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.