Electronic Structure of Binuclear Metal Carbonyl Complexes BY WILLEM EVERT AND PET ROS HEIJSER JAN BAERENDS Scheikundig Laboratorium Vrije Universiteit De Boelelaan 1083 Amsterdam The Netherlands Received 20th July 1979 This article describes LCAO-Hartree-Fock-Slater calculations on the binuclear metal carbonyls Mn2(CO)lo Fe2(C0)9 and Co2(CO)*. The calculations which are carried out within a double zeta STO basis are used to investigate the electronic structure of the carbonyls and to calculate a number of physical properties. It is found that in Mn2(CO)lo the two Mn(CO)5 fragments are bonded by a single Mn-Mn bond but that in Fe2(C0)9 and CO~(CO)~ the bonding effects arise from a strong interaction between metal &orbitals and n* levels of the bridging ligands.Neither in the iron complex nor in the cobalt com- plex is there any evidence for a direct metal-metal bond. The calculated ionisation potentials and U.V. data agree reasonably well with experimental values when these are available. n* Populations of bridging and terminal carbonyls fit well into a correlation with i.r. stretching frequencies previously obtained. 1. INTRODUCTION In the thriving field of metal-metal bonded systems the bi- and poly-nuclear car- bony1 complexes are the classic examples. We investigate in this paper' the series Mn2(CO)lo Fe,(C0)9 and Co,(CO), which cover the possibilities of just a single M-M bond [Mn,(CO),,] or a straight M-M bond assisted by bridging CO groups [Fe,(C0)9] and a bent M-M bond plus bridging groups [Co,(CO),].The geo- metrie~,-~ are specified in table 1 and the structures are sketched in fig. 1. We note that Mn2(CO)10 has D4d symmetry having the equatorial CO groups of the two Mn(CO)5 fragments staggered. The rotation barrier is estimated to be 32 kcal m01-l.~ The Fe2(C0)9 molecule has three bridging carbonyls in the equatorial plane which have staggered positions with respect to the sets of terminal car-bonyls on each Fe atom. The symmetry of the complex is D3h. Each Fe atom is almost octahedrally surrounded by CO ligands. Putting two perfect octahedra together with one face in common would result in a Fe-cb,idge-Fe angle of 70.5'. The Fe-Cb-Fe angle is 77.6'. The structure of the Co,(CO) isomer investigated here which is the one present in the solid state is similar to that of Fe2(C0)9.There is just one bridging carbonyl missing. The symmetry is C2u. Comparison with the Fe2(C0)9 data shows that apart from the absence of a third bridging carbonyl there is very little change in geo- metry. The co-cb-co angle (83") is slightly larger than the Fe-cb-Fe angle. It is important to note our choice of coordinate axes as drawn in fig. 1. The metal-metal axis is always the z-axis. In Fe,(CO) there is one bridging carbonyl along the x-axis. In Co,(CO) it is this carbonyl that is missing. In the C,,sym-metry of Co,(CO) the C2axis is in our coordinate system the x-axis not the z-axis. A considerable amount of experimental work has been done on these systems including u.v.-p.e.s. and ESCA,'-I1 u.v.v.,I2-l4 i.r.and Ramar~,'~-~' mass e.~.r.,~''~~ BINUCLEAR METAL CARBONYL COMPLEXES TABLE 1 .-GEOMETRIES OF BINUCLEAR CARBONYLS distance/A angle/" Mn2(CO)10 Mn-Mn 2.923 MnMnC, 86.2 Mn-C, 1.792 MnC,,O, 180 Mn-C, 1.831 Cax-Oax 1 .151 Ceq-Oeq 1.157 Fe2(C0)9 Fe-Fe 2.523 FeFeC 120.9 Fe-cb 2.016 FeCbFe 77.6 Fe-C 1.838 FeCbOb 141.2 cb-ob 1.176 FeC,Ot 177.1 ct-0 1.156 thermodynamic measurement^,^^-^^ Mossbauer ~tudies~~J~ ~pectrornetry,~~-~~ and a Co n.m.r. in~estigation.~' Theoretical treatments 7~13941-47 do not go beyond qualitative and semi-empirical studies. The absence of more detailed information on Fe,(CO) and CO~(CO)~ such as MO energies and composition is particularly noteworthy. There is almost universal agreement on the bonding in Mn2(CO)lo but the elec- tronic structure of Fe2(C0)9 and Co2(CO) is more controversial.The EAN (or 18-electron) rule requires a direct M-M bond in all cases. We will briefly discuss in section 3 some qualitative descriptions of the bonding in these systems and then pass on to the present Hartree-Fock-Slater results. 2. COMPUTATIONAL APPROACH The results described in this paper have been obtained with LCAO-Hartree- Fock-Slater calculations. The LCAO-HFS method has been described previ- ously.48*49 It is characterized by the use of the Xa potential (always with a =0.7) and the application of special numerical techniques. The latter afford an essentially ab initio solution of the one-electron HFS equations (no muffin-tin approximation).The quality of the SCF calculation is thus determined by the quality of the basis set. We have used a double-zeta Slater type orbital basis as obtained from Clementi's tables.50 Extensive basis set tests on Cr(C0)6 have demonstrated this basis set to be The important difference with ab adequate for the present type of in~estigation.~~ W. HEIJSER E. J. BAERENDS AND P. ROS 0 I 0 0 o-oo-o \\ \ \ 0 FIG.1.