摘要:

Electronic Structure of Heavy Metal Diatomics from urb Initio Relativistic Effective Core Potential Studies BY HAROLD BASCH Department of Chemistry Bar Ilan University Ramat Gan Israel Received 31st July 1979 Calculated electronic structure results and ideas for the metal-metal bonded systems Ptz Pd, Cu, Ag, Au, AgAu Ni2C2H4 and Ni (n = 1-6) are discussed. In this work ab initio effective core potentials have been used to replace the chemically inactive atomic core electrons including the dominant relativistic effects for the heavier metals. The fact that a special Faraday Symposium is devoted to diatomic metals and metal- lic clusters is the result of the increased interest and activity in the area of metal-metal bonding that has developed especially over the past several years.Although once considered as belonging within the exclusive domain of the solid state physicist the focus of attention on the detailed electronic structural properties of a finite group of metal atoms and its interaction with other atoms and molecules has brought this area within reach of recently developed quantum chemical techniques. Small metal particles typically have enhanced catalytic activity.' A well known example is in silver halide photography where small silver atom clusters are believed to be the active agents in the development of the latent image by the developer.2 An understanding of the metal-metal bond is also of importance for binuclear and poly- nuclear metal complexes and their photochemical behavio~r.~~~ The role of the metal-metal bond in heterogeneous catalysis and its precursor adsorbate surface chemisorption step also awaits elucidation.In this paper we will present a survey of calculated electronic structure results and ideas on metal-metal bonded systems obtained using ab initio effective core poten- tials (ECPs) to replace the chemically inactive atomic core electrons including rela- tivistic effects for the heavier atom^.^^^ The use of ECPs substantially reduces the dimension of the problem to be solved in the basis set expansion self-consistent field (SCF) method used here by allowing all atoms in the same group of the periodic table to be directly treated as isoelectronic systems. This approach is in basic accord with the wide body of chemical experience and knowledge embodied in the periodic table.EFFECTIVE CORE POTENTIAL The atomic effective core potentials are obtained by first transforming the canoni- cal Hartree-Fock atomic orbitals for a given atomic state-configuration into nodeless pseudo-valence orbitals which are then used to numerically invert the atomic Hartree- Fock equations to obtain the ab initio core potential. For more detailed descriptions of these methods recently published papers in this area should be cons~lted.~-~ The atomic ECPs are then used directly in molecular electronic structure calcula- HEAVY METAL DIATOMICS tions on the valence electrons (VEs) only. For the purpose of calculating core-core repulsion energies the core electrons on each atom are treated as point charges which reduces the actual atomic nuclear charge to the number of valence electrons.Aside from the well-understood frozen core approximation inherent in this pro- cedure a number of additional questions can be raised about the method of generation and use of these ECPs in a molecular environment. (1) How sensitive are the obtained potentials to the atomic state-configuration used to generate them ? How transfer- able is a given atom potential among different charge states (anionic and cationic) of the atom in the molecule? (2) What is the proper method of enforcing the correct long range behaviour of the ECPs? Recent w0rk~9~' has shown that the conventional methods5** tend to introduce spurious long range tails into the potentials.Although ad hoc procedures have been proposed9*'' for eliminating these tails in the atomic case the problem involves a region of space that is relatively unimportant for the atom but is of critical importance in a molecular environment. Therefore a purely atomic criterion for enforcing the proper long range behaviour may be inadequate. (3) When do core-core repulsions as a function of internuclear distance become important to the determination of the potential energy curve? Also in this regard how important is the incorporated non-orthogonality between a given core and other centre valence electrons? (4) What basis set dependence and corresponding accuracy is to be expected from using the ECPs? Although it might be possible to give formal answers to all the above posed questions the best response probably lies in testing the generated ECPs in a molecular environment by comparison with all electron (AE) and ultimately with experimental results.Such a comparison is shown in tables 1 and 2 for the square planar CuC1,- complex. In these tables the results using three types of ab initio single configuration TABLE EQUILIBRIUMBOND DISTANCE (Re) AND HARMONIC FORCE CONSTANT 1 .-CALCULATED (k) FOR SQUARE PLANAR CuClf--~~ ~ ~~ system state core basis Re/A k1a.u." CUCl -'Alg AE AE 2.22 1.467 ECP AE 2.20 1.130 ECP ECP 2.23 1.214 CUCI$ -2B1 AE AE 2.42 1.421 ECP AE 2.43 1.236 ECP ECP 2.44 1.266 From a fit of energy = aR2 + bR + c with k = 2a. TABLE2.-RELATIVE ELECTRONIC STATE ENERGIES FOR SQUARE PLANAR CUc1,"-(IN ev) ~~~~~~ ~ ~ ~ system state location of energy d-hole AE core ECP core ECP core Demuynck et aLi2 AE basis AE basis ECP Basis (BS 11) CUClz -2B1g 3dx2-y2 0 0 0 0 2Alg 3dz2 1.29 1.13 1.16 1.30 2B2g 3dXY 0.96 0.95 0.97 1 .oo 'Eg 3dXZ.YZ 1.19 1.11 1.13 1.23 -2.66 2.61 2.62 -CUCI$ -'A H.BASCH 151 SCF calculations are displayed. As the reference calculation the completely all electron treatment in both the basis set size and representation of the core electrons uses 77 basis functions contracted from 190 Gaussian primitives."*''* Two types of core ECP calculations are shown for comparison with the AE result; one using the complete AE basis described above and the second using the much more compact VE only basis which consists of only 100 primitive Gaussians contracted to 53 basis functions.13t Table 1 shows the SCF calculated equilibrium Cu-C1 bond distances (Re)and har- monic force constants (k) for the square planar CuCli- and CuC1,- complexes in their respective ground states.The variation in the calculated Re using the same basis set but different ways of treating the core is no larger than 0.02 A and switching to the smaller VE basis does not increase the error in Re. The use of the AE basis in a VE calculation is of course grossly inefficient and is just intended to give a basis for comparison between the AE and ECP cores using the same basis set. Table 2 gives the calculated relative energy ordering the d-holes states and lowest ionization energy for the square planar CuCli- ion.The absolute error in substitut- ing an ECP for explicit treatment of the core electrons is at most ~0.16 eV in the rela- tive energies and again does not grow by introducing the more compact VE basis. In fact in general the ECP (basis)/ECP(core) results are closer to the AE/VE numbers than are the mixed AE/ECP values which probably shows the importance of matching the basis set to the method. In summary these two tables show that the proper use of ab initio ECPs in place of core electrons can be expected to lead to calculated quantities which are very close to the corresponding AE results. RELATIVISTIC EFFECTS The use of ECPs would thus seem to open all of the periodic table to ab initio electronic structure calculation by eliminating the need to represent the core electrons by expansion basis functions.However relativistic (R) effects grow increasingly im- portant as the atomic number (2)increases. Such effects as they modify the valence electron wave functions and energies would be expected to contribute to the differ- ences in chemical and physical behaviour that is observed between compounds of atoms in the same column but different rows of the periodic table.14 Thus the in- creasing usefulness of the ECP method with increasing Z coincides with the increasing importance of relativistic effects. Naturally this coincidence of trends has pointed the way to the development of relativistic ECP rnethod~.~*'~~'~ The relativistic ECPs are generally generated as /-dependent potentials (thereby neglecting spin-orbit coupling) for use in conventional (non-relativistic) molecular SCF calculations.The core potentials include the important direct core relativistic effects and the valence electron orbitals therefore show quantitatively all of the spatial * For the copper atom AE basis the los basis primitives of Ross et al." were augmented by the two outermost s-type Gaussians (with exponents 0.32 and 0.08) suggested by Demuynck et al. [ref. (12)]. Analogously to the 4"et of Roos et al. [ref. (ll)] was added a single set of d orbitals with exponent 0.2. Contraction coefficients were taken from atom SCF calculations on the neutral Cu(*D)state. Thus the final basis is (12s8p5d)contracted to [5s44p2d]. The AE chlorine atom basis was obtained by optimizing the exponents and contraction coefficients of a (10s7p)/[3s3p]basis for the ground 'P state except for the outermost p-type primitive which was kept with a fixed primitive exponent of 0.1.t The ECPs for the C1 and Cu atoms are from ref. (10) and (13) respectively. The VE basis for Cu uses (a)the 4 smallest s-type exponents of the AE basis contracted [3'] from a VE atom calculation (6) the 2 smallest p-type exponents from the AE basis uncontracted and (c) the (5d)/[2d] basis from the AE calculations. HEAVY METAL DIATOMICS scaling effects (contraction or expansion) and electron binding energy shifts (to higher or lower energies) obtained from the AE relativistic Dirac-Fock calculation^.^^,^^ This method is expected to be successful because direct relativistic effects on the valence electrons in the valence region seem to be small.A striking example of the importance of including relativistic effects in heavy atom compounds is the PtH diatomic mo1ecule6"8 shown in table 3. Experimentally the TABLE 3.4ALCULATED AND EXPERIMENTAL SPECTROSCOPIC PROPERTIES OF PtH" method state RelA DJkcal mol-I coe/crn-' NR 2A 1.76 23.0 1233 zc 1.52 38.1 1758 R 2A 1.47 (1.49) 65.0 (61.8) 2260 (2289) 2c 1.46 (1.47) 59.3 (55.8) 2257 (2288) experimentb zA 1.53 2377 The wave functions are optimum double configuration (bonding pair correlated) with the ECP on the Pt atom expanded through 1 = 2 except for the values in parenthesis which use the Pt atom ECP expanded through I = 3.R. Scullman Arkiu Fys. 1965,28,255; B. Kaving and R. Scullman Physica Scripta 1974 9 33. ground state of PtH is a 2A52. Using a non-relativistic (NR) ECP for the Pt atom predicts a 2C ground state. On the other hand using the R core potential the proper 2A ground state is obtained along with good agreement with experiment for Re and the harmonic stretching frequency me. This substantial difference between the NR and R PtH results can be traced directly to the corresponding errors in the calculated NR energies of the Pt atom shown in table 4. In contrast to the experimentally found and R calculated (J-averaged) TABLE 4.-RELATIVE ENERGIES OF THE PLATINUM ATOM ELECTRONIC STATES (IN ev) configuration state experimental" Dirac-Fockb Hartree-Fock" (J-averaged) (J-averaged) 5d96s1 3D 0 0 0 5d'O 'S 0.51 1.12 -1.41 5ds6s2 3F 0.67 0.46 3.28 a C.E. Moore Atomic Energy Levels vol. 111 NBS Circular 467 (1971). J. P. Desclaux Comp. Phys. Comm. 1975,9 31. C. Froese Comp. Phys. Comm. 1972,4 107. 5d96s1(30) ground state the NR Hartree-Fock method predicts 5d10 (IS)to be the ground state-configuration of the Pt atom. As has been argued20 the 5d'O (IS) dissociation limit energetically favours the 2C state over the 'A state in PtH and there- fore the spurious stability of the Pt atom 'S state in the NR approximation gives % as the ground state of PtH. The bonding description of the Ni group monohydrides (MH) shows a competition between the metal nd and (n + 1)s orbitals as to which is the primary metal bonding orbital.For Ni the M-H bond is formed using primarily the metal 4s orbital for Pt it is essentially the 5d orbital and in palladium the bonding is mixed 4d/5s.19*20 It is probably due to this competition that the relativistic effects are so important for the heavier metals since they stabilize the (n + 1)s and destabilize the nd electrons H. BASCH 153 relative to the NR approximation. Thus for the bare metal diatomics and clusters where the metal atoms are in formally zero oxidation states relativistic effects will generally have to be taken into account for an accurate description of the molecular systems. This same nd/(n +-1)scompetition has been found in the Ni, Pd and Pt2 series” except that here the transition to significant nd orbital participation in the bond occurs between Pd and Pt rather than between Ni and Pd as in the case of the corresponding metal hydrides.This difference in orbital description of the M-H and M-M bonds is also apparent from the photoemission energy distribution and difference spectra of Demuth,’ for clean metals and hydrogen chemisorbed on metal surfaces. Thus the photoemission energy distribution curves for the clean metal (1 11) surface show great similarity between nickel and palladium. On the other hand the photoemission difference spectra between the hydrogen saturated and clean metal surfaces are con- gruent between the palladium and platinum metal curves and differ significantly from the H,/Ni difference spectrum. These experimental results can be taken as supporting the metal-metal and metal-hydrogen bonding picture obtained for the diatomic molecules from ab initio electronic structure calculations and suggest the possible role to be played by diatomics as models for the larger systems.BARE METAL DIATOMICS AND BIMETALLICS Recent ab initio results on the metal diatomics Ni2,22-26 Au,,,’ Zn,29 and Cu228930 have been reported. The studies on Ni, which are the most extensive are hampered by a scarcity of experimental information with which to compare calculated values. In addition the complex maze of densely packed electronic energy levels for this open d-shell transition metal diatomic defies the best of efforts to determine even the electronic ground state. A complicating factor is the importance of the metal atom states to the accurate determination of the diatomic molecular states., Thus intra- atomic correlation energy is found to be an important factor in the energetics of interatomic metal-metal interactions.This complication essentially rules out the possibility of using the Hartree-Fock method straightforwardly to obtain quantitative results for these systems. The group IB metals (Cu Ag and Au) diatomics with their closed shell dt0con-figuration for the ground-state atom are reasonably well characterized experimentally and have well-defined electronic ground states. It is also expected that intra-atomic correlation effects will be less important to the diatomic molecule states since the importance of the nd orbital in the bonding description is minimal for all these atoms.Also the Cu and Ag atom diatomics are still sufficiently small that they can also be handled by (NR) all electron techniques. In addition the question of whether Ag has to be treated relativistically or not can be addressed. Thus the series Cu, Ag, and Au2allows a comparison of AE with ECP methods and R with NK core potentials a study of the basis set dependence of results and a look at the importance of con- figuration interaction (CI). Such a comparison is shown in table 5 where the basis set labelling is explained in table 6. The ODC (optimal double configuration) wave functions are of the form (omitting core orbitals) to allow for proper dissociation to the ground state atoms. Further details of the HEAVY METAL DIATOMICS TABLE 5.-RESULTS OF SCF AND CI CALCULATIQNS ON CUz Agz AU AND AgAu molecule R/NR core basisa calculation Re/A De/eV w,/cm-l CUZ NR AE 52F ODC 2.44 1.16 338 NR ECP 34F ODC 2.49 0.76 282 NR ECP 34F CI 2.33 1.30 340 Agz NR NR experimentalb AE ECP 72F 34F ODC ODC 2.22 2.84 2.89 2.05 0.76 0.51 269 21 8 164 NR ECP 34F CI 2.73 0.95 226 R ECP 34F ODC 2.76 0.61 222 R EGP 34F CI 2.62 1.12 242 R ECP 48F ODC 2.73 0.65 21 3 R ECP 52F ODC 2.75 0.63 219 R ECP 54F ODC 2.75 0.63 21 7 AU2 R experimentalb ECP 34F ODC 2.5 2.65 1.68 0.85 207 236 R ECP 34F CI 2.60 1.34 166 AgAu R experimentalb ECP 40F ODC 2.47 2.65 2.34 0.90 191 266 See table 6.Spectroscopic Constants for Selected Homonuclear Diatomic Molecules ed. S. N.Suchard and J. E. Melzer (Aerospace Corporation El Segundo California 1976). TABLE 6.-BASIS SET DESCRIPTION core label primitives" basis functions ~~ ~~~~ AE 52F (1 2S7p5d) [5'3 p2d] 72F (19'1lPSd) [6"4P3d] ECP 34F (3'lPNd) [2"1 p2a1 40F (3s2pNd) [2S2P2d] 48F (3S3P5d) [3 3 p2d] 52F (3'3P5d) [2s2p 3 dl 54F (3S2p5dl [2"1 P2d1 f] f "ForCuandAgN= 5andforAuN=4. potentials and basis sets will be published el~ewhere.~',~~* The CI calculations include energy-~elected~~ single and double excitations from all the orbitals in the 2 parent configurations in (1) into the /120, 2a,} 3a, 3a,,2n and 27tgmolecular orbitals. In table 5 there are sets of corresponding AE and VE calculations (NR) for both Cu and Ag,. Interestingly enough the results are very similar for these two dia- tomics.Thus it appears that the use of an ECP for these systems consistently causes the equilibrium M-M bond length to be overestimated by ~0.05A the bonding energy (D,)underestimated by z 33% and co to be underestimated by z 33%; all * The details of the calculations are as follows The AE basis for the Cu atom is similar to the one described for the CuClz- calculations except that because of the zero metal atom oxidation state the Sd set and 4s orbital primitives (Cu 'Sstate) were taken from Wa~hters.~' The basis set for the NR silver atom was contracted optimized specially for this work. The NR and R silver atom ECPs as well as the R gold atom ECP were generated as described previou~ly,~~~*~~,'~ with the potential expanded through I = 3.The basis sets for these atoms were taken from analytic fits to the numeric pseudo-valence orbitals and the contraction coefficients from atom calculations using the respective ECPs. H. BASCH 155 relative to the AE results. Overall the ECP calculations seems to predict a less stable molecule. The agreement here between AE and VE calculated results is thus substantially less than that found for CuC1;- discussed previously. Aside from possibly subtle basis set effects one possible source of these differences may lie in the importance of charge transfer (ie.,Ag+Ag-) structures in describing even the closed shell ground state.28 Such ionic structures would be expected to be less well described with an ECP core than with the AE core.The effect of using the R instead of the NR potential for Ag is seen to cause a Substantial decrease in Re and increases in both D,and a, all indicating a strengthen- ing of the Ag-Ag bond. This trend is in accord with the primary 5s orbital charac- ter of the bond which is known to be stabilized and contracted by the relativistic terms in the atom.17 The importance of including relativistic effects for second row transition metal atoms at least when they are 5s orbital bonded is therefore estab- lished. A study of the influence of basis set on the R/ECP results for Ag, also in table 5 shows that even a set of.f-type functions apparently causes no substantial changes in the calculated values of the spectroscopic parameters again showing the relative unimportance of the d electrons to the bonding.On the other hand CI is found to be very effective in bringing the calculated Re and D closer to their experimental values as has also been observed for Ni2.25-26 The (NR) Cu, (R) Ag and (R) AuZ ECP/34F calculations consistently show the same trends in the spectroscopic constants and properties as are found for the corre- sponding experimental values. Thus Re increases and then decreases in going from Cu2to Ag and then to Au,. In this same direction D,is calculated to decrease and then increase being largest for Au in accord with experiment. In analogous agree- ment with experiment the value of co is calculated to decrease from Cu to Ag and then increase for Au, with Cu being the largest. For the corresponding C1 wave function the calculated trends are close to experiment except for the prediction of a substantial decrease in we in going from Ag to Au,.In general this preliminary study shows that even for the s-bonded group TB metals the quantitatively accurate description of the metal-metal bond is a non-trivial problem. There are no known experimental values for the calculated spectroscopic proper- ties in table 5 for AgAu. The Calculated ODC values for D,and co are larger than either of the corresponding homonuclear diatomic property values as expected. These systems require further study. CLUSTER COMPLEXES One of the interesting applications of the metal diatomic systems is as localized bonding models for the low density limit chemisorption of small molecules on transi- tion metals.34 In addition the current wide interest in binuclear metal coordination complexes is at least in part due to their potential usefulness for the conversion of solar energy to the production of H,.35 It is also becoming widely believed that there is a close relationship between the chemisorbed form of an adsorbate on a metal surface and its appearance as a ligand in binuclear and polynuclear metal coordina- tion complexes.36 A recent has described the interaction of an ethylene molecule with the Ni species.In particular the n type complex with the Ni bond axis perpendicular to the molecular plane of the ethylene (with the hydrogen atoms moved back slightly out of plane) was found to lead to a stable cluster-complex.In table 7 the energetics HEAVY METAL DIATOMICS TABLE 7.-ENERGIES OF REACTIONS' reaction AEIeV (1) Ni2C2H4-+ Ni2 + C2H4 0.31 (2) Ni2C2H4-+ Ni 4-NiC2H4 1.S6 (3) Ni2-+ 2 Ni 1.18 (4) NiC2H4-f Ni + C2H4 -0.07 ~~ 'Based on results reported in ref. (34). of several reactions involving the possible dissociation components of Ni2C2H4 are given based uniformly on the pair correlated wave functions described in that work at a fixed Ni-C distance of 2.10A. This table shows that at the theoretical level described NiC2H4 has an essentially zero dissociation energy [reaction (4)]and that the dissociation energy of Ni2C,H4 to Ni + C2H4 is only 0.31 eV [reaction (I)]. However if we concentrate on what happens to the Ni-Ni bond in Ni2C2H4 relative to the bare Ni [reactions (2)and (3)] we see that the Ni-Ni bond in Ni2C2H4 is stronger than in Ni,.Thus the bonding of C2H4 to Ni seems to be due at least in part to a strengthening of the metal-metal bond. The ground state electronic structure of the Ni entity is believed to 8,38,3n:n$la,220,2(4s) (2) where the corresponding bonding and antibonding 3d orbital partners are equivalently occupied. This arrangement of the electronic structure should lead to a net anti- bonding contribution of the 3d electrons to the 24 (4s) bond. As has been described by Hoffmann and ~o-workers~~*~~ in d10 systems the repulsive interaction of an anti- bonding orbital can be relieved by mixing in empty orbitals on the same or other atoms which can hybridize the antibonding electrons away from each other.Thus any mechanism for chemisorption or coordinate complexation involving an M-M bonded system in the second half of the transition series where antibonding orbitals are occu- pied must take into account the possible strengthening of the metal-metal bond as energetically facilitating the process. Gray 39 has actually suggested that the energy gained for the metal-metal bond in this way could be used to facilitate dissociative chemisorption of hydrocarbons across a metal-metal bond. METAL CLUSTERS A recent ab initio study2' of small nickel atom clusters of up to six atoms has re- vealed an interesting pattern in the preferred electronic and geometric structure of these clusters.Actually as was mentioned before for bare M-M bonds the relative ordering of the atom states is an important factor in the proper electronic structure description of the cluster states and their ge~metries.~O-~~ The Hartree-Fock method for example places the 3d84s2(3F) state-configuration 1.83 eV below 3d94s1(3D) whereas experimentally these two states are essentially degenerate. Such a poor description of the isolated nickel atom states wouId cast serious doubt on the electronic and geometric structure SCF results for the nickel atom clusters. This problem was circumvented by using a single-zeta representation of the 3d orbitals with the Gaussian primitive contraction coefficients frozen for the Ni atom 3D state. In this way using a (3s1p4d)/[2s1p1d] basis the 3Fand 3D states are calculated to be very close in energy as is observed experimentally.H. BASCH 157 The cluster calculations showed that the single 4s electrons per nickel atom com- bine to form the primary bonding orbitals of the clusters and that the form of these cluster orbitals can be predicted from a three dimensional Huckel-type interactions matrix with overlap. This means that it is a priori possible to predict where in the cluster the 4s electrons will have high and low densities for a given cluster size and geometry. In the on the Ni2C2H4 cluster-complex on the 7r geometry de- scribed above it was found that the back nickel atom acts as a sink of 4s electron density making the contact nickel atom 4s electron deficient.Thus ethylene as an adsorbate will look for 4s electron deficient sites on the nickel surface to which to bond. However a small cluster size representation of the nickel atom surface will have these sites pre-determined by the cluster size and geometry and not necessarily connected in any realistic manner with a real surface. Thus relative site stabilities for adsorbates obtained using a small cluster representation of the metal may be unconnected to the real situation on a metal surface. One possible solution to this problem is to use a positively charged metal cluster. In this way the role of the metal hinterland to the surface as a 4s electron sink in chemisorption is simulated. The specificity of high and low 4s electron density sites in the neutral cluster should thereby be diminished by the energetic need to spread the remaining 4s electron density as much as possible so as to minimize atom-atom repulsions within the positively charged cluster.Such an approach has been used recently by Walch and G0ddard.~'9~' This research was supported by grants from the United States-Israel Binational Science Foundation (B.S.F.),Jerusalem and the Israel Commission for Basic Research Jerusalem. Parts of this work were carried out in collaboration with Drs. Sid Topiol Marshall Newton and Jules W. Moskowitz. G.C. Bond in Electronic Structure and Reactivity of Metal Surfaces ed. E. G. Derouane and A. A. Lucas (Plenum Press N.Y. 1976). F. Trautweiler Photogr. Sci. Eng. 1968 12 138. F. A. Cotton Accounts Chem.Res. 1978 11 225. W. C. Trogler and H. B. Gray Accounts Chem. Res. 1978 11 232. L. R. Kahn P. Baybutt and D. G. Truhlar J. Chem. Phys. 1976,65 3826. H. Basch and S. Topiol J. Chenz. Phys. 1979 71 802. C. F. Melius B. D. Olafson and W. A. Goddard Chem. Phys. Letters 1974,28,457. S. Topiol J. W. Moskowitz and C. F. Melius J. Chem. Phys. 1978 68 2364. P. J. Hay W. R. Wadt and L. R. Kahn J. Chem. Phys. 1978 68 3059. lo H. Basch M. D. Newton J. Jafri J. W. Moskowitz and S. Topiol 1.Chem. Phys. 1978 68 4005. l1 B. Roos A. Veillard and G.Vinot Theor. Chim. Acta 1971 20 1. l2 J. Demuynck A. Veillard and U. Wahlgren J. Amer. Chem. Sac. 1973 95 5563. l3 S. Topiol J. W. Moskowitz and C. F. Melius J. Chem. Phys. 1978 68 2364. l4 P. Pyykko Adu. Quant.Chem. 1978 11 353. l5 Y.S. Lee W. C. Ermler and K. S. Pitzer J. Chem. Phys. 1977 67 5861. l6 L. R. Kahn P. J. Hay and R. D. Cowan J. Chem. Phys. 1978 68 2386. l7 J. P. Desclaux and Y.K. Kim J. Physique 1975 88 1177. l8 H. Basch D. Cohen and S. Topiol Theory of Molecular Structure and Bonding ed. R. Paunez and E. A. Halevi (Weitzmann Science Press Jerusalem 1979). l9 R. P. Messmer D. R. Salahub K. H. Johnsodand C. Y.Yang Chem. Phys. Letters 1977 51 84. 2o S. G. Louie Phys. Rev. Letters 1979 42 476. 21 J. E. Demuth Surface Sci. 1977 65 369. 22 T. H. Upton and W. A. Goddard 111 J. Amer. Chem. Soc. 1978 100 5659. 23 I. Shim J. P. Dahl and H. Johansen Int. J. Quantum Chem. 1979 XV 31 1. 24 J. Harris and R. D. Jones J. Chem. Phys. 1979 70 830. 25 H.Basch M. D. Newton and J. W. Moskowitz to be published. 158 HEAVY METAL DIATOMICS 26 J. D. Noell M. D. Newton and P. J. Hay to be published. ''Y. S. Lee W. C. Ermler K. Pitzer and A. D. McLean J. Chem. Phys. 1979 70,288; W. C. Ermler Y.S. Lee and K. S. Pitzer J. Chem. Phys. 1979,70,293. 28 P. J. Hay T. H. Dunning Jr and R. C. Raffenetti J. Chem. Phys. 1976 65 2679. 29 P. Joyes and M. Leleyter J. Phys. B 1973 6 150. 30 R. N. Dixon and I. L. Robertson MoZ. Phys. 1978 36 1099. 31 A. J. H. Wachters J. Chem. Phys. 1970 52 1033. 32 H. Basch to be published. 33 H. Basch J. Amer. Chem. SOC. 1975 97 6047. 34 H. Basch M. D. Newton and J. W. Moskowitz J. Chem. 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ISSN:0301-5696    

