Experimental and Predicted Stability of Diatomic Metals and Metallic Clusters BY KARLA. GINGERICH Department of Chemistry Texas A & M University College Station Texas 77843 U.S.A. Received 17th October 1979 The experimental bond energies of atomic and polyatomic metals and intermetallic compounds are reviewed and discussed in terms of various empirical models of bonding such as the Pauling model of a polar single bond the valence bond approach for certain multiply bonded intermetallic molecules and the atomic cell model. Illustrations emphasize recent Knudsen effusion mass spectro- metric results. For ligand-free diatomic metals a maximum dissociation energy of 640 & 40 kJ mol-I is predicted. 1. INTRODUCTION The investigation of diatomic metals and intermetallic compounds has been a major objective of our research for more than a decade.Our early emphasis was to test the applicability of the Pauling model of a polar single bond' to diatomic inter- metallic compounds. The determination of the dissociation energies of previously unknown homonuclear diatomic molecules permitted application of the Pauling model to the intermetallic molecules of these elements since these values are needed in the models' application. In our experimental work on testing the Pauling model we emphasized diatomic intermetallic compounds for which a sizeable ionic contribution to the dissociation energy was expected because of a large electronegativity difference in the component atoms e.g. rare-earth-gold intermetallic compounds.These compounds also in- cluded the largest measured bond energies ~340 kJ mol-' between two metal atoms known at that time. Other large dissociation energy values were measured for AlAu and UAu and for the gold compounds with the metalloids boron and silicon.2 The applicability of the Pauling model was soon extended to polyatomic intermetallic molecules.39 The Pauling model is not expected to apply to multiply bonded molecules. Mul-tiple bond formation between two different metal atoms and thus bond energies of possibly more than 420 kJ mol-' was according to a suggestion by Bre~er,~ expected for molecules formed between a group IV transition metal e.g. zirconium and platinum. The corresponding condensed intermetallic compounds are known to be very stable because in Brewer's view the transfer of one or more of the paired d-electrons of the platinum to the vacant d-orbitals of the group IV transition metal will make more valence electrons available on both atoms and thus permit strong mul- tiple bonding.An experimental test to confirm the expected large dissociation energies was difficult particularly because of the tremendously reduced activity of the group 1V metal in the corresponding condensed alloy and because of the high chemical reactivity of the group IV transition metals. Thus at first we confirmed Brewer's expectation qualitatively through a spark source mass spectrometric st~dy,~ the results DIATOMIC METALS AND METALLIC CLUSTERS of which also led us to the choice of the Ti + Rh system for measuring the first inter- metallic multiply bonded transition metal molecule under equilibrium conditions.6 Next the high temperature mass spectrometric equilibrium studies were extended to combinations between a rare earth metal or an actinide metal and a platinum metal.7 The results of these investigations could be interpreted in terms of an empirical valence bond approach for multiply bonded platinum metal intermetallic molecules with Group 111 to Group V transition metals or lanthanide or actinide metals.8 This valence bond approach accounts for many molecules with assumed double and triple bonds.Quadrupole bonding appears partially achievable but also restricted by the directional requirements of orbital overlap in the diatomic m~lecules.~ As a conse-quence of this limitation the maximum bond energy between any two ligand-free metal atoms could be predicted as 670 j-84 kJ mol-'.' Most compounds of platinum however cannot be quantitatively treated for lack of a suitable valence state.The range of validity and the weakness of the model have recently been critically discussed.1o The model has guided us in finding a score of additional very stable intermetallic molecules. It can account for or be used to predict the dissociation energies of z 200 diatomic intermetallic molecules with multiple bonds. The atomic cell model by Miedema and collaborators" for quantitative description of heats of formation of solid alloys and heats of mixing of liquid alloys has recently been extended to diatomic molecules.12 Miedema will discuss the model in detail at the present Symposium.lo3 The atomic cell model appears to be more general than either the Pauling model of a polar single bond or the valence bond model for certain multiply bonded intermetallic molecules; it encompasses both of them.It may be ap- plied with certain reservations to all metallic molecules including metalloids. Certain refinements of the model will however be needed and we are therefore engaged in an experimental programme to determine the bond energies of homonuclear and hetero- nuclear metallic molecules in order to provide a broader basis for the refinements of the various empirical models. Parallel to our efforts in measuring and understanding the bond energies of diatomic metals we have been extending our work on small metallic