P. R. Mitchell University of Kent at Canterbury

Canterbury, England and R. V. Parish I The

University of Manchester Institute of Science and Technology

Monchester, M60-IQD, England I The eighteen-electron rule (alias the

nine-orbital, rare gas, or effective atomic number rule) is widely used for the rationalization of the stoichi- ometries and structures of transition metal complexes, particularly carhonyls and organometallic compounds, on the basis that complexes in which the valence shell of the metal atom has eighteen electrons have greater stability than those with less or more valence electrons. A theoretical treatment has been given,' based on the assumption that the rule will be followed if the elec- tron cloud of the metal atom resembles that of the next rare gas, but there is to our knowledge no satisfactory qualitative explanation in the literature for this in- creased stability. I t is the intention of this article to provide such a rationalization, and to outline the scope of the rule.

The eighteen electrons to which the rule refers are those which would be housed in the nine valence shell orbitals of the metal atom (five (n - l)d orbitals, one ns orbital, and the three np orbitals) or, more precisely, in the molecular orbitals formed from these atomic orbitals. These electrons comprise those donated by the ligands together with the d electrons of the metal ion in the appropriate oxidation state. Thus, hoth CO(NH&~+ and Cr(CO)6 conform (for different rea- sons) to the rule in having six 3d electrons plus 12 donated electrons, a total of 18. Other examples are given in Table 1. Carbonyl complexes which contain

Table 1.

bridging carbonyl groups and/or metal-metal bonds are less straightforward. Metal carbonyls (with the exception of V(CO)s) are observed to. be diamagnetic, and those metals which would have an odd number of valence electrons give polymeric carbonyls in which the odd electrons are paired up by the formation of metal- metal bonds. I n these cases it is best to regard the

'CRAIG, n. P., AND D O Q G E ~ , G., J . Chem. Sac., 4189 (1963).

Eighteen-Electron Rule

metal atom as having an oxidation state of zero, when each bridging CO group and each metal-metal bond may be deemed to supply one electron to each metal atom. Hence, Fe2(CO)9 (I) follows the rule, since each Fe(O) atom has a 3ds configuration, six electrons are supplied by the three terminal CO groups, and one each by the bridging CO groups and the Fe-Fe bond, making a total of 18 electrons available to each iron atom. Similarly, in [a-CsHSCr(CO)a]z (11) there are six electrons from the Cr(O), plus six from the terminal CO groups, plus five from the cyclopentadienyl ligand, and one from the metal-metal bond. Note that it is .not necessary to know whether or not the CO groups are bridging to test the eighteen-electron rule: both forms of C O ~ ( C O ) ~ (I11 and IV) satisfy the rule.

The rule is followed by the vast majority of carbonyls and their derivatives [V(CO)6 and the hexanuclear carbonyls of cobalt and rhodium are the major excep- tions], and also by many complexes of the second and third row transition metals. For example, 1 r C l ~ ~ - (5d6) and MO(CN)~&- (4d2) are hoth eighteen-electron complexes, but hoth may he oxidized to give products with only 17 electrons (IrClsz- and MO(CN)~~-) . This type of deviation from the eighteen-electron rule is common for the second and third row transition ele- ments but, interestingly, occurs very rarely with the carbonyl complexes. For the first row metals, the carbonyls and related complexes again conform hut the vast majority of other complexes show scant regard for the rule; the occurrence of eighteen-electron complexes here appears fortuitous, and examples of complexes containing both less and more than eighteen electrons are common (Table 2).

It thus appears that we have three groups of com- plexes to consider.

Volume 46, Number 12, December 1969 / 81 1

Toble 2. Typical Complexes of First ROW ' - Transition Metals

(1) A group in which the electronic configurations are corn- plelelv unrelated to the eighteen-electron rule.

(2) A group of complexes which follow the rule at least in so far ss that they nerrer have more than eighteen electrons.

(3) Complexes which c o n f m rigorously to the rule.

A satisfactory explanation of these three types of he- havior may be obtained on the basis of a simple mo- lecular orbital treatment of the metal-ligand bonding.