DOI:10.1039/FS9801400149

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Theoretical Study of the Electronic Structure of the Transition Metal Dimers Sc2,Cr, Mo and Ni BY CAROLWOOD,MARK DORAN AND IANH. HILLIER Chemistry Depart men t University of Manchester Manchester Ml 3 9PL AND MARTYN F. GUEST S.R.C. Daresbury Laboratory Daresbury Warrington WA4 4AD Received 20th July 1979 MCSCF calculations of the potential energy curves of the ground states of the transition metal species Sc, Cr, Mo2and Niz are described. The ground state of Scz is calculated to be ’C; corre-sponding to the orbital occupancy o~(s)a~(d)~~(d)o~(s).In Ni the metal-metal bonding is due to the doubly occupied o,(s) orbital a number of very closely spaced states arising from the weakly interacting pair of nickel d9configurations. In Cr and Mo a major feature of the bonding is the reduction in the order of the “ sextuple ” bond due to correlation effects particularly in Cr,.Bind-ing energies of all four diatomic species are calculated and compared with available experimental data. Transition metals play an important role in chemisorption and catalysis and there is growing interest both experimental and theoretical in the electronic structure of small clusters of these elements. The isolation in argon matrices of transition metal diatom species and higher aggregates has allowed spectroscopic studies to be made of these species.l-s In recent years many calculations on the electronic structure of such clusters have been reported. Thus aggregates of the metals Ni Ag Au Pd Cr Mo and Cu have been studied using semi-empirical molecular orbital methods9-15 and the scattered-wave (SW) Xcc method.l69” These techniques have also been em- ployed to investigate the interaction between gases and models of metal surfaces.’s-22 In this paper we consider the calculation of the electronic structure of the transition metal dimers Sc, Cr2 Mo and Ni by ab initio molecular orbital techniques.Al-though calculations on larger aggregates of transition metals will probably be re- stricted to more approximate methods particularly by pseudo-potential techniques we consider that more accurate calculations on the metal dimers are necessary both to obtain a satisfactory description of their particular mode of bonding and to provide “ bench-marks ” against which the more approximate calculations may be judged.This set of metal dimers was chosen to provide a representative sample of these species and because their dissociation energies have been determined e~perirnentally.~~-~~ Whilst the present work was in progress an investigation of the reaction Ni + H2+ Ni2H2 which included calculations on Ni, using ab initio methods with an effective core potential was rep~rted,~’ together with GVB calculations of Ni,28 which also used an effective core potential. TRANSITION METAL DIMERS COMPUTATIONAL DETAILS BASIS SETS The calculations were carried out using atomic bases of Gaussian type functions. For the first row transition metal atoms the (12s6p4d) basis of Roos et al.29was con- tracted to (5s2pld) and augmented with an additional s p and d function with the following exponents 0.45 0.26 and 0.15 for Ni; 0.24 0.13 and 0.08 for Sc; 0.4 0.4 and 0.2 for Cr.These additional primitive Gaussian functions were added following the conclusions of ROOS~~ concerning the inadequacy of the (12s6p4d) basis in the valence region. Hay3' has shown that the addition of an extra d function to this basis provides an improved description of the 4s13dnf1configuration relative to the 4s23dnconfiguration of the atom. The relative energies of the 4s23dnand 4s13dnS1 configurations of these atoms calculated with this basis are compared with the experimental separations 31 and with those resulting from near Hartree-Fock calcula-tion~~~ in table 1. The basis used in the calculations on Mo was the (27sl3p9d) basis of Huzinaga3' contracted to (8s4p3d).TABLE 1.-CALCULATED AND EXPERIMENTAL RELATIVE ENERGIES (a.U.) OF THE STATES OF ATOMIC Sc Cr AND Ni numerical this work Hartree-Fock experimental 0.0 0.0 0.0 0.008 0.047 0.001 (-0.001)" 2D(4s23d')"{ 4F(4s13d2) 0.0 0.02 0.0 0.037 0.0 0.052 7S(4S13d5) 0.0 0.0 0.0 cr{ SD(4s23d4) 0.059 0.047 0.035 a On averaging the J components of each state. COMPUTATIONAL METHODS In this work we are concerned with the determination of potential energy curves for these diatomic species so that single determinantal wavefunctions which do not dissociate correctly will be inadequate for this purpose. Multiconfigurational wave-functions which include at least those configurations leading to correct dissociation were calculated by standard configuration interaction (CI) methods,33 and in many cases the orbitals used to construct such expansions were optimized by the multi- configuration self-consistent field (MCSCF) method previously described.34 In this way a compact wavefunction of high accuracy can be obtained.A more restrictive MCSCF method the antisymmetric product of strongly orthogonal geminals (APSG) method,35 was used to obtain correlated wavefunctions for the closed-shell configura- tions of Cr and Mo2. We now discuss the calculations carried out on the individual diatomic molecules. C. WOOD M. DORAN I. H. HILLIER AND M. F. GUEST 161 COMPUTATIONAL RESULTS GROUND STATE OF SC To determine the ground state of Sc several states with different spin multi- plicities were examined.The procedure adopted was to perform MCSCF calculations for a number of selected states with S = 0 1 and 2 corresponding to the orbital occupancies shown in table 2. The molecular orbitals la and la,* may be regarded as the 4s bonding and antibonding orbitals the ten remaining valence MOs (2o, ln, ln, 16, la, 2a,) having mainly d character. In atomic Sc the 4s orbital is lower in energy than the 3dorbitals and this suggests that both the la and la MOs may be occupied in the ground state of Sc,. The selected orbital occupancies were obtained by occupying the 4s bonding orbital la and then distributing the remaining valence electrons amongst the lo, 2a, In and 16 MOs thus creating configurations with the maximum number of bonding orbitals occupied.The MCSCF calculations performed on these states were each to the same level of approximation and included all the important correlating excitations for each of them being double and quadruple excitations to the unoccupied internal orbitals. In all the MCSCF and CI calculations for Sc the core orbitals were kept fully occupied and in the MCSCF calculations only internal excitations were considered. The MCSCF wavefunction for each state has only one dominant configuration in the bonding region (typically z80%). The MCSCF energies are presented in table 2. A minimum in the MCSCF TABLE 2.-SCF AND MCSCF ENERGIES (a.u.) OF SELECTED STATES OF Sc electronic state configuration SCF energy MCSCF energy 'x; 10,210,220,2 -1516.477 -1516.578 1x; 10;1n4 -1516.478 -1516.590 3m7 10;2a,210:17T -1516.570 3xc 10;20;1n; -1516.437 -1516.573 5x; 10,22o30;1n; -1516.533 -1516.619 5As 10;2a; 1nf16; -1516.572 energy of the 5C; state occurs at 2.57 A and the energies of all the states are given at this bond length.If the ground state of Sc is a singlet or a triplet it must formally dissociate to 2D(~2d1) + ,D(s2d1). The lowest dissociation products from a quintet state of Sc are ,D + 4F(~1d2), and from a septet 4F+ 4F. From these considerations the ground state of Sc is unlikely to be a septet state since a relatively large binding energy would be required to make it lower in energy than states which were bound with respect to a lower dissociation limit.For this reason MCSCF calculations were not performed on any septet states of Sc,. The MCSCF energies of the singlet and triplet states in table 2 are all higher in energy than the separate atoms ,D + ,D,the lowest being the lZ; (loilzi). To improve the description of the lZ; state relative to the ,D + ,D limit a CI calculation was performed using the MCSCF vectors as basis MOs. The CI expansion included all double single and some quadruple excitations from the determinant la,21zi to * The orbital numbering in this paper does not include the core orbitals. TRANSITION METAL DIMERS the first twenty unoccupied orbitals. However this only lowered the energy of the state by 0.014 a.u. still leaving it higher in energy than the 2D + 2Ddissociation limit.On the basis of the MCSCF calculations it is proposed that the ground state of Sc is 5X~ (la,22a~ln303. The MCSCF curve (fig. 1) has a minimum at 2.57 A and is bound by 29 kJ mol-I with respect to the dissociation limit 2D+ 4F. -0.44 -0.48 ? -0.52 t -0.56 >r E" K d a -0.60 0 c 0 c -0.64 I1 I I 1 I 2.1 2.5 2.9 3.3 3.7 4.1 R /B FIG.1.-Potential energy curves of 5C; ground state of Sc2. An improved description of the 'Z; state was obtained by using the MCSCF vectors as basis MOs for a larger CI calculation. The CI expansion which ensured correct dissociation behaviour included all configurations which could be generated from the internal set of orbitals with the general valence description s2d4or s3d3and all other single and double excitations from la~2a~la~ln~ to the unoccupied orbitals (30,.. . 16, 2ng. . . 26,). The CI curve for the ground state shown in fig. 1 has a depth of 109 kJ mol-1 with respect to 2D+ 4Fatoms and 53 kJ mol-I with respect to two 2Datoms to be compared to the experimental value for the dissociation energy of 124 & 20 kJ m01-I.~~ From the CI curve the equilibrium bond length is 2.6 A. The results of this present work are not in agreement with the findings of previous workers. Cooper et a1.l3performed Extended Hiickel calculations and proposed a (la,21n:) ground state and an equilibrium bond length of 2.2 A. Busby et aL7 also used this method for their calculations which they performed at a bond length of 2.3 A.They proposed a 5A (la~2a~In~16~) ground state. Both the 'Z and the 5As states have been shown to be higher in energy in the bonding region than the proposed ground state (table 2). GROUND STATE OF Ni2 The ground state of the Ni atom is 3Fc~rre~p~nding to a configuration (Ar)4s23d* while the first excited state is 3Dcorresponding to a configuration (Ar)4s13d9. How-ever on averaging the J components of each state (corresponding approximately to ignoring spin-orbit coupling) the ground state is 3D(~1d9) while 3F(s2d*)is only 0.03 163 C. WOOD M. DORAN I. H. HILLIER AND M. F. GUEST eV higher. In both these states the partially filled 3d shell is more tightly bound than the 4s electrons This indicates that the interactions of two Ni atoms will be domin- ated by the 4s electrons on each centre.In this case two s2dsatoms will interact in a repulsive manner as they approach one another but two s1d9atoms can interact in a bonding manner. An s2d8atom coupled with an s1d9atom will lead to a total of three electrons in the 4s shell and would not be expected to bond as strongly as in the s'd -s1d9 case. The basic picture for the lower Nizstates will thus be of a single 4s bond analogous to the alkali metals or H,. The determination of the ground state of Ni2 therefore reduces to a problem of finding the most favourable coupling between the 3d electrons on each centre. A strong candidate for the ground state of Ni is 'Xi (I ail n,41n,41(Ti16:2a,2)* and indeed has been calculated to be the ground state using the SCF-Xcr-SW rnethod.20p22 However using semi-empirical MO method^'^^'^ the ground state is found to be 3Z; (1aila,21 ?Ti1 ?T;1 8; 16ff203.The present work was begun by performing SCF calculations on these two states for R(Ni-Ni) = 2.3 .$,twice the covalent radius and using these MOs in CI calcula-tions in which the core orbitals were kept occupied and only excitations amongst the internal orbitals were considered. For the calculation of the singlet states the CI expansion included all such closed shell configurations and all single and double excitations from the orbital occupancy la~ln~1n~ld~l(Tff2a~. The expansion of the triplet states included all single and double excitations from the 3Z; SCF configuration. Thus these two CI expansions include all the configurations with S = 0 or 1 respec-tively which can be produced by doubly occupying the 4s bonding orbital zag and permuting the remaining 18 valence electrons amongst the 3d bonding ar,d anti- bonding MOs.The striking feature of the results of both calculations (tables 3 and 4) is the small energy differences between the various states. This highlights the main problem encountered in trying to determine the ground state of Niz that is the low- lying states are all very close together. These preliminary calculations indicate the triplet states to be lower in energy than TABLE 3.-RESULTS OF THE CI CALCULATION ON THE SINGLET STATES OF Ni AT 2.3 A root state energy/a.u. important configurations 1 IX; -3009.0598 1a;2a,21ntfli n;lS;184 10;20;1 ntf1 nil S;l slf1a," 241ntf1 n;1 S;l s;10," 2 A9 -300!J.0407 la$20:1 ntfl~~;18i1&10~ 1a,220;1ntf 1 n;1 Sil Stf 10 1a;24 n;1 n;1 SilStf 1a,' '44 3 -3009.0398 10,220; 17.~21 nil Sil Stf10; 1a;2a,21 nil n;1 S;ls:l a 1 a,22a.3 nlfl n;1 s;1 s:1a; 4 lrs -3005.0302 10,220,21n:1 nil S$l Sfl a," I 1 a,220;1 n;ll nil S,2l S4,l a 5 'C,+ -3~09.0302j 6 'c -3009.0286 1~,22a:1n:1 n;l Sil S:~CT," 7 'nu -3009.0265 10,22~,21~~1~~16~1Stfl~~ 1a;2a;1 n:n 7riI s;1s:10," * Here the MOs 1o,,1ouy1nuy1ngy16 and 16 refer to the MQs arising from the 3d atomic orbitals and 20, 20 to the 4s orbitals.164 TRANSITION METAL DIMERS TABLE 4.-RESULTS OF THE CI CALCULATION ON THE TRIPLET STATES OF Niz AT 2.3 A root state energy/a.u.important configurations 1 -3009.1133 1 a,22a,21 nil nil 821 Sjlo,” 1 a,22a,2l nil nil s;1 sj10; 2 -3009.1 1 1 9 3 -3009.1 1 1 9 4 -3009.11 17 1 0,2203 np;l n;1s;1 s;1 a,” 1 a,22a,21 nlf1 nil s,21 s91a; 5 -3009.1 115 10,220,21 njl nil s;1 s;1 a,” la,22a,21 nil n;1 s;1 s:1 a,” 6 -3009.1109 7 -3009.1097 8 -3009.1094 J 9 -3009.1077 10,2203 nj1 n;1s; 1 s;1 0,’ 10;2a,21 nil nil s;1 st1 (7 10 -3009.1067 1 42a; 1 n 1 n;1 ail Splla 1a;2a,21 ntfln;ls;ls;lO,Z 10,2203 nlf1 nil sj1 s:1 a,’ 11 -3009.1067 12 -3009.105 1 1 0,224 n 1n;1 8491 s;f 1a,” 13 -3009.1046 } 14 -3009.1014 1 0,220; 1n:1n; 1 s;1 sj1a 15 -3009,0978 1a;2a;1 nj1 n;1 s;1 sjla,‘ 16 -3009.0526 1 0,2203 n:1 nil s;1 sj10,220,‘ singlet states with the same orbital occupancies.However it was subsequently found that this was largely due to the different basis MOs used in the two calculations. To obtain a uniform description of the lowest states produced by these initial calcula- tions a series of fairly limited CI calculations was performed in which only the SCF MOs for the 3X~ state were taken as basis MOs (table 5). Each state was described by a small expansion of configurations which included the essential orbital occupancies (tables 3 and 4) with only their important correlating excitations (i.e. ag2 -+a 7ti -+ n; 6; 36;) as there are only a small number of dominant configurations. The object of these calculations was to provide an adequate description of each state in the bond- ing region so that the ground state might be identified.To improve the description of these states MCSCF calculations were performed with the same set of configurations. The results of these MCSCF calculations (table 5) show that there are a number of singlet and triplet states lying very close together with energies approximately 33 kJ rno1-l below the 3F + 3Fdi~~~ciation limit. These results also show that the favoured orbital occupancies are those in which there are two holes in the 6 sub-shell. The 3ru, resulting six states (Irg,‘C,C IC; 3C;, ”:) are extremely close in energy and it is not possible on the basis of these calculations to be definitive about which is the ground state. From this group of states the lTSwas chosen for a more detailed study.265 C. WOOD M. DORAN I. H. HILLIER AND M. F. GUEST TABLE 5.-CI AND MCSCF CALCULATIONS ON SOME OF THE LOW-LYING STATESOF Niz [R(Ni-Ni) = 2.3 A] state dominant configuration CI energy/a.u. MCSCF energy/a.u. -3009.1 180 -3009.1395 -3009.1 181 -3009.1396 -3009.1139 -3009.1380 -3009.1 174 -3009.1384 -3009.1 176 -3009.1 390 -3009.1 152 -3009.1 394 -3009.1 1 1 1 -3009.1268 -3009.1 1 30 -3009.1 347 -3009.1119 -3009.1275 -3009.1 122 -3009.1342 -3009.1 125 -3009.1 324 -3009.101 8 -3009.1264 -3009.1096 - -3009.1094 - -3009.1079 - -3009.108 1 - The MCSCF calculations described above were performed for the ITs state over a range of bond lengths. The MCSCF orbitals were then used in the CI calculations in which all internal configurations of ITs symmetry were included giving the potential 0.22 1.7 2.1 2.5 2.9 3.3 3.7 4.1 4.5 R/B.FIG.2.-Potential energy curves for Ni, (a) SCF curve for 3C; state (la~2a~ln4,1n~16~164,la,2); (b)CI curve for state (la$?a,21n4,1~~16",ls~lo,'). 166 TRANSITION METAL DIMERS curve (fig. 2) and ensuring at least formally correct dissociation. The lowest calcu- lated dissociation limit is ‘F + ’&‘and therefore the state of Ni found to be the ground state should go continuously to that limit. However at a bond length of 4.5A the atoms in the lrqstate of Ni still adopt an s1d9Configuration and the potential curve at this distance lies above the 3F + ’F limit. We might expect therefore a curve cross- ing at a longer bond length if the is the ground State so that the correct dissociation limit is achieved.However a detailed examination of the long range behaviour of the states of Ni would require an improved description of the atomic states. The poten- tial curve produced for the ISqstate gives a dissociation energy of 50 kJ mol-l with respect to ’F + 3F and an equilibrium bond length of 2.36 A. The experimental estimate of the binding energy of Ni is 231 kJ mol-l. GROUND STATES OF Cr AND Mo In the case of Cr and Mo, where 12 valence electrons are to be accommodated in 12 valence MOs it is not practical computationally to decide the ground state elec- tronic configurations. However complexes containing the Cri+ and Mo~+entities are found to be diamagnetic and in such complexes it is considered that the Mi+ electron configuration is ai(d)n:(d)d:(d) corresponding to a formal quadruple metal- metal bond.It is thus likely that the configuration in Cr and Mo corresponds to the “ sextuple bond ” .~(s)a,”(d).~(d)6~(d).At a bond length of 1.9A the SCF calculation of this configuration for Cr yields an energy 1 a.u. above that of the atoms in the 7S(4s13d5) state. A similar situation is found for Mo where at a bond length of 2.0 A the energy of the SCF wavefunction is 0.35 a.u. above that of the isolated atoms. Such a result reflects the lack of left-right correlation in the SCF wavefunction which does not dissociate correctly to ‘S atoms. With a bond of such high multiplicity the error in the SCF wavefunction is considerably greater than that found for Ni and Sc (fig.1 and 2). To ensure correct behaviour of the wavefunction at the dissociation limit requires nearly 1000 bonded functions and represents a calculation that it is not practical for us to carry out at present. For this reason we have used the APSG method which yields a multiconfigurational wavefunction that dissociates to metal atoms not in their lowest energy configuration but to a weighted average of all the atomic states arising from the sldsconfiguration. The corresponding average atomic energy for chromium and molybdenum is calculated to be some 0.1-0.15 a.u. above that of the 7Satomic state. Such an APSG calculation is equivalent to an MCSCF calculation that takes account of the intra-pair correlation energy arising from the 092 -+ at n,2 -+ ni and 6 -+ 6 excitations and from other multiple excitations.The results of the SCF and APSG calculations on Cr and Mo are shown in fig. 3 and 4 respectively. From these calculations including correlation equilibrium bond lengths of 1.9and 2.1 A and binding energies (with respect to the average energies of the s1d5atomic configurations) of 143 and 430 kJ m01-l for Cr and Mo, respectively are found. The formal description of the M-M bond in these two diatomic species may be discussed by the decomposition of the APSG wavefunctions in terms of their com- ponent configurations (table 6). In the case of Mo the sextuple bond configuration contributes nearly 50% to the multiconfigurational wavefunction whilst for Cr this value is only 19%.The dominant correlating configuration arises from the 8 -+ 6% excitation and reflects the weak interaction between the atomic dxyand dx2-y2 orbitals in these molecules. We may estimate an appropriate M-M bond order (P)in terms of the occupation C. WOOD M. DORAN I. H. HILLIER AND M. F. GUEST -0.5 -0.4 0.3 -n =! 0.2-N a3 0 0.1 -(v + U >r 0-F C -0.1 -d b + 0 -0.2--0.3 -I I 1 I I I 1 FIG.3.-Potential energy curves for Cr2. -I 2 0.7} 1.7 2.0 2.3 2.6 2.9 3.2 3.5 3.8 RJA FIG.4.-Potential energy curves for Mo2. TRANSITION METAL DIMERS TABLE 6.-sUMMARY OF APSG CALCULATIONS ON Cr2(R = 1.9 A) AND Mo~(R= 2.0 A) configuration percentage in wavefunction Crz MO2 numbers (al,a,) of the bonding and corresponding antibonding orbital of each geminal giving P = 2 (aI2-a2”.fJ,%8 ‘This definition of P which merely provides a “ count ” of the number of bonds and provides no indication of the relative strengths of the components of each bond gives a value of 4.6 for the Mo and 3.3 for Cr, in line with the smaller contribution of the sextuple bond configuration to Cr compared with Mo,. DISCUSSION A major aim of the theoretical description of transition metal diatoms is the deter- mination of the ground state configurations which have not generally been determined experimentally. This presents a theoretical difficulty since a number of closely spaced states may arise due to the degeneracy of the atomic d orbitals and their small energy separation from the corresponding atomic s orbitals.The ground state configuration may not correspond to a maximum occupancy of the most bonding molecular orbitals since such an occupancy usually corresponds to a lowering of the spin compared with that of the isolated atoms. The actual configuration adopted will therefore correspond to a balance between the bonding energy and the spin energy. The latter contribu- tion is not considered in Huckel calculations which will predict a ground state corre- sponding to maximum occupancy of the most bonding orbitals. The calculations reported here on Sc and Ni have aimed to obtain an accurate description of these effects by means of quite small expansions of multideterminantal wavefunctions in which the individual orbitals are optimized.In both molecules such a multideterminantal description is necessary to achieve bonding and as expected the calculated binding energies are sensitive to the size of the CI expansion being considerably smaller than the experimental values although the calculated bond lengths are relatively insensitive to the size of the expansion. In the case of Ni, our predicted bond length 2.36 A is shorter than that in the bulk metal (2.49 A) and is to be compared with the value of 2.04 derived from calculations using an effective core-potential. Note that although our calculations predict different ground state configurations from those given by more approximate methods recent density functional calculations36 also yield a T; ground state for Sc and predict a number of closely spaced states for Ni,.In the case of Cr and Mo, we have not carried out the large number of calcula- tions required to determine the ground state configuration of these molecules. How-ever having assumed a ‘C,+ “ sextuple-bond ” configuration we find that a single determinant gives molecular energies with larger deviations from the atom energies C. WOOD M. DORAN I. H. HILLIER AND M. F. GUEST than was found for Sc or Ni, due to the greater formal bond order in Cr and Mo,. The inclusion of correlation effects by the APSG method reduces the bond order to near 3 and 5 for Cr and Moz respectively and yields bond energies of 143 and 430 kJ mol-l. These values are in very good agreement with the corresponding experi- mental e~timates~~v~~ of 151 and 406 kJ rnol-l respectively.Note added in proof A recent more extensive ab initio study of Ni237 comes to similar conclusions to those presented here. We thank the S.R.C. for support. R. A. Teichman 111 M. Epting and E. R. Nixon J. Chem. Phys. 1978,68,336. W. Schulze H. U. Becker R. Minkwitz and K. Manzel Chem. Phys. Letters 1978,55 59. T. A. Ford H. Huber W. Klotzbucher E. P. Kundig M. Moskovits and G. A. Ozin J. Chem. Phys. 1977,66,524. T. C. Devore A. Ewing H. F. Franzen and V. Calder Chem. Phys. Letters 1975,35,78. M. Moskovits and J. E. Hulse J. Chem. Phys. 1977 66 3988. E. P. Kundig M. Moskovits and G. A. Ozin Nature 1975 254 503. ’R. Busby W. Klotzbucher and G.A. Ozin J. Amer. Chem. Soc. 1976,98,4013. W. Klotzbucher and G. A. Ozin Inorg. Chem. 1977 16,984. R. C. Baetzold J. Chem. Phys. 1971 55 4355. lo R. C. Baetzold J. Chem. Phys. 1978 68 555. l1 R. C. Baetzold and R. E. Mack J. Chem. Phys. 1975 62 1513. j2 R. C. Baetzold J. Catalysis 1973 29 129. l3 W. F. Cooper G. A. Clarke and C. R. Hare J. Phys. Chern. 1972,76 2268. l4 A. B. Anderson J. Chem. Phys. 1976 64,4046. A. B. Anderson J. Chem. Phys. 1977,66 5108. l6 R. P. Messmer S. K. Knudson K. H. Johnson J. B. Diamond and C. Y.Yang Phys. Rev. B 1976,13,1396. l7 J. G. Norman Jr H. Kolari H. B. Gray and W. Trogler Inorg. Chem. 1977,16,987. l8 A. B. Anderson and R. Hoffman J. Chenz. Phys. 1974,61,4545. l9 G. Blyholder J. Chem. Phys. 1975 62 3193. 2o N.Rosch and T. N. Rhodin Phys. Rev. Letters 1974 32 11 89. 21 N. Rosch and D. Menzel Chem. Phys. 1976 13,243. 22 I. P. Batra and 0. Robaux J. Vac. Sci. Technol. 1975 12,242. 23 A. Kant and B. Strauss J. Chem. Phys. 1966,45,3161. 24 A. Kant J. Chem. Phys. 1964 41 1872. 25 G. Verhaegen S. Smoes and J. Drowart J. Chem. Phys. 1964 40,239. 26 S. K. Gupta R. M. Atkins and K. A. Gingerich Inorg. Chem. 1978,17 321 I. 27 C. F. Melius J. W. Moskowitz A. P. Mortola M. B. Baillie and M. A. Ratner Surface Sci. 1976 59 279. 28 T. H. Upton and W. A. Goddard 111 J. Amer. Chem. Soc. 1978,100 5659. 29 B. Roos A. Veillard and G. Vinot Theor. Chim. Acta (Berlin) 1971,20,1. 30 P. J. Hay J. Chem. Phys. 1977 66 4377. 31 C. E. Moore Atomic Energy LeueIs (Nat. Bur. Standards Circular 467) 1952.32 S. Huzinaga J. Chem. Phys. 1977 66 4245. 33 S. F. Boys C.M. Reeves and I. Shavitt Nature 1956,178,1207; C. M. Reeves Comm. A.C.M. 1966,9 276; G. H. F. Diercksen and B. T. Sutcliffe Theor. Chim. Acta (Berlin) 1974,34 105. 34 J. Kendrick and I. H. Hillier Chem. Phys. Letters 1976 41 283. 35 V. R. Saunders and M. F. Guest in Quantum Chemistry the State of the Art ed. V. R. Saunders and J. Brown (S.R.C. London 1975) p. 119. 36 J. Harris and R. 0.Jones J. Chem. Phys. 1979,70,830. 37 I. Shim J. P. Dahl and H. Johansen Int. J. Quantum Chem. 1979 15 31 1.

