Organometallics 1983,2, 435-447
Polyhedral Skeletal Electron Pair Theory-Its Nonconical Fragments
435
Extension to
David G. Evans and D. Michael P. Mingos’ Inorganic Chemistry Laboratory, Univers#y of Oxford, Oxford OX1 3QR, &eat Britain Received August 25, 1982
Molecular orbital calculations supplemented by symmetry and perturbation theory arguments have been utilized to evaluate the effect of introducing C% M(CO)4fragments into metal polyhedral cluster compounds derived from conical M(COI3fragments. Electron-counting rules for predicting the geometries of these lower symmetry species are provided, and site preferences and conformational consequencesof the bonding model are developed. Although we remain a long way from understanding the electronic structures of transition-metal cluster compounds in sufficient detail to be able to reliably predict their occurrence and electronic and chemical properties; the last 10 years has seen the development of simplified bonding schemes derived primarily from symmetry arguments and semiempirical molecular orbital calculations, which have provided a conceptual framework for rationalizing (and indeed a t times even predicting) the gross geometrical features of such compounds.’ The complex of ideas, which has been collectively described as the polyhedral skeletal electron pair theory,2 has proved to be particularly effective for rationalizing the structures of a wide range of cluster compounds involving transition-metal carbonyl and cyclopentadienyl components, metallocarboranes, and metallohydrocarbons, and is particularly successful when applied to structures in which conical fragments such as M(CO)3or M(q-C5H5)occupy the vertices of the polyhedronS3 This success can be attributed to the isolobal connection4s5between such fragments and main-group fragments such as B-H and C-H. However, at its most fundamental level the success of the polyhedral skeletal electron pair approach can be traced to the fact that the total electron count in a cluster, be it derived from main-group or metal carbonyl fragments, is decided primarily by the number of antibonding skeletal molecular orbitals derived from the s and p orbitals of the vertex atoms. These antibonding molecular orbitals are unavailable for either metal-ligand or skeletal bonding by virtue of their high-lying nature and (1)For recent reviews see: K. Wade, “Transition Metal Clusters”, B. F. G. Johnson, Ed., Wiley-Interscience, Chicheater, 1980. R. E. Benfield and B. F. G. Johnson, Top. Stereochem. 12,253 (1981);W. C. Tmgler and M. C. Manning, Coord. Chem. Rev., 38, 89 (1981). D.M.P. Mingos In ‘Comprehensive Organometallic Chemistry”, F. G. A. Stone and G. Wilkinson, Eds.; Pergamon Press, Oxford, 1982. (2)The term polyhedral skeletal electron pair theory was first introduced in R. Mason, K. M. Thomas, and D. M. P. Mingos, J. Am. Chem. SOC.,95,3802(19731,but the basic concepts were developed in R. E.W i l l i i , Znorg. Chem., 10,210 (1971);K.Wade, J. Chem. SOC.,Chem. Commun., 792 (1971);Inorg. Nucl. Chem. Lett. 8,559,563(1972);D. M. P. Mingos, Nature (London), Phys. Sci., 236,99 (1972);R. Mason and D. M. P. Mingos, MTPZnt. Rev. Sci.: Phys. Chem., Ser. Two, 11,121 (1975). (3)A recent breakdown of this approach for MCp fragments has been discussed in D. N. Cox, D. M. P. Mingos, and R. Hoffmann, J. Chem. Soc., Dalton Trans., 1788 (1981);and K.Wade and M. O’Neill, Inorg. Chem., 21,461 (1982). (4)The term isolobal was fmt introduced by M. Elian,M. M. L. Chen, D. M. P. Mingos, and R. Hoffmann, Inorg. Chem., 15,1148 (1976),but some of its origins can be traced to J. Halpern, Discuss. Faraday SOC., 46,7(1968);J. E.Ellis,J. Chem. Educ., 53,2(1976)and references given under 2. (5)Recent papers dealing with the isolobal principle include R. Hoffmann, Nobel Lecture, 1981;Science (Washington, DC), 211, 995 (1981);F. G.A. Stone, Acc. Chem. Res., 14,318(1981);D. M. P. Mingos, Trans. Amer. Crystallogr. Assoc., 16,17 (1980);T.A. Albright, ibid., 16, 35 (1980).