-Geometries of Mn,(CO)lo (a),Fez(C0)9(b)and CO,(CO)~ (c). The position of the coordin- ate axes is shown in (d). initio Hartree-Fock calculations is in the use of the Xa potential. An evaluation of the LCAO-HFS method49 led to the conclusion that the Xa potential if applied with the same care as the Hartree-Fock potential (i.e.,comparable basis set quality etc.) leads to results that are at least as close to experiment as Hartree-Fock results.BINUCLEAR METAL CARBONYL COMPLEXES 3. QUALITATIVE DESCRIPTION OF THE ELECTRONIC STRUCTURE In Mn2(CO)lo the local symmetry around each Mn atom is that of a distorted octa- hedron so the d orbitals split to a first approximation into a t2 and e set. If we consider the Mn(CO) fragment only the e set will split further into a dz2 with sym- metry a in the local C4,group and a higher lying 3d,~-~z of b symmetry [see fig. 2 and ref. (47a)l. The dz2 can mix in 4s and 4pz which also have a symmetry. We may use the seven valence electrons of the Mn atom for filling the low-lying t2gset of orbitals which will be involved in the backbonding interaction with the CO 7c* orbitals.The remaining electron occupies the a dsp hybrid which may combine with its partner on the other Mn(CO) fragment to form a simple two-electron M-M bond. The only point of controversy with respect to this simple bonding scheme has been the possibility of the equatorial CO groups interacting with the other Mn atom which would make them " semi-bridging ".41944 The qualitative bonding model of Fe,(CO) is much more complicated than the scheme sketched for Mn2(CO)lo. In all papers on this problem with one e~ception,~~ a direct Fe-Fe bond is a priori accepted. In a paper published in 1953 Dunitz and Orge152 mention the " net formation of an iron-iron bond ". In inorganic text- book~~~-~~ a direct Fe-Fe bond is casually accepted on the basis of the 18 electron rule.Finally Braterman states " This bond is real not formal ".45 A simple qualitative bonding model of Fe2(C0)9 e.g. that described in ref. (7) and (43 starts by assuming the iron atoms in the complex to be approximately octa- hedrally surrounded by carbonyl groups. In first approximation the 3d orbitals of each iron atom split into a t2gand an e set. In our coordinate system the tLg set (ener- getically the lowest orbitals) will consist of the 3dzz 3dX2-,2 and 3dxyorbitals (in fact the 3dz2 is a pure tz orbital in this coordinate system while the remaining tes orbitals have mainly 3dX2-,,zand 3dxycharacter). In the local C3,symmetry around the iron atoms these orbitals are indicated as a and e orbitals respectively (see fig.5). The re- maining 3d orbitals mainly 3dxzand 3dyz,are the e orbitals in octahedral symmetry and will also be found as an e set in the local C3 symmetry. In this qualitative bond- ing model these latter orbitals are now assumed to hybridise with the iron 4s and 4p orbitals (d2sp3)into six hybrid orbitals pointing to the carbonyls. Now we can start making bonding orbitals and placing the electrons. The electrons which we have available are eight valence electrons of each iron atom (4s and 34 and two electrons from each carbonyl group. The terminal CO(C0,)Sa orbitals combine with three iron hybrids; these orbitals are filled with the 50 electrons. The bonding interaction between the metal hybrids and the bridging carbonyls must be of another type.Some authors' assume a normal bond between the metal atoms and sp2-hybridized carbon of CO describe the bonding in terms of three centre two-electron bonds. In the latter model the plus combination of the two hybrids pointing to a bridge carbonyl forms a bonding combination with the Cob 50which is occupied by the two 50 electrons. The minus combination of the hybrids interacts with the 7t* of Cob thus forming a three-centre two-electron bond. In this model as well as in the first each metal atom provides one electron for the bond forma- tion with each of the bridging carbonyls. Since the metal atoms start with eight valence electrons (3d64s2),this leaves us with five electrons at each iron atom that are to be placed in the t2,-type orbitals.Four electrons will fill the e orbitals (3dX2-y2 3dxy); these orbitals are available for backbonding purposes. The last electron of each iron atom is placed in the bond- ing combination of the 3dz2 orbitals of both atoms thus providing a direct single iron-iron bond. W. HEIJSER E. J. BAERENDS AND P. ROS In all these models the plus combination of the 3d,z orbitals is responsible for the Fe-Fe bond the minus combination is supposed to be an orbital with such a high energy that it will be empty. [In Braterman's the (3dz2-3dz2) level must be higher than the three-centre bonding levels]. A bonding scheme for Fe,(CO) without a direct Fe-Fe bond has to our knowledge only been suggested in a paper by Hoffrnann and co-workers on " triple-decker sandwiches ".46 These authors assume the interaction between the e orbitals and the bridging carbonyls to be re- sponsible for the stability of the complex.In their bonding scheme the tZsorbitals are considered to be Fe-Fe nonbonding orbitals. In section 5 we will further consider their results. A description