ISSN:0301-5696    

DOI:10.1039/FS9801400159

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Structure and Electronic Properties of Copper Clusters An Ab Iizitio LCAO-MO-SCF Study BY CHRISTIAN BACHMANN AND ALAINVEILLARD JEAN DEMUYNCK E.R. no 139 du C.N.R.S. Institut Le Bel Universitk L. Pasteur 4 rue B1. Pascal 67000 Strasbourg France Received 5th Jzcly 1979 The structure and electronic properties of copper clusters Cu (n = 2-5,8 and 13) have been studied through ab initio LCAO-MO-SCF calculations with a Gaussian basis set (12 7 5) contracted to [5,3,2]. The linear structure is more stable than the two- and three-dimensional structures for n = 3 and 4 but becomes less stable for n 3 5. Since for Cu8 the band of 3d levels and the 4s levels are well separated and for CulJ the two bands just begin to overlap the distribution of energy levels in these clusters appears to be rather different from that in the bulk metal.This is also a consequence of the fact that most of the atoms in the cluster CuI3 are surface atoms. The binding energy increases quasi-linearly with the number of atoms in the cluster up to n = 8. A knowledge of the electronic structure of metallic clusters containing up to a few tens of atoms is important for the following reasons. (i) Metal catalysts are usually found in the form of dispersed microcrystallites with a high surface/volume ratio The relationship between the electronic and structural properties of these clusters usually <10 A in size and those of the bulk metal is far from clear. A thorough understanding of the electronic and structural properties of these small metal particles is probably necessary in understanding how these metal aggregates act as catalysts.(ii) A number of experimental techniques such as the technique of con- densation within a matrix at low temperature has been developed recently for the experimental study of small metallic clusters with <10 For instance it has been possible to follow the changes in the U.V. and visible absorption spectra as a func- tion of the size of the agg~-egate.~.~ (iii) There is a strong interest in the chemistry of polynuclear organometallics with several metal-metal bonds (called molecular clusters by the chemists) as potential homogeneous catalysts. The possible relation- ship between the role of molecular clusters in homogeneous catalysis and the role of metallic clusters in heterogeneous catalysis has already been Many quantum mechanical studies deal with the electronic properties of transition metal clusters containing up to a few tens of atoms (large clusters including up to a thousand atoms have been studied in the tight-binding appro~imation).~ However nearly all the previous studies rely on semi-empirical methods.Both the extended Huckel method and the CNDO method have been used to investigate the electronic structure of transition or noble metal clusters (Ni Cu Pd Ag Au) of up to 55 atoms.10-20 Recently the SCF-Xa-scattered wave method has been used to investi- gate transition metal clusters of 8 and 13 atoms (Ni Cu Pd and Pt).21$22 The same method has been used to study the clusters of Li atoms (Li to Li13)23and of A1 atoms (up to A143).24 However the conclusions of these semi-empirical studies have been the subjects of controversy for instance regarding the rapidity with which the electronic C.BACHMANN J. DEMUYNCK AND A. VEILLARD properties of the clusters approach their bulk counterparts with increasing size. Ac-cording to Extended Hiickel and CNDO calculations the binding energy per atom increases slowly with the size of the clusters the binding energy being 4to 4of the bulk value for a 55 atom cluster. In contrast the SCF-Xcc calculations suggest that the bulk density of states (for transition metals) is largely attained for a cluster of 13 atoms.21 Ab initio calculations dealing with the electronic structure of metallic clusters are very scarce and have been restricted to clusters of lithium and beryllium atom^.^^-^^ We report here the results of an ab initio LCAO-MO-SCF study of clusters of copper atoms Cu with n between 2 and 13.In this study we have tried to answer the follow- ing questions (i) how do the electronic structure and binding energy per atom vary with cluster size and geometry; (ii) do the binding energy per atom and the density of states (DOS) structure approach those of the bulk metal for small clusters; (iii) what is the most stable structure for a cluster with a given number of atoms? A pre- liminary account of this work has been published previously.28 METHOD AND CALCULATIONS Ab initio LCAO-MO-SCF calculations have been carried out with four different basis sets of contracted Gaussian functions.Calculations for the clusters of up to eight atoms were carried out with basis set I (BSI) which is a Gaussian basis set (12 7 5) contracted to [5 3 23 (minimal basis set for the inner shells and the 4p shell double- zeta basis set for the shells 3d and 4s). A larger basis set (BSII) (13 8 5) contracted to [6,4. 21 (minimal basis set for the inner shells double-zeta for 3d and 4p triple-zeta for 4s) has also been used for Cu,. Another large basis set used for Cu and denoted BSIII is made of basis set I incremented with polarization functions namely a set of s p and d functions along the Cu-Cu axis and off the nuclei. A smaller basis set (BSIV) (12 7 4) contracted to [S 3 13 (minimal except for the 4s orbital which is split) was used for the cluster Cu, since the corresponding calculation with BSI would have exceeded the present possibilities of our open-shell SCF program.The Gaussian basis set (12 7 5) corresponds to the basis set (12 6,4) of ref. (29) incremented with one p function of exponent 0.25 and one d function of exponent 0.2. The (13 8 5) basis set has one additional s function of exponent 0.02 and one addi- tional p function of exponent 0.1. The (12 7 4) basis set is similar to the (12 7 5) set except for the exponents of the d functions which have been reoptimized. Different geometries have been considered for n = 3,4 5 and 8. For the 13-atom cluster the cubo-octahedral geometry shown in fig. I is the structure corresponding FIG.1.-Cubo-octahedral cluster containing 13 atoms.STRUCTURE OF COPPER CLUSTERS to the local arrangement ot atoms in the face-centred cubic (f.c.c.) crystalline metal. The Cu-Cu distance has been optimized for a limited number of structures corre- sponding to n = 2 3 4 and 8. Otherwise a fixed distance of 2.40 A has been used. The calculations were carried out with the system of programs A~terix.~~?~~ The open-shell SCF treatment is based on the restricted Hartree-Fock formalism proposed by Guest and Saunder~.~~ All one- and two-electron integrals were computed with single-word accuracy on the Univac 1110 (word of 36 bits). The SCF calculations were carried out with double-word accuracy for the clusters up to Cu,. For CuI3 the SCF calculation was carried out with single-word accuracy.NUMERICAL RESULTS In table 1 are reported the calculated SCF energies for Cu2 as a function of the interatomic distance and of the basis set used. The ground-state energies for the different structures and different sizes of clusters are given in table 2 together with TABLE 1.-SCF ENERGIES (IN a.u.) FOR Cu2 AS A FUNCTION OF THE BASIS SET USED AND OF THE INTERATOMIC DISTANCE (IN A) BSI BSII BSIII BSIV r E r E r E r E 2.29 -3271.0493 2.291 -3271.084 85 2.25 -3271.677 00 2.35 -3268.867 76 2.34 -3271.0496 2.341 -3271.085 14 2.30 -3271.677 81 2.40 -3269.868 02 2.40 -3271.0493 2.391 -3271.084 57 2.35 -3271.677 96 2.45 -3269.867 90 re=2.34 re=2.3 33 re=2.327 re=2.41 the optimized Cu-Cu distance whenever calculated and the binding energy per atom.The energy values and binding energies per atom of table 2 have been obtained with basis set I and a fixed Cu-Cu distance of 2.40 A except for CuI3 where they corre- spond to basis set IV. A calculation for Cu (Oh symmetry) has also been carried out FIG.2.-Orbital energies (in a.u.) for the occupied orbitals 3d and 4s of the linear clusters Cu,, n = 2-5. Open-shell orbitals are indicated by an asterisk. TABLE 2.-SCF ENERGIES OPTIMIZED Cu-Cu DISTANCES IONIZATION POTENTIALS AND BINDING ENERGIES PER ATOM FOR THE CLUSTERS Cu (WITH BASIS SET I UNLESS OTHERWISE STATED ENERGY VALUES FOR A FIXED CU-cu DISTANCE OF 2.40 A) ~ ~~ energy of optimized binding energy ionization n structure electronic the ground Cu-Cu distance per atom potential state state /a.u.IA /kcal mol-l /eV 2 linear -3 271.0493 2.343 9.7 5.7" (6.1') z 3 linear -4906.5753 2.35 10.0 5.4" 2 bent (120") -4906.5704 8.9 03h -4906.5700 2.41 8.9 4 linear -6542.1180 12.7 5.4" (5.6') square planar (&) -6 542.1128 2.43 11.9 5.2" tetrahedral (Td) -6 542.1016 10.2 IX = 150" -6542.1124 11.9 02' a = 1200 -6542.1099 11.5 5 linear -8 177.6437 12.3 trigonal bipyramid (&h) -8 177.6591 14.2 square pyramid (C4") -8 177.6560 13.8 4.6" body-centred square (&) -8 177.6384 11.6 8 cube (Oh) -13 084.321 2.43 19.5 5.9' -13 079.537" 11.5 square antiprism (D4d) -13 084.333 20.4 5.5' 13 cubo-octahedron -21 254.314" 14.6 a Calculated as the difference of the energies for the ion Cu,' and the cluster Cu,.'Calculated according to Koopmans' theorem. With basis set IV. 174 STRUCTURE OF COPPER CLUSTERS with basis set IV thus allowing for a comparison of the results obtained with basis sets I and IV. Fig. 2 is a plot of the orbital energies for the occupied orbitals 3d and 4s (closed-shells and open-shells) of the linear clusters Cu, n = 2-5. Fig. 3 is a plot of the same orbital energies for the two- and three-dimensional clusters Cu, n = 3-5 8 and 13 (Cu has also been included for the sake of comparison). Table 3 shows the depend- ence of the orbital energies of Cu on the basis set used. Fig. 4 shows the density of occupied states for the cluster CwI3 (each energy level has been represented through a Gaussian function with a broadening parameter CJ = 0.005 a.u.).TABLE 3.-oRBITAL ENERGIES OF CUz (IN a.U.) FOR THE ORBITALS 3d AND 4s AS A FUNCTION OF THE BASIS SET USED BSI BSII BSIII BSIV og (4s) UU -0.225 -0.461 -0.223 -0.459 -0.223 -0.469 -0.221 -0.471 n -0.470 -0.468 -0.478 -0.482 6 -0.481 -0.479 -0.489 -0.491 6 nu -0.487 -0.501 -0.485 -0.498 -0.494 -0.506 -0.496 -0.510 og(34 -0.511 -0.508 -0.516 -0.519 -* e" s) il 0 0 FIG.3.-Orbital energies (in a.u.) for the occupied orbitals 3dand 4s of the two- and three-dimensional clusters Cun,n = 3-5 8 and 13. Open-shell orbitals are indicated by an asterisk. DISCUSSION BOND LENGTHS AND GEOMETRIES The results of table 1 show that the calculated bond length for Cu is rather sensi- tive to the basis set used. The calculated bond length decreases (from 2.41 to 2.33 A) when the quality of the basis set increases (in the order BSIV BSI and BSIII).We C. BACHMANN J. DEMUYNCK AND A. VEILLARD & 1a.u. FIG.4.-Density of occupied states for CuI3(orbital energies in a.u.). estimate that the theoretical bond length in Cu at the Hartree-Fock limit would be close to 2.3 A. The experimental bond length is 2.22 A.33 Our calculations do not support the results of Joyes and Leleyter; these authors report an equilibrium bond length of ~2.2 A with a basis set of Slater (minimal basis set except for the d orbitals which are split) (their SCF energy of -3270.4 a.u. is higher than the SCF energies reported in table 1 for the basis sets I to 111). Calculations close to the Hartree-Fock limit usually tend to produce bond lengths which are accurate to a few hundredths of A and generally too short.35 However the discrepancy for Cu is probably larger of the order of 0.08 A with the calculated bond length too long.We tentatively ascribe this behaviour to the neglect at the SCF level of configurations of the type (4~0)~ together with the configurations arising from the atomic states 3d94s2 (including the configuration formed from the 4s orbitals34 will probably lengthen the bond). The calculated value of 1.1 mdyn A-' for the harmonic force constant in Cu is nevertheless in good agreement with the experimental value of 1.32 mdyn A-1.33 The computed bond lengths for the clusters Cu fall within two groups namely 2.34-2.35 A for the linear structures and 2.41-2.43 A for the two- and three-dimen- sional structures.This is exemplified for the Cu cluster (table 2) with the distance for the linear structure 0.06 A shorter than the corresponding value for the triangular structure. Potential energy curves for Ag, based on Extended Huckel calculations also show larger internuclear distances for the cubic and planar geometries compared to the linear geometry." A similar trend is also apparent in the calculations of Anderson.18 This increased bond length in the two- and three-dimensional structures is probably a consequence of the presence of filled antibonding levels; the anti- bonding character of these levels is comparatively larger in the non-linear structures,'O but may be reduced by increasing the internuclear distance.The internuclear separa- tions calculated for the two- and three-dimensional structures show little change with the size of the cluster. The distance of 2.43 A calculated for n = 8 differs appreciably from the value of 2.56 A for the bulk metal. Goddard et al. have optimized the bond length for a cluster of 13 Ni atoms and find a Ni-Ni distance of 2.41 A to be compared to the value of 2.49 A for the bulk For n = 3 and 4 the linear structure is slightly more stable (by z 3 kcal mol-l) than the two-dimensional structure of D3,,or D4hsymmetry. However for n = 5 the linear structure becomes less stable (by ~9 kcal mol-l) than the trigonal bipyramid. I76 STRUCTURE OF COPPER CLUSTERS We conclude that the linear structure is more stable than the two- and three-dimen- sional structures only for the smallest aggregates with n = 3 and 4.Our calculations do not support the conclusions of Extended Hiickel calculations that the linear struc- ture represents the most stable geometric form up to 30 or 50 The experimental evidence although scarce seems to be in agreement with the results of the ab initio calculations. Ag is probably linear since the corresponding Raman spectrum shows only one line.,' The e.s.r. spectra of a species Ag,' or Agj+ has been analysed by assuming two pairs of inequivalent silver atoms this being consistent with a linear ge~metry.,~ Both the anion Pbg- and the cation Bi:+ appear to have a trigonal bipyramidal struct~re.~~~~~ The Ag cluster has an octahedral structure.41 Thus the structural evidence points to a change from the linear structure to the three- dimensional structures probably between 4 and 5 atoms.Support for a change from the linear to the three-dimensional structure between Ag and Ag also comes from the observation by Schulze et al. of a decrease in the energy of the lowest ab- sorption band from Ag to Ag, followed by an increase from Ag to Ag and a subse- quent decrease from Ag to Ag6.5 The authors attribute this change in the trend of the excitation energy to a change of structure (cf. below). The greater stability of the linear chains in the extended Hiickel calculations has been assigned by Baetzold to the presence of filled antibonding levels the antibonding character of these levels being increased in the non-linear structures.1° Examination of the orbital energies for Cu show that this analysis is correct the open-shell orbital energies for Cu are respectively -0.028 a.u.for the D3hstructure and -0.108 a.u. for the linear structure. However there are two opposing factors which favour a greater stability of the two- and three-dimensional structures and which soon become predominant. First the antibonding interaction just mentioned for Cu becomes nonbonding for Cu4 (in the sense that the molecular orbital displays out-of-phase amplitude on non-adjacent atoms see for instance the open-shell orbital e of Cu4 square-planar in fig. 5). This causes a relative stabilization of the two-dimensional n -0.114 n -0.198 * ,0363 -0.282A .0.304 w-FIG.5.-Highest-occupied orbitals of the linear clusters CUZ-CUS and of the two- and three-dimen- sional clusters Cu3-Cu5.Their orbital energies are given in a.u. C. BACHMANN J. DEMUYNCK AND A. VEILLARD 177 structure as shown by the open-shell orbital energies of Cu3 DSh and CU~D~~ -0.028 and -0.096 a.u. respectively. The second factor and probably the most important one is that the number of bonding interactions for a given cluster is much larger in the two- and mostly three-dimensional structures than in the linear structures (see for instance the in-phase bonding orbitals of fig. 5). This is typified by the change in the energy of the bonding in-phase orbital in the series Cu3 Cu4 and Cu5 -0.24 -0.25 -0.26 a.u.respectively for the linear structures and -0.28 -0.30 -0.36 a.u. for the two- and three-dimensional structures. ORBITAL ENERGIES AND BINDING ENERGIES Examination of table 3 shows that the orbital energies of Cu2 are relatively insensi- tive to the basis set used. Fig. 2 and 3 show the build-up of a relatively narrow and dense band of 3d levels together with a relatively wide 4s band (with usually a small admixture of 4p orbitals). For Cu8 the 3d band and the 4s levels are well separated. For C~13 the two bands just begin to overlap with the a, level being the lowest level with s-character and just at the top of the d band Thus our results do not support the conclusion inferred from the SCF-Xa calculations that “already in the Cu8 aggregate the d band is totally overlapped by the sp band as in the solid ”.21 For C~13 the two levels t2gand e located slightly below the d band correspond to d orbitals which are bonding between the central atom and outer atoms of the cubo- octahedron but which are primarily localized on the central atom.However the splitting off of these two d orbitals from the bottom of the d-band is much smaller in our calculation (about 0.02 a.u.) than in the SCF-Xa calculation (more than 0.1 a.u.). In the SCF-Xa study by Messmer et al. it is stated that “ while the main band of d levels in C~13 corresponds closely to the d band characteristic of bulk copper the two deep-lying d levels have no close counterpart in bulk copper and are artifacts of the deeper potential energy of the central atom of C~13 compared with the surface atoms of the cluster”.We believe that the correspondence made between the main d band in C~l3 and the d band characteristic of bulk copper is erroneous. The central atom in C~13 is surrounded by twelve atoms hence the strongly bonding interactions resulting in the t2s and e levels at lower energies while each “ surface ” atom is sur- rounded by only four atoms. The central atom in Cu13 is in a situation analogous to that found for the atoms of the bulk copper. We conclude that the two levels tZgand e of Cu13 represent the origin of the d band of bulk copper (together with the corresponding antibonding levels) while the main band of d levels in Cu13 corresponds rather to surface states of bulk copper. There is some experimental evidence that the energy levels of clusters of the size considered here are different from those of the bulk metal at variance with the conclusions of the SCF-Xa calculations and in agreement with the results of the ab initio calculations.In the U.V. photoelectron spectroscopy of palladium particle arrays (probably much larger than the present clusters) the width of the Pd valence band was found to be a sensitive function of particle size.42 From a study of the absorption bands of silver clusters Schulze et al. concluded that more than ten atoms are necessary to change the electronic properties of silver clusters from a molecular type towards a metal type’ (however Ozin considers that silver clusters containing from 6 to 15 silver atoms exhibit both molecular and bulk optical characteristics).4 On the other hand the ionization potential appears rather insensitive to the size of the cluster.For the closed-shell systems these ionization potentials were calculated STRUCTURE OF COPPER CLUSTERS either according to Koopmans' theorem or as the difference of the energies of the neu- tral species and of the ion (the relaxation effects are then accounted for but they appear to be relatively unimportant). Only the latter procedure can be used for the open- shell systems. The calculated values centre around 5 eV and do not show any sig- nificant trend with the number of atoms. They appear rather close to the work func- tion of 4.7 eV for bulk copper. The binding energies per atom calculated with basis set I increase practically linearly with the number of atoms up to n = 8.A similar trend is found between the clusters of 8 and 13 atoms with basis set 11. Thus in terms of binding energy the properties of the clusters should be rather different from those of the bulk metal. The binding energy of 20 kcal mol-' calculated for Cu with basis set I is well below the experimental value of 80 kcal mol-1 for the bulk metal (however part of the difference should be traced to the SCF approximation which underestimates the binding energies). Note added in proof Since this paper was submitted we have completed the calculations (with basis set IV) for the cluster Cu13 with two different structures the cubo-octahedron and the icosahedron. The icosahedron has a lower energy (-21 254.286a.u.for 6Ag)than the cubo-octahedron (-21 254.219 a.u. for 6A,and -21 254.200 a.u. for 2T2g) (these energy values correspond to a double-word accuracy). Thus a cluster of thirteen atoms should prefer an icosahedral arrangement rather than the cubo- octahedral arrangement corresponding to the f.c.c. structure of the bulk metal. Furthermore there may be a close correspondence between the structures of the naked clusters and those of the mole- cular clusters. In this respect one may note that (i) the structure of a trigonal bipyramid is rather common for organometallics with five metal atoms; (ii) a square antiprismatic arrangement of the eight copper atoms has been found in the octameric o-anisylcopper (I); 43 (iii) an icosahedral arrange- ment of thirteen gold atoms has been reported for the cation Au13 (d~pm),.~~ This work has been supported through the A.T.P.no2454 of the C.N.R.S. Calcu-lations have been carried out at the Centre de Calcul du C.N.R.S. in Strasbourg-Cronenbourg. l J. R. Anderson Structure of Metallic Catalysts (Academic Press London 1975). M. Moskowits and J. E. Hulse J. Chem. Phys. 1977,66 3988. M. Moskowits and J. E. Hulse J. Chem. Phys. 1977 67,4271. G. A. Ozin and H. Huber Inorg. Chem. 1978 17 155. W. Schulze H. U. Becker and H. Abe Chem. Phys. 1978,35 177. B. J. Garrison N. Winograd and D. E. Harrison J. Chem. Phys. 1978,69 1440. E. L. Muetterties Bull. SOC. chim. belg. 1975,84,959. * J. M. Basset and R. Ugo in Aspects of Homogeneous Catalysis ed.R. Ugo (D. Reidel Dord- recht 1977) vol. 3 p. 137-183. M. B. Gordon Th2se de Doctorat de 3Pme Cycle (UniversitC Scientifique et MCdicale de Gren- oble 1978). lo R. G. Baetzold J. Chem. Phys. 1971 55,4363. l1 D. J. M. Fassaert H. Verbeek and A. Van der Avoird Surface Sci. 1972,29 501. l2 R. G. Baetzold J. Catalysis 1973 29 129. l3 G. Blyholder Surface Sci. 1974 42 249. l4 R. C. Baetzold and R. E. Mack J. Chem. Phys. 1975 62 1513. l5 R. C. Baetzold J. Phys. Chem. 1976 80 1504. R. C. Baetzold J. Chem. Phys. 1978 68 555. l7 A. B. Anderson and R. Hoffmann J. Chem. Phys. 1974,61,4545. A. B. Anderson,'J. Chem. Phys. 1976 64 4046. l9 A. B. Anderson J. Chem. Phys. 1978 68 1744. 2o J. D. Head and K. A. R. Mitchell Mol. Phys. 1978 35 1681. 21 R.P. Messmer S. K. Knudson K. H. Johnson J. B. Diamond and C. Y.Yang Phys. Rev. B 1976 13 1396. 22 N. Rosch and D. Menzel Chem. Phys. Letters 1976,13,243. C. BACHMANN J. DEMUYNCK AND A. VEILLARD 179 23 J. G. Fripiat K. T. Chow M. Boudard J. B. Diamond and K. H. Johnson J. Mol. Catalysis 1975/76,1,59. 24 D. R. Salahub and R. P. Messmer Phys. Reu. B 1977,16,2526. 25 C. W. Bauschlicher D. H. Liskow C. F. Bender and H. F. Schaefer J. Chem. Phys. 1975 62 4815. 26 R. F. Marshall R. J. Blint and A. B. Kunz Phys. Reu. B 1976,13 3333. ’’P. Fantucci and P. Balzarini J. Mol. Catalysis 1978 4 337. 28 C. Bachmann J. Demuynck and A. Veillard Gazzetta 1978 108 389. 29 B. Roos A. Veillard and G. Vinot Theor. Chim. Acta 1971,20 1. 30 M. BCnard A.Dedieu J. Demuynck M.-M. Rohmer A. Strich and A. Veillard Asterix a System of Programs for the Uniuac 1110 unpublished work. M. BCnard J. Chim. phys. 1976,73,413. 32 M. F. Guest and V. R. Saunders Mol. Phys. 1974,28 819. 33 N. Aslund R. F. Barrow W. G. Richards and D. N. Travis Arkiu Fys. 1965,30 171. 34 P. Joyes and M. Leleyter J. Phys. B 1973 6 150. 35 See for instance J. A. Pople in Modern Theoretical Chemistry. Applications of Electronic Structure Theory ed. H. F. Schaefer (Plenum Press New York 1977) vol. 4 p. I. 36 Quoted in T. H. Upton and W. A. Goddard J. Amer. Chem. SOC. 1978,100 5659. 37 W. S. Schulze H. V. Becker R. Minkwitz and K. Manzel Chem. Phys. Letters 1978,55,59. 38 R. S. Eachus and M. C. R. Symons J. Chem. SOC.A 1970,1329. 39 J. D.Corbett and P. A. Edwards J.C.S. Chem. Comm. 1975,984. 40 R. C. Burns R. J. Gillespie and W. Luk Inorg. Chem. 1978 17 3596. 41 Y.Kim and K. Seff J. Amer. Chem. SOC., 1978,100,6989. 42 R. Unwin and A. M. Bradshaw Chem. Phys. Letters 1978 58 58. 43 A. Camus N. Marsich G. Nardin and L. Randaccio J. Ovganometal. Chem. 1978 174 121. 44 F. A. Vollenbroek Thesis (Nijmegen 1979).