their inward hybridization and therefore set an upper limit on the total electron count for a particular polyhedral arrangement.6 For example, if a particular geometric arrangement of vertex atoms leads to the formation of 2n such orbitals, where n is the number of vertex atoms, then the total electron count in a main-group cluster will be 2(4n - 2n) = 4n electrons and will be 2(9n - 2n) = 14n electrons for a transition-metal carbonyl cluster compound. The difference in electron count merely reflects the presence of the additional five d orbitals in the latter case. Table I summarizes the consequences of this simple principle for several important classes of metal and main-group polyhedral molecules, e.g., closo-triangulated polyhedra, electron precise polyhedra, and, for completeness sake, some inorganic ring and nonbonded aggregates.’ Some illustrative examples are also given in this table, but a more extensive discussion of the applications of this methodology are to be found in ref 1. Although this generalized principle works surprisingly well for polyhedral molecules which have the isolobal fragments M(CO)3, M(q-C5H5),B-H,or C-H at the vertices, it is less successfully applied to cluster compounds derived from CzuM(CO)4and M(C0)2fragments (or related fragments such as Pt(PF&)J. The problems which are encountered with such fragments may be illustrated by the following examples from osmium and platinum cluster chemistry. In the first example O S ~ ( C O ) (1) ~ ~the C~ total electron count is 74 and the observed square-pyramidal structure is consistent with the (14n + 4 ) electron count predicted by the polyhedral skeletal electron pair approach for a nido octahedron (see Table I). The second example 2g has the same total electron count but the introduction of an Os(CO), fragment has resulted in the observed edge-bridged tetrahedral structure. The platinum compound 3 derived from PtLz fragments has the same skeletal geometry as 2 but a total of only 70 valence electrons.1° These differences can be interpreted in terms of the frontier molecular orbitals of the OS(CO)~, OS(CO)~, and Os(CO), fragments illustrated in Figure 1. The derivation of these frontier molecular orbitals and their usefulness in interpreting the stereochemical and chemical properties (6)D. M. P. Mingos, J. Chem. SOC., Dalton Trans., 133 (1974);J. W. Lauher, J. Am. Chem. SOC.,100,5305(1978);A. J. Stone, Inorg. Chem., 20, 563 (1981);G.Ciani and A. Sironi, J. Organomet. Chem., 197,223 (1980). (7)See, for example: P. R. Raithby in ‘Transition Metal Clusters”, B. F. G. Johnson, Ed., Wiley-Interscience, Chichester, 1980,for a recent review of the structures of transition-metal clusters. (8)C. R. Eady, B. F. G. Johnson, J. Lewis, and T. Matheson, J. Organomet. Chem., 57,C82 (1973). (9)C. R. Eady, B. F. G. Johnson, and J. Lewis, J. Organomet. Chem., 57,C84 (1973). (10)J.-P. Barbier, R. Bender, P. Braunstein, J. Fischer, and L. Ricard, J. Chem. Res., Synop., 230 (1978).
0276-7333183123Q2-Q435$Q1.5Q/O0 1983 American Chemical Society
Evans and Mingos
436 Organometallics, Vol. 2, No. 3, 1983
i?
Os!CCiL
cs!cO:3
OS(COi2
Figure 1. A comparison of the frontier molecular orbitals of OS(CO)~, OS(CO)~, and Os(CO), fragments.
[P~.~(CO)~(PR~)A]
ligand. The following examples illustrate the usefulness of this relationship.'J2 This approach is less readily ap-
(?)
of these fragments have been discussed in considerable detail elsewhere, particularly by Hoffmann and his coworkers and ourselvesll and therefore only those features which are germane to the current analysis will be discussed in the following section. The isolobal connection between M(C0)3and B-H fragments has its origins in the 2e(hy(xz,yz)) and 2al(hy(s-z)) out-pointing hybrid orbitals of the conical fragment, which bear a resemblance to the frontier orbitals of either B-H or C-H (see Figure 1).l1The addition or removal of a carbonyl ligand from M(CO)3 leads to a loss in the correspondence between these fragments and B-H, since the lower symmetry fragments have only a single hy(xz) orbital in addition to the higher lying al(hy(s-z)) orbital. The lost hy(yz) component can be traced in each case (see Figure 1)to the lower set of orbitals which are generally considered to be nonbonding as far as cluster bonding is concerned.6J1 Since the hy(xz) and hy(s-z) orbitals resemble the al and bz orbitals of the methylene singlet state, the Os(CO), and Pt(CO), fragments have been described as isolobal with CH2. The wide ramifications of this analog9 have been explored in Hoffmann's Nobel prize l e ~ t u r e . ~ Since this paper is in large measure concerned with the total electron count in cluster compounds derived from such fragments, it is necessary to note that for Os(CO),, OS(CO)~, and OS(CO)~ fragments the total electron count is 16, 14, and 12, respectively. Therefore although Os(CO), is isolobal and pseudoisoelectronic with CH2, the corresponding M(C0)2fragment is Os(C0):- or Pt(CO), with two electrons fewer. Consequently replacement of Os(CO), by Pt(C0)2leads to a decrease in total electron count of 2. The isolobal connection can provide a useful way of resolving some of the bonding problems associated with the introduction of Os(CO), fragments into the cluster since this moiety can be partitioned from the cluster and treated by analogy with CH2 as a two-electron-bridging (11)T. A. Albright, R. Hoffmann, J. C. Thibeault, and D. L. Thorn, J. Am. Chem. SOC.,101,3801 (1979);D.M. P. Mingos, J. Chem., Soc., Dalton Trans., 610 (1977);M. I. Forsyth, D. M. P. Mingos and A. J. Welch, ibid., 1674 (1980);D.M. P. Mingos and C. R. Nurse, J. Organomet. Chem., 184,281(1980);R.Pinhas, T. A. Albright, P. Hofmann, and R. Hoffmann, Helu. Chim. Acta, 63, 29 (1980).