of the bonding model of Co,(CO) is very much the same as in the case of the iron complex. If we assume that in cDz(co)8 a co(co,),fragment has local C3"symmetry then the angle between the C3axis belonging to this fragment and the Co-Co axis turns out to be only (approximately) 5". Apparently the molecule does not fold open at the removal of one of the bridging carbonyls. Therefore it is often assumed that the bonding interaction which was provided for by this carbonyl is taken over by a direct Co-Co bond.in simple bonding models two possibilities for a metal-metal bond have been proposed viz. a " straight " and a " bent " metal-metal bond. In such bonding models [e.g. described in ref. (45)] CO,(CO) is treated as analogous to Fe,(CO), i.e. the metal atoms are assumed to be d2sp3hybridised. Five of the six hybrids are involved in the bonding to the (terminal and bridging) carbonyls while the sixth one points to the empty bridging site. Of the remaining d orbitals (the tZgset) the 3dZz also plays a role in the metal-metal bonding. When all orbitals except the sixth hybrid and the 3dz2 of both Co atoms are occu- pied as they are in the Fe,(C0)9 case three electrons are left at each cobalt atom.We still have four orbitals available to accommodate these electrons uiz. the plus and minus combinations of the 3dz2 orbitals of both cobalt atoms and the plus and minus free hybrid combinations. The plus combinations which are both of Co-Co bond-ing character will be occupied in any event. Now one Co-Co antibonding orbital must be filled. if the antibonding hybrid combination is filled the hybrids of both cobalt atoms can be considered as lone pairs pointing to the empty bridging site while a straight metal-metal bond results from the bonding 3dz2 combination completely analogous to the classical Fe,(CO) picture. However if the antibonding 3dZz orbital is filled a bent metal-metal bond is formed by the bonding combination of the hybrids.4. QUANTITATIVE (HFS) DESCRIPTION OF THE ELECTRONIC STRUCTURE OF Mn2(CO)lo In order to investigate the electronic structure of Mn,(CO), we carried out HFS calculations on Mnz(CO),, MXI(CO)~ Mn and CO. The orbital energies of the relevant valence orbitals of Mn(CO) and of Mn,(CO), are shown in fig. 2. Levels in columns labelled Oh and Clv are arbitrary but show the symmetry splitting of the levels in the different symmetries. Clearly the t,,-derived levels of the Mn(CO) fragment i.e. 1le and 2b2,hardly split in the Mn,(CO), molecule. The singly occu- pied HOMO of Mn(CO), the e,-derived 17q level forms a bonding (17a1)and anti- bonding combination (17bZ) in Mn,(CO)lo. Below the closely spaced set of d levels we find as in the mononuclear carbonyl~,~~ the predominantly CO 50 171 levels be- ginning at =-0.38 a.u.These have some 3d character in accordance with the Mn-CO 0 bonding. The 40 and 30 CO orbitals are found at = -0.5 and -1.0 BINUCLEAR METAL CARBONYL COMPLEXES 0 I I I 0.o I I -271‘ -0.1 12e3 17bz -0.2 a.u4 -0.3 +56 -10e -10e3 -0.4 I 1 I I1 I 1 I 1 -0.5 I 46 Mn-atom FIG.2.-HFS orbital energies of Mn(CO)5 Mnz(CO)loand CO. The first three columns show the splitting of the Mn atomic orbitals in different symmetries. TABLE2.-cALCULATED COMPOSITION (%) OF SOME Mn2(CO)loORBITALS Mnz orbital transf. to (C0)1 energy Mn(C0)5 transformation to Mn and CO orbitals orbital /a.u. orbitals 17bz -0.127 17a 66.9 Mn 44.6 CO, 8.2 CO, 47.2 19Ul 10.1 3d22 41.3 50 5.5 50 11.8 20~1 19.5 2n 36.5 17al -0.235 1701 96.1 Mn 57.9 CO, 2.6 CO, 39.5 3d2z 26.5 ln 6.3 4s 3.3 2n 35.4 4Pz 23.8 ~ lle3 -0.237 lle 98.8 Mn 65.9 CO, 15.4 CO, 18.7 3dxz,).2 65.1 2n 13.0 2n 15.7 ~ llel -0.250 lle 99.3 Mn 57.2 CO, 14.8 CO, 28.0 3dx2,y2 56.9 2n 12.0 2n 22.2 8ez -0.254 2bz 99.5 Mn 52.1 CO, 0 CO, 47.9 3dx?-y2,xy 52.1 In 8.0 2n 39.2 FIG.3.-(a) 17al Orbital of Mn(C0)5 in a plane containing Mn two equatorial and the axial CO.Contour values (a.u.) 0.00 fO.O1 10.02 f0.04 10.06 f0.08 hO.10 10.15 &0.20. Positive and zero contours solid lines; negative contours dashed lines. (6) The t2,-derived al orbital of the Fe(CO)3 fragment in the XZ plane. BINUCLEAR METAL CARBONYL COMPLEXES \ / FIG.4.-(a) Density difference between Mnz(CO)lo and two Mn(CO)5 fragments.(b)The Mn C and 0 atoms in the XZ plane. Contours (a) 0.00 10.005 10.01 10.02 f0.03 k0.04 h0.05 f0.075 fO.100; (b) see fig. 3(a). W. HEIJSER E. J. BAERENDS AND P. ROS a.u. respectively. The lowest virtual orbitals have mainly CO 2n character except for 17b2 of course. If we analyse both Mn,(CO), and Mn(CO) in terms of the Mn and CO orbitals the resulting populations turn out to be very similar so we may assume that the elec- tronic structure of the two Mn(CQ) fragments does not change much upon bond formation. This is strikingly confirmed by analysing the Mn2(CQ),o density and orbitals in terms of Mn(CO)5 orbitals (table 2). All doubly occupied MII(CO)~ orbitals remain doubly occupied in Mn2(CO)lo indicating that both the bonding and antibonding combinations are occupied.The 17a orbital is almost purely the bond- ing Combination of