ISSN:0301-5696    

DOI:10.1039/FS9801400170

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Dependence of Stability Bond Strength and Electronic Structure of Dimetal Units upon Atomic Number Oxidation Number and Chemical Environment BY BRUCEE. BURSTEN COTTON AND F. ALBERT Department of Chemistry Texas A & M University College Station Texas 77843 U.S.A. Received 6th August 1979 The electronic structures of the Cr and Mo units in the form of neutral diatomic molecules charged diatomic molecules and coordinated by ligands have been investigated by SCF-Xa-SW calculations supplemented by projection of the Xa MOs in atomic orbital basis sets (the PXa pro-cedure). The results are compared with the experimental data on Cr, Mod and the many CP2L and Mo1',L, complexes. This paper addresses the similarities and differences between the " naked " diatomic metal clusters as they are known in the gas phase or in inert-gas matrices and the " clothed " ones that is those in stable chemical compounds where they form bonds to ligand atoms.The naked ones have the advantages of relative simplicity but are more difficult to study because of the low concentrations and the inconvenience of applying standard physical techniques. The clothed ones can be made and studied more conveniently in a range of formal oxidation states but the presence of other atoms and bonds creates some complications. Taking the dimolybdenum unit as an example we have for Mo,(g) a secure value1 of @,,(406 20 kJ mol-l) some disparate estimates2y3 (315 cm-l and 477 crn-l) for vMo-Mo; earlier MO computations3 have suggested a bond order as high as six with YM~-M~z 2.1 A and Dho-Moz 326 kJ mol-I.The most recent spectroscopic data4 on Mo,(g) have been analysed to give rMo-Mo = 1.929 A DMo-Mo = 397 60 kJ mo1-l and vMo-Mo = 477 crn-l. Compounds containing Mo-Mo triple and quadruple bonds have bond lengths ranging from a low of 2.037(3) A in Mo2[(C5H4N) NC(0)CH3]45 to 2.457(1) 8 in Mo,[(F,P)~NCH,]~C~~ which contains a twisted triple bond.6 vM0-Mo values range from ~300 to 426 cm-I and a wealth of information both experimental and theoretical is available on the electronic structures of these bonds. The Cr,(g) molecule is said to have rCrdCr= 1.685 A,4 which is difficult to reconcile with the reported @98 of only z 150 kJ m~l-',~ and distances of 1.83-2.54A ~-~~ found in Cr24+ compounds.8 This short value of Y~ will be correct only if the assumption that the spectrum from which it is derived9 is due to Cr rather than CCrC or OCrO is correct.* While it has been recognized from the startg that this point * If the observed spectrum is due to CCrC or OCrO the C-Cr or 0-Cr distances would have to be x1.78 or % 1.54 A respectively.We emphatically disagree with the statement that these are so implausible as to allow an ips0 facfo rejection of these species. CCrC is not a less likely product of photolysis of Cr(C0)6 than Cr and since Cr-C is 1.91 A in Cr(C0)6 where there are six Cr-C bonds and each C atom also forms a multiple bond to oxygen a Cr-C distance of "1.78 A in CCrC is not a priori unreasonable. B. E. BURSTEN AND F.A. COTTON can be checked conclusively by repeating the measurements with isotopic labelling such an experiment (which would not be difficult) has not yet been done. We shall describe here calculations performed on MO,~+and Cr24+ species with q varying from 0 to 4. The objectives are (1) to compare corresponding molybdenum and chromium species and (2) for each one to investigate the dependence of the bond- ing on the internuclear distance and the charge. COMPUTATIONAL METHODS All calculations were performed using the SCF-Xa-SW method of Slater and Johnson.".'l Starting parameters were chosen as in earlier Xa calculations l2 on Mo and Mo;+. The overlapping atomic-sphere radii used were chosen to be 25 % greater than tangential-sphere radii and the outer-sphere radii were chosen to touch the atomic spheres.This choice of sphere radii results in consistently good virial ratios.13 The calculations were iterated until the largest change in the molecular potential was <0.0005 a.u. The converged calculations were projected onto a Slater atomic orbital (STO) basis using the projected Xa (PXa) method.14 To avoid biasing the PXa results a very flexible even-te~pered'~ valence STO basis was used for all calculations. For Cr atoms the basis consisted of five uncontracted 3d STOs ([ = 0.5 1.0 2.0 4.0 and 8.0) three uncontracted 4s STOs (c = 1.0 2.0 and 4.0) and three uncontracted 4p STOs ([ = 1.0 2.0 and 4.0). For Mo atoms the same exponents were used for the 44 5s and 5p STOs. In all cases the use of these basis sets resulted in an overlap of >0.99 between the LCAO MOs and the corresponding Xa MOs.RESULTS AND DISCUSSION NEUTRAL DIMERS We begin with Mo for which Norman et al. have already reported12 an Xa-SW calculation that led them to propose an Mo-Mo bond order of six. This calculation was done with Mo-Mo distances greater than the 1.929 A now reported from experi- ~ent.~ This short distance implies that the bond order is greater than four. We have reinvestigated the electronic structure at the experimental distance. The orbital energies and the Mulliken percent characters l6 of the valence orbitals of Mo (dMo-Mo1.929 A) obtained from the PXa treatment are given in table 1. = TABLE1.-ORBITAL ENERGIES AND PXa MULLIKEN PERCENT CHARACTERS OF THE VALENCE ORBITALS OF MO orbital efeV %4d %5s %5P 1% -0.53 131 -31 1OU -1.38 24 125 -49 16 -2.49 100 -2oga -3.58 9 112 -21 16 -4.51 100 1ZU -6.24 98 -2 1U -7.00 84 0 16 a Highest occupied orbital.STABILITY OF DIMETAL UNITS B. E. BURSTEN AND F. A. COTTON FIG.1.-Contour plots of the 10 (a),1nu(b),16 (c) and 20 (d) orbitals of Mo2at 1.929 A. Interior contours close to the atomic centres have been omitted for clarity. All plots are in the xz plane. The contour values are kl f2 f3 k4 rt5 = k0.015 10.030 10.060 10.120 10.240 respectively. STABILITY OF DIMETAL UNITS For a singlet ground state the twelve valence electrons should form a closed shell (10,)~ (lnJ4 (20,)' configuration corresponding to two a two n and two 6 bonds between the Mo atoms as previously found by Norman et al.at the longer Mo-Mo bond distances. Before presenting a detailed analysis of the six metal- metal bonds however some comment on the seemingly anomalous Mulliken percent characters (i.e. >lo0 or <0) of the 2a, la and ln orbitals is in order since such intuitively displeasing results tend to indicate deficiencies in the STO basis used for the LCAO projection. However it was precisely to avoid this difficulty that a very flexible basie set was used. The 2ag la and In orbitals are very diffuse containing respectively only 23 20 and 50% of their charge density within the atomic spheres. Mulliken population analysis however assumes that orbitals largely retain atomic character thus allowing the charge density to be equitably divided among the contri- buting AOs.l6 Unfortunately this approximation breaks down for very diffuse orbitals not only in the present case but in semi-empirical and ab initiu LCAO-MO calculations on transition metal systems as well7 Contour plots of the la, In, 16 and 20 orbitals are presented in fig.1. The la orbital as expected," is dominated by the metal 4dz2 AOs. There is appreciable (16%) mixing of Mo 5p character as well however. Although not obvious from the contour plot the A0 coefficients of the projected 1a orbitals indicate that this mixing results in 4d2*-5p bonding interactions via the 442 doughnut a result which will be discussed in more detail later. The In, and 16 orbitals clearly represent bonding interactions between the 4dx,,y and 4dx2-y2,xyAOs respectively.The 20 orbital is dominated by 5s-5s bonding interactions accounting for its resemblance to a diffuse Rydberg orbital but the 4dz2 AOs also participate with coefficients opposite in sign to the 5s AOs. This causes a polarization of the density in a direction perpendicular to the Mo-Mo bond (cf. the oblate contour at the centre of the plot). The 5p orbitals also mix in to give a 5s-5p2 bonding interaction strengthening the overall bonding in the orbital. Although it is clear that there are six bonding interactions in Mo2,it is important to make a distinction between the number of metal-metal interactions and the strengths of these interactions/ Whereas the number controls the magnetic properties of the molecule it is the strengths that determine the bond length and bond energy.The complexity of the contour plots of the orbitals precludes their use in estimating the relative strengths of the a ;rc and 6 interactions but the projected LCAO orbitals produce an informative representation of the bonds. It is generally assumed that the extent of bonding between two atoms in an orbital is related to the amount of shared charge in the inter-atomic region. This is the under- lying assumption in the use of Mulliken overlap population^^^ to estimate relative bonding strengths. However the breakdown in the conventional Mulliken analysis for the diffuse 20 orbital leads us to employ the following modification. For a molecular orbital v consisting of AOs on atoms A and B we write The charge density distribution in the orbital given by the square of v,,(r),will consist of one-centre terms involving only AOs on either atom A or atom B and the two- centre cross terms which we will call the overlap distribution OD@) B.E. BURSTEN AND F. A. COTTON Multiplying OD(r) by the occupation of the orbital and integrating overall space gives the Mulliken overlap population (MOP) MOP = n I OD(r) dr = 2 2 cp cy Sij ly where Sljis the overlap integral’’ between xf and xy. However the use of Sljis the source of difficulty for diffuse orbitals,17 so we prefer to display OD(r) directly thus focusing on the distribution between the atoms. Fig. 2 and 3 present surface plots of OD(r) for the four occupied MOs of Mo,.The la overlap distribution not surprisingly is indicative of a large charge concentra- FIG.2.-Overlap distribution function for the la (a)and 1 n,,(6) orbitals of Mo at 1.929A. The xz plane has been plotted with z increasing from the bottom corner to the right corner of the plot. The position of one of the atoms is indicated by the dot on the lower plot. STABILITY OF DIMETAL UNITS FIG.3.-Overlap distribution function for the 16 (a) and 20 (b) orbitals of Mo at 1.929 A. The positions of the atoms are indicated by the dots on the upper plot. tion between the atoms. The smaller peaks on either side of the Mo atoms result from the complex nodal structure of the Mo 4d 5s and 5p AOs and are not of im-portance in this discussion.The large “ wells ” off the end of each Mo atom result from overlap of the diffuse 5pz orbital on one Mo with 4dz2 orbital on the other MO. Since as noted earlier the 5pz orbitals mix into the la MO to produce bonding between the atoms via the 4dz2 “ doughnut,” the 5pz-4dz2 overlap off the ends of the molecule must be negative. It is important to note that Mulliken analysis of this orbital would consider these “ wells ” as antibonding contributions to the MO an assumption which seems unsatisfying. The ln overlap distribution consists of two large peaks on either side of the nodal plane of the orbital and small features around the atoms due again to the nodal B. E. BURSTEN AND IF. A. COTTON structure of the 4d AOs. From a comparison of the la and lnuoverlap distributions it would appear that the a bond is probably stronger than one rc bond but less strong than the sum of both rc bonds and reminds one of the relative a and n bond strengths in hydrocarbons.The 16 overlap distribution is distinguished by its flatness suggesting an insensi- tivity of the 6 interaction to the metal-metal bond length and presumably also the converse i.e. that the metal-metal bond length is relatively insensitive to the amount of 6 interaction." Thus it seems doubtful that the extremely short bond length of Mo relative to Mo"L species owes much to the addition of another 6 bond. On the other hand the 20 overlap distribution indicates a fairly substantial buildup of density along a ridge running through the centre of the Mo-Mo bond and we con- clude that this second a bond may actually be stronger than the 6 bonds even though it lies at higher energy.The existence of this second CT bond in conjunction with the absence of ligand effects may largely account for the very short bond in Mo,. For Cr we have performed calculations at internuclear distances of 1.685 and 1.80 A. The orbital energies of the two Cr calculations are compared with those of Mo in fig. 4. At both distances a bond order of six is obtained in complete analogy 0 -9 In 1 a ............--.. _.l._.............--- -0. -.%.*. . ........-(.*- -2 Ib -.-- .........---.*.* ......-.. -3 Mo,(1.929 ,&I Cr2(1.685 A1 Cr2(1.800AJ FIG.4.-Molecular orbital energies of Mo2 at 1.929 A and Cr2at 1.685 and 1.800 A.with Mo,. The slight upward shifts of the lo, In and 16 levels in Cr relative to Mo probably result from both a slight increase in the metal d orbital energy and slightly weaker bonding. The la orbital rises by nearly 1 eV indicating that the main a bond in Cr is probably weaker than that in Mo,. This is consistent with predictions from extended Huckel calculations2' of the M bond energies2 for M0 (79 kcal mol-l) and Cr (61 kcal mol-l) although the predicted value for Mo is so much lower than the experimental value (97 & 5 kcal mol-l) that the results of such extended Huckel calculations are of dubious value. It is also notable that the drop in STABILITY OF DIMETAL UNITS energy of the 20 orbital of Cr relative to that of Mo, a change which is consistent with the observation that the atomic ionization potential of Cr 4s electrons is greater than that of Mo 5s electrons,22 appears to agree with the shifts in the electronic spectra of matrix isolated Mo and Cr2.The first allowed excitation presumably the 20 -+ la (52 t'Z;) transition is blue-shifted from 19530 cm-l in Mo to 21 930 cm-I in Cr . With the exception of the 20 orbital lengthening the Cr-Cr bond from 1.685 to 1.80 A results in the expected changes uiz. the bonding orbitals rise in energy while the antibonding levels drop. The 20 orbital behaves curiously showing a slight decrease in energy upon bond lengthening as might be expected for an antibonding orbital. The reason is that the increase in bond length greatly changes the character of the 20 orbital; nearly all of its 3dz2 character is lost at 1.80A resulting in an essen- tially nonbonding 4s-4s MO with slight mixing in of 4p character very similar to the onorbital proposed for multiply bonded compounds.18 That the orbital remains at very nearly the same energy would seem to indicate that the second o bond in Cr2 even at 1.685 A is not as strong as that in Mo, but this is inconsistent with the extremely short Cr-Cr bond and supports our view that the reported distance should be checked.QUADRUPLY CHARGED DIMERS Theoretical study of charged M2units is important because they form the basis ofa myriad of M"L quadruply bonded corn pound^^^^^^ in which the effects of the ligands upon the molecular and electronic structures are still incompletely understood.Thus depending upon the number geometry basicity and n-bonding capabilities of the ligands the formally quadruply bonded dichromium(r1) complexes span a remarkably wide range of CrCr bond lengths from 1.83 to 2.54 A.8 In this section we will first examine the electronic structure of the base M;+ units comparing them to the neutral dimers and investigating the effects on the molecular orbitals of changing M-M bond length. The valence molecular orbital energies of Mo;+ are shown next to those of Mo in fig. 5. The bond length of 1.929 A has been retained to facilitate the comparison even though the shortest known Mo-Mo quadruple bond5 is more than 0.1 A longer than this. The calculation on Moi+ employed Dlth rather than Dmh symmetry allowing us to selectively occupy the two different components of both the 6 and 6 representations.Thus the 6 representation of Dmh splits into b, + b, under symmetry in which the former uses dX2+2 orbitals as a basis and the latter uses dx,,orbitals. This breaking of symmetry will be helpful in our simulation of ligand donation effects in the next section. It should be noted that the spherical averaging of the XCC-SWmethod guarantees that the (b,, bZg)and (bl, bZu)set of orbitals will remain degenerate as they should. There are a number of interesting features in fig. 5. The ground configuration of Moi+ which we have constrained to correspond to a 'A, ground state is alg2e:b2s2 (or equivalently alg2e,4b,,2)corresponding to one O two n and one 6 bond for a total bond order of 4.This is the expected result. What is surprising however are the orbital shifts upon the removal of four electrons from Mo,. The most prominent feature is the large upward shift of the 2al orbital of Moi+ relative to the 20 orbital of Mo,. This shift has been attributed by Norman et all3 to greater stabilization of the Mo 4dAOs relative to the Mo 5s AOs. The lalgand la, MOs of Mo~+ exhibit large stabilization and destabilization respectively relative to their counterparts in Mo,. This strongly suggests that the main component of the Mo-Mo o bond is B. E. BURSTEN AND F. A. COTTON 5 4 3 2 1 eV 0 -1 -2 -3 -4 -5 M02 FIG.5.-Molecular orbital energies of MoZ and Moi+ at 1.929 A.The zero of energy has been as-signed to the average of the 6 and 6" orbital energies. strengthened upon the removal of electrons from the diatomic unit most probably because of a contraction of the Mo 4d22 orbitals in the charged species. In Mo they are diffuse enough to allow significant overlap of the positive lobe on one Mo 442 with the negative torus on the other one but contraction induced by making the atoms positive increases the positive overlap and results in more effective 4d22-4dz2 inter-action. The leu and leg MOs of MO;+ exhibit analogous downward and upward shifts albeit not as great as those of the la, and la, levels and a similar explanation is applicable. That the 4dx,,, AOs in Mo are too large for optimal interaction is apparent in fig.2(b),OD@)for the ln MO. There are clearly valleys off the ends of the molecule indicative of the over-extension of the 4dX,,, AOs on one atom to the far side of the other atom an effect which will be Iessened by contraction of the 4d orbitals. The 6 and 6" MOs of Mo;+ shift very slightly upward and downward relative to those of Mo, evidence for a very slightly weaker 6 interaction in the charged species. This shift is again consistent with a contraction of the Mo 4d orbitals since the geometry of dxy,x*-y2 orbitals dictates that their overlap will montoni-cally decrease with increasing compactness of the orbitals. The very small magnitude of the shift shows the insensitivity of the 6 interaction to changes in atomic charge as well as changes in bond length.To investigate the energetics of the orbitals of M;+ as a function of metal-metal bond lengths we have performed calculations on Cr;+ at 1.85 2.00 and 2.15 A. The orbital energies for the three calculations are shown in fig. 6. Increasing the metal- metal distance results in smooth nearly linear upward shifts of the bonding orbitals and downward shifts of the antibonding orbitals with slopes in the order cr E TC >6. STABILITY OF DIMETAL UNITS 1.85 A 2.00 A 2.15 A FIG.6.-Molecular orbital energies of Cr$+at 1.85 2.00 and 2.15 A. The zero of energy has been assigned to the average of the lbzgand lbl orbital energies. The Ib2 orbital is the highest occupied orbital in all three calculations. PRESENCE OF LIGANDS If we assume an electronic configuration for M;+ of (a1,)2(e,)4(b2g)2, i.e.the metal d,2 d,, dyzand dxyAOs are half-filled (neglecting for now the higher lying s and p AOs) the interaction of ligands with the Mi+ unit can occur in three different ways. (1) The ligands can donate charge to the empty dxz-y2,s orp orbitals. (2) The ligands can donate charge into the antibonding blu,e or aZUorbitals. (3) The ligands can accept charge from the occupied metal levels. The effect of the first of these will be to reduce the effective positive charge on the metal atoms without significantly affecting the bond order. The second and third interactions will each reduce the bond order of the metal-metal bond besides causing a reduction or increase respectively in the positive charge on the metal atoms.The geometry of the ligands and their electronic requirements will dictate the relative importance of these three types of interaction . We have chosen to demonstrate the effect of ligands on the dimeric unit by performing a PXa calculation on [MO~CI~]~-, in which only the first two effects will be possible Calculational details are given el~ewhere.~~~~~ The PXa total Mulliken orbital populations are given in table 2 referred to the coordinate system in fig. 7. These are compared to "idealized " Mo;+ wherein 5s and 5p contributions to the filled levels are ignored resulting in a (~~)~(xz)~(yz>~(xy)~ configuration on each Mo atom. The main component of Mo-CI boHding is donation from the C1 3px orbitals to Mo 4d,~-~zand 5s orbitals the bonding B.E. BURSTEN AND F. A. COTTON TABLE 2.-BONDING AND ANTIBONDING CONTRIBUTIONS TO THE ATOMIC ORBITAL POPULATIONS OF [IVf02c&]4-bonding antibonding total Mo24-t a 0.99 0.09 1.08 1.o 0.36 0.31 0.67 0.0 1.oo 0.09 1.09 1.o 1.oo 0.09 1.09 1.o 1.oo 0.09 1.09 1.o 0.15 0.12 0.27 0.0 total 4.50 0.79 5.29 4.0 C1:b 3s 1.96 3Px 1.78 3PY 3Pz 1.98 1.96 total 7.68 a See text. See fig. 7 for the reference coordinate system. x FIG.7.-Coordinate system of [Mo2Cl8I4-. C1" is the chlorine atom used for the population analysis in table 2. (big or a,,) contribution being slightly greater than the antibonding (b2uor a2u). There are smaller C1 to Mo donations from the 3s 3py and 3p orbitals the effect of which is to make the 4dzz 4dxy,4dxzand 44 A0 populations greater than one.Any charge in these AOs in excess of the half-filled configuration must result from MOs which are metal-metal antibonding as indicated in tabie 2. The net result of all the bonding and antibonding effects is a reduction of the Mulliken bond order from 4.0 (1.0 0,2.0 n,1.0 S) in Mo:+ to 3.71 (0.93 0 1.82 TI,0.96 S) and a reduction of the charge on the Mo atom from +2.0 to +0.71. The chloride ions have donated 0.94 e per Mo atom via mode (1) and 0.35 e per Mo by mode (2). Another way to study the first mode of ligand-metal bonding i.e. ligand 0 donation without metal-metal bond order reduction has been accomplished by investigating the energetics of Crh+ and MoZ+ (q = 4 3 2 1 0) at 1.850and 1.929 A respectively.Charge is reduced from 4-4 by introduction of equal amounts of elec-tron density to the b, and b2uorbitals resulting in no change in the metal-metal bond order and simulating the effect of idealized simple donation to the metal dXz-,,z STABILITY OF DIMETAL UNITS orbitals. The calculated differences in the o and o*,7t and n*,and 6 and 6* orbital energies are summarized in table 3. Several interesting trends are evident. The TABLE3.-vARIATION OF THE O-O* 71-71* AND 6-6" ORBITAL ENERGY DIFFERENCES (ev) FOR QUADRUPLY BONDED M%+ 4 Crg+ 0-0* 71-71 * 6-6 " o-o* Moj+ n-n* 6-6 * 4.0 5.73 3.39 0.69 8.94 6.50 1.54 3.O 5.35 3.70 0.88 8.01 6.51 1.75 2.0 4.82 3.91 1.10 6.96 6.38 1.94 1.o 3.95 3.92 1.33 5.73 5.94 2.11 0.0 2.46 3.74 1.21 4.37" 4.74" 2.21" a This value is from a calculation which was ill-behaved and is not fully converged.o-o* energy separation in both species decreases monotically with decreasing positive charge corroborating the proposal in the previous section that the dz2 orbitals of the neutral atoms are too extended for optimal bonding at short distances. In contrast the n-n* separations in both molecules are not a monotonic function of the charge. Rather the n-n* separation maximizes at a particular degree of simulated donation indicating that the 7t-bonding can be optimized. The 6-6* separation is monotically increasing with increasing donation except for the Cr;+ (q = 0) calculation. This is surprising in that the 6-6" interaction should increase with increasing diffuseness of the Cr 3d orbitals.A possible explanation of this anomaly is a dominance of the 6 and 6* orbital energies by the charge residing in the dX2-,,2 orbitals for it must be remembered that the quadruple bond has been preserved ; the electron configuration (als)2(eJ4 (b2s)2(bJ2 (b2u)2 formally corresponds to one o bond two 7t bonds two 6 bonds and one 6 antibond. Upon comparing the Cr;+ calculations to those of Mo$+,it is seen that both the o-o* and n-n* energy separations span a wider range for Moj+ and that the n-n* separation in Mo;+ maximizes at a greater positive charge. All of these trends indi- cate that the Mo 4d orbitals in Mo;' are less contracted than the Cr 3d orbitals in Cr$+ at the chosen bond distances.Although a more judicious choice of Mo-Mo bond length would have been 2.00 to 2.05 A the orbital separations are expected to decrease only slightly and we expect the compact character of the Cr 3d orbitals to be general. These simulations of the effects of simple o donation by ligands although ad- mittedly simplistic can be used to explain several puzzling trends in the structural chemistry of quadruply bonded compounds. For example the replacement of the chloride ions in [M02C&l4- by methyl groups which are stronger charge donors results in a lengthening of the metal-metal bond from 2.139 A in K4M02C18. 2H2027 to 2.147 A in Li,Mo,(CH& 4THF." It might appear then that chloride ion is a better ligand for the formation of quadruple bonds than is the methide ion.However the situation is very different for chromium for which the complex [Cr2(CH&j4- exists28 but the analogous octachloro compound does not. It is very likely if not entirely certain that this is the result of thermodynamic factors and an attractive explanation is in the electronic differences between Cr and Mo in quadruply bonded complexes. Increased donation by the methyl groups decreases the charge on the Mo atoms beyond the optimal point resulting in orbitals which are too diffuse and causing the Mo atoms to move further apart to compensate. The Cr atoms on the other hand require greater donation than Mo atoms and chloride ions may be in- B. E. BURSTEN AND F. A. COTTEN capable of delivering enough density to the Cr atoms to stabilize a quadruple bond.This argument has of course neglected completely the second mode of ligand-metal interaction which we discussed earlier. It is apparent that modes (2) and (3) of ligand interaction with Mi+ units can also be easily simulated by calculations with varying degrees and distributions of added electron density. Such calculations will be made in the future to develop a compre- hensive description of the electronic effects of ligands on multiple metal-metal bonds. This work has been supported by the National Science Foundation through a research grant and a National Needs Postdoctoral Fellowship to B. E. B. S. K. Gupta R. M. Atkins and K. A. Gingerich Znorg. Chem. 1978 17 321 I. W. Klotzbucher and G.A. Ozin Inorg. Chem. 1977 16 984. W. Klotzbucher G. A. Ozin J. G. Norman Jr and H. J. Kolari Inorg. Chem. 1977 16 2871. Yu. M. Efremov A. N. Samoilova V. B. Kozhukhovsky and L. V. Gurvich J. Mol. Spectr. 1978,73,430. * F. A. Cotton W. H. Ilsley and W. Kaim Inorg. Chem. 1979,18 2717. F. A. Cotton W. H. Ilsley and W. Kaim J. Amer. Chem. Soc. 1980 102 1918. 'A. Kant and B. Strauss J. Chem. Phys. 1966 45 3161. A. Bino F. A. Cotton and W. Kaim J. Amer. Chern. Soc. 1979 101 2506 and references therein. Yu. M. Efremov A. N. Samoilova and L. V. Gurvich Optics and Spectroscopy 1974 36 654. lo J. C. Slater The Selfconsistent Field for Molecules and Solids Quantum Theory of Molecules and Solids (McGraw-Hill New York 1974) vol. 4. l1 K.H. Johnson Ann. Rev. Phys. Chem. 1975 26 39. l2 J. G. Norman Jr H. J. Kolari H. B. Gray and W. C. Trogler Znorg. Chem. 1977,16,987. l3J. G. Norman Jr J. Chem. Phys. 1974 61,4630. l4 B. E. Bursten and R. F. Fenske J. Chem. Phys. 1977,67 3138. K. Ruedenberg R. C. Raffenetti and R. D. Bardo Energy Structure und Reactivity Proceed- ings of the 1972 Boulder Seminar Research Conference on Theoretical Chemistry ed. D. W. Smith (Wiley New York 1973) p. 164. l6 R. S. Mulliken J. Chem. Phys. 1955 23 1833. l7 J. H. Ammeter H.-B. Burgi J. C. Thibeault and R. Hoffmann J. Arner. Chem. Soc. 1978 100,3686. l8 F. A. Cotton Znorg. Chem. 1965 4 334. l9 R. S. Mulliken J. Chem. Phys. 1955 23 1841. 2o F. A. Cotton J. M. Troup T. R. Webb D. H. Williamson and G. Wilkinson J.Amer. Chem. Soc. 1974 96 3824. 21 R. Hoffmann J. Chem. Phys. 1963 39 1397. 22 C. E. Moore Atomic Energy Levels (Nat. Bur. Stand. Circ. 467 vol. I1 and 111 1952 1958). 23 F. A. Cotton Chem. SOC.Rev. 1975 4 27. 24 F. A. Cotton Accounts Chem. Res. 1978 11 225. 25 5. G. Norman Jr and H. J. Kolari J. Amer. Chem. Soc. 1975 97 33. 26 B. E. Bursten Ph.D. Thesis (University of Wisconsin Madison Wisconsin 1978). 27 J. V. Brencic and F. A. Cotton Inorg. Chem. 1969 8 7. 28 J. Krausse G. Marx and G. Schodl J. Organometul. Chem. 1970 21 159.