and intermetallic clusters with emphasis on group IV and group V homonuclear molecules and on small intermetallic clusters involving these elements.This work has the purpose of con- tributing to the understanding of certain catalylic processes in which such small metal clusters are believed to play an important role. In the following discussion some comments concerning the Knudsen cell mass spectrometric method will be made since it has been by far the most commonly used experimental technique for determining bond energies of diatomic metals and metallic clusters. Then a brief review and a tabulation of the dissociation energies of diatomic metals and the atomization energies of metal clusters will be given.Using these experimental data the various empirical models of calculating bond energies will be discussed and compared. 2. EXPERIMENTAL The bond energies of diatomic metals and small metal molecules have been determined mainly by the well established Knudsen cell mass spectrometric method. In our laboratory the measurements have been performed with a Nuclide Corporation 12-90 HT mass spectro- meter that resembles the one described by Chupka and 1ngh~am.l~ The mass spectrometer and the experimental technique have been described previously.'" The Knudsen cell containing the sample is heated by radiation from a non-inductively wound thoriated tungsten spiral resistance heater. This heater permits attainment of K.A. GINGERICH temperatures up to % 3000 K. Temperatures are measured by focusing a calibrated optical pyrometer on a black-body hole in the bottom of the Knudsen cell. Measured temperatures are corrected for the optical absorption of the viewing window and deflection prism used. The optical pyrometer can be calibrated at the freezing point of gold under in situ experimental conditions. Identification of the ions with the corresponding molecular precursors is usually done by measurement of their mass-to-charge ratio isotopic abundance distribution shutter profile appearance potential and ionization efficiency. The measured ion currents are correlated with the corresponding partial pressure^.'^*'^ From these partial pressures reaction enthalpies are obtained by the third law method using the equation AH' = -RTln Kp -T[A(G; -H;)/TJ and when a large enough temperature range can be covered in addition by the second-law method from the relation dln K,/d(l/T) = -AH,/R.Further details of the instrument experimental procedure and data evaluation are given elsewhereY7*l4 and in pertinent reviews 15*16 and in the individual papers quoted. 3. REVIEW OF EXPERIMENTAL BOND ENERGIES The dissociation or atomization energies of ligand-free gaseous diatomic metals and small metal clusters are presented in tables 1-4. Unless stated otherwise the compilation by Gurvich et a1.I' has been taken as a basis for the values listed. These authors present the latest critical evaluation available for the types of molecules covered.Other reviews have been by Siegel," Gaydon,I9 Drowart,*' Drowart and TABLE.-DISSOCIATION ENERGIES D& OF HOMONUCLEAR DIATOMIC MOLECULES (IN kJ mol -l). I [FROM REF. (17) INTEGRATED WITH NEW VALUES]. 101.o 21.2 DIATOMIC METALS AND METALLIC CLUSTERS TABLE2.-ATOMIZATION ENERGIES Do",OF POLYATOMIC METALS (IN kJ mOI-') molecule Do" ref. molecule Do" ref. Bi 365 f 13 27,30 IPbj 221 .+ 16 45 Bi 595 f 8 27-29 Pbj 415 f 16 45 Ge 639 I20 32-34 Sn 480.7 f 17 44 Ge 999 i-25 32-34 Sn 757.7 f 20 44 Ge 1343 & 42 34 Sn 1024 & 25 44 Ge6 1703 h 54 34 Sn6 1329 & 30 44 Ge7 2013 63 34 Sn7 1612 & 35 44 Li 173.6 * 16.7 51 TABLE 3.-DISSOCIATION ENERGIES D OF DIATOMIC INTERMETALLIC COMPOUNDS (IN kJ mOl -') molecule Do0 ref.molecule Do" ref. AgAl 172 f 17 17 CdIn 134 17 AgAu 200.8 f 10.5 17 CeIr 580.7 I 25 86 AgBi 192 42 17 CeOs 503 L-33 64 AgCu 169.5 f 10.5 17 CePd 318.4 f 17 76 AgDy 124 f 19 52 CePt 551.0 & 25 86 AgEu 123.0 f 12.5 47 CeRh 545.6 f 25 86 AgGa 177.8 f 6.3 2 CeRu 527 & 25 64 AgGe 170.7 i-21 35 cocu 163 & 21 17 AgHo 119.7 5 17 48 CoGe 230 f 21 17 AgIn 163.2 f 6 2 CrCu 155 f 25 17 AgLi 173.6 -C 6.3 53 CrGe 165.7 & 29 65 AgMn 96 f 21 17 CsHg 4.8 26 AgNa 136.0 f 10.5 54 CsLi (69) 26 AgSn 134 f 21 17 CsK (47) 26 AlAu 322.2 f 6.3 55 CsNa (41) 26 AlCu 209 f 17 17 CuDy 140 i 19 31 AlLi 172.0 f 14.6 56 CuGe 197 i 17 17 AlPd 250.6 f 12.0 57 CuHo 139 f 19 31 AuBa 251.1 f 10 58 CuLi 189.3 f 8.8 53 AuBe 280 17 CuNa 172.4 & 16.7 66 AuBi 293 f 8.4 17 CuNi 201 f 21 17 AuCa 238 17 CuSn 168 & 10 77 AuCe 335 f 21 17 CuTb 187 -i 19 31 AuCo 218 f 17 17 EuRh 231.8 f 34 47 AuCr 209 I 17 17 GaLi 129.3 f 14.6 56 AuCu 224.3 & 5.1 32 GeNi 276 13 17 AuDy 254 5 20 52 GePd 259 f 17 17 AuEu 238.9 f 10.5 47 HgK 5.8 26 AuGa 230 f 38 17 HgLi 10.1 26 AuGe 270.4 f 5.0 32,35 HgNa 5.3 26 AuFe 188 4 21 17 HgRb 4.7 26 AuHo 263.6 f 33 42 InLi 86.6 f 13.4 56 AuLa 335 f 21 17 IrLa 573 & 12 67 AuLi 280.8 f 6.5 53 IrTh 570.7 f 42 8a AuLu 328.4 i 17 50 IrY 452.8 + 16 62 AuMg 243 f 42 17 KLi 78.2 i 4.2 68 AuMn 188 f 13 17 KNa 61.0 f 4.2 68 AuNa 212.1 f 12.6 54 LaPt 496 & 15 69 K.A. GINGERICH 113 TABLE3.-continued molecuIe Do ref.molecule D ref. AuNd 297 f 21 17 LaRh 524.7 f 16.7 7c AuNi 251 f 21 17 LaY 197 f 17 17 AuPb 126 & 42 17 LiNa 86.6 & 6.3 68 AuPd 151 & 21 17 LuPt 397.5 3I 34 7a AuPr 305 f 21 17 MoNb 448 & 25 70 AuRh AuSc 228.9 & 29 276.6 & 17 47 59 NaRb PtTh 54.8 4 3.8 546.6 * 42 17 8a AuSn 251 & 8 60 PtTi 394 2c 11 71 AuTb 289.5 f 33 42 PtY 470 3 8 37 AuU 318 & 29 17 RhSc 440.3 f 10.5 72 AuV 238 & 12 61 RhTh 510 4 21 73 AuY 304.1 i 8.2 62 RhTi 387.0 f 14.6 41 BaPd 220.0 f 5.0 58 RhU 516 i17 73 BaRh 257.4 5 25 58 RhV 360 i29 74 BiGa 155 f 17 63 RhY 441.8 & 10.5 72 BiPb 134 & 8 17 RuTh 587.9 f 42 9 BiSn 206.3 f 8.4 27 RuV 410 f 29 74 BiTl 117 & 13 17 TABLE4.