Mn(CQ)5 17a,orbitals. This fully confirms the qualitative picture of a single fragment-fragment bond. It is perhaps not completely justified to de- scribe this bond as Mn-Mn as the 17a orbital contains a significant percentage of equatorial CO character (39.5 % mostly 2n). The large CO 2n contribution is visual- ized in fig. 3(a) where the 17a1orbital of Mn(CO) is plotted in a plane containing the Mn atom and two equatorial and the axial CO groups. The rather extended charac- ter of the 17a orbital is also reflected in a relatively small increase in charge density along the Mn-Mn bond axis upon bond formation as is evident from a plot [fig.4(a)]of the difference between the density of Mn,(CO)10 and the sum of the densities of the two Mn(CO)5 fragments. We do not wish to conclude from the strong involve- ment of CO, 2n in the 17~2 orbital that the equatorial COs are semi-bridging. A density difference map with Mn C and 0 atoms subtracted from the Mn,(CO), density [fig. 4(b)]shows that the equatorial carbonyls differ very little from the axial carbonyls particularly when compared with truly bridging carbonyls as in Fe,(CO) (vide infra). We finally note that our calculations are in complete agreement with the qualitative treatment of Elian and including the Mn 3dZz 4pz hybridisation and the involvement of CO 2n, orbitals.5. QUANTITATIVE (HFS) DESCRIPTJON OF THE ELECTRONIC STRUCTURE OF Fe2(C0)9 We may analyse Fe,(CO) in terms of two Fe(CO) fragments and three bridging COs. The orbital energies of the important valence orbitals of Fe,(CO) and of its fragments are presented in fig. 5 which also shows the splitting of the levels in the respective symmetries. The levels shown are separated by a considerable gap from the CO 50 In derived set which comes below -0.34 a.u. The t,,-derived orbitals range from 17~;-1le”. It is important to realize that a22 “ t2g” orbitals are filled both the plus and minus combinations. In particular the (3dz2 + 3dz2) combination (17a;) and the (3dzz -3d22) combination (13~;)are closely spaced and both occupied (see table 3 for the composition of these levels).This is a rather striking difference with the Mn,(CO), case where the interaction between these two orbitals (17a and 17b2in D4J is the crucial factor in the explanation for the metal-metal bond. The direct Fe-Fe bond in the qualitative bonding is based on the same type of splitting as in Mnz(CO), and therefore disagrees with the present result. The difference in be- haviour of the dzz (or rather dz2-p2-2n hybrid) orbital in Mn,(CQ), and Fe,(CO) can be understood from the fact that in Mnz(CO), it is an e,-derived orbital separated by the ligand field splitting from the t2,-derived orbitals whereas in Fe,(CO) it is a t,,-like orbital. The relatively high-lying ey-type dz2 hybridises if allowed by symmetry con- BINUCLEAR METAL CARBONYL COMPLEXES 0,C -0.3 0 -. 0 -0.2 -0.3 FIG.5.-HFS orbital energies (valence levels) for Fe(CO)3 [Fe(C0)J2 Fe2(C0)9 and CO. The columns Fe(AT0M) and Fe(Oh)do not contain calculated values but only display the symmetry splitting of Fe AOs. siderably with the 4pz and also mixes strongly with the nearby equatorial CQ 271 orbitals [see fig. 3(a)]. A large overlap between such extended orbitals belonging to the two Mn(CO) fragments results. In contrast the low-lying t2,-derived 4 in Fe(CQ,)3 2 does not show much s,p hybridisation. Fig. 3(b)shows very clearly how heavily this orbital (as a “ tag” orbital) is involved in backbonding to the terminal carbonyls and how strikingly reduced its amplitude in the +z direction is compared with the Mn(CQ) orbital in fig.3(a). There is a next higher a orbital in the Fe(CO,) fragment mostly 4s and 4p with some dz2 character which is much more like the 17U1 in Mn(CO),. This is also evident from its strong stabilization in [Fe(C0,)J2 (see fig. 5). It is however not occupied and is mainly important as an acceptor orbital. The 16e’and 1le” are the plus and minus combinations of the remaining “ tag” orbitals which are largely 3dX2-,,zand 34 and thus have their largest amplitudes in planes perpendicu- lar to the Fe-Fe axis and parallel to the xy plane with the bridging carbonyls. They show the normal backbonding to terminal carbonyls and are virtually Fe-Fe non-bonding. If the two Fe(CO,) fragments are not kept together by a direct Fe-Fe bond the complex must derive its stability from the presence of the bridging carbonyls.This is indeed the case. In the hypothetical [Fe(CO,),] molecule the “ e ” orbitals will split up in a n bonding e’ and a n antibonding e” orbital. It is evident from fig. 5 that the e” is strongly stabilized by interaction with the e” orbital resulting from the 27~11orbitals of Cob(11 indicates parallel I_ perpendicular to the Fe-Fe axis). The W. HEJJSER E. J. BAERENDS AND P. ROS 221 TABLE3.