on two main ideas (1) that the use of outer d orbitals of the central atom is so slight that they may be neglected altogether, and (2) that the persistent recurrence of bond angles close to 90° and 180° in AB molecules suggests that orbitals perpendicular to one another, namely, p orbitals, are being used. 

Both the three-center bond model and the correlation diagram treatment, as just outlined, omit all central-atom orbitals except the s and p orbitals of the valence shell. Indeed the three-center bond model neglects even the s orbital except as a storage place for one electron pair. They can be described as very restricted or incomplete MO treatments. They are also inexact, even within their self-imposed limits, since numerical accuracy is neither sought nor obtained in their usual applications. It would not, of course, be sensible to strive for numerical precision after such sweeping assumptions have been made at the outset. On the other hand, the hybridization or directed valence treatment assumes very full involvement of outer d orbitals whenever more than four pairs of electrons must be accommodated. This extreme assumption is also unlikely to be accurate. Finally, the VSEPR model resorts to a simple electrostatic model, which, however successful it may be, can scarcely be taken literally. 

It is not clear how far from this optimum situation one may go and still expect major contributions to bonding from the outer d orbitals. More extensive and detailed studies will be required to refine our understanding of this problem. The foregoing considerations do clearly suggest that com-pounds in. which d orbitals might be used are most likely to be formed with the more electronegative ligand atoms (F, O, Cl) and this is in accord with observation. 

While the role of central atom d orbitals in the formation of a bonds to outer atoms has been a controversial subject, there is another role for d orbitals where their actual participation has been more generally accepted for some time, although here, too, the exact extent of that participation is subject to some differences of opinion. 

A survey of all of the available data on the stability of halide complexes shows that generally the stability decreases in the series F>Cl>Br>I, but with some metal ions the order is the opposite, namely, Ftheoretical explanation for either sequence or for the existence of the two classes of acceptors relative to the halide ions has been given. It is likely that charge/radius ratio, polarizability, and the ability to use empty outer d orbitals for back-bonding are significant factors. From the available results it appears that for complexes where the replacement stability order is Clbond strength is Cl >Br >1, so that ionic size and polarizability appear to be the critical factors. 

The C—F bond energy is indeed very high (486 kJ mol-1 cf. C—H 415, and C—Cl 332 kJ mol"1), but organic fluorides are not necessarily particularly stable thermodynamically rather, the low reactivities of fluorine derivatives must be attributed to the impossibility of expansion of the octet of fluorine and the inability of, say, water to coordinate to fluorine or carbon as the first step in hydrolysis, whereas with chlorine this may be possible using outer d orbitals. Because of the small size of the F atom, H atoms can be replaced by F atoms with the least introduction of strain or distortion, as compared with replacement by other halogen atoms. The F atoms also effectively shield the carbon atoms from attack. Finally, since C bonded to F can be considered to be effectively oxidized (whereas in C—H it is reduced), there is no tendency for oxidation by oxygen. Fluorocarbons are attacked only by hot metals, e.g., molten sodium. When pyrolyzed, fluorocarbons tend to split at C—C rather than C—F bonds. 

There are also important cases in which the ligands have both empty and filled n orbitals. In some, such as the Cl", Br and I- ions, these two types are not directly interrelated, the former being outer d orbitals and the latter valence-shell p orbitals. In others, such as CO, CN and pyridine, the empty and filled n orbitals are the antibonding and bonding pn orbitals. 

As mentioned above such simple conclusions are not easily drawn in the case of transition metal compounds because of charge transfer into d as well as into outer metal orbitals. In addition, bonding mechanisms may be significantly different in different coordinations. A meaningful comparison between M and later transition elements is also difficult to draw. One or more of oxidation state, spin state, structure, or coordination geometry are generally different. It does appear, however, that the Ad and 5d covalency is similar in chlorides and bromides of the elements Pd and Pt for which significant comparisons are available. 

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