-ATOMIZATION ENERGIES D OF POLYATOMIC INTERMETALLIC COMPOUNDS (IN kJ mol -I) molecule D; ref.molecule Do0 ref. AlAu2 506.3 i 25.1 3 AuSn 486 -& 18 60 A12Au 460.2 Zt 20.9 3 AuSn 786 f. 25 60 A1 2Pd 492.4 &-24 57 Au,Sn 542 i 18 60 Au2Ba 552 & 21 75 Au2Snz 871 f 25 60 Au~Eu 549.4 f 16.7 47 Au2Tb 582 & 42 42 AuGe 531.9 f 10 32 Bi2Sn 427.6 i 10.5 27 AuGeJ 897 & 20 32 Bi,Sn 644.3 & 16.7 27 AuGe4 1295 I30 32 CuGe 506.0 i25 76 Au2Ge 534.9 5 12 32 CuSn2 391 & 25 77 Au2Ge2 927 & 14 32 CuzSn 452 & 25 77 Au~Ho 533 & 42 42 RhTiz 996 =t42 41 AuZLU 602.1 & 33.5 50 Goldfinger,” Gingerich,2*22 Cheetham and Barrow,23 Ro~en,~~ Barrow 25 and Huber and Herzberg. 26 4. EMPIRICAL CORRELATIONS OF BOND ENERGIES AND COMPARISON WITH EXPERIMENT Bond energies of metal molecules are among the most difficult properties to calcu- late from first principles.Ab initio calculations are rather scarce and limited to a few examples involving metals with low atomic numbers. Approximate theoretical treatments such as density functional theory and the SCF-Xor-SW method or semi- empirical calculations such as the extended-Huckel (EH) and CNDO techniques have no useful predicting power as far as bond energies are concerned. Therefore one has to rely on empirical methods for the prediction of unknown bond energies of diatomic metals and metallic clusters. In this section the results of various empirical methods DIATOMIC hl ET ALS AND METALLIC CLUSTERS are compared with the corresponding experimental values and relative merits and limitations of the empirical approaches are discussed.4.1. HOMONUCLEAR DIATOMIC METALS As can be seen from table 1 the dissociation energies of diatomic representative metals are more or less well known. Gaps or large uncertainties exist for the diatomic molecules of the group IIA and IIB metals and the transition metals. The group IIA and group IIB molecules are believed to be of the van der Waals type and will not be further discussed here. Some of the transition metal molecules are also of the van der Waals type e.g. Yb, very likely Eu and possibly Mn,. The others have chemical single bonds or muItiple bonds. Several early empirical correlations for interpreting or estimating dissociation energies of homonuclear diatomic metals relate the dissociation energy to the heat of vaporization of the atom and the excitation energy (promotion energy) of the ground state atoms to their valence state.Griffith78 introduced the concept of excitation energy (promotion energy) into the discussion of the cohesive energy of transition metals. Verhaegen et al. 79 related the atomization energy of the metal and the dis- sociation energy of the dimer through cc = AH&p(M)/DE(M2). Kant and associates have used a correlation between dissociation energies valence state promotion ener- gies and empirical valence state dissociation energies to account semiquantitatively for the observed dissociation energies of the 3d transition metals" and the lanthanide metals.46 Krasnovsl first predicted the dissociation energies of the 4d and 5d transition metal molecules using the empirical relation AH;,, -D8 = const -const = C (1) with an empirical value of C = 65 -l 10 kcal mol-' for the Y to Pd series based on the experimental and DG of the end members Y and Pd.His value C = 45 kcal mo1-l for the La to Pt series was solely based on La,. He suggested that possibly C > 45 which appears to be confirmed by the recent determination of DE(Pt,) in our lab~ratory,~~ which leads to C = 50. In an alternative approach Miedema and Gingerich have recently demonstrated that there is a relation between the dissociation enthalpies of homonuclear diatomic molecules D:,the heat of vaporization of the metals in the condensed phase AH:,, and the surface energy of the pure metals y and have also predicted dissociation energies for the 4d(Y-Pd) and 5d(La-Pt) transition metals.They have used these predicted values as a basis for calculating the dissociation energies of diatomic inter- metallic compounds by the atomic cell on which Miedema will report elsewhere at this Symposium.103 A third set of 4d and 5d transition metal dimer dissociation energies has been calculated by Brewers2 using a modification of the bonding energies he has used in the bulk In table 5 the estimated values by the three methods for the dissociation energies of 4d and 5d transition metal dimers are compared. Also included have been the recently measured values by Gupta et al. which were not available at the time of the predicted values li~ted,~~,~~*~~ as well as other estimates.Gupta and Gingeri~h~~ 71984*85 also predict the dissociation energy of Ta to be larger than that of Nb2 and possibly larger than that of W2. It should be pointed out that the dissociation energies of Mo and Nb2 are probably K. A. GINGERICH 115 TABLE 5 .