60 electrons
:5>
plied to polyhedral cluster compounds which have M(CO), fragments at a vertex, e.g., Os6(CO)16or Ru4H2(CO),, (6).13314 Therefore this paper attempts to interpret the geometric features of cluster compounds containing M(CO), fragments by considering in more detail the frontier molecular orbitals of such fragments. B o n d i n g Capabilities of t h e M(CO), Fragment. Although the M(CO), and M(C0)2 fragments may be classified as being isolobal with CHz, a more careful examination of the frontier molecular orbitals of these fragments which are illustrated in Figure 2 suggests that (12) J. Lewis and B. F. G. Johnson, Adu. Znorg. Chem. Radiochem., 24,255 (1981)and references therein. (13)P. F. Jackson, B. F. G. Johnson, J. Lewis, M. McPartlin, and W. J. Nelson, J. Chem. SOC.,Chem. Commun., 920 (1978);D.B.W.Yawney and R. J. Doedens, Inorg. Chem., 11,838 (1972). (14)C. R.Eady, B. F. G. Johnson, J. Lewis, B. E. Reichert, and G . M. Sheldrick, J. Chem. SOC.,Chem. Commun., 271 (1976).
Organometallics, Vol. 2, No. 3, 1983 437
Polyhedral Skeletal Electron Pair Theory
[o~~~co)l~3
[R%H2 (CO),,l
($1
this analogy must be used with caution since both fragments have within their d manifold the yz orbitals 7 and 8. These orbitals correlate with the hybrid hybz) orbital
a (9)
(7)
of the M(CO)3fragment (9). The orbitals 7 and 8 do not contribute as effectively as 9 to metal-metal bonding because of their lower energies and unhybridized character, but their presence cannot be totally ignored as the simple application of the isolobal analogy would suggest. The problem is compounded for the M(C0)2fragment by the occurrence of the py orbital 10 which has the same symmetry characteristics as 9 and can, if the metal d-p promotion energy is small, make a significant contribution to skeletal bonding. A more complete comparison of the bonding capabilities of M(CO)4and M(C0)2fragments is given in a subsequent paper.15 The ambiguity in classifying the Os(CO), fragment becomes more pronounced when the distortional mode illustrated in 11-13 is considered. If the equatorial OC\ \
c2v
c2v
C4V
111)
(12)
(13)
Os-CO angle is opened out from its initial value of 105' as the axial OC-Os-CO angle is reduced, then the axially symmetric Os(CO), fragment illustrated in 14 is generated.16 The distortional mode represented in 11 has the OC
(. 1
)
effect of stabilizing hy(xz) and destabilizing y z (see Figure 2). In the Clulimit, these orbitals represent degenerate components of the d-p hybrid orbitals e(hy(xz,yz)). A ClU (15) D. G. Evans and D. M.P. Mingos, to be submitted for publication. (16) M.Elian and R. Hoffmann, Znorg. Chem., 14,1058 (1975); J. K. Burdett, J. Chem. SOC.,Faraday Trans. 2, 70, 1599 (1974).
2 c 2v OSKO)~
CLV
-
OS(C0)4
Figure 2. Schematic illustration of the effect on the frontier molecular orbitals of the CZU CQ distortion of an OS(CO)~ fragment. In the CZUgeometry the equatorial C-Os-C angle is 105O and in the CllVgeometry the ligands make an angle of 120° with respect to the C4axis. Particularly noteworthy is the large destabilization of the bl component, derived from yz.