-CALCULATED COMPOSITION (%) OF SOME Fe2(C0)9ORBITALS orbital Fe2(C0)9orbital energy/a.u. Fe cob and Cot/% 1712’ -0.048 Fe 16.7 Cob 36.8 cot 46.5 3dx~-y2,xy 9.2 50 9.2 2n 46.5 4Px 1 Y 6.3 2n-1 28.9 14a; -0.077 Fe 45.1 cob 23.3 cot 31.6 3dzz 38.6 2n-11 23.O 2n 31.6 12e” -0.166 Fe 54.6 cob 30.1 cot 15.3 3dxz,Yz 49.7 2n-11 26.0 50 6.5 2n 8.O 1 le” -0.201 Fe 67.0 cob 9.2 cot 23.8 3dx2-y2,xy 53.8 2n-II 6.2 2n 21.7 3dXZ,YZ 11.0 134 -0.206 Fe 66.3 cob 9.8 cot 23.9 3dzz 56.7 2n-11 6.5 2n 20.9 4Pz 12.4 16e’ -0.213 Fe 65.1 Cob 12.8 cot 22.1 3dx2-yz,xy 44.7 2Z-1 8.7 2n 19.6 3dXZ,YZ 19.7 174 -0.223 Fe 72.8 cob 4.2 cot 23.0 3dz 71.3 2n 19.0 e’ and a orbitals are destabilized by interaction with the 50 of cob reflecting the normal a-donation from cob to empty Fe 3d and 4s 4p orbitals.The three-centre Fe3d(eg)-2n-II-Fe3d(eg) bond we have found is analogous to the one proposed in Braterman’s qualitative model the important difference being the complete lack of 4s and 4p contribution in our 12e” orbital.Instead of a d2sp3 hybrid it is an essentially pure 3d orbital of e character in the local octahedral en- vironment of Fe that interacts with 2n-11. It is interesting to see whether density difference maps give a picture of the bonding in Fe2(C0)9 which is in agreement with our conclusion. Fig. 6(a)shows the difference in the XZ plane (containing the iron atoms one bridging and two terminal carbonyls) between Fe2(C0)9 and the Fe atoms (spherically symmetric atomic density of configur- ation [Ar](3~i)~(4s)~) and the CO molecules. Fig. 6(b) shows the same density differ- ence in the XY plane containing the three bridging carbonyls. In fig. 6(a) the very large cob 2n-11 population is particularly conspicuous in agreement with the special role this orbital plays in the bonding.The negative regions around the C-0 bond axes [see also fig. 6(b)]reflect the a-donation. The terminal carbonyls show a “ normal ” pattern as in Mn,(CO)lo or Cr(CO),.51 We note that along the Fe-Fe bond axis there is a negative density difference. This alone is not of course sufficient evidence for the absence of a direct Fe-Fe bond but it stresses the difference with the Mn2(CO)lo case. We finally note that the BIN UCLEA R METAL CARBON YL C0MPLEX E S FIG.6.-Density difference between Fe2(C0)9 and the Fe atoms and CO molecules. Contour values; see fig. 4(a). (a)XZ plane (b) XY plane (with three bridging COs). W. HEIJSER E. J. BAERENDS AND P. ROS possibility that there is not a direct Fe-Fe bond in Fe,(CO) has been recognised by Hoffmann and Excellent discussions of the electronic structure of the M(CO) fragment may be found in ref.(47). 6. QUANTITATIVE (HFS) DESCRIPTION OF THE ELECTRONIC STRUCTURE OF CO,(CO) Fig. 7 shows the orbital level diagram of Cs2(C0) and its fragments. For future reference we note that an index 1 on the irreducible representation symbol for an orbital means symmetric with respect to the XY plane of the bridging carbonyls FIG.7.-HFS orbital energies (valence levels) for CO(CO)~ CO,(CO)~ [CO(CO)~]~ and CO. First two columns show splitting of Co AOs. 2 antisymmetric. But a and b are symmetric with respect to XZ a and bl anti-symmetric. The “ tZg” orbitals ranging from 27a to 23b, are completely analogous to those in Fe,(CO) (see table 4 for population analysis).Again the plus and minus combination of the predominantly dz2 orbitals 28a and 23b2,are close in energy and both occupied. All “ t2,” orbitals are involved in backbonding to the terminal carbonyls. The net effect of the whole “ t2g’’set with respect to the Co(CO,),- Co(CO,) interaction is at best non-bonding. The “ e ” orbitals show an interesting difference from the Fe,(CO) case. The e” orbitals of the D,,symmetry are now split into an a and a b orbital (I 3a2and 246,). Just as in Fe,(CO) these orbitals are stabilized by interaction with the 271-11 orbitals. The 6 orbital is symmetric with respect to the XZ-plane and has its largest density in 224 BINUCLEAR METAL CARBONYL COMPLEXES TABLE4.-cALCULATED COMPOSITION OF SOME cO2(co)~ORBITALS orbital orbital energy Co cob and Cot/% /a.u.30al -0.114 CO 23.2 cob 7.6 cot 69.2 3dx2-y2 9.4 {: 3dxz 11.1 2n-1 7.6 2562 -0.128 CO 36.0 cob 25.8 cot 38.2 3dz2 26.1 2n-11 25.5 2n 37.8 4s 2.6 4Pz 5.7 24b2 -0.228 CO 61.8 cob 17.3 cot 20.9 3dx2 46.1 2n-11 13.2 50 11.0 4Px 7.3 2n 7.5 1 3a2 -0.235 CO 40.6 cob 42.9 cot 16.5 3dxy 3dyz 20.4 15.3 1n-11 2n-11 12.2 30.8 5a 2n 8.2 7.0 29al -0.254 CO 59.1 cob 0.2 cot 40.7 3dxz-yz 23.8 50 6.9 3dxz 9.4 In 11.4 4Px 7.3 2n 22.3 4Pz 13.0 2362 -0.263 CO 73.1 cob 1.2 cot 25.7 3dzz 50.1 In 8.4 3dX2-,z 14.0 2n 17.0 4Pz 10.3 ~ ~ ~~ 1 2a2 -0.272 CO 80.0 cob 0.4 cot 19.6 3dXY 29.6 ln 6.5 3dYZ 49.6 2n 12.5 17bl -0.272 CO 69.1 cob 6.8 cot 24.1 3dxy 43.0 In 8.1 34% 22.8 2rr 15.8 2262 -0.281 CO 76.6 cob 4.3 cot 19.1 3dzz 15.3 In 6.5 3dXz-yz 36.5 2n 12.2 3dxz 23.1 28al -0.282 CO 77.7 cob 8.9 cot 13.4 3dzz 65.6 2n 9.4 4Px 5.8 27al -0.293 CO 65.8 cob 20.4 cot 13.8 3dxz-zY 28.0 In-1 10.6 2n 8.6 3dx.z 32.5 2~-I 9.5 W.HEIJSER E. J. BAERENDS AND P. ROS the direction of the empty bridging site (which is on the -x axis). It therefore inter- acts somewhat less with the 271-11 of the bridging carbonyls as is evident from the smal- ler 271-11 population in 246 than in 13a (see table 4). Fig. S(a) and (b)contain plots