-COMPARISON OF VARIOUS ESTIMATED DISSOCIATION ENERGIES OF SYMMETRIC 4d AND 5d TRANSITION METAL DIMERS ~~ M estimated D:(Mz)/kJ mo1-l Miedema and other exp. Do"(Md /kJ m0l-l a Krasnov 81 Gingerich12" Brewer 82 estimates ~~~~ Zr 335-293 309 293 Hf 431-314 304 335 Nb 448-360 371 335 502 503 -I 1036 Ta 590-393 395 377 Mo 385-322 325 293 41gS4 397 A 6385 404 f2040 W 661-423 452 397 535 & 6367 Tc - 3 30 272 Re 586-385 3 76 410 Ru - 327 293 0s 598-392 405 397 Ir 481-335 333 385 Pt 377 -28 5 278 358 & 737 a Experimental values obtained subsequent to estimated values listed.slightly lower than reported because of electronic contributions of possible low-lying excited states which had not been considered in arriving at the experimental values. Brewer 86 has reevaluated the experimental value for D;(Mo2)40 assuming population of excited states to correspond to an electronic degeneracy of 5 at 2900 K which leads to 365 40 kJ mol-' for D"(M0,). While there is no doubt about some electronic contribution to the free energy functions of Mo and Nb at the temperatures of measurement Brewer may have somewhat overestimated this contribution in case of Mo,(g) in view of the high experimental second-law value,4o Dg = 407 & 33 kJ mol-I.Even if one takes a small lowering of the dissociation energies for Mo and Nb into account the recent experimental values by Gupta et al. for these two molecules and for Pt show that the estimated values by the three empirical methods12"*8'*82 listed in table 5 appear to be too low but give the trends within each period cor- rectly. 4.2. DIATOMIC INTERMETALLIC COMPOUNDS In this section the application of empirical models of bonding to diatomic inter- metallic compounds is illustrated and discussed. The models considered are the Pauling model of a polar single bond,' the valence bond model for certain inter- metallic transition molecules with multiple bonds,' and the atomic cell model.lZb 4.2.1.PAULING MODEL OF A POLAR SINGLE BOND The Pauling model of a polar single bond' can generally be applied to interpret the dissociation energies of intermetallic molecules ,0p8' except in two cases (a)The values calculated by the model are lower than the experimental values for multiply bonded molecules. For such intermetallic molecules the valence bond approach and the atomic cell model to be discussed below are applicable. (b) It has been found experimentally that combinations of the copper subgroup transition metals with alkali or alkaline earth metals have lower dissociation energies than the values calculated DIATOMIC METALS AND METALLIC CLUSTERS by the model. These findings parallel the observation by Pauling' for the alkali hydrides.Similar can also be shown for mercury compounds with alkali metals using the data in tables 1 and 3. According to the model the bond energy D(A-B) of a diatomic molecule AB may be expressed by the relation D(A-B) = +[(D(A-A) + D(B-B)] + 96(xa -xB)'(in kJ mol-') (2) where D(A-A) and D(B-B) are " single bond " energies of component elements A and B respectively and x,,and xBare the respective electronegativities. In the appli- cation of the Pauling model in our laboratory we have preferred the Pauling scale' of electronegativities since it is based on bond energy measurements. The first term in eqn (2) gives the covalent contribution to the bond energy; the second term gives the "ionic resonance " energy which is always positive.Pauling also gives an alternate " geometric mean " version D(A-B) = [D(A-A) x D(B-B)]f + 125.5(~ -xB)2(in kJ mol-I). (3) A set of single bond energies for all non-transition elements has been calculated by Sanderson.8s Pauling' also gives values for the single-bond energies (in kJ mol-') for Ge (157.3) Sn (143.0) and Bi (105) which are pertinent to the present discussion and which differ from the corresponding dissociation energies for Ge, Sn and Biz respectively listed in table 1. Usually the dissociation energies of the transition metal dimers are taken as single-bond energies for lack of a reliable knowledge of the latter. This places an additional restriction on the application of the model especially where 4d and 5d transition metals are involved for most of which the dimers are expected to have multiple-bond character.Additional uncertainties in the use of the model come from the availability of different electronegativity scales and the dependency of the electronegativity of the valence ~tate.'*~'*~~ The range of applicability of the Paul- ing model to intermetallic molecules has been greatly extended during the last decade as a consequence of the experimental determination of the bond energies of many new diatomic metal molecules. The application of the Pauling model has also been demonstrated for triatomic intermetallic molec~les.~~~~ In this case the model is applied to each individual heteronuclear bond and the contributions of the various bonds are added to yield the atomization energies.The results for triatomic molecules are illustrated in section 4.4 below. For a comparison of calculated values with experimental dissociation energies of diatomic intermetallic compounds (see table 3) reference is made to the review 2.8 7 and to the original 31935A2 ,52.54,55,59,69.91-97 literature The intermetallic compounds of gold have been most thoroughly studied both by mass spectrometry and by optical spectroscopy. Since gold is the most electro- negative metal on the Pauling scale a sizeable ionic contribution to the bond energy is expected especially for combinations with the more electropositive metals. In table 6 the values obtained using eqn (2) are shown in brackets together with the experimental values (rounded to integers) taken from table 3.The calculated values for the alkali and alkaline earth compounds have been taken from Gingerich and In calculating the remaining values the Pauling electronegativities Finkbeir~er.