ISSN:0301-5696    

DOI:10.1039/FS9801400180

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Dynamic and Static Stereochemistry in Dirnolybdenum and Ditungsten Compounds Containing a Central (M=M)“+Unit BY MALCOLM H. CHISHOLM Department of Chemistry Indiana University Bloomington Indiana 47405 U.S.A. Received 4th September 1979 The chemistry of molybdenum and tungsten in oxidation state +3 is now dominated by compounds containing a central (M=M)6+ core with metal-to-metal distances in the range 2.2-2.3 A. The molecular orbital configuration of the triple bond is dn4arising from the mutual interaction of metal atomic d,z (0)and d,, d,,(n) orbitals. In compounds containing the central (MEM)~+ core the metal atoms may be bonded to three four five or six ligand atoms. Examples of each are given and for a given coordination number the preferred geometry is discussed.Low temperature n.m.r. studies support the view that the structures found in the solid state are also present in solution. Variable temperature n.m.r. studies reveal a wealth of knowledge concerning the dynamic behaviour of these molecules in solution. For example (i) M2(NR2)6 and Mz(NR2)4Yz molecules (Y = halide alkyl or alkoxy group) are molecular propellers; (ii) rotational barriers about metal-to-metal triple bonds in MzY4Xz(M=M) compounds are comparable to those in related Si2Y4X2 and P2Y4 com-pounds; the latter contain a central element-element 0-bond of length 2.2-2.3 A; (iii) molecules of the type L(R0)3M=M(OR)3L’ contain OR groups which are cis and trails to the neutral ligands L and L’. Site exchange between cis and ti’aans groups occurs on the n.m.r.time-scale by a threshold mechanism which does not involve exchange of OR groups between the two metal atoms. This is compared to the fluxional properties associated with MX5 compounds (D3,,+D4J. Finally the absence of any complex containing a central M4I2+ tetrahedral arrangement is noted. The closest approach to such a compound is seen in the tetranuclear Complexes Mo~(,x-F)~(OBU~)~ and Mo~(,LL- F)3(p-NMe2)(OB~t)8 which contain a bisphenoid of molybdenum atoms having two short Mo-Mo distances (2.26 A) and four long Mo-Mo distances (3.75 A) corresponding to localized triple and non-bonding interactions respectively. “ There are literally thousands of chromium(Ir1) complexes which with very few exceptions are all hexaco~rdinate.’’~ This is not surprising in view of the fact that ligand field stabilization favours an octahedral geometry for a d3 ion.Since ligand field stabilization energies increase sizeably in going from the first to the second row and again from the second to the third row within a triad of transition metals one might have anticipated an abundance of molybdenum(Ir1) and tungsten(II1) hexaco- ordinate complexes. Rather interestingly the reverse trend is observed there is but a handful of well authenticated mononuclear molybdenum(Ir1) complexes and to this author’s knowledge not one mononuclear complex is known for tungsten(Ir1). Does this mean that the argument based on ligand field stabilization is fallacious? Certainly not. If we consider the d6 configuration for example we find an abun- dance of six-coordinate octahedral 2nd and 3rd row transition metal complexes e.g.IP PtIV complexes. The main difference between the d3 and d6 systems rests with the former being paramagnetic and the latter diamagnetic and since within any triad of metals for given oxidation state Z+,the effective nuclear charge exerted on the valence electrons decreases down the series then the d3 orbitals in an octahedral en- vironment t& become more diffuse and available for metal-metal bonding. This is M. H. CHISHOLM well demonstrated in the structures of the M2C1;-ions which share a common con- facial bioctahedral geometry D3h,and where the M-M distances change from 3.12 A (M = Cr) to 2.67 (M = Mo) to 2.41 (M = W).2'3 Indeed W2C1$- is diamagnetic and Pauling4 introduced the canonical structures W=W and WgW as part of a resonance hybrid description for the anion.However the types of compounds described in this accowt are of a simpler nature in that there are no atoms directly bridging the two metals. SYNTHESES Though this account does not dwell on syntheses or reactivity patterns of the com- pounds to be described it is worth noting that the basic M& compounds [M = Mo or W X = R(P-elimination stabilized alkyl) or NMe,] are derived from metathetic reactions involving either MoCl, MoCl, wC16 or WC14. Though the details of these reactions are now known we have presented a strong case for the fact that the M2X6 compounds are not formed by the coupling of two reactive mononuclear species.6 The most synthetically useful compounds are the dimethylamido Compounds M,(NMe,),,7y8 from which literally scores of dinuclear compounds con- taining the central (MEM)~ have been prepared.Some of these reactions are sum- + marized in scheme 1. where R =Me CHzCMe3 M -Mo R = Bur PrF or Mo2( OZCNMez)4 (m) + 1-alkene f alkane R = Et i-Pr n-Bu MO~(OR)~L~;= an amine L SOLID-STATE STRUCTURES M2X6COMPOUNDS (x = R NR2AND OR) All these compounds have a central staggered ethane-like M2C6 M2N6or M206 group having virtual D3d~ymmetry.~Two views of the Mo,(NMe,) molecule are shown in fig. 1. The M-NC planes are aligned with the Mo-Mo-N planes thus maintaining Dfdsymmetry and giving rise to six proximal N-methyl groups those lying over the metal-metal bond and six distal N-methyl groups.There is also a large class of M2X,(NR2)4compounds e.,q.,X = halide alkyl or alkoxide group.5* These may be viewed as 1 ,Zdisubstituted ethane-li ke molecules. The halides all crystallize in the anti-rotamer and maintain this in hydrocarbon solutions.lO?ll Fig. 2 shows the * The compounds where X = OR(R = But Pr' Et and Me) have only recently been made and behave in solution like the corresponding alkyls X = CH,R.9 196 STEREOCHEMISTRY IN COMPOUNDS CONTAINING (MEM)6C lb) 2C(13) N(121 lC(12) wbZC(12) FIG.1 .-Two ORTEP views of the Mo,(NM~,)~ molecule (a) almost perpendicular to the Mo-Mo axis; (b)almost along the Mo-Mo axis. In this and in all other structural figures thermal ellipsoids are drawn at the 50% probability level.molecular structure of W2C12(NEt2)4 lo again the N-ethyl groups are arranged in proximal and distal sets. The solid state structures of W2Me2(NEt2)412 and Mo2Me2- (NME2),13also show the anti-rotamer. M2X6L2 COMPOUNDS Mo~(OS~M~~)~(HNM~~)~'~ lS are two examples of nitrogen and W2(OPri)6(py)2 donor adducts to M2X6-type molecules. The geometry about each metal is essentially square planar and the two M03N units are joined in such a manner that they are partially staggered with respect to each other. A view down the W-W bond of the W206N2 skeleton of the W2(OPri),(py) molecule is shown in fig. 3. In the Mo~(OBU~),(O~COB~')~ molecule there are a pair of cis-02COBut ligands which bridge the MozMo bond.' This imposes a virtually eclipsed geometry on the Mo2040& skeleton.In the W2(NMe2)4(PhN3Ph)2 molecule the diphenyltriazenido group is bidentate but does not bridge the WzW bond." An ORTEP view of the molecule is shown in fig. 4 note that the molecule has a C2axis of symmetry. M. H. CHISHOLM FIG.2.-An ORTEP view of the WzC12(NEt2)4 molecule. Note the central W,C12N skeleton has virtual Czusymmetry. N1 02 FIG.3.-The Wz06N2 skeleton of the W2(OPri)6(py)2 molecule viewed down the metal-metal bond. 198 STEREOCHEMISTRY IN COMPOUNDS CONTAINING (MZEM)6t FIG.4.-An ORTEP view of the W2(NMe2)4(PhN3Ph)2 molecule emphasizing the C2 axis of symmetry. Irrespective of the nature of the groups present we have found that when four atoms are coordinated to each metal in an (M=M)'j+ compound the four atoms lie at least roughly at the corners of a square plane.Typically the M-M distance is ~0.02 8 longer in these compounds than in the simple M2X6 compounds.* What about five atoms coordinated to each metal? Where will the fifth ligand position be? Well we only have one structurally characterized example so it is certainly premature to claim a general trend. The central skeleton of the W,(CH,) (02CNEt2)4 molecule is shown in fig. 5. There is a pair of bridging O,CNEt ligands which imposes an eclipsed geometry with respect to each end of the molecule.ls There is also a pair of bidentate O,CNEt ligands and the carbon atom of the methyl group makes up a pentagonal coordination for each tungsten.Although one cannot generalize from a single case the structure of W2(02CNMe,)6l9 is so closely related to that of W2(CH3)2(02CNEt2)4 that it is at least tempting to say that a pattern is beginning to emerge. The central W,(O,C) skeleton is shown in fig. 6. The relationship between the structure of W2(CH3)2(02CNEt2)4 and W2 (O,CNMe,) is most striking the methyl carbon is replaced by an oxygen atom of an axially aligned O,CNMe group. The other oxygen forms a weak/long bond in the axial position. 'Thus it appears that the central (M=M)6+ unit upon expanding the coordination number of each metal from 3 to 4 to 5 goes from trigonal to square planar to penta- gonal planar and only reluctantly will accept a sixth ligand atom in the axial position (axial with respect to the M-M bond).REMARKS ON BONDING In all the compounds a simple analysis of the symmetry types of orbitals required to form M-M and M-L bonds and a consideration of the symmetry properties of * See ref. (56) for a tabular listing of M-M distances containing the central (MEM)~+group. M. H. CHISHOLM FIG.5.-The central W2C2(02C)4 molecule emphasizing that the skeleton of the W2(Me)2(02CNEt2)4 molecule has virtual Czvsymmetry. 09 FIG.6.-The central wz(Ozc)6 skeleton of the W2(02CNMe2)6 molecule emphasizing that the molecule has virtual Czvsymmetry. the metal valence shell orbitals leads to a satisfactory formulation of electronic structure. We may assume that the M=M bond is formed primarily by overlap of metal dZ2 orbitals to give the component and metal dxzand dyzorbitals to give the rc components.This is in accord with the assumption originally made and subse- quently supported by SCF Xcc calculation^^^ for the quadruple bond in Re,Cl;- and Mo,Cli-. Furtheriiiore the detailed electronic structure of Mo,X compounds (X = 200 STEREOCHEMISTRY IN COMPOUNDS CONTAINING (M=M)6' R NMe and OH) was the subject of a recent SCF Xcc SW calculation and here the calculated and observed p.e. spectra were in good agreement.20 Then in M2X6 molecules the metal may use sp2or sd2hybrids to form the three tri- gonal bonds. When X = NR2 or OR ligand to metal n-bonding may also occur to two of the metal orbitals not used in a-bonding.The maximum M-N bond order is therefore 13 in M2(NMe,) compounds and each metal attains a valence shell of 16 electrons. 798 In M2X4L2molecules the four planar bonds may use s px,py d,z_,z-hybrids. In W,(Me),(O,CNEt,) the five quasi-planar bonds may use tungsten s px,py,dx2-y2 and dxyatomic orbitals and in W2(0,CNMe2)6 the additional use of the tungsten pz orbital may be employed to form the weak axial W-0 bond (2.67 A). Such a qualitative picture may be viewed as satisfactory to the extent that it readily accounts for the observed diamagnetic nature of the compounds and the short nature of the Mo-Mo distances which are only ~0.1 8 longer than those found in compounds containing MoZMo bonds. * Furthermore all the compounds are yel- low or orange resulting from a tailing into the visible of higher energy (u.v.) charge transfer bands.Lastly it should be noted that a triple bond consisting of a (T component and two equivalent n-components has cylindrical symmetry and imposes no restriction upon geometry [cf. Re,Cli-where the 6 component of the M-M bond imposes an eclipsed geometry of the two ReCI; units]. The observed geometries for all of the afore- mentioned compounds appear to be totally dominated by the steric requirements of the ligands. All the M2X6 and M2X6L2 compounds adopt staggered geometries because steric repulsive interactions dominate. Only in Mo,(OBu'),(02COBut)2 W2(Me)2(02CNEt2)4 and W2(02CNMe2)6 which contain bridging OCO groups are the geometries eclipsed. DYNAMICAL SOLUTION BEHAVIOUR Since all the compounds are diamagnetic their dynamical solution behaviour is readily investigated by variable temperature n.m.r.spectroscopy. The dialkylamido compounds reveal the expected but rarely before observed diamagnetic anisotropy associated with a triple bond. Variable temperature n.m.r. studies reveal that these molecules are " cheerleader " molecules they whirl as they twirl.? Detailed descriptions concerning the rotations that occur around the M-N bonds and the M=M bonds have been presented elsewhere as has the assignment of proximal and distal resonance^.^^ It is sufficient here to exemplify the phenomenon. Fig. 7 shows the high temperature and low temperature limiting 'H n.m.r. spec- trum of W2C12(NEt2) in [2H,]tol~iene. At high temperatures >130 "C proximal + distal ethyl exchange is rapid on the n.m.r.time-scale while at low temperatures <-16 "C,proximal and distal resonances are frozen out. Three further points are noteworthy. (1) The high-temperature limiting spectrum corresponds to an ABX3 spectrum and the low-temperature limiting spectrum to two ABX3 spectra. Evi-dently the mechanism of proximal $ distal exchange does not remove the diastereo- topic nature of the methylene protons. (2) The spectra correspond to the presence of only the anti rotamer in solution. This is the rotamer found in the solid state; * See ref. (56) for a recent tabular listing of M-M distances in compounds containing a central MEM bond. 7 At Indiana University they cheer " Go Big Red ".M. H. CHISHOLM 201 ~~ 6.O 5.0 4.0 3.0 2.0 1.o 0.0 8 / p.p.m. FIG.7.-(a) High (150 "C) and (b) low (-18 "C) temperature limiting 'H n.m.r. spectra of anti-W2C1,(NEt,) obtained in [2H8]toluene at 100 MHz. see fig. 2. (3) There is a large chemical shift separation between proximal and distal methylene proton resonances z2.5 p.p.m. The separation between proximal and distal methylene carbon resonances is much larger z 30 p.p.m. The variable temperature n.m.r. spectra of M2R2'(NR2)4compounds R' = Me Et i-Pr n-Bu CH,CMe and CH,SiMe, and R = Me and Et are more complex A because both anti and gauche rotamers exist in equilibria in ~o1~tion.~~*~~*~~ gauche M2R2'(NR2)4molecule has C2 symmetry and thus has two types of NR groups two are anti to R' and two are mutually anti.The low temperature limiting 'H n.m.r. spectrum for W,(CH,CMe,),(NMe,) in [2H,]toluene is shown in fig. 8. 202 STEREOCHEMISTRY IN COMPOUNDS CONTAINING (MEM)6t i FIG.&-Low temperature limiting 'H n.m.r. spectrum of a mixture of anti andgauche W2(CH2CMe3)2 (NMe2)4 obtained at -65 "C and 270 MHz. Note the relative concentrations of gauche to anti rotamers are z 10:1 and that the methylene protons of the neopentyl ligand are an AB quartet in which the chemical shift separation of the Ha and Hb protons is very large. Note (1) The gauche-rotamer predominates. (2) The methylene protons of CH2CMe ligands are diastereotopic and form an AB pattern. (3) The chemical shift separation of the Haand Hbprotons is now exceedingly large [cf the N(CH2CH,) spectra shown in fig.71. The latter presumably reflects the fact that in the gauche rotamer the pair of bulky CMe groups impose a preferred conformation in which the methylene protons occupy sites which are quite different with respect to the M-M triple bonds' diamagnetic anisotropy. Since the M2R2(NRJ4 molecules appaiently prefer to crystallize in the anti- rotameric form it has been possible to measure the energy of activation for anti-to- gauche isomerization in these molecules. This is slow on the n.m.r. time-scale and can be followed by monitoring the approach to equilibrium EA falls in the range 20-24 kcal mol-l depending upon specific R and R' combination^.^" A point which now naturally arises is by what mechanism does anti +gauche isomerization occur a simple rotation about the M-M bond or by an intramolecular mechanism in which NR2 groups are transferred from one metal atom to the other by way of the formation of dialkylamido bridges cJ2 metal carbonyl site exchange in cluster metal carbonyls? This question is best answered by the examination of a molecule of the formula M2X5Y.Here the X groups naturally fall into three classes as shown below. y\ If rotation about the MEEMbondis frozen out on the n.m.r. time-scale then one should observe 3 different X signals. If rotation is fast on the n.m.r. time-scale then X(2) and X(3) become equivalent but remain distinct from X(1). Finally if exchange of X groups between the two metal atoms occurs rapidly then all X groups become equivalent.We have been able to synthesize molecules of this form. For example when M. €1. CHISHOLM Mo,(C,H,),(NMe,) is treated with tert-butanol in benzene the fascinating reaction shown below occurs 21* Examination of the IH n.m.r. spectrum of MO~(C~H,)(OBU*)~ at -65 "C and 270 MHz shows two types of OBu' groups in the integral ratio 2:3. This is consistent with the view that rotation about the W-W bond is still rapid on the n.m.r. time- scale and furthermore that alkoxy group exchange between metal atoms is slow. Further support for facile rotation about M=M is seen in the low-temperature 'H n.m.r. spectra of M2Me2(OB~t)4 Here we have not yet been able to freeze out anti + gauche isomerization on the n.m.r. time-scale even using high field spectrometers.We attribute the difference in EA to rotation about the M=M bond in compounds of the form M2R2'(NR2)4 and M2R2'(OBu*)4to the cogging effect of the NR2 groups in the former. The compounds M2(NR2)6 and M2X2(NR2)4 which we refer to as cheerleader molecules correspond stereochemically to 1,I ,2,2-tetra-aryl substituted ethanes and in solution behave as molecular propeller^.^^ When the blades are removed as in M,R,(OBU')~ and M,R(OBu') compounds then rotation about the M=M bond becomes much more facile EA < 7 kcal mol-I. Indeed the rotational barriers appear close'iy related to tetra-alkyl silanes R,HSi-SiHR and tetra-alkyl diphosphines R2P-PR2 which in solution also prefer the gauche conforma-tion.26 This comparison is all the more impressive when one recognizes that the Si-Si a-bond distance is ~2.3 A (Mo-Mo is 2.2 A) and the P-P a-distance is 2.2 A (W=W is 2.3 A).Thus we believe that our work has provided the first experimental demonstration that for a non-linear molecule containing a triple bond composed of one 0and two equivalent 7c components the rotational barrier is limited only by the steric factors associated with the substituents on the two elements which are united by the triple bond. Molecules of the type M2(OR)6L2 contain two types of OR groups on each metal atom namely those which are cis and trans with respect to the ligand L. In all cases which we have examined thus far the low temperature limiting n.m.r. spectra reveal two types of OR groups in the integral ratio 2 :1.Perhaps even more fascinating is our observation that the low temperature limiting 13Cn.m.r. spectrum of the W2(OPri),- (py) molecule shows three methyne carbon signals OCH(CH3), in the integral ratio 1 :1:1 which is what is expected for a W206N2 skeleton that has virtual C sym-metry namely the pyridine ligands are adjacent to each other as shown in fig. 3. Al-though in the crystal there are six distinct oxygen atoms it is easy to see that a slight twisting about the WrW bond brings about a time-averaged molecule with an apparent C axis of symmetry thereby making the oxygen atoms fall into three sets (01 OS) (03 07) and (02 06). It then follows that there should be three sets of me- thyne carbon atoms. At room temperature on the n.m.r.time-scale all M2(0R)& molecules show only one type of OR group. This is consistent with rapid (n.m.r. time-scale) cis + trans isomerization. Once again however one would like to answer the question " How is this achieved?" In order to probe such an intriguing matter one must design a * We note in ref. (22) that when the reaction is carried out using the labelled compound Mo2-(CH2CD3),(NMeJ4 with Bu'OH the ethane that is eliminated is exclusively CH,DCD,. The result- ing ethyl ligand is CZH3D2formed from Bu'OH + CD2 :CH2 and has a statistical distribution of deuterium atoms on the cc and p ethyl carbons. 204 STEREOCHEMISTRY IN COMPOUNDS CONTAINING (MrM)6f molecule of the form M2(0R)6L1L2 in which L and L2are two different donor ligands then each end of the molecule is effectively labelled M(1) and M(2).One must also design a molecule where it is possible to show that L1and L2do not hop between the two metal atoms either by an intra- or inter-molecular mechanism. In this regard ligand dissociation must be ruled out otherwise M(l) and M(2) would become equivalent. We think we have been fortunate enough to obtain such a molecule. Crystallo-graphically we have shown that acetylene^,^^ allenes29 and dialkylaminocyanimides 29 add across the M=M bond in the Cp2M02(C0)430 compound in the manner shown in fig. 9. Now it so happens that Mo2(OR) compounds also react with all of the f ;N\ I Mo' FIG.9.-Schematic representations of the Cp,Mo2(C0)4(un) molecules where A un = RC ECR; B un = allene and C un = Me2NCN emphasizing the coordination of the central Mo,(un) group.above. Unfortunately no crystallographic data are at present available on the ad- ducts. Nevertheless if we make the assumption that in the Mo2(oPri),(NCNMe2) one molybdenum atom receives a lone pair of electrons from the terminal nitrogen atom while the other molybdenum atom receives a pair of electrons from the C=N ;It-bond and furthermore that this causes the NCNC2 unit to become planar with a fairly high energy barrier (n.m.r. time-scale) to rotation about the central C-N bond then we are home and dry. This may seem like too much to assume but the amazing fact is that the low-temperature 'H n.m.r. spectrum shown in fig. 10 is entirely consistent with these assumptions.There are four methyne proton resonances labelled A-D in fig. 10 respectively. The methyl region of the OPri ligands is more M. H. CHISHOLM complex and consists of three well separated doublets marked E-G and three over- lapping sets marked H in fig. 10. Six methyl resonances are indeed expected accord- ing to our assumption since (i) each molybdenum atom is labelled (ii) there are cis and trans OPr' ligands with respect to the NCNMe ligand and (iii) the methyl groups FIG.10.-Low-temperature limiting 'H n.m.r. spectrum of Mo2(0Pri)6(NCNMez) obtained at -45 "C 220 MHz in [2H,]toluene. The methyne proton resonances are indicated A B C and D and the methyl resonances E F G and H. The signals marked with an asterisk are due to Mo,( OPri)6 (M =M).of the cis-OPr' ligands are diastereotopic. There are also two signals of equal intensity for the N-methyl protons which is expected for a planar C,NCN group with restricted rotation about the central N-C bond. [This latter observation is directly analogous to the low-temperature limiting spectrum observed for Cp2M02(CO) (NCNMe,)].29 The only other resonances seen in the spectrum (fig. 10) are assignable to (i) small amounts of Mo,(OPr') which is present as an impurity and (ii) residual protons in the [2H,]toluene solvent. On raising the temperature the methyne proton resonances B and D start to broaden and then coalesce as do three of the methyl doublets namely the doublets indicated by F G and one from H in fig. 10. At this temperature site exchange of three of the OPr' ligands is fast while the other three are still frozen out on the n.m.r.time-scale. There are still two signals of equal intensity for the N-methyl protons which implies that the Mo,(NCNC,) unit is not fluxional. We believe the most reason- able interpretation of the dynamic behaviour of the molecule at 16 "Cis that alkoxy group exchange is occurring rapidly at one molybdenum atom but not at the other. Furthermore it is reasonable to suppose that the rapid site exchange involves the alkoxy groups which are coordinated to the least sterically crowded molybdenum atom namely the one which receives a nitrogen lone pair. On raising the temperature above 16 "C site exchange between the other set of OPr' ligands sets in and finally (>80 "C) all OPr' ligands become equivalent and the N-methyl resonances collapse to a single resonance.This is consistent with the view that the Mo,NCNC unit becomes fluxional in a manner which equilibrates both molybdenum atoms this was found for Cp,Mo,(CO),(NCNMe,). All these tem- perature dependent processes do not involve free Mo,(OPr-i), which is present in solution and are thus considered intramolecular processes. Indeed a plausible explanation for the above and indeed all the M2(0R),L2 compounds is that the ends of the molecules undergo facile square-based pyramidal + 206 STEREOCHEMISTRY IN COMPOUNDS CONTAINING (M=M)6i-trigonal bipyramidal interconversions of the type well known for mononuclear ML5 complexes.32 The only major difference is that for the dinuclear compounds M=M there seems to be a marked preference for the square-based pyramid and thus the trigonal bipyramidal form is either a relatively unstable intermediate or a transition state for cis + trans isomerization shown below.M M M The W,(02CNMe,) molecule displays a particularly fascinating dynamical solution behaviour." Each O,CNC unit is planar and one can reasonably assume* that EA for rotation about the central C-N bond is zl6 kcal mol-l. Thus the carbon resonances of the methyl groups can be used to monitor the motions of the oxygen atoms. Furthermore by using 13CQ2 in the preparation of the compound (see scheme 1) one can readily monitor the three types of carboxylic carbon atoms.? Three distinct chemical processes can be detected which are in increasing order of energy of activation (1) the exchange of O(12) and O(11) sites.This is tantamount to an intramolecular substitution reaction in which an entering axially aligned ligand 0(12) substitutes one of the ligands in the pentagonal plane O(11); (2) Exchange of terminally bonded carbamate groups i.e. 13C resonances associated with C(5) and C(6) coalesce and (3) finally above room temperature exchange between bridging and terminally bonded carbamate ligands become fast on the n.m.r. time-scale. The dynamic behaviour of W2Me2(OzCNEt2)4 also parallels that of W2(0,CNMe,) in solution but here there are only two types of carbamato ligands :bridging and ter- minal. Below room temperature the solid-state structure (fig.5) is frozen out on the n.m.r. time-scale. However above 50 "C rapid exchange of bridging and terminal ligands occurs.19 In contrast to the carbamato complexes which readily exchange bridging and ter- minal groups the W2(NMe2)4(PhN3Ph)2 (see fig. 4) molecule appears relatively rigid in s01ution.l~ The molecule contains a C,axis of symmetry and may be considered as a member of the class of gauche-M,X,(NMe,) molecules but with X = the bi- dentate triazenido group. There are therefore two types of NMe groups and at -45 "C and 220 MHz the IH n.m.r. spectrum clearly shows four N-methyl reso- nances of equal intensity two proximal (downfield) and two distal (upfield). On raising the temperature there is a pair-wise collapse to give ultimately two lines at 100 "C which means that even though rotations about the M-N bonds become fast on the n.m.r.time-scale the C2axis of symmetry is rnaintained.l7 Enantiomerization involving either gauche to gauche or gauche to anti to gauche transformations does not occur rapidly on the n.m.r. time-scale. This could have been caused either by a simple rotation about the W=W bond or by the formation of an intermediate in which the two 1,3-diphenyltriazenido ligands bridged the M-M bond cJ the structure of NO,(QB~~)~(Q,COB~~),.~~ The difference in both the static and dynamic stereo- chemistry of the Mo2(OBut),(O,COBut) and W2(NMe2)4(PhN3Ph)2 molecules is once again determined by the steric demands of the ligands bonded to the central * Simple organic carbamate esters Me2NC(0)OR show a barrier to rotation about the C-N bond of 16 kcal mol-l 33 1-Note the molecule has virtual Czvsymmetry.M. H. CHISHOLM 207 (MEM)~+ unit. The M-NC units in M2X2(NMe2)4 compounds are effectively cogged in such a way that even though rotations about M-N bonds may be fast on the n.m.r. time-scale rotation about the M=M is hindered. This fact can be used to advantage in investigating the mechanisms of substitution reactions at these dinuclear centres. For example the observation that anti-W,Cl,(NEt,) reacts with LiCH,- SiMe (2 equiv.) in benzene to give anti-W,(CH,SiMe,),(NEt,) which then slowly isomerizes to a mixture of anti-and gau~he-W,(CH,SiMe,),(NEt,)~indicates that the alkyl-for-chloride ligand exchange must proceed with retention of stereochemistry at tungsten.34 Mi2+CLUSTERS For some time now we have been trying to establish that the dimerization of two (M=M)6+ containing compounds can lead to Mi2+ cluster compounds containing a central tetrahedral M4 unit.Indeed it seemed that for a given ligand X or combina- tion of X Y ligands there should be an equilibrium of the type shown below.6 As the steric bulk of an alkoxy ligand is reduced polynuclear [Mo(OR),], com- pounds are formed e.g. for R = Et and Me.35 These are diamagnetic which indi- cates the existence of metal-metal bonds but as yet no X-ray structural information is available. The closest approach to a tetrahedral Mi2+cluster was recently found in the reac- tion between Mo,(OBU')~ and PF (2 equiv.) which leads to a black compound of empirical formula Mo(F)(OBu'),.In one preparation of this compound crystals suitable for detailed X-ray work were obtained. The unit cell was found to contain one molecule of Mo4(~-F),(OBut),and two molecules of Mo~(,u-NM~~)(,u-F),(OBU~)~.~~ The latter compound was a total surprise to us and we attribute the presence of the di- methylamido ligand to incomplete alcoholysis in the preparation of the starting material Mo,(OBu') (see scheme 1). ORTEP views of the Mo~(,u-F)~(OB~') and Mo~(,u- NMe2)(~-F),(OBut) molecules are shown in fig. 11 and 12 respectively. In both molecules the Mo~ unit is a bisphenoid having two short Mo-Mo distances 2.26 8 (averaged) and four long Mo-Mo distances 3.75 A (averaged). Evidently a fluoride-for-tert-butoxide reaction induces a Lewis base association reaction by the formation of metal-ligand bridges.While substitution of the small and more electronegative fluoride ligand might well be expected to promote a Lewis base association reaction,35 the choice of bridging ligands which is established namely F NMe > OBu' is surprising to us. It seems as if the localized M=M units (2.26 A) are held apart by the fluoride bridges-though we have no way of knowing at this time whether these molecules are formed under kinetic or thermodynamic control. Finally however it should be noted that the geometries about the Mo2F404 and Mo2NF304 units (M=M) are virtually identical to the local Mo,O,O' skeleton of the Mo,(OB~~)~(O,COB~~), (MEM) molecule.There are two molybdenum atoms held together by a metal-to-metal triple bond (no bridging groups) and each molybdenum atom is coordinated to four ligands which lie roughly in a square plane. 208 STEREOCHEMISTRY IN COMPOUNDS CONTAINING (MEd't~f)~' Cl111') c (1 21') C(211') c(111') c ( 221') FIG.11.-The central skeleton of the Mo~(,u-F)~(OBU')~molecule. M. H. CHISHOLM C(211) "'1 d >' c (A11) I' FIG.12.-The central skeleton of the Mo4(p-NMez)(p-F),(0Bu')amolecule. For financial support of this work we thank the Research Corporation the donors of the Petroleum Research Fund administered by the American Chemical Society the National Science Foundation the Office of Naval Research the Marshal H. Wrubel Computing Center and the Tax Payers of the State of Indiana.This author is also grateful for all the talented co-authors referenced in this work and in particular to Prof. F. Albert Cotton who was instrumental in promoting this work uia collabora-tion during this author's term at Princeton University. F. A. Cotton and G. Wilkinson in Advanced Inorganic Chemistry (Interscience Publishers 3rd edn 1972) section 25-C-4 p. 830. F. A. Cotton Rev.Pure Appl. Chem. 1967 17 25 and references cited therein. R. Sailant and R. A. D. Wentworth Inorg. Chem. 1969 8 1226 and references cited therein. L. Pauling The Nature of the Chemical Bond (Cornell University Press 3rd edn 1960) p. 437. For recent reviews of chemistry associated with these compounds see (a)M. H.Chisholm and F. A. Cotton Accounts Chem. Res. 1978 11 356 and (b) M. H. Chisholm Transition Metal Chem. 1978 3 321. M. H. Chisholm M. W. Extine R. L. Kelly W. C. Mills C. A. Murillo L. A. Rankell and W. W. Reichert Inorg. Chem. 1978 17 1673. 210 STEREOCHEMISTRY IN COMPOUNDS CONTAlNlNG (MZdVf)6+ M = Mo M. H. Chisholm F. A. Cotton B. A. Frenz W. W. Reichert L. W. Shive and B. R. Stults J. Amer. Chem. Soc. 1976 98 4469. M = W M. H. Chisholm F. A. Cotton M. Extine and B. R. Stults J. Amer. Chem. Soc. 1976 98,4477. M. H. Chisholm and J. Garman results to be published. lo M. H. Chisholm F. A. Cotton M. W. Extine M. Millar and B. R. Stults J. Amer. Chem. SOC. 1976,98,4486. l1 M. H. Chisholm F. A. Cotton M. W. Extine M. Millar and B. R. Stults Inorg.Chem. 1977 16,320. l2 M. H. Chisholm F. A. Cotton M. W. Extine and B. R. Stults Inorg. Chem. 1976,15,2244. l3 M. H. Chisholm F. A. Cotton M. W. Extine and C. A. Murillo Inorg. Chem. 1978 17,2338. l4 M. H. Chisholm F. A. Cotton M. W. Extine and W. W. Reichert J. Amer. Chem. SOC., 1978 100,153. l5 M. Akiyama M. H. Chisholm F. A. Cotton M. W. Extine D. A. Haitko D. Little and P. E. Fanwick Inorg. Chem. 1979,18,2266. l6 M. H. Chisholm F. A. Cotton M. W. Extine and W. W. Reichert J. Amer. Chem. Soc. 1978 100,1727. l7 M. H.Chisholm J. C. Huffman and R. L. Kelly Inorg. Chem. 1979,18 3554. l8 M. H. Chisholm F. A. Cotton M. W. Extine and B. R. Stults Inorg. Chem. 1977 16,603. l9 F.A. Cotton Accounts @em. Res. 1978 11 225 and references cited therein.2o F. A. Cotton G. G. Stanley B,. J. Kalbacher J. C. Green E. Seddon and M. H. Chisholm Proc. Nat. Acad. Sci. 1977 74 3109. M. H. Chisholm D. A. Haitko and C. A. Murillo J. Ameu. Chem. Soc. 1978,100,6262. 22 M. H. Chisholm and D. A. Haitko J. Amer. Chem. Soc. 1979 101 6784. 23 R. D. Adams and F. A. Cotton in Dynamic Nuclear Magnetic Resonance Spectroscopy ed. L. M. Jackman and F. A. Cotton (Academic Press N.Y. 1975) p. 489. 24 M. H. Chisholm and D. A. Haitko results to be published. 25 K. Mislow Accounts Chem. Res. 1976 9 26. 26 S. G. Baxter D. A. Dougherty J. P. Hummel J. F. Blount and K. Mislow J. Amer. Chem. Soc. 1978 100 7795. 27 W. I. Bailey M. H. Chisholm F. A. Cotton and L. A. Rankel J. Amer. Chem. Soc. 1978,100 5764. 28 W. I. Bailey M.H. Chisholm F. A. Cotton C. A. Murillo and L. A. Rankel J. Amer. Chem. Soc. 1978 100 802. 29 M. H. Chisholm F. A. Cotton M. W. Extine and L. A. Rankel J.Amer. Chenz. Soc. 1978,100 807. 30 R. J. Klinger W. Butler and M. D. Curtis J.Amer. Chem. Soc. 1975,97,3535; 1978,100,5034. 31 M. H. Chisholm and R. L. Kelly Inorg. Chem. 1979,18,2321. 32 A. D. English S. D. Ittel C. A. Tolman P. Meakon and J. P. Jesson J. Amer. Chem. Soc. 1977 99 117 and references cited therein. 33 E. Lustig W. R. Benson and N. Duy J. Org. Chem. 1967 32 851. See also discussion in M. H. Chisholm and M. W. Extine J. Amer. Chem. Soc. 1977,99 782. 34 M. H. Chisholm and M. W. Extine J. Amer. Chem. Soc. 1976,98 6393. 35 M. H. Chisholm F. A. Cotton C. A. Murillo and W. W. Reichert Inorg.Chem. 1977,16,1801. 36 M. H. Chisholm J. C. Huffman and R. L. Kelly J. Amer. Chem. Soc. 1979,101 7100.