of the 13a2and 24b2 orbitals in the DIAG(ona1) plane (DIAG is a plane containing the cobalt atoms and a bridging carbonyl).Both orbitals show the typical bridge bond through the 271-11 the 24b2 being less than the 13a2. The important difference from Fe,(C0)9 is in the behaviour of the a and b,orbitals corresponding to the e' set in Fe,(C0)9. These orbitals are symmetric with respect to the XY-plane a is also symmetric with respect to the XZ plane but b is not. In Fe,(CO) the e' set was destabilized mostly by interaction with the three low lying cob 50 orbitals (the a-donation). Here the b is similarly destabilized but the a, having its largest density in the direction of the missing carbonyl is not. It is found as 29a, below the 24b2and 1 3a corresponding to the e" set in Fe2(C0)+ This orbital can be considered as a Co-Co bent bonding orbital as is clearly demonstrated in fig.8(d) where the 29a is plotted in the XZ plane. It is however not possible to conclude that there is a Co-Co bent bond as the 24b2orbital is the minus combina- tion of the same " e " type orbitals (in the local Co octahedral environments) which form the 29~2,as a plus combination. The 24b2 could contribute as we have seen to the bridge bond through the remaining two carbonyls but it is still the antibonding partner of 29a,. This is demonstrated by the plot of 24b2in the XZ plane [fig. S(c)]. The question whether there is some net bent bonding interaction is a subtle one as of course the 3d and 4p contributions to 29a and 24b2 are not identical. It is interesting in this respect to consider density difference maps. Fig. 9 shows the calculated density difference between Co,(CO) and the CO molecules and Co atoms (configuration [Ar](3~!)~(4s),)in the XZ plane (a) XY plane (b) and DIAG plane (c).Again very striking is the large cob 2rn-11 population [fig. 9(c)]. Compari-son of fig. 9(b) with the corresponding Fe,(C0)9 plot shows an increased 271-1 population. The terminal carbonyls are entirely normal. The metal-metal region is particularly interesting. Just as in Fe,(C0)9 we do not find a density increase along the metal-metal axis. The positive density difference in the bent bond region is so small [between the zero and +0.005 e (a.~.)-~ contours] that we can conclude that a bent bond is not observed in the density difference plots. We finally note that related studies on Co,(CO) and the isoelectronic Fe,(CO)i- have been made by Hoffmann and c~workers.~~~~~ Although these authors did not specifically address the question of straight as compared with bent metal-metal bonds and although there are significant differences in the details of level orderings we may infer from their data that there would be agreement on the essential points.These authors refer to a bent bond in the bridged isomer of Co2(CO), but it is clear from their orbital energy diagram47b that they do not only occupy the bent bonding a orbital (i.e. 29a,) but also the antibonding b partner (ie. 2432). We also observe that the analogy between bridged Co,(CO) and other bridged binuclear systems of the general formula M2(C0)6X2,57 with X2= HC-CH S, [PR,] or [SMe], which has been used to carry over conclusions for CO,(CO)~ to these does not really hold.In most of these X2bridges there is a low lying orbital of b sym-metry which destabilizes the 24b2orbital so that it can become the LUMO if M=Fe. The 29a then provides the bent metal-metal bond in agreement with the conclusions of Teo et aLS7 Such a b2orbital is for instance the occupied ln-ji orbital in acetylene [see ref. (47b)l. In (CO,) there is indeed a b combination of the ln-11 orbitals but it is too low in energy and too strongly localized on the 0 atom to have an appreciable effect on 24b2. BINUCLEAR METAL CARBONYL COMPLEXES I. I W. HEIJSER E. J. BAERENDS AND P. ROS FIG.8.-Plots of valence orbitals of CO,(CO)~. Contours see fig. 3. (a)13a2 in the DIAG plane through the two Co atoms and a bridging CO; (6) 2462 in the DIAG plane; (c)246 in the XZ ulane (d) 29a in the XZ olane.!L8 BINUCLEAR METAL CARBONYL COMPLEXES A W. HEIJSER E. J. BAERENDS AND P. ROS FIG.9.-Density difference between CO~(CO)~ and the Co atoms and CO molecules. Contours see fig. 4(a). (a) XZ plane; (b) XY plane containing the bridging carbonyls (the +sign in the centre indicates the Co-Co axis); (c)DIAG-plane containing the two Co atoms and a bridging C atom. 7. COMPARISON OF THEORETICAL AND EXPERIMENTAL P.E.S. U.V.V. I.R. AND RAMAN DATA A first test on the calculated level schemes as far as the occupied orbitals are concerned can be done by comparing with photoelectron spectra which have been published for Mn,(CO), in the gas-phase'." and for condensed Fe,(CO) and Co (CO)s.ll We have calculated the ionisation potentials with Slater's transition-state pr~cedure,~' which includes relaxation of the ion just as a ASCF calculation in Hartree- Fock theory.The CO 30 4aand 50 + In. bands are completely analogous to those in mononuclear carbonyls and have been studied before.56 In agreement with ex- periment we find a