~~~ were used adjusted for common valence" (e.g. to 1.7 for Ge Sn and Pb from 1.8 and 1.4 for U instead of 1.7). The use of 1.4 for Sc and 1.3 for the remaining rare- earth elements instead of 1.5 for Sc and 1.1-1.2 for the lanthanides has been discussed el~ewhere.~~"?~ The values in table 6 given in parenthesis have been calculated by the atomic cell K. A. GINGERICH TABLE 6.-cOMPARISON OF EXPERIMENTAL VALUES FOR DIATOMIC INTERMETALLIC COMPOUNDS OF GOLD WITH THOSE CALCULATED AFTER THE PAULING MODEL [ ] AND THE ATOMIC CELL MODEL 0 - Li 281 13491 Na 212 Mg243 1362 1 1251 I (207) CaK - Sc Ti Mn Fe 1 Co I Ni I Cu I Zn 238 277 188 I3041 12861 [2521 (405) (332)- (2101 (1273 Rb Sr Y Zr Tc 304 13051 -cs Ba (393) La (452) Hf (234) Re 251 335 :337] - 13481 (421) 1420) (255) 269) (244) (234) 11391 (6 9) Fr Ra Ac 318 13161 model IZa and will be discussed below.For Ge and Sn Pauling's single bond energies were used to calculate the covalent contribution. In all other cases the experimental dissociation energies were taken. The latter likely correspond to a bond order higher than 1 if they are >200 kJ mol-' and in these cases one notes from table 6 that the calculated values are consistently higher than the experimental ones (AuV AuLa AuCe AuRh). The agreement observed for AuNi is trivial since there is only a very small ionic component to the bonding.According to unpublished data obtained by Dr. G. D. Blue the dissociation energy of AuMg is considerably lower than the spectroscopic estimate listed in table 6. From the estimated data for AuPb it also appears that the spectroscopically derived experimental value is much too low. 4.2.2. EMPIRICAL VALENCE BOND METHOD FOR CERTAIN MULTIPLY BONDED TRANSITION ELEMENT MOLECULES A discussion of the applicability and limitations of the empirical valence bond method for certain multiply bonded molecules between electronegative and electro- positive transition metals,s has recently been presented.I0 In this method each of the two atoms forming the molecule is promoted to a valence state with two to four un- paired electrons that is suitable for multiple bond formation.Electron pair bonds are then allowed to form between the unpaired electrons of the two atoms in their valence states. The resulting bond energy per electron pair per mole is then taken the same as the determined valence state bonding enthalpy per mole per electron for the corre- sponding type of electrons in the respective condensed metal. The individual values for the latter are taken from the Brewer curvess3 which show the variation of s orp and DIATOMIC METALS AND METALLIC CLUSTERS d valence state bonding enthalpies per mole of electrons with atomic number and with principal quantum number and in the case of d-electrons also with the number of d-electrons participating in the bonding.Wengert 95 has conveniently tabulated such values obtained from the Brewer curves. The bonding energies of all bonds formed are then added. From this sum the sum of the valence state promotion energies is subtracted. The resulting value represents the calculated dissociation energy. The necessary valence state promotion energies are taken from the literat~re.~~*~' They are evaluated in a manner analogous to the one shown by Bre~er.*~*~~ Sample calculations have been given else~here.~*'~~~~ The experimental values of diatomic molecules of platinum metals with groups 111 and IV (including thorium) transition metals and with vanadium are compared in table 7 with the values calcu- TABLE 7.-cOMPARISON OF EXPERIMENTAL DISSOCIATION ENERGIES WITH VALUES CALCULATED USING EMPIRICALVALENCE BOND AND ATOMIC CELL MODELS.(VALUESARE IN kJ mol-I.) molecule (exp.1(see table 3) Do"(calculated) valence atomic bond model8 cell model1zb IrLa 573 * 12 565 537 IrTh 571 5 42 556 555 IrY 453 rt 16 451 522 LaPt 496 i15 423 573 LaRh 525 & 17 540 470 PtTh PtTi 547 342 394 * 11 456 360 588 494 PtY 470 & 8 316 555 RhSc RhTh 440+ 11 510 + 21 387 527 467 484 RhTi 387 f 15 427" 397 RhV 360 i29 460 362 RhY 442f 11 424 452 RuTh 588 & 42 657 496 RuV 410 5 29 569 382 ~~~ @ Revised value see ref. (71). lated by the empirical valence bond model. For these molecules values calculated by the atomic cell model12b have also been included.Additional comparisons with experimental values have been given elsewhere for BaRh BaPt LuPt RhU and the cerium compounds with all platinum metals." The experimental data in ref. (10) and in table 7 show that the calculated dis- sociation energies for the intermetallic molecules with platinum which have been based on an assumed double bond are lower than the experimental values. The latter are closer to those expected from an assumed triple bond but since platinum has no suitable valence state for triple-bond formation they have to be compared with the experimental values for the corresponding iridium compounds. Molecular orbital considerations lo can be used to explain the lower than calculated dissociation energies for RhV and RuV (for RuV a quadruple bond was assumed; with an assumed triple bond the same value as given for RhV would have been obtained).Thus optimum bonding can be expected for RhSc by assuming all electrons being paired with none in antibonding orbitals. One additional electron has to go into an antibonding K. A. GINGERICH orbital in case of RuV and two additional electrons in case of RhV weakening the bond in the observed sequence. 