ISSN:0301-5696    

DOI:10.1039/FS9801400194

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

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. The same holds true for the isomers with and without bridging carbonyls of CO,(CO)~.~~~ It is not possible to decide on the preference for one or the other type of cluster without taking into account all important energy terms including repulsions between CO m01ecules.~~ Such terms will also have to be taken into account quantitatively if one wants to study the details of the geometry of one particular isomer e.g.the question why the bridged Co2(CO) isomer does not fold open or the staggered versus eclipsed conformation of carbonyls on different metals. It is a matter for future investigation whether SCF calculations of the Hartree-Fock-Slater type can provide insight into these more subtle questions. Based on W. Heijser Ph.D. Thesis (Vrije Universiteit Amsterdam 1979). L. F. Dahl E. Ishishi and R. E.Rundle J. Chem. Phys. 1957 26 1750. L. F. Dahl and R. E. Rundle Acta Cryst. 1963 16 419. A. Almenningen 6.G. Jacobsen and H. M. Seip Acta Chem. Scand. 1969 23 685. H. M. Powell and R. V. G. Ewens J. Chem. Soc. 1939 286. F. A. Cotton and J. M. Troup J.C.S. Dalton 1974 800. ’G. G. Sumner H. P. Klug and L. E. Alexander Acta Cryst. 1964 17 732. S. Evans J. C. Green M. L. H. Green A. F. Orchard and D. W. Turner Disc.Faraday SOC. 1969,47,112. B. R. Higginson D. R. Lloyd S. Evans and A. F. Orchard J.C.S. Faraday II 1975,71 1913. lo D. F. van de Vondel L. F. Wuyts G. P. van der Kelen and L. Bevernage,J. Electron Spectr. Rel. Phenom. 1977,10 389. E. W. Plummer W. R. Salaneck J. S. Miller Phys. Rev. 1978 B18 1673. R. T. Lundquist and M. Cais J. Org. Chem. 1962 27 1167.R. A. Levenson and H. B. Gray J. Amer. Chem. SOC.,1975 97 6042. l4 H. B. Abrahamson C. C. Frazier D. S. Ginley H. B. Gray J. Lilienthal D. R. Tyler and M. S. Wrighton Inorg. Chem. 1977 16 1554. Is N. Flitcroft D. K. Huggins and H. D. Kaesz Inorg. Chem. 1964 3 1123. BINUCLEAR METAL CARBONYL COMPLEXES l6 F. A. Cotton and R. M. Wing Znorg. Chem. 1965 4 1328. l7 R. W. Cattrall and R. J. H. Clark J. Organometal. 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ISSN:0301-5696    