band of metal d i.p.s well separated from the CO bands. The metal d i.p.s are given in table 6. For Mn,(CO),o we compare them with the available gas-phase data' and with some semi-empirical calculations. The agreement with experiment is not sufficient to unambiguously assign the three experimental peaks. In the case of Fe,(CO) and Co,(CO) the experimental results give a band around 7.6 (half-width w1.5 eV) for condensed Co,(CO) and the same for condensed Fe,(CO), but with a shoulder at 6.5 eV.This last result agrees with the calculated larger separa- tion between the HOMO (12 e")and the other d orbitals in Fe,(CO) than in Co,(CO),. The condensed phase results have to be corrected with +(0.6 -1.4) eV for polarisa- tion effects in order to make comparison with our calculations possible. Information on the virtual spectrum may be obtained from U.V.V. spectra. The experimental spectrum of Mn2(CO),013 shows an intense band at 3.69 eV which has been assigned as the 17a + 17b2(a -+a*)transition and a shoulder at 3.31 eV which BINUCLEAR METAL CARBONYL COMPLEXES TABLE 5.-EXPERIMENTAL (GAS-PHASE) AND CALCULATED IONISATION POTENTIALS (IN ev) semi-empirical data orbital exp.' this work SCCC44 EH43 EH13 1 7al 8.02 8.80 9.65 7.92 8.10 1 le3 8.35 8.84 9.66 8.29 8.34 'Ie1}8e2 9.03 9.169.37 10.03 9.95 8.42 8.41 8.60 8.26 orbital calc.i.p. orbital 12e" 6.91 8.77 1 le" 7.80 8.85 13a; 7.95 9.32 1612' 8.13 9.54 1 7a; 8.48 9.82 9.82 10.08 10.09 10.41 TABLE 6.-EXPERIMENTAL AND CALCULATED ELECTRONIC TRANSITIONS IN c02(c0)~ e~perimental'~ calculated v/cm -lev assignment /eV assignment 26 460 3.28 dn +o* 2.81 2432 -+ 2562 (29 000) (3.60) 3.60 29Ui-f 2532 (32 100) (3.98) 35 460 4.40 t3+a" 4.2 28ul +2562 TABLE7.--CCT STRETCH FREQUENCIES AND 2n GROSS ORBITAL POPULATIONS FOR BINUCLEAR METAL CARBONYL COMPLEXES.THEEXPERIMENTAL DATA ARE WEIGHTED AVERAGES OF THE OBSERVED STRETCH FREQUENCIES. v,,/cm-l 2n-population CO 2143.2 0.000 Fe2(CO)' terminal 2047.3 0.523 bridge 1853.0 0.691 CO~(CO)~ terminal 2043.6 0.468 bridge 1857.0 0.782 ~~ ~~~ ~ ~ ~ ~ a Weighted average of the axial'and equatorial carbonyls. W. HEIJSER E. J. BAERENDS AND P. ROS 231 is supposed to be the 1 le -+17b2 transition (dn -+a*). We have calculated the 17a -f 17b2 excitation at 3.0 eV and the 1 le -+ 17b2 at 0.15 eV lower. The M -+ L charge transfer transitions are not well resolved but come above 4 eV. There is no doubt about this assignment the a -+o*excitation being used extensively for photo- lysis of M2(C0)10 systems.59 The electronic spectrum of Co,(CO) in solution has been reported at 298 and 50 K.14 At room temperature the bridged and non-bridged isomers are believed to be in equilibrium with about equal concentrations.At 50 K the equilibrium has shifted completely to the bridged isomer we are studying. From the changes in the spectrum upon cooling the band at 3.54 eV(28 570 crn-l) has been assigned to a a-+a* transition in the non-bridged isomer and the band at 4.40 eV (35 460 cm-') to a CT -+a*transition in the bridged isomer. The shift to higher energy in the bridged isomer has been considered to be in accordance with the smaller Co-Co bond length in this isomer. We do not agree however as is clear from the foregoing with the implicit assumption that in both isomers there is a large spacing between a bonding occupied o(essentially dz2 + d,~)and its antibonding partner a*(essentially dz2 -d,z).This is probably true for the non-bridged isomer in which the single Co-CO bond resembles the Mn-Mn bond in Mn,(CQ), [cJ the treatment of the C30M(CQ)4 fragment in ref. (47a)l. In the bridged isomer however both these a and a* levels have been found to be occupied (28a1 and 23b2). In view of the multitude of excitations that are theoretically possible it is difficult 21 00 2000 c I 5 \ ;r 1900 1800 0.4 0.5 Q.6 0.7 Q.8 p2 TI-FIG.10.-CO 2n gross orbital populations as a function of CO stretching frequency in a number of mononuclear and binuclear metal carbonyi complexes. The solid line has been obtained for the mononuclear carbonyl~.~~ 0,mononuclear metal carbonyls; 56 0 Mn2(CQ)10; A Fe2(CQ)9; x ,C02(CO)*.BINUCLEAR METAL CARBONYL COMPLEXES to assign the observed maxima at 26 460 and 35 460 cm-l. The first may be the 24b2-+ 25b2. If we denote the LUMO as D* which might be defended in view of its still significant amount of dzz -dz2 character (although is it bridge bonding through the 271-I/!) then 24b2 -+ 25b2 is indeed a dn -+ o* transition. A transition of D -+ o* type is then 28a1 -* 256,. It is calculated as 4.2 eV (33 800 cm-'). The resolution of the experimental spectrum is not sufficient to allow more detailed assignments. Let us finally consider the i.r. and Raman data. It is interesting to verify whether the good correlation found by Baerends and RosS6 between the experimental CO stretch vibration frequencies and the 2n gross orbital populations still holds for bi- nuclear metal carbonyls and in particular whether it is possible to differentiate between terminal and bridging carbonyls.In Mn2(CO)10 it is not possible to