fragment with the frontier orbitals illustrated in Figure 2 is more correctly described as being isolobal with either CH- or BH2-. Therefore, the precise designation of the isolobal nature of the M(CO)4fragment is sensitive to the gradient of the potential energy surface connecting 11 and 14 and the magnitude in the difference in the bonding abilities of the hy(xz) and yz orbitals in 11. The latter will depend on the orbital characteristics of the cluster moiety to which Os(CO), is bonded. The extended Huckel calculations, which are described in the Appendix, suggest an energy difference separating 11 and 14 of 2.6 eV. The greater stability of the C2"fragment can be related to the fact that the destabilization of yz (see Figure 2) far outweighs the stabilization associated with hy(xz). From the analysis provided above it is clear that the bonding capabilities of the Os(CO), fragment will be influenced primarily by the hy(xz) and hy(s-z) orbitals in Figure 1. These interactions are likely to be maximized for coplanar arrangements of osmium atoms, and therefore it is such molecules that will be considered initially. Two-Dimensional Cluster Compounds. The simplest two-dimensional cluster species is the triangle, and therefore this analysis begins with a consideration of the alternative O S ~ ( C Ogeometries )~~ illustrated in 15, 16, and 17. Both 15 and 17 are based on CZvfragments (although in the latter cluster this results in substantial steric crowding). Furthermore, they may both be derived from 16, which is based on conical Os(CO), fragments, by appropriate distortions of the O C - 0 ~ 4 0bond angles. With
438 Organometallics, Vol. 2, No. 3, 1983
Evans and Mingos
Table I. Summary of the Total Number of Valence Electrons for Polyhedral Molecules and Ring Compounds” main-group hydrides isolated atoms held together by bridging groups ring compds electron precise polyhedra arachno polyhedra (deltahedra)c nido polyhedra (deltahedra) closo polyhedra (deltahedra) capped polyhedra (deltahedra) with m capping groups
examples
8n 6n 5n 4n 4n 4n 4n
transition-metal carbonyls 18n
(n 2 3) ( n even 2 4) + 6 (n> 4) t 4 (n2 4) t 2 (n> 5 ) + 2 + 2m ( n > 5 )
P A , s, cubane, P, BnHn+6 BnHn+4 BnHnz-
no examples
16n ( n > 3 ) 15n ( n even > 4) 14n t 6 1411t 4 14n + 2 14n + 2 t 2m
a The total number of valence electrons is expressed in terms of the number of polyhedral atoms n. polyhedra have three edges radiating from each vertex. Deltahedra have triangular faces exclusively.
examples
CU,X,( AsRJj,-OS3(CO),,
Ir4(CO)12 OS,C(CO)l, Os,( GO),52OS,(CO),,
Electron precise
molecular orbitals illustrated in 18 and 19 which experience the first-order perturbation theory stabilization described above. In the final CPOlocal geometry of Os(CO), the a/
d21’
(
6
,
Figure 3. Comparison of the bonding molecular orbitals for OS,(CO)~~ derived from ClU fragments (16) and CZOOS(CO)~ fragments (15).
use of Stone’s notation6 and mode of analysis the skeletal bonding molecular orbitals derived from the 2a1 and e(hy(xz,yz))frontier orbitals of the conical M(CO), fragment illustrated in Figure 2 may be represented as radial and a-surface molecular orbitals. For 16 the radial bonding molecular orbitals derived from the al orbitals are represented by a bonding al’ and a pair of antibonding e’ orbitals. The a-surface molecular orbitals derived from e(hy(xz,yz)) give rise to the bonding e’ and a;’ molecular orbitals and the antibonding e’’ and a; orbitals as shown in Figure 3. For a 48-electron cluster such as Os3(CO)12 the orbital populations are (a;’)2(e’)4(e’’)4(al’)2corresponding to a net Os-Os bond order of 1since the out of plane a interactions are cancelled out by the simultaneous electron occupation of a; and e”. Within the framework of first-order perturbation theory the conversion of a ClUM(CO)4fragment into one of Czu symmetry may be represented by a substantial decrease in the Coulomb integral for the y z component of the e set (i.e., it becomes more negative) and a decrease in the resonance integrals between yz orbitals on adjacent osmium at0ms.l’ These effects can readily be assimilated into the interaction diagram shown in Figure 3. For the conformation shown in 15 the hy(yz) components of the e sets of the individual Os(CO), fragments lie perpendicular to the Os, plane, and therefore it is the a/ and e’’ (17)E. Heilbronner and H. Bock, “Das HMO Model1 und seine Anwendung”, Verlag Chemie, Weinheim, 1968.
’61
e//
(19!
and e’’ orbitals approximate to being nonbonding. The cluster metal-metal bonding is therefore dominated by the e’ and al’ levels shown in Figure 3. Previously we have reported photoelectron spectral resultsls which have demonstrated that the bonding picture illustrated in Figure 3 is essentially valid. Since the stabilization energy associated with e” and a; when taken with that associated with a