DOI:10.1039/FS9801400211

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. J. Winn (Berkeley)said The mechanism for Ag photoaggregation in a rare- gas matrix is consistent with the known potential energy curves for the isovalent alkali- metal-rare-gas diatomics.lq2 These molecules are characterized by extremely weak ground-state binding energies and extremely long bond lengths. Optical excitation in the molecular bonds (which lie slightly to the red of the corresponding atomic reson- ance lines) produces a continuum fluorescence which extends well to the red of the absorption. This fluorescence is due to bond-free emission from the rather more strongly bound shorter bond-length excited states to the repulsive wall of the ground state. In the matrix experiment an observation of the dispersed fluorescence result- ing from excitation in the atomic line may reveal the Sam2 qualitative features in sup- port of the mechanism.Similarly an analysis of this fluorescence could indicate the magnitude of the repulsive kick given to the Ag on such a relaxation. J. H. Goble and J. S. Winn J. Chem. Phys. 1979,70,2051. J. Tellinghuisen A. Ragone M. S. Kim D. J. Auerbach R.E. Smalley L. Wharton and D. H. Levy J. Chem. Phys. 1979,71 1283. Dr. ReF. Barrow (Oxford) said I would like to ask if anything is known about triplet states of Ag, which might perhaps be expected to be seen in absorption in a low-temperature matrix. Prof. H. A. Skinner (Manchester)said The dissociation energy of only one of the molecules investigated by Kasai and McLeod is known i.e. D,"(AuMg) = 243 kJ mol-l.This is included in table 6 of the paper by Gingerich. It is a reasonably strong bond implying that the antibonding electron a,*is insufficient to neutralize the bonding power of the 0,2 electron pair which is strengthened by the ionic character of the AuMg bond. Estimated Do0 values for AuZn AuCd and AuHg by Gingerich and Miedema are less than for D;(AuMg) but even in the weakest of these (AuHg) the calculated bond strength is of the order 100 kJ mol-". In triatomic molecules Au2M Cu,M (M = Mg Zn Cd Hg) ionic structures [Au-M+Au-1 [Au-M+-Au] and the dicovalent [Au-M"-Au] (from a diva-lent excited state of M) may contribute to the bonding and it would be of interest to know bond strengths in molecules of this type. The triatomic Au,Ba molecule has been investigated (table 8 of the paper by Gingerich) and the average bond-energy in this (276 kJ mol-l) is larger than Diin BaAu (251 kJ mol-I).Dr. P. H. Kasai (Z.B.M.) said The ionic term makes a large contribution to the stability of AuMg. This is reflected in the small value of A/& determined for this molecule (fig. 10 of our paper). The ground state of an intermetallic molecule AB arising from the atoms A(ns') and B(n's2)may not be always 'C(aiafl>as observed for the present series of molecules. A plausible alternative state is 21J(cr~n1) where rc represents the orbital resulting from the bonding combination of the np and n'p atomic orbitals. We have observed the e.s.r. spectrum of NaZn in the 2C state (a,2az1) but failed to detect the signal attribut- able to NaMg from the matrices containing Na and Mg atoms.The failure may be GENERAL DISCUSSION due to the state of NaMg. An EHT molecular orbital calculation also supports this contention. Prof. H. A. Skinner (Manchester) said The identification of the ground-state configurations and multiplicities of certain dimetals by Montano is a most welcome breakthrough. In one case namely Fe, the dissociation energy D,"= (100 & 21) kJ mol-1 has been measured. Such weak bonding is difficult to reconcile with the quadrupole bonding to be expected of a singlet ground state but is less surprising given the 7C ground state now proposed. Accordingly five electrons singly occupy the a,*,ring* and 6 antibonding orbitals and only the singly occupied do bonding orbital has its antibonding counterpart vacant.All other bonding orbitals are in effect " neutralized " by antibonding electrons and the net bonding is provided by the single do electron. D,"values are not yet known for FeCo FeCu FeMn and FeNi; Miedema's estimates (table 1 of his paper) place FeCo > FeCu > FeFe in agreement with Montano's order of " bond strength " but there is marked disagreement for FeNi. Montano finds retention of the 3d64s2configuration of Fe in the FeNi mole- cule but it is perhaps relevant to recall that the d9sconfiguration in Ni lies very near to the d8s2ground state. This should counterbalance the bonding disadvantage of the d6s2configuration of Fe. Dr. P. A. Montano (Morgantown)said I turn first to Prof.Skinner's question about the weak bonding and high multiplicity of the iron diatomic molecules. The weak bonding of Fe is not very surprising. From their mass spectroscopic work Kant and coworkers have determined a small dissociation energy for Fe,; moreover the isomer shift observed for the Fe molecule isolated in solid rare gases (-0.14 mm s-l) indicates a weak bonding between the two atoms. This isomer shift value is close to the one observed for the iron monomer in solid rare gases (3d64s2 atomic configuration). The C character of Fe is well determined from the sign of the electric field gradient. The spin per atom was determined by carrying out Mossbauer measurements in the presence of an external field; a ferromagnetic coupling was observed.In order to find a consistent description of the electronic ground state of this molecule we carried out EHMO calculations. Due to the large amount of experi-mental information we were able to obtain the ground state 7C and to find a value of 1.5 eV for the dissociation energy (1.3 eV is the measured value). We were also able to explain the observed optical transitions for Fe in solid argon1 EHMO/eV exp/eV n; + n 3.07 3.37 0,-+ 0 2.7 2.98 n; -+ n 2.2 2.32 The interatomic equilibrium distance in Fe was calculated using EHMO as 2 A; in recent EXAFS measurements we found a value of 1.9 A. Indeed the electronic configuration of the ground state dissociation energy and optical transitions of Fez can be well explained within a simple EHMO picture.This does not mean that the EHMO approach is useful for all the diatomics; a good handling of the EHMO cal- culations was possible for Fe due to the weak bonding and large amount of experi- mental information available. More accurate theoretical calculations are needed. Prof. Ozin commented about the site symmetry on the monomeric species iso- lated in solid rare gases. In our studies of iron atoms isolated in rare gas solids we have not observed any evidence for a non-cubic site symmetry. This non-cubic site symmetry will manifest itself by producing an electric field gradient at the 57Fe nucleus. From our measure- GENERAL DISCUSSION ments in the presence of large magnetic fields no evidence of any non-cubic component in the crystal field was detected.However we know that multiple trapping is possible and that the iron atom can be trapped in an interstitial site but retaining octahedral symmetry. It is worth mentioning that Jacob et a1.2 have observed a non-cubic com- ponent in the crystal field of europium atoms isolated in solid argon. Concerning the discussion about ab initio and Xcc-SCF calculations initiated by ProfXotton I would like to remark that the test of the validity of any theoretical cal- culation is its agreement with the experiment. A very good example of fundamental discrepancy between experiment and theoretical calculations is the recent paper by Jones and Harris. This paper has been considered by many as one of the most out- standing calculations of diatomic molecules; however in the case of Fe the ground- state symmetry and dissociation energy are in disagreement with the experiments.This of course indicates that carrying out very complicated and expensive calculations does not imply better results. For example in a semi-qualitative way Xcc-SCF cal-culations by Johnson and coworkers predict an increase in the magnetic moment at the iron atom as the particle size decreases ; this has been corroborated by the experi- ments. It is extremely important to try to carry out theoretical calculations on mole- cules where a large amount of experimental information is available. Since all the approximations used for small molecules are subject to ill defined uncertainties the validity of the theoretical calculation will be ultimately in its agreement with the experimental results.T. C. de Vore et al. Chem. Phys. Letters 1975 35 78. M. Jacob H. Micklitz and K. Luchner Phys. Letters 1976 57A,67. Dr. E. R.Buckle (Shefield) said Evaporation of metal at low pressure is evidently regarded as a good method of producing " naked " clusters for these spectroscopic studies. A difficulty will arise with the larger aggregates containing a few hundred atoms say as these are not present in saturated vapour in significant numbers. Un-less encouraged to grow by heterogeneous nucleation on a surface such particles can only be made to grow by aerosol condensation as in the formation of smoke and fume. The condensation of evaporated atoms into nuclei and the growth of the nuclei into larger and larger particles is dependent on the interplay of gradients of vapour pressure and temperature which extend outwards from the source forming a boundary 1ayer.l A front of enlarging particles is continuously advancing through this layer which at ordinary pressures is at most only a few mm thick.If the temperature out- side the layer is low enough the final type and size of particle observed is that which emerges from the layer. The earliest stages of cluster-building are to be looked for inside the layer up to and immediately beyond the point at which the critical super- saturation is achieved. Only under very stable conditions of heating and external flow will the location of this point be constant in time. The observed variations in the types of particle produced in the presence of natural convection2 suggest that stable conditions may only be achievable in stagnant conditions when the layer expands to fill the space between the source and sink of heat.The boundary layer expands also when the pressure is reduced and at the same time convection is less of a problem. The emerging particles are in this case smaller but it is not yet known from experi- ments if the size can be continuously decreased by working at lower and lower pressures. Attempts are in progress to follow the evolution of particles through the layer by laser microbeam ~cattering.~ E. R. Buckle and K. C. Pointon Faraday Disc. Chn. SOC.,1976 61 92. * E. R. Buckle and P. Tsakiropoulos J. Muter. Sci. 1979 14 1421. E. R. Buckle J. Microscopy 1978,114 205.GENERAL DISCUSSION Prof. K. A. Gingerich (College Station) said Dr. Montano’s interpretation of the measured isomer shift (IS) in terms of relative bond strength is very interesting. How reliable is this method in predicting relative (and possible absolute) bond strengths ? The sequence of bond strengths FeCo (strongest)>FeCu > FeMn > FeFe > FeNi is unexpected especially with respect to FeNi and to a lesser extent FeMn. The atomic cell model (Miedema’s paper table 1) predicts 129 125,80 100 (experimental) and 169 kJ mol-l respectively for these molecules. Application of the Pauling model as described in my paper results in the same relative stabilities for these intermetallic molecules as does the atomic cell model.If Dr. Montano can derive something definite about the relative bond strengths from his IS measurements this would be very important since his method would be indicative of details in the electronic structure of these intermetallic molecules. An experimental determination of the dissociation energies would be important in view of the apparent discrepancy between Dr. Montana’s results and those predicted by the above mentioned empirical models. Dr. P. A. Montano (W. Virginia) said I do not think the isomer shift can be used in general to determine bond strengths since several factors affect the electron density at the nucleus. For diatomic molecules (in iron) we have a competition between 3d and 4s orbitals’ participation in the bonding. For example if the d-orbital population at the iron atom increases a more positive isomer shift is observed; a similar effect is observed if the 4s-electron population decreases.It is difficult to predict strictly the bonding on the basis of the isomer shift alone. However we have used a simple argument for describing the isomer shifts trend of the iron-diatomic molecules. It is based upon the assumption that the closer the electron configuration at the iron is to 3d64s2,the weaker is the bond to the neighbouring atom. Accidental cancellation effects cannot be excluded in the present interpretation. I will not recommend the method as a substitute for the standard dissociation energy measurements. Dr. A. R. Miedema (Eindhoven)said I would like to make a general comment in relation to the final four papers.The stability of matrix-isolated clusters can be different from that of vacuum clus- ters. This difference is something like the interfacial adhesion energy at a metal-inert gas interface the relevant interface area being the surface area of one mole of metal atoms. The interfacia! adhesion is expected to be expressible by A~J~M-2@y*+yM+ (A is = the inert gas M is the metal with 03 0.4). That such a treatment can be correct even for interfaces of atomic dimensions can be verified by analysing the heats of adsorp- tion of rare gases on metallic substrates. Indeed heats of adsorption for say Xe on metals vary as yM+. For metals embedded in Xe adhesion energies (per unit molar surface area) are given in table 1.For other matrix molecules Kr A and Ne these values are to be multiplied by 0.7 0.5 and 0.2 respectively. TABLE1.-ADHESIVE ENERGY -Ead,FOR A MOLE OF INDIVIDUAL METAL ATOMS EMBEDDED IN Xe (IN kJ mol-’) Ag 36 Mn 37 Au 45 Fe 40 c11 27 co 36 Ni 37 GENERAL DISCUSSION We conclude that stabilities of polymers compared to those of free atoms will be somewhat reduced in a matrix relative to the situation for vacuum clusters. In critical situations where chain and more closed packed modifications have comparable energies it can be important that in a matrix a chain produces the larger interfacial adhesive energy effect. Dr. E. R. Buckle (Shefield)said (1) Having seen the diagram of Schulze's apparatus I would ask if he is sure that his micrographs show gas-condensed (Le.aerosol) par- ticles and not ones that have grown on the collecting surface. Surface-grown par- ticles present on the substrate might be different from particles grown in the matrix. (2) Conditions for aerosol condensation do not necessarily exist over an evaporat- ing surface especially at reduced pressures. The problem would not arise if foreign seeds were present in the gas phase and impurities emitted by the heater sometimes provide such heterogeneous nuclei. The presence of impurity would of course defeat the object where this is to study the smallest naked clusters. The high va- pour flux densities necessary for self-nucleation can be achieved without danger of contamination if the specimen is made self-supporting and heated in a small area by a pulsed laser beam.(3) Another consideration is the size of cluster to be expected in an evaporation- condensation technique. Besides the temperature and vapour pressure gradients the transit time of the growing centres through the boundary layer is important in determining their final size. Short transit times and steep gradients can be achieved in nozzle expansions and preparations containing vary small clusters in useful num- bers have been obtained by evaporation of metal into high-speed flows.' D. D. McBride and P. M. Sherman A.Z.A.A. Jouvnai 1972 10 1058. Dr. W. Schulze (Berlin) said (1) Surface grown particles present on the substrate are of course different from those grown in the matrix. The size of the former is governed mainly by the number of condensed atoms whereas their density on the surface is nearly independent of the amount of condensed metal.If however pre- formed clusters are condensed the mean size is independent of the amount of con- densed metal but this is definitely not true of their density. This behaviour has been found in our experiments and we are certain that the micrographs show gas-conden- sed particles. (2) The effect of impurities in the aerosol condensation was negligible in these ex- periments since the tantalum boat was carefully outgassed before it was filled with silver and a residual pressure z Torr was obtained in the vacuum vessel. Aero-sol condensation was then carried out an an Ar pressure of lo-' -10° Torr and a silver vapour pressure of the same order.An advantage of the gas aggregation technique is that low vapour-flux densities are sufficient for self-nucleation. In this technique the evaporated metal atoms are efficiently cooled down by collisions with colder noble-gas atoms allowing a sufficient supersaturation for self-nucleation to be reached easily. Another advantage of this technique is that large amounts of metal (grams or more) can be transformed into clusters quantitatively and continuously with an extremely simple experimental arrangement. (3) The transit time of the growing nuclei through the boundary layer is of great importance in determining their final size. A further reduction of this time would allow us to reduce the final cluster size to <10 A.The paper cited by Dr. Buckle where in a nozzle experiment metal was evaporated into high speed flows shows however that only clusters with mean diameters E 100 8 have so far been formed with this method. Nevertheless we agree that the shortest transit times and steepest gra- GENERAL DISCUSSION dients possible can be achieved in nozzle expansions. Such experiments are currently under way in our laboratory. Prof. K. A. Gingerich (College Station) said In response to an informal query by Dr. Miedema I wish to say that the empirical valence bond model for certain multiply bonded diatomic intermetallic transition element molecules has not yet been applied to triatomic intermetallics. The only known triatomic molecule between a platinum metal and a d-electron deficient transition metal is Ti,Rh.And for this molecule the reported atomization energy’ may only be an upper limit. It is expected that the empirical valence bond model would have to be significantly modified to make it applicable to triatomic intermetallic molecules. D. L. Cocke and K. A. Gingerich J. Chem. Phys. 1978,60,1958. Dr. R. F. Barrow (Oxford)said Simple molecular orbital theory works very well for light diatomics and it would be surprising if Be turned out to have more than a small dissociation energy since the ground-state configuration is la,21a,”2a,220,2 ‘2:. Dr. A. R. Miedema (Eindhoven)said It strikes me that the predicted value for the dissociation energy of Be is extremely small even smaller than that for Mg and Hg,. From my analysis (fig.5) of heats of vaporization dimer energies and metal surface energies (although for Be the latter is less certain than for metals in general) it would follow that Be can be quite stable. Jones has predicted Be to be quite stable from local-density type calculations. That Be deviates from other divalent metals might in the terminology of the paper of Brewer and Winn be related to the fact that going from Hg to Cd Zn Mg and Be the 5p promotion energy decreases (from 449 to 360 386 262 and 263 kJ respectively) while the solid cohesive energy increases drastically AH,, = 60 112 130 145 and 320 kJ mol-I for Hg Cd Zn Mg and Be respec- tively. Prof. J. Winn (Berkeley)said There are several aspects of the bonding in alkaline earths that warrant special treatment and the bonding in Be is one of the most out- standing.We have not attempted a calculation of the bonding of Be from a 2s2p configuration for two reasons the excitation energy to this valence configuration is uncertain and the bonding energy gained from this configuration is uncertain. One finds1 the Be2s2p 3P levels 31.63 kK above the 2s2 ‘S ground level and the 2s2p ’P level 61.62 kK above IS. The large separation between these two levels makes the assignment of a valence state promotion energy uncertain. When one asks what the bonding effectiveness of a single 2p electron might be from such a valence state one notes that the bonding energies (per electron per atom) of H, B2 and A1 are 52 33 and 20 kK respectively. It is tempting to say that one should expect valence state binding in Be to be at least as large as B (i.e.at least 33 kK) which would more than offset the 2s2p 3P promotion energy of 31.6 kK. If such were the case Be would then be similar in bonding to Ba, which we have discussed as being weakly bound but deriving this binding from an excited valence state. On the other hand the 2s2p IP level is so far away from the 3Plevel that assignment of a valence state promo- tion energy cannot be done with any certainty within the realm of our model. More accurate theories must be applied to Be,. Of those calculations done to date only that of Jones2 shows any appreciable binding. This binding energy 4.1 kK is some seven times larger than the binding energy of Mg,. In contrast ab initio SCF-SCEP calculations by Dykstra et a1.,3at 8.5 bohr show a binding of at GENERAL DISCUSSION 241 most 65 kK and very recent ab initio calculations by Dunning4 over the range from 20 bohr to less than 5 bohr show a binding on the order of 200 5 200 K.These latter calculations would certainly have noticed a binding as great as even 1000 K were Be to be bound by an energy of that magnitude. (Liu and McLean' calculate an energy of 1100 K for Be,.) The implication is that the calculation by Jones greatly overestimates the binding and perhaps the cause of the error can be traced to the failure of the density functional method to yield atomic Be energies to sufficient accu- racy especially the 2s2p IP level. C. E. Moore Atomic Energy Levels (U.S.Government Printing Office Washington D.C. 1949) vol. 1; K. V. Subbaram R. Vasudev and W. E. Jones J. Opt. SOC. Amer. 1975,65,318. R. 0.Jones J. Chem. Phys. 1979 71 1300. C. E. Dykstra H. F. Schaefer I11 and W. Meyer J. Chem. Phys. 1976 65 5141. Thomas H. Dunning personal communication January 1980. B. Liu and A. D. McLean J. Chem. Phys. 1980 72,3418. Prof. H. A. Skinner (Manchester) said Prof. Gingerich refers to various correla- tions that have been noted between the dissociation energies Do (M, g) and the enthalpies of sublimation (atomization) of metals. I would draw attention to these in a general way noting that the enthalpy of formation AH,"(M,g) at 0 K measures the binding energyper atom in the solid metal and 3Di(M, g) measures the binding energyper atom in the diatomic M2 gaseous molecule.Consider the ratio defined by [AH,"(M,g) -+Dg(M, g)]/AH,"(M,g). The ratio approaches unity in the case that M,(g) is a weakly bonded " van der Waals " molecule; for all metals the ratio must be a positive fraction > 0 otherwise the condensation M,(g) -+ 2M(c) would not occur at normal temperatures. Values of the ratio for selected elements (including a few non-metals) calculated from AH,"(M,g) values given by Gurvich et aZ.,l and Di values from Gingerich are listed below C2(% +1 0.575 ') 0.75 -2 0.64 0.76 Nb2 0.65 0.77 Si2 0.66 0.77 Na2 0.67 0.79 Li 0.68 0.80 Pt2 0.68 0.80 MO2 0.69 0.81 Sn2 0.69 0.86 AU2 0.70 0.87 cu2 0.72 0.88 Ag2 0.72 0.96 Ni 0.73 0.97 Rh2 0.745 0.98 At one extreme the Group I1 dimetals (Cd, Ca, Mg,) have ratio values 0.96- 0.98 expected of essentially " van der Waals " type M molecules.These are dis- cussed in more detail by Brewer and Winn in their paper. At the other extreme the lC,+ ground state of C, with ratio = 0.575 has a bond length2 = 1.2425 A indica-tive of multiple bonding it is longer than the triple bond in acetylene but shorter than the C=C double bonds in ethylene and allene (the excited 374 state of C2 has re = 1.3119 A and lies only w7 kJ mol-I above the ground state). The alkali metals and Cu, Ag and Au, in which the bond is presumably single have ratio values of 0.67-0.72. In so far as these ratios are typical few of the dimetals are effectively multiple-bonded and the first-row transition metals (Sc, Ti, Cr, Fe and Co,) appear to be even less than singly-bonded.Brewer and Winn attribute the weak bonding to the need to promote to appropriate valence states but difficulties remain GENERAL DISCUSSION in that Mo and Cr can in principle form multiple bonds from ground-state atoms and the reported bond lengths imply a high degree of multiple bonding. Nevertheless the ratios for Mo and Cr are larger than for the multiple-bonded C molecule and as large or larger than those for the single-bonded Group 1 dimetals. We may use the data on small clusters (given by Gingerich) to examine values of the ratio [B.E. (metal) -B.E. (cluster)]/B.E. (metal) where B.E. is binding energy per atom. Values are listed below (Li 2 0.68) 0.575) Li 0.63 0.37 0.64) 0.69) (Pbz 0.80) 0.43 0.47 Pb3 0.62 0.33 0.37 Pb4 0.47 0.28 0.32 -0.24 0.27 0.23 0.24 -0.53) 0.42 0.29 The ratio is seen to fall with increasing size of the cluster in all cases and must necessarily approach zero when the cluster size becomes large enough effectively to reproduce true metallic bonding.For n = 7 in Sn and Ge clusters it is clear that the cluster is still far removed from the " true metal " and a considerable increase in cluster size would be needed to bridge the gap. Nevertheless there is a dramatic change from the dimetal to clusters containing only 4 or 5 atoms. L. V. Gurvich G. V. Karachevstev V. N. Kondratiev Y.A. Lebedev V. A. Medvedev V. K. Potapov and Y. S. Khodeev Bond Energies Zonization Potentials and Electron Aflnities (Nauka Moscow 1974).L. Veseth Canad. J. Phys. 1975 53,299. Prof. K. A. Gingerich (College Station) said The dissociation energy for Cu of 108 kJ mol-' atom-' is in agreement with the unpublished experimental value of 98 kJ mol-1 atom-' as obtained by K. Hilpert and K. A. Gingerich by Knudsen cell mass spectrometry. Dr. E R. Buckle (Shefield) said The observation of a correlation between molar surface free energy and evaporation enthalpy for liquids has quite a long history. It seems to be traceable to theoretical reasoning put forward by Stefan.l For the solid metals the quantity N*yV:/AH has a value of ~0.15 at the melting point, much the same value as calculated from fig. 4 in Miedema's paper.The correlation of y with (AHv/Vm)"has even been proposed3 although the units are not compatible. Hex-agonal and rhombohedra1 metals (which include divalent metals) gave n = 0.62 and the cubic and tetragonal metals n = 0.93 but it would be imprudent to draw conclu- sions from this about different kinds of interatomic binding. In section 2 the starting point taken resembles Volmer's well-known calculation of the free energy of formation of a gaseous aggregate from g separate gas atoms. This may be written wg= yo -gw GENERAL DISCUSSION where 0 is the surface area of the cluster and W the free energy per bulk molecule for evaporation into the supersaturated vapour. In molar quantities AGg = Fg -AG where AGg = NWgIg Fg = NyOg/gand AG = NW,.Experimental values of the critical supersaturation for condensation of a variety of molecular liquid aerosols are found to be in harmony with Volmer's theory when Fgis calculated with data for the macroscopic liquid even though the critical cluster or nucleus is predicted to contain as few as 16 molecule^.