4.2.3. ATOMIC CELL MODEL The atomic cell model proposed by Miedema and GingerichlZb for calculating enthalpies of formation of diatomic intermetallic molecules is more general than either the Pauling model of a polar single bond or the valence bond method for intermetallic molecules with multiple bonds discussed above. It is based on a model description by Miedema and associates that was originally designed to account for the heat of formation of metallic alloys both in the solid and the liquid state.The enthalpies of formation of the diatomic intermetallic molecules are derived from the difference in electronegativity AVO*and that in the electron density at the boundary of the Wigner-Seitz atomic cell An,, using the symmetric dimers as reference states. In simplified form if the metals are of approximately equal size and do not contain p valence electrons the dissociation energy D(A-B) may be expressed by D(A-B) = -$[D(A-A) + D(B-B)] + P(Av*)~-Q(An$D2 (4) where P and Q are empirical constants. This relation may be compared with that of Pauling for a polar single bond [eqn (2)]. The second term corresponds to Pauling's ionic resonance contribution but uses the same electronegativity values as Miedema and associates used for the condensed alloys.Particularly noteworthy is the third (repulsive term) lacking in Pauling's formula. For diatomic molecules between transi- tion metal atoms and polyvalent main group atoms a fourth constant term must also be added (as in the formula for condensed alloys) to account for bond strengthening due to hybridization. Miedema will give a more detailed account of this model at this Symposium.103 Comparisons of model calculations with experimental values have been presented in our original paper.12b In table 6 a comparison of experimental dissociation energies with those calculated using the atomic cell model or Pauling model is made for intermetallic compounds with gold.The atomic cell model as has been noted for the Pauling model yields over-large dissociation energies for molecules of Group I B transition metals with alkali or alkaline earth metals. However if the value of the ionicity parameter P [eqn (4)] is reduced by a factor of 0.65 the agreement with the experimental values for alkali compounds with group IB metals becomes good.12b For the molecules with one of the magnetic metals Cr Mn Fe Co and Ni the atomic cell model yields over-small dissociation energies whereas the Pauling model gives quite good agreement in these cases. The atomic cell model has not yet been applied to the lanthanide and actinide-gold compounds (except thorium) for which the Pauling model gives good agreement with experiment.In table 7 values for dissociation energies calculated by the atomic cell model are compared with experimental values and those calculated by the valence bond model. As can be seen the values calculated for the platinum compounds are higher than the experimental values. This has been attributed to a barrier for charge transfer for metals of high electronegativity at the end of a transition metal series such as Pt and Au (see table 6) when these metals are combined with much more electropositive partners such as the group I11 transition metals.12b For RhV and RuV the atomic cell model reproduces the experimental values well unlike the valence bond model. A significant advantage of the atomic cell model is seen in its applicability to intercombinations of transition metals in the central region of the transition series to which the Pauling model and the valence bond model cannot be applied.In com- DIATOMIC METALS AND METALLIC CLUSTERS menting on the relative merits of the three empirical models discussed here the atomic cell model is most generally applicable to intermetallic compounds whereas the Pauling model and the valence bond approach may give more accurate predictions in their specific areas of applicability. Another advantage of the atomic cell model is seen in its direct relation to the bonding in the corresponding condensed alloys which can be expressed in quantitative terms. Further experimental results are expected to permit refinements of all models but especially of the atomic cell model.4.3. MAXIMUM BOND ENERGY BETWEEN TWO METAL ATOMS Both the valence bond model and the atomic cell model predict similar maximum bond energies between two metal atoms. The highest values calculated by the valence bond model assuming quadruple bond formation are between 630 and 670 kJ mol-1.8" The observation that quadruple bonding is not fully achieved led to the conclusion that the maximum possible bond energy between two ligand-free metal atoms is 670 & 84 m01-I.