Consider the common case of an octahedral complex, MLB. The combination of the six-ligand a orbitals with a d%p3 set of .metal orbitals of appropriate symmetry gives six bonding and six antibonding molecular orbitals (Fig. The bonding MO's will accommodate the 12 electrons which may be considered as being donated by the ligands, and it is the relative energies of the next available orbitals which are critical in determining to which of the three above groups the complex will belong. These orbitals are the nonbonding ta, orbitals and the antibonding e,* orbitals. The energy separation be- tween these two sets is the conventional ligand field splitting energy, A,. For many complexes of the first row metals A. is relatively small, and the e,* orbitals will be only weakly antibonding. Hence these orbitals will be available for occupation without much loss of energy by the complex as a whole. There will there- fore be no restriction on the number of d electrons sup- plied by the metal atom and any number, up to ten, can be accommodated. The total number of electrons available to the metal atom may be, in principle a t least, anywhere from 12 to 22; examples are given in Table

2. Thus, case (1) above corresponds to a relatively small A, value.

As A. increases, the energy of the e,* orbitals in- creases, and there will come a point a t which it is no longer energetically feasible to have electrons in these orbitals. The complex would then be effectively re- stricted to a maximum of six nonhonding electrons, and the presence of more electrons than this would lead to rearrangement and the formation of a complex of lower coordination number. Thus, the criterion for not ex- ceeding eighteen electrons (case (2)) is that A. shall be large, i.e., there must be a large ligand field splitting. For any particular ,ligand, large A. values are found when the metal is in a high oxidation state, or when the metal belongs to either the second or third transi- tion series. When the metal is in a high oxidation state its radius is small, the ligands approach closely, and the bonding interactions are strong. In metals of the sec- ond and third rows, the d orbitals are larger and more diffuse (than the 3d orbitals) and will interact more strongly with the ligands. Table 3 shows a number of complexes of the second and third row metals with up to 18 electrons, but very few complexes of these metals have ever been shown conclusively to have more than eighteen electrons.

Similar effects are seen when the ligands are high in the spectrochemical series, e.g., cyanide ion. Thus, hexacyano complexes are formed with metal ions having up to six d electrons, e.g., V(CN)? (d2), Cr(CN)63- (d3), Mn(CN)a3- d 4 , Fe(CN)sa- (d5), Fe(CN)e4- (dB), and Co(CN)e3- (d6), but the corresponding co- balt(I1) complex (d') is Co(CNh- and nickel(I1) (d3) gives Ni(CN)? and NI(CN)~~-. In these cases we presume that i t is possible to have less than the maximum number of nonbonding electrons precisely because these are essentially nonhonding and their addi- tion or removal will have relatively little effect on the stability of the complex.

Although the argument used above was developed using the example of an octahedral complex, precisely similar results are obtained for other coordmation numbers (Fig. 2). If the coordination number is m (m > 4), then (m - 4) d orbitals are required to form MO's with the ligand a orhitals. There will thus be (m - 4) low-lying antibonding 6rbitals and (9 - m)

Figure 1. MO diogram for an octohedrol complex (c bonding).

'The e bonding MO's are shown as a. degenerate set. This is not correct, but the relative energies of the a,,, e , and 11% sets are not known. The bonding LMO'S in Figures 2 and 3 are shown in this way for similar reasons.

812 / Journal of Chemical Education

Figure 2. MO diagrams lo bonding) for [A) tetrahedral, ( B ) trigonal bipyramidd, ond (C) rquore ontiprismatis complexes.

nonbonding orbitals. The energy separation between these two groups of orbitals will depend on the degree of metal-ligand u bonding as discussed above. The situe, tion is more complicated for tetrahedral complexes (m = 4), since MO schemes can be set up using either d3s or spa sets of metal orbitals. In practice both sets will be used and the 1, MO's will involve both d and p orbitals. However, in all cases the ligand field split- ting energy, A,, is small, so that the electronic configura- tion is not restricted and examples are known with 0-10 d electrons. Square planar complexes are con- sidered later.

Thus, when the ligand field effect (u bonding) is strong, the maximum number of nonbonding electrons will be governed by the coordination number and, con- versely, the mmimum coordination number will be governed by the number of nonbonding electrons.

It is, however, very noticeable that with ligands a t the top of the spectrochemical series, e.g., carbon mon- oxide, trifluorophosphine, the eighteen-electron rule is followed rigorously almost without exception. These ligands are thought to have their place a t the top of the series because they are capable of forming strong a bonds with the metal. The orbitals on the metal which are used in such a bonding are just those which, up to now, we have considered as being nonbonding. Using the octahedral complex as our example again, we now have three tz, orbitals which have become rela- tively strongly bonding by interaction with T orbitals on the ligands (Fig. 3). Thus, while it is still imperative not to have electrons in the unstable e,* orbitals, it is equally important to have the maximum possible num- ber of tz0 electrons, since removal of these electrons would destabilize the complex by loss of bond energy. I n octahedral carbonyl complexes, then, there are nearly always six d electrons, as in V(CO)s; Cr(CO)s and Mn(CO)6+. In other cases, the coordination num- ber and the number of d electrons are complementary in the same way-the d orbitals not involved in u bond- ing will form T bonds and will be full. Now the co- ordination number is exactly determined by the elec- tronic configuration of the metal, and vice versa, and we find compounds such as BrMn(CO)s, I;Fe(CO)a (both d6), Fe(CO)5 (d8) and Ni(PF& (d13. When the metal has an odd number of electrons, the odd electron is