^ Onc explanation would be the mutual cancellation of size-dependence of y and V,. Alternatively the effect of size on both y and V could be minimal until g decreases to even smaller values. See e.g. J. R. Partington An Advanced Treatise on Physical Chemistry (Longmans London 1962) vol. 2 p. 148. H. Jones Metal Sci. J. 1971 5 15. A. V. Grosse Science 1963 140 781. J. L. Katz and T. L. Virkler Faraday Disc.Chem. Soc. 1976 61 83. Dr.E. J. Baerends (Amsterdam)said The relativistic contraction of bond lengths is a general phenomenon. It is generally ascribed to the well known contraction of atomic valence orbitals due to relativity. In a series of recent calculations we treated relativisitic effects by perturbation theory which allows a more detailed analysis of this phenomenon. Some results of these calculations are represented in table 2 from which it can be seen that the relativistic contraction is adequately described in the perturbative treatment .l TABLE2.-CALCULATIONS OF BOND DISTANCES (Re) DISSOCIATION ENERGIES (De = -AE) AND VIBRATIONAL FREQUENCIES (we) FROM RELATIVISTIC-HFS CALCULATIONS AND NON-RELATIVISTIC HFS CALCULATIONS (FIGURES IN PARENTHESES) ON Au2 Ag, Cu2 H&+ Cd:+ Zn$+ AuCs AND Cs2 compound Re/A DJkcal mol-1 we/cm-HFS EXP HFS EXP HFS EXP cu2 2.24(2.26) 2.22 53(51) 45 & 2 274(268) 266 Ag2 2.52( 2.67) -47(40) 37 f2 203(184) 192 Ah 2.44(2.90) 2.47 58(27) 52 & 2 201(93) 191 + Znt 2.40(2.42) -30( -30) -187(183) -Cd; 2.73(2.84) -34( -39) -160(141) -+ Hg:+ 2.63(3.12) -11( -46) -182(107) -AuCs 3.53(4.00) -28(21) -69(51) -cs2 5.20( 5.1 7) -12(10) -51(49) -From these perturbative calculations however a different explanation of the bond contraction emerges.Due to relativity we have first order corrections to the non-relativisitic hamiltonian i.e. the mass-velocity Darwin and spin-orbit operators R2 R2 2J7; + .L" S' (VV xP> 8 s 2 = -v4 + GENERAL DISCUSSION where V; is the sum of the nuclear and electronic potentials the latter being calculated from the zero-order (non-relativistic) orbitals v/:.The first order correction to the atomic orbitals tyt represents the contraction of the orbitals. The first order correc- tion to the energy is given by E' = Ei(v/qlh'ltyio) =I h'(l)p"(l 1') dzl. 141' We note that this correction is independent of the ty and the concurrent first-order change in the density p'( 1 1') which only shows up in second order E2 = 3 I hl(l)pl(l 1') dz,. J 141' /bl 0.15 0.05 0.10 0.05 0.oo 0.00 h F al -0.05 -0.02 -0.05 -0.10 -0.25 c 4.5 5.0 5.5 4.5 5.0 Rla u. R1a.u FIG.1.-(a) Relativistic corrections (first- and second-order) to the total bonding energy in Au2 as a function of the internuclear distance.The first-order correction is split in a part due to core- valence orthogonalization (A&) and a part due to valence orbital interaction AEv. (i) AE; (ii) AE2 (iii) AEE,. (b) Kinetic energy and polential energy (only the contribution due to core-valence orthogonalization) with their respective corrections as a function of internuclear distance. (i) Tcv( + Vcv)(x 5 x (iv) -V2Tcv + V2VLv,(v) Vcv(x 5 x x5 x (ii) V2Vcv (iii) (Tcv (vi) -V2TCv. GENERAL DISCUSSION This result is of course due to the stationarity of E" against variations in the orbitals. The effect of relativity on the bonding energy and bond length is deter- mined by the difference of the relativistic correction for the molecule and the constitu- ent atoms A and B AEREL= Ah'' + AE2.AE2is relatively small compared with AE' and its effect on bond length is negligible by virtue of its flatness [see fig. l(a)]. The first-order correction is determined only by piB pi and pj so the bond contraction is not due to the orbital contraction. The actual cause of the bond contraction can be understood by a closer analysis of AE'. We will first consider the kinetic energy and its relativistic correction the mass-velocity energy. It is well known that when the internuclear distance decreases the kinetic energy rises primarily due to the requirement of orthogonality of the valence orbitals of A on the core orbitals of B and vice versa. The mass-velocity correction however has the opposite sign (cj the classical expression p2/2rnfor the kinetic energy and -p4/8mc for the mass-velocity term) and is roughly proportional to the kinetic energy (see fig.1). The effect of the mass-velocity term is therefore to counteract the rise in kinetic energy upon bond shortening. This results in a bond contraction. The potential energy and the Darwin correction on it have opposite signs and partly cancel the effect of the kinetic energy terms. The net effect is however a contraction. It is to be noted that the bond length is rather sensitive to the small relativisitic corrections because of the flatness of the non-relativistic total energy at the equilibrium distance. (a)T. Ziegler J. G. Snijders and E. J. Baerends unpublished results; (h)J.G. Snijders and E. J. Baerends Mol. Phys. 1978,36 1789; (c) J. G. Snijders E. J. Baerends and P. Ros Mol. Phys. 1979 38 1909. Dr. I. H. Hillier (Manchester)said In reply to Prof. Ozin's comments on our paper we do not consider that the similarity in the absorption spectra of Mo2 and Cr necessarily points to the same ground-state electronic configuration of these molecules since the same orbital transition may take place in both molecules even if their ground- state configurations differ. Prof. K. A. Gingerich (College Station) said I wish to ask Dr. Hillier how his results compare with those obtained by Harris and Jones' for the first transition series dimers in terms of ground-state and excited-state electronic configurations and energy levels of the latter as well as of calculated dissociation energies.Also would he please comment on the relative merits of his MCSCF calculations and those by Harris and Jones using the local spin density (LSD) approximation? We are very interested in knowledge of the electronic structure of transition metal dimers such as multiplici- ties of ground states and low-lying excited states and energy levels of the latter since the lack of this knowledge causes the single largest uncertainty in the experimental values for their dissociation energies as obtained by high-temperature mass spectro- metry. J. Harris and R. 0.Jones J. Chem. Phys. 1979 70 830. Dr. A. R. Miedema (Eindhoven)said In Prof. Veillard's picture of going gradually from free atoms to a solid upon increasing the number of atoms in a cluster it may be of interest to calculate the variation of the degree of hybridization of the various GENERAL DISCUSSION d-states with increasing number of atoms.In the solid metal the contribution of the d-band to the cohesive energy exists because there is significant d-s or d-p hybridiza-tion. It would be interesting to know in which way the total d-band hybridization (or the contribution of the 10 “ d ” states to the cohesive energy) varies with cluster size. In addition I would like to suggest that when comparing dimer interatomic distances with interatomic spacings in the solid metals the relevant quantity for the latter is Vm+(Vm is molar volume) rather than the actually measured crystal structure de- pendent interatomic distance.Prof. A. Veillard (Strasbourg) said There is indeed an increasing hybridization of the d-levels as the number of atoms in the cluster increases as shown by the results of a population analysisfor these d-leuels. In the diatomics Cu, these d-levels are made of pure d-orbitals with practically no hybridization (this result is independent of the basis set). For Cu8 the contributions of the 4s- and 4porbitals to these levels amount respectively to 0.03 and 0.02 e for each Cu atom. These numbers increase to 0.05 and 0.05 for each peripheral Cu atom in the cluster CuI3. We believe that this trend does not represent a basis set effect but rather an intrinsic property. A more detailed analysis will be given in a subsequent publication.Prof. K. A. Gingerich (College Station) said If one scales Veillard’s calculated binding energies in moll1 atom-’ for Cu and linear Cu (the favoured structure) to the experimental value for Cu (95.1 kJ mol-l atomv1) one obtains good agreement of his calculated value for Cu 98 kJ mol-’ atom-’ with the unpublished experimental value by K. Hilpert and K. A. Gingerich of 98 kJ mol-l atom-l. Dr. C. D. Garner (Manchester) said Could Prof. Cotton indicate the reason(s) for expecting that a metal-metal interaction may be stronger in a compound in which the metal atoms are in a positive oxidation state as compared with the corresponding interaction in the neutral diatomic molecule [e.g. Mo,(O,CCH,)~ as compared with Mo2l. Are there any reasons for suggesting that a 6 interaction in particular may be strengthened upon oxidation; the Xa calculations imply a very weak &overlap yet in [Mo2C1814- the &overlap is generally agreed to be the reason for the eclipsed conformation of the two MoCl units.Prof. H. A. Skinner (Manchester) (partly communicated) Thermochemical studies on “ clothed ” metallic clusters can only provide values for the total binding enthalpy of the molecule; as Prof. Cotton has remarked the separation from this total of the part due to the metal-metal bonds in the molecule remains essentially an arbitrary procedure. In the special case of hydrocarbons for which there is an abundance of thermochemical data on similar molecules several sophisticated pro- cedures have been examined in detai1,l but only the simplest of procedures can be applied to “ clothed’’ metal clusters due to the very limited thermal data as yet available.Moreover a novel factor with metals (as opposed to carbon) is the variable valence of a metal in its different compounds. We may examine two different examples to illustrate the problem. The entb alpies of the disruption processes Mo,(NMe2)&)+ 2Mok) + GNMe,(g) <i> and Mo(NMe2)4(g)j Mo(g) + 4NMe2(g) (ii) GENERAL DISCUSSION were measured as 1929 & 28 and 1021.6 & 19 kJ mol-l respectively. Transfer of the average (Mo-NMe,) bond enthalpy in Mo(NMe,) into Mo,(NM~,)~ leaves ~396 kJ mol-' for the contribution from the (Mo = Mo) bond in Mo,(NMe,),. This is of similar order to the dissociation energy (reported by Cingerich) in the " naked " Mo molecule.However it is questionable that transfer from Mo(NMe,) is justified. Other possible " reference " compounds e.g. Mo(NMe,), Mo(NM~,)~ Mo(NM~,)~ and Mo(NMe,), have yet to be prepared and there are reasons to expect that the (Mo-NMe,) bond enthalpy contribution will vary with n in the series Mo(NMe2),. The second example involves the compounds Mo(pd), Mo,(pd),(acet) and Mo,(acet) [(pd) = pentane-2,4-dionate ; (acet) = acetate] for which AH",g) values of -1199 -1650 and -1806 kJ mol-l respectively have been obtained. The disruption processes Mo(pd),(g) + M4g) + 3Pdk) ; AH1 Mo,(pd),(acet),(g) 32Mo(g) + 2pd(g) + 2(acet)(g) ; AH2 Mo,(acet),(g) -+ 2Mo(g) + 4(acet)(g) ; AH3 have AHl = 1199 + AH,"(Mo g) + 3AH,"(pd g) AH2= 1650 + 2AH,"(Mo g) + 2AH,"(pd g) + 2AHy(acet g) and AH3 = 1806 + 2AH,"(Mo g) + 4AH,"(acet g).Values are reported for AH,"(Mo g) = 658 rt_ 2 kJ mol-l and for AH,"(acet g) = -217 & 10 kJ mol-' but no experimental value is available for AH,"(pd g). This disadvantage may be by-passed as follows rewrite the disruption energies in the form AH1 = 1857 + 3AH,"(pd)= 6D(Mo-O)* AH2 = 2532 + 2AH,"(pd) = B(MoSMO) + 4D(Mo-O)* + dD(Mo-0) and AH3 = 2254 = D(MozMo) + 8D(Mo-O) where D(Mo-0)" measures the Mo-0 contribution in Mo-pd bonding and B(Mo-0) the similar contribution in Mo-acetate bonding. If we now assume that D(Mo-O)* is the same in Mo(pd) as in M~~(pd),(acet)~ and that ~(MOSMO) is unchanged in Mo,(acet) from its value in Mo,(a~et),(pd)~ these equations yield D(MoEMo) = 334 kJ mol-'.Once again we arrive at a value weaker than Do in the diatomic molecule but again there remains the question of the validity of transfer from a reference molecule [in this case Mo(pd),] in which the formal valence of the metal is different from that in the dimolybdenuin complex. More examples are needed before a " correct " procedure can be agreed. Several investigations are in progress with this objective in view; one of these involving the complexes Mo,(mhp),(acet),_ (n = 0 1 2 3 4) is almost completed5 (mhpH = 6-methyl-2-hydroxypyridine). J. D. Cox and G. Pilcher Thermochemistry of Organic and Organometallic Compounds (Aca-demic Press N.Y. 1970). * F. A. Adedeji K.J. Cavell S. Cavell J. A. Connor G. Pilcher H. A. Skinner and M. T. Zafarani-Moattar J.C.S. Faraday I 1979 75 603. K. J. Cavell C. D. Garner G. Pilcher and S. Parkes J.C.S. Dalton 1979 1714. K. D. Cook and J. W. Taylor Int. J. Mass Spectrom. Ion Phys. 1979,30,93. M. T. Zafarani-Mottar Ph.D. Thesis (Manchester University 1979). Prof. M. H. Chisholm (Bloomington) said The claim that " cheerleader molecules whirl as they twirl " is well demonstrated in variable-temperature 'H n.m.r. studies of the compound 1,l-Mo~(NM~,),(CH,S~M~,),(M~M).~ At 220 MHz and at tempera- GENERAL DISCUSSION tures below -38 "C in [2H,]toluene the spectrum is entirely consistent with the adoption of the frozen-out structure shown below. Me/N\ Me There are three types of trimethylsilylmethyl groups R(l) R(2) and R(3); the methylene protons associated with R(3) are diastereotopic and appear as an AB quartet while those associated with R(1) and R(2) appear as single resonances in accord with the existence of the*molecular plane of symmetry which contains the anti-C-Mo-Mo-C atoms.There are also proximal and distal N-methyl reso- nances. On raising the temperature the proximal and distal N-methyl signals coalesce to a sharp singlet as rotation about the Mo-N bonds becomes rapid and the AB quartet collapses with one of the methylene protons singlets leading to a simple 3 1 pattern for both the methylene and methyl groups of the trimethylsilylmethyl ligands above 80 "C (see fig. 2). These observations provide direct evidence of the facile rotation about a triple bond which being cylindrical in nature should have only a sterically imposed rotational barrier.M. H. Chisholm and I. P. Rothwell J. Amer. Chem. SOC.,in press. Prof. H. A. Skinner (Manchester) said The calculations of Baerends indicate that there is a genuine metal-metal bond in Mn2(CO),o but that there is no effective metal-metal bonding in Fe2(CO),. The question I raise relates to the bond lengths in these compounds; for whereas the Mn-Mn bond length in Mn2(CO)lo (re = 2.923 A) is decidedly longer than the nearest-neighbour contacts in manganese metal (8 at 2.58 A; 4 at 2.67 A) and is longer than expected for a single Mn-Mn bond the Fe-Fe separation in Fe,(CO) (re = 2.523 8.)is identical with the nearest-neighbour contacts in metallic iron (Al cubic close packed arrangement) and is consistent with a single Fe-Fe bond in this molecule.Dr. J. Evans (Southampton) said It is well known that mass spectra of transition metal carbonyls ionised by a 70 eV electron beam demonstrate apparent stepwise carbonyl loss. Can Dr. Winn explain why his experiment appears instead to give synchronous loss of all CO ligands? Prof. J. Winn (Berkeley) said Sequential carbonyl loss is observed not only in positive ion mass spectra of metal carbonyls,' but also in low-energy dissociative electron attachment experiments2 and one photon absorption e~periment,~ in both flash photolysis and in matrix isolation. In our experiments it must be remembered that atomic fluorescence occurs at the earliest some few nanoseconds after the energy- transfer collision.Thus our data are consistent not only with a simultaneous release of all ligands but also with a rapid (sub-nanosecond time-scale) sequential release of ligands providing these sequential dissociations impart no net momentum to the metal atom product. The distinguishing feature of these experiments is therefore the rapid loss of all carbonyls and the question of simultaneity is almost one of seman- tics on this timescale. The answer must come from the potential-energy hypersurface for the activated carbonyl; is this surface unbound in all metal-ligand bond co- GENERAL DISCUSSION 249 95 * c 62 -38 I I 1 I 2.5 2 .o 1.5 1.o p.p.m. FIG.2.-Methylene proton signals of a solution of 1,I-MO~(NM~~)~(CH~S~M~~)~ in [ZH8]toluene recorded at various temperatures in the range -38-+95 "C and at 220 MHz.The signals arising from ['H8toluene methyl impurities are denoted by an asterisk and reveal a slight loss of resolution in both the high and low temperature limiting spectra shown in this figure. ordinates or are we merely seeing the unimolecular decay of a superenergized state which rapidly concentrates an excess of energy in the metal-ligand bonds? Certainly the latter picture is more appropriate for the description of 70 eV electron bombardment ionisation where a slow timescale sequential unimolecular fragmentation is observed. The difference between ionisation and single-photon absorption dissociation on the one hand and electronic energy transfer via collision on the other hand is the subtle difference in the final electronic configuration of the energized carbonyl.Ionisation removes at threshold an electron from an m.0. which has metal d-and CO 2n-character. This certainly weakens the metal-ligand bonding but does not grossly disrupt the CO a-donation framework. Photo-chemical excitations in the U.V. are d to n* charge transfer bands which flow charge GENERAL DISCUSSION away from the metal centre. In contrast electronic energy transfer will result in charge transfer toward the metal centre as an electron is promoted from the n back-bonding framework to an excited s (or d depending on the metal) orbital on the metal. This transfer is expected in analogy with many electronic energy transfer collisions which proceed by a two-electron energy exchange process.The transitory collision intermediate is rather ionic in nature due to the effective electron affinity of the metastable rare gas. The resulting excitation with a unique direction of charge flow in the carbonyl makes the suspicion of a totally repulsive state a rather likely one. M. R. Litzow and T. R. Spalding Mass Spectrometry of Tnovganic and OrganornetulIic Com- pounds (Elsevier New York 1973) chap. 1I. M. S. Foster and J. L. Beachamp J. Amer. Chem. SOC.,1975,97,4808. A. B. Callear Proc. Roy. Soc. A. 1961,265 71; M. Poliakoff and J. J. Turner J.C.S. Faraday 11,1974 70,93. Prof. H. A. Skinner (Manchester) said Gurvich and co-workers examined the spectra following flash photolysis decomposition of saturated vapours of Cr(CO) and Mo(CO) (and of mixtures of the two) at room temperature.The absorption spectra following photolysis showed transient bands attributed to the dilnetals Cr, Mo and CrMo. The decomposition of metal carbonyls via metastable rare gas collisions is a unique process and the proposed mechanism (leading directly to metal atoms) leaves no room for transient intermediates. Have the Gurvich bands been sought ? Yu. M. Efremov A. N. Samoilova and L. V. Gurvich Chem. Phys. Letters 1976 44 108. Dr. E. J. Baerends (Amsterdam)said It was pointed out by Prof. H. Skinner that the Fe-Fe bond in Fe,C09 is rather short. This has been considered for a long time to be a strong indication for the presence of bonding interactions between the Fe atoms.In reply to Prof. Skinner's comment we may say that the extent to which bonding interactions between the metal atoms are present is rather difficult to assess. In the Fe2(C0) fragment we have as valence orbitals the n-bonding e' set (filled) the 0-bonding a; (empty) and n-antibonding e" (empty). The bonding a; and e' sets mix with bridge donor orbitals (the ai and e' from CO 50) and the antibonding e" set mixes with bridge acceptor orbitals (the eft from CO n*). There is some ambiguity in looking at these interactions which primarily represent the Fe-C bonds from the point of view of metal-metal bonding. Nevertheless one might argue that a net direct metal-metal bonding effect is present if the occupied metal- bridge a; and e' orbitals contain more metal character than the occupied metal-bridge e;' orbitals.This is however by no means the case. The 12 eff is a real mixture of metal and cob 2n orbitals having 54.6% metal character. We have to compare this with the admixture of metal character into the cob 50 orbitals. The latter occur in the dense manifold of CO 50 In orbitals below -0.34 a,u which all have varying amounts of both bridge and terminal CO character and small amounts of metal character. Even the sum of metal-metal bonding contributions (~25%) is not nearly so large as the 54.6% in the metal-metal antibonding 12 e". So even from this point of view there is no reason to maintain a Fe-Fe bond. The actual factors governing the M-M bond length in bridged binuclear complexes have recently been considered in an excellent study by Swmmerville and Woffmann.' We may also refer to a recent study by who reaches conclusions in agreement with ours on the metal-metal bonds in the CO bridged systems Cp,Fe(CO) and Fe3(CO)12.R. Sumrnerville and R. Hoffmann J. Anzev. Chem. SOC.,1979 101 3822. M. BCnard Iiiorg. Chem. 1979 18 2782.

ISSN:0301-5696    

DOI:10.1039/FS9801400235

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

INDEX OF NAMES" Abe H. 87 Armstrong S. 94 Bachrnann C. 170 Baerends E. J. 211 243 250 Barrow R. F. 235 240 Basch H. 149 Brewer L. 126 Buckle E. R. 237 239 242 Bursten B. E. 180 Chisholm M. H. 194 247 Cotton F. A. 180 Demuynck J. 170 Doran M. 159 Evans J. 248 Garner C. D. 246 Heijser W. 211 Hillier 1. H. 159 245 Jayasooriya U. A. 94 Kasai P. H. 65 235 McCombie J. 94 McLeod D. 65 Miederna A. R. 136 238 240 245 Montano P. A. 79 236 238 Norris D. 94 Ozin G. A. 7 Ros P. 211 Schulze W. 87 239 Skinner H. A. 235 236 241 246 248 250 Springall .J. P. 94 Veillard A. 170 246 Gingerich K. A. 109,238,240,242,245,246 Winn J. S. 102 126 235 240 248 Grinter R. 94 Wood C. 159 Guest M. F. 159 * The page numbers in heavy type indicate papers submitted for discussion.

ISSN:0301-5696    

DOI:10.1039/FS9801400251

出版商:RSC    

年代:1980

数据来源: RSC