separate axial and equatorial stretching vibrations because of strong mixing but Bor and Sbrignadel10~~ find the axial and equatorial C-0 force constants to be practically identical (,tax = 16.3 and k, = 16.5 mdyn A-l). Our calculated 27t populations also show only small differences 0.596 (ax) and 0.569 (eq) in accordance with our previ- ous conclusion that the equatorial carbonyls do not have a bridging function. Bridg-ing carbonyls give stretching frequencies of w1850 cm-I and have much higher 271 populations (0.69-0.78).In table 7 we collect the relevant data and in fig. 10 we plot the results for the binuclear metal carbonyls with respect to the curve we found for mononuclear carbonyls. The terminal carbonyls have populations in the range of neutral mononuclear ~arbonyls,~~ but the bridging carbonyls have populations approaching those of heavily backdonating metals like Fe d10 in Fe(CO)i-. Both the terminal and bridging carbonyls fit well into the correlation found for the mono- nuclear carbonyls. 8. DISCUSSION It is often stated that organometallic complexes frequently obey the EAN rule carbonyl complexes in perhaps 99% of all cases. There are nevertheless many " CO-deficient " polynuclear complexes in which the right electron number can only be obtained by postulating localised electron-pair M-M bonds which contribute additional electrons to the electron count of both metals.Fe,(CO) is an illustration for one Fe atom there are apart from its own 8 elec-trons only 9 carbonyl electrons making 17 in total. An electron pair bond between the Fe atoms brings the electron count to the required 18. This procedure can be followed in the known M3and M4carbonyl clusters where one postulates edge bonds in the metal triangles and tetrahedra but it breaks down in M6clusters.60*61Accord-ing to our results the rule is not even applicable to binuclear carbonyl clusters. This is somewhat unexpected. Still the 18 electron rule has not been observed empirically by counting the numbers of carbonyls and known metal-metal bonds but the latter were hypothetical introduced in order to maintain the 18 electron hypothesis.If we do not accept the 18 electron rule (plus a M-M bond) can we still (or for the first time) understand why there are 9 carbonyls in the Fe dimer and only 8 in the Co dimer? From our level scheme (fig. 5) it is clear that a hypothetical Co,(CO) molecule would require two electrons in the high-lying 14a; orbital [the LUMO in Fe,(CO),]. It is evident from our discussion of Co,(CO) how this unfavourable situ- ation is avoided. By dismissing one of the bridging carbonyls the plus combination of d orbitals pointing to the vacated site is no longer destabilized by the filled CO 50 but can descend (as 29a,) to the occupied levels accommodating the additional pair of electrons.As a corollary one would also expect the isoelectronic Fe2(CO);- to be stable. This is perfectly in order Fe2(CO);- is indeed well known.62 233 W. HEIJSER E. J. BAERENDS AND P ROS It appears from our results that simple molecular orbital energy diagrams are a powerful means of analysing and explaining bi- and poly-nuclear metal carbonyl stoichiometries. A case in point is the wide occurrence of clusters with the same number of electrons and the same geometry but with different metals [as indeed CO,(CO)~and Fe,(CO)i-]. As an example we mention the M2(CO)lo type with M = Mn Tc or Re to which also belong M2(C0)1; with M = Cr Mo W and MM’(C0)G with M = Cr Mo W M’ = Mn Re. Similar observations have been made for the larger clusters and can be understood immediately from a common “ stable ” orbital level pattern with an appreciable HQMO-LUMO separation as observed in the three examples treated in this paper.In order to understand MO level patterns and to build them up qualitatively it is essential to realise that it is not sufficient to recognise the directional properties of the metal d levels in a metal carbonyl fragment but it is necessary to be aware of the ligand field splitting in the d set which is primarily due to the extent to which a d orbital is destabilised by CO 50 orbitals or stabilised by 2n orbitals. We have seen the importance of this in the C3,M(CO)3 fragment where the dz2 is to be considered as a primarily backbonding orbital inactive with respect to metal-metal bonding.This has also been observed by Hoffmann and for the M(CO) and the isolobal MCp fragments where it is important in understanding the electronic structure of M4(CO)12 and M,Cp clusters. Although simple qualitative MQ considerations guided by some calculations in order to assess the relative importance of possible contributing orbitals may be quite helpful in understanding carbonyl clusters they have obvious limitations. In the case of M3(C0)12 clusters with M = Fe Qs Ru the structure of Fe,(CO), is different from the other two the latter having no bridging carbonyls. Both types of structure can nevertheless be rationalized on the basis of qualitative MO considerations. 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