'PAWLING, L., J . C h m . Soe., 1461 (1948).

paired up by the formation of a metal-metal bond (often accompanied by the formation of CO bridges): Mnz(CO)lo (d7), CO~(CO)~ (dg), although a few mono- meric, seventeen-electron complexes are known, e.g., V(CO)o and [Mo(CO)~(P~~PCH&HZPP~,),~+ (d5). When extensive metal-metal bonding occurs, as in metal cluster compounds like CO~(CO)I~ the MO dia- gram is complicated, but in all cases the stable MO's are fully occupied and there is a large energy gap be- tween these and the lowest unoccupied orbital.

There is one major exception to the eighteen-electron rule which does not fit the above treatment. Metals with d8 configurations frequently form square planar, four-coordinate complexes, even when the metal is in a high oxidation state (e.g., AuC1,-) or when the ligands are high in the spectrochemical series (e.g., Ni(CN)42-, Rh(C0)zCL-). These complexes might be expected to be five-coordinate; while examples of this coordina- tion number may be found, they are relatively rare. Two factors probably combine to produce this result.

The coordination number adopted by a metal atom in a complex will depend on two (major) factors. Firstly, there must be available orbitals of suitable energy and symmetry. Secondly, we expect the elec- troneutrality principlea to apply, in that the formal

Figure 3. MO diagrom for an octahedral complex b and r bondingl.

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positive charge on the metal ion should be approxi- mately neutralized by the negative charge donated by the ligands. The electroneutrality principle would lead us to expect the higher coordination number when (a) the metal is in a relatively high oxidation state, and could tolerate the donation of charge by five ligands, or (b ) the ligands are nonpolarizahle (e.g., F-, 0%-) and would not transfer much charge to the metal, or (c ) the ligands can form a acceptor bonds, removing some of the charge placed on the metal by c bonding.' Thus, complexes of the d g metals are most likely to be five- coordinate when many of the ligands form strong s bonds, as in Fe(CO)s, Fe(CNRh. Ligands which form weaker s bonds, e.g., phosphines, cyanide ion, tri- chlorostannate(I1) ion, mostly give four-coordinate complexes, but a few five-coordinate complexes are known, e.g., (Ph3P)Jr(CO)H, Ni(CN)sa-, Pt(SnC1dn3-.

However, for all five metal orbitals (one d orbital, the s, and the three p orbitals) to be used for effective c bonding with the ligands, it is required that these orbitals should have comparable energies. In crossing each transition series from Group IVA to IB, the energy separation between the (n - 1) d and np orbitals increases sharply, and it becomes increasingly unlikely that all of the metal p orbitals will be used. It has also been shownvhat this energy separation increases with increasing positive charge on the metal ion. Thus,

in the later Groups, where the d8 configurations arise, we require a low positive charge on the metal atom to allow full use of the p orbitals and a t the same time a relatively high positive charge to enable the coordin* tion of five ligands without violating the electroneu- trality principle. The most favorable compromise would again be the carbonyls, where the oxidation state is low and the ligands a bonding.

We may summarize the position as follows: For complexes in which ligand field effects are relatively small, there will be no correlation with the eighteen- electron rule. Where strong ligand field effects arise primarily by a bonding, the rule will be followed in that the number of electrons does not exceed eighteen but may be less. The rule will be rigorously followed when the ligands are strongly s bonding. In the square planar complexes, one p orbital is unused. Since this orbital has relatively high energy, we again have the situation that all strongly bonding and all nonbonding (or s bonding) orbitals are occupied and all unstable orbitals are empty.

'An increase in coordination rn~mber does not necessarily mean that there will be an increase in the charge donated to the met,al. I n some cases the metal-ligand bond distance increases as the coordination number increases, and t,he bonds become more ionic.

NYHOLM, R. S., P70~. Chem. Sac., 273 (1961).

81 4 1 Journal of Chemical Educaiion