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. 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