~ The atomic cell model yields maximum bond energies for intermetallic molecules of iridium (IrZr 588; IrHf 555; IrTh 555) osmium (OsZr 574) and platinum (PtSc 571 ; PtZr 621 ; LaPt 573; HfPt 584; PtTh 588).12* Here the values are given for molecules with a predicted dissociation energy of more than 550 kJ mol-'.As discussed earlier12' and as confirmed for LaPt,69 the calcu- lated values for the platinum-containing molecules with the more electropositive metals tend to be too high. On the other hand there will be a small upwards revision for the bond energies since the new experimental evidence quoted in table 5 indicates that the dimer dissociation energies of the 4d and 5d transition metals are higher than the estimated values1*" used as a basis for the calculations. However the downward correction for D"(PtZr) is expected to be larger than this upward correction thus 620 kJ mo1-' the highest value obtained by the atomic cell model may be con- sidered an upper limit value and is in agreement with the upper limit value based on the valence bond model.For the homonuclear transition metal molecules the highest estimates (see table 5) are 66lS1and 538'2a kJ mo1-' respectively both for W2where the latter value was based on eqn (4) in ref. [12(a)l. The experimental evidence for the isoelectronic molecules RhY and Mo (see table 4) suggests that D;(W,) is not larger than that of the isoelectronic molecule IrLa (573 -& 12 kJ mol-I). The dissociation energy of Ta is expected to be possibly larger than that of W2,36but not by much. Thus 600 & 40 kJ mol-' is considered to be a safe upper limit for the maximum dissociation energy of a symmetric diatomic metal molecule. Current knowledge from experi- ment and from the empirical models of bonding suggests that the actual upper limit for a diatomic intermetallic molecule is lower than the upper limit of 670 & 84 kJ mo1-l given earlier' and a revised upper limit of 640 rf 40 kJ mol-' (or 150 & 10 kcal mol-I) is proposed.It is of interest to compare this upper limit for the bond energy between two ligand- free metal atoms with the maximum bond energy expected for quadruply bonded pairs of metal atoms in dinuclear transition metal complexes of Moil Cr" TclI1 and Re1('." In early estimates of the strength of quadruply bonded metals e.g. for Re,Cli- Cotton99u had suggested that the bond energy holding the pair of metal atoms together may be as high as 400 kcal mol-' (1674 kJ mol-I). In all early discussions9'" the strongest argument for the high bond energy had been the very short observed bond distance in conjunction with the observed geometrical arrange- ment of the ligands.Cotton had qualitatively related the bond shortening to the bond strength.'" The experimental calorimetric determination of the bond strength K. A. GINGERICH between such pairs of metal atoms in a complex compound is difficult and the results quite uncertain since attribution of the measured heat effects has to be made to all bonds in the corresponding complex compounds. About ten years ago this author had therefore graphically related the bond strength to the bond shortening."' In these estimates the known dissociation energies D;,and equilibrium separations re,of the molecules Cu, Au2 AlAu RhC and PtC had served as a basis for an empiri- cal plot of bond shortening against bond energy.The bond shortening was based on the Pauling' metallic single bond radii or 12-coordinate radii respectively as a reference. For the largest bond shortening known at that time,Io2 in molybdenum(rr) acetate [Mo(O,CCH,),], a bond energy of 740 kJ mol-' resulted from both methods. For the first established quadruply bonded complex compound (Re,C1,)2-,100 360 kJ mol-l resulted using the 12-coordinate metallic radii as a reference or 520 kJ mo1-I using the metallic single bond radii. These results showed that such quadruple bonds were not the strongest chemical bonds known as had been widely assumed at that time. The recent experimental determination of the bond length r(Mo-Mo) = 1.929 Ag5and dissociation energy Dg(Mo,) = 404 -& 20 kJ m~l-',~' indicate that the bond energies between quadruply bonded metal atoms in complex compounds are actually smaller than the largest bond energies found in ligand-free metal dimers provided the experimental bond distance for gaseous Mo is correct.4.4. POLYATOMIC METAL MOLECULES For polyatomic metals (table 2) and intermetallic compounds (table 4) the bond additivity concept has frequently been used to interpret the experimental atomization energies. In case of the intermetallic compounds the Pauling model has been success- fully used in addition (see table 8). The electronic structures of each family of poly- 8.-COMPARISON OF EXPERIMENTAL AND CALCULATED VALUES USING THE PAULING TABLE MODEL FOR TRIATOMIC SYMMETRIC MAu2 INTERMETALLIC MOLECULES.(VALUESARE IN kJ mol-l.) DE(MAu2) molecule calc." exp.' AlAu2 528 506.3 f25.1 Au2Ba 674 552 i21 Au~Eu 482 549.4 k 16.7 Au2Ge 472 534.9 rt 12 AuZHO 534 533 f 42 Au~Lu 592 602.1 & 33.5 Au2Sn 502 542 f18 AuzTb 580 582 f42 = - a Using Do0 D(M-M) + D(Au-Au) + 192(xA x~)~; Taken from table 4. atomic metals (and metalloids) give rise to special trends in bond energies (and geometries) for each family e.g. group IV or group V polyatomic molecules. For specific details reference is made to the individual literature quoted in tables 2 and 4. The lack of spectroscopic data concerning their electronic and molecular structure limits the insight into the bonding that can be gained from available atomization energies.Theoretical and semi-empirical calculations have been contributing to qualitative or semi-qualitative estimates of stabilities geometry and spectra of small clusters. It is expected that in the near future the experimental and theoretical DIATOMIC METALS AND METALLIC CLUSTERS methods will mutually aid in gaining a deeper understanding of the nature of small metal clusters. Note added in proof In his paper at this Symposium,103 Miedema has treated the metals Ni Pd Pt or Au differently in the prediction of the dissociation energies of heteronuclear diatomic transition metal molecules from the original paper by Mie- dema and Gingerich.lzb The values listed in table 1 of Miedema's paper103 include a correction for resistance to charge transfer of the metals Ni Pd Pt and Au when combined with the more electropositive transition metals.In table 9 the values for those intermetallic molecules of gold and platinum for which a correction has been made by Miedernalo3 are listed together with the experimental values (table 3) and previously estimated values (tables 6 and 7). As can be seen from table 9 the refine- ments to the atomic cell model by Miedema have led to an improvement in all the calculated values. This is particularly the case for the platinum compounds for which the values calculated by the atomic cell model now agree with the experimental values except for TiPt for which it almost agrees. Thus for diatomic platinum com- pounds with electropositive transition elements the atomic cell model appears to be superior to the empirical valence bond model.TABLE9.-cOMPARISON OF EXPERIMENTAL VALUES FOR THE DISSOCIATION ENERGIES (IN kJ mol -l) OF DIATOMIC INTERMETALLIC COMPOUNDS WITH THOSE CALCULATED BY VARIOUS EMPIRICAL MODELS D;,calculated molecule D& exp. table 3) (see -atomic cell model ref. (126) ref. (103) model Pauling bond model valence AuSc 277 i17 405 369 286 AuY 304 & 8 393 359 305 AuLa 335 3= 21 421 362 348 AuTi 332 314 252 AuZr 452 420 AuHf 420 393 AuTh 423 392 369 AuV 238 12 322 314 252 AuNb 381 373 AuTa 383 376 LaPt 496 i15 573 484 423 PtTh 547 & 42 588 508 456 PtTi PtY 394 f11 470 + 8 494 555 441 470 360 316 HfPt 584 516 PtSc 571 488 PtZr 621 544 Also included in table 9 are values for platinum intermetallic molecules that have been mentioned in section 4.3 in connection with the estimation of the maximum bond energy between two metal atoms and for which Miedema has presented refined K.A. GINGERICH estimates. These refined values are ir,support of the qualitative conclusions drawn in section 4.3 above. In table 2 of their paper Brewer and Winn104 present different estimated dissocia- tion energies from those values listed in table 5 of this paper given by Brewer.' Expressed in kJ mol-' for comparison with Brewer's values quoted in table 5 these are Zr, 333; Hf, 333 & 50; Ta, 349 & 50; W, 482 & 66; Re, 312 & 82; Ru, 308; Os, 366 & 50; and Ir, 349 & 50.Except for the lower estimates for Ta, Re and Os, these more recent estimates by Brewer and Winn are closer to the corresponding estimates by Miedema and Gingerich 12b and by Krasnov.81 This article has the nature of a summary and revicw of more than a decade's effort. A number of colleagues have contributed at the various stages as can be seen from the list of references. In particular the author wishes to thank Drs. G. D. Blue U. V. Choudary D. L. Cocke S. K. Gupta R. Hague J. Kordis A. R. Miedema B. M. Nappi M. Pelino and V. Piacente Mr. J. E. Kingcade Jr and his wife. Dr. Gupta had in addition contributed to this manuscript with valuable discussions. The ex- perimental work at Texas A & M University has been generously supported through research grants by the National Science Foundation and the Robert A.Welch Foundati on. L. Pauling The Nature of the Chemical Bond (Cornell University Press Ithaca N.Y. 3rd edn 1960). K. A. Gingerich J. Cryst. Growth 1971 9 31. K. A. Gingerich D. L. Cocke H. C. Finkbeiner and C.-A. Chang Chem. Phys. Letters 1973 18,102. L. Brewer personal communication 1968. ' K. A. Gingerich and R. D. Grigsby Metallurg. Trans. 1971 2 917. K. A. Gingerlich and D. L. Cocke Chem. Cotnm. 1972 536. K. A. Gingerlich High Temp. Sci. 1971 3 415; D. L. Cocke and K. A. Gingerich J. Phys. Chem. 1972 76 2332 4042; D. L. Cocke K. A. Gingerich and J. Kordis High Temp. Sci. 1973 5 474. a (a)K. A. Gingerich Chem. Phys. Letters 1973 23 270; (6) K. A.Gingerich J.C.S. Faraday II 1974 70 471. K. A. Gingerich Chem. Phys. Letters 1974 25 526. lo K. A. Gingerich Int. J. Quantum Chern. Symp. 1978 12 489. l1 A. R. Miedema R. Boom and F. 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Wengert Thermodynamic Stabilities of Certain Intermetallic Contpoiinds Mude From Traiisitiott Elenients UCRL-I 8727 Berkeley CA 1969. 96 C. E. Moore Atotnic Etiergy Levels Natl. Bur. Stand. Circ. 467 vol. 1-3 1949 1952 1958. 97 L. Brewer J. Opt. SOC. Anzer. 1971 61 1101. 98 L. Brewer High Stretigth Materials ed. V. F. Zackay (Wiley New York 1965) pp 12-103. 99 (a)F. A. Cotton Accounfs Chert?. Rex 1979 2 240; (b) F. A. Cotton Chem. Soc. Rev. 1975 4 225; (c) F. A. Cotton Accounts Clietn. Res. 1978 11 25; and literature quoted therein.loo F. A. Cotton Inorg. Chetn. 1965 4 335. K. A. Gingerich invited paper presented at the Joint Conf. of the Chem. Inst. of Canada with the Amer. Chem. SOC. Symp. on Structure and Chemistry of Compounds with Metal-Metal Bonds Toronto Canada (1970). Also quoted in ref. (8a). lo' D. Lawton and R. Mason J.Amer. Chem. SOC.,1965,87,92I. Io3 A. R. Miedema Faraday Disc. Chetn. SOC.,1980 14 136. Io4 L. Brewer and J. S. Winn Faraday Disc. Chent. SOC.,1980 14 127.