Electron Spin Resonance Study of Intermetallic Molecules CUM and AuM (M=Mg Zn Cd and Hg) AND DONALD BY PAULH. KASAI~ MCLEODJR Union Carbide Corporation Tarrytown Technical Center Tarrytown New York 10591 U.S.A. Received 21st August 1979 A series of intermetallic diatomic molecules CUM and AuM (M = Mg Zn Cd and Hg) generated in argon matrices was examined by e.s.r. spectroscopy. For all the CUM and AuM examined the hyperfine coupling tensors to the Cu and Au nuclei were isotropic. The unpaired electron resides in an orbital given essentially by an antibonding combination of the valence s orbitals of Cu (or Au) and M atoms. Coupling interactions observed with magnetic Cd and Hg nuclei and the analysis of the g tensor indicate a small admixture ( % 10%) of the valence pz orbital of the atom M in each CUM and AuM examined.The nature of metal-metal bonds found between metal atoms in complex coordina- tion compounds1 as well as those existing between ligand-free metal has been the subject of many recent investigations. The homonuclear diatomic molecules of various metals have been examined by mass spectroscopy of the vapour phase3 and by optical spectroscopy using the matrix isolation techniq~e.~ Electron spin resonance (e.s.r.) spectra of heteronuclear intermetallic diatomic molecules if ob-served would be particularly elucidative of the interaction between the pair of metal atoms. When metal atoms M are condensed in inert gas matrices at liquid helium tem- perature the diatomic species MZ are found in a quantity much larger than that expected from the vapour phase compo~ition.~ The diffusion of metal atoms within the quasi-liquid surface layer existing during the deposition must be responsible for the extra dimerization process.It follows that a sufficient amount of heteronuclear diatomic molecules may be generated in rare gas matrices by cocondensation of two different atoms. Recently we reported an e.s.r. study of AgM (M = group I1 metal) generated by this cocondensation technique in argon mat rice^.^ The present paper describes the result of the extension of the matrix-isolation e.s.r. study to include CUMand AuM (M = Mg Zn Cd and Hg). The e.s.r. spectra of CUM and AuM are expected to be characterized by extremely large hyperfine interactions with the Cu and Au nuclei and hence to provide more sensitive probing of the semi-filled orbital.The observed e.s.r. spectra revealed that the hyperfine coupling interaction is indeed large but is essentially isotropic. As in the case of AgM the electronic configurations of CUM and AuM are concluded to be a;a*,'where a and a,*are the bonding and antibonding a orbitals arising essentially from the valence s orbitals of Cu (or Au) and the atom M. -f To whom correspondence should be addressed. Present address IBM (78V-906) Box 390, Poughkeepsie New York 12602 U.S.A. E.S.R. OF INTERMETALLIC MOLECULES EXPERIMENTAL The cryostat-spectrometer assembly that would permit trapping of high temperature vapour phase species in a rare-gas matrix at -4 K and observation of the resulting matrix by e.s.r.has been described earlier.6 In the present series of experiments two metal atoms were vaporized from two independently resistively heated tantalum cells. The tantalum cells contained the metals in granular form and were heated to a temperature at which the vapour pressure of the respective metal would be 0.1-0.5 Torr. In the case of Au in order to prevent alloying with the Ta cell Au metal was placed inside an alumina tube capped with a molybdenum plug and then placed inside the Ta cell. The gold vapour effused through an opening drilled through the Ta and alumina walls. The frequency of the e.s.r. spectrometer locked to the sample cavity was 9.42 GHz and all the spectra were obtaiiKd while the matrices were maintained at -4 K.RESULTS SPECTRA AND ANALYSES The e.s.r. spectra of Cu atoms (3d1'4s') and Au atoms (5dl06s1)isolated in argon matrices have been studied earlier.7 The spectra are characterized by extremely large hyperfine interactions with the nuclei of spin $ i.e. 63Cu (natural abundance = 69% I = 3,p = 2.2206&) 65Cu (natural abundance = 31% Z = 3,p = 2.3790&) and I9'Au (natural abundance = loo% I = 4,p = 0.1439pN). The splittings of energy levels of an isotropic system with S = 3and I = $ in a magnetic field Hcan be readily obtained from the Breit-Rabi solution of the spin Hamiltonian (1) X=gPH*S+AZ*S (1) and are illustrated in fig. l(a). Ar f2 ft FIG.1.-(a) Splitting of energy levels of a system with S = 4and I = $ in external magnetic field.Observable transitions are indicated for the two cases Av > 2A and hv < 2A. (b) Dependence of the resonance fields (gpH//Av)upon the hyperfine coupling coupling constant (A/hv)for the system given in (a). P. H. KASAI AND I). MCLEOD JR 67 As can be seen from fig. 1 the e.s.r. spectrometer frequency v must be larger than the zero-field splitting (I + +)A in order to observe the '' normal '' (21+ 1) hyperfine components of the e.s.r. transitions AMs = & 1 AMI = 0. If the zero-field splitting is larger than the spectrometer frequency only two transitions are observable; one corresponds to the highest field hyperfine component of the normal e.s.r. transition (AMs = &l MI = -I) and the other corresponds to an n.m.r.transition (M = _-i MI = -I ++ -I + 1). The Breit-Rabi solution also yields the following ex- pressions for the resonance positions of the normal e.s.r. transitions and the particular n.m.r. transitions discussed above. (21+ l)a -2 (3) q(n.m.r.) = 2-a where Dependencies of the reduced resonance fields y(Mz)and y (n.m.r.) upon the reduced hyperfine coupling constant a are illustrated in fig. l(b). The hyperfine coupling constants of Cu atoms isolated in an argon matrix are 6.151 and 6.587 GHz for 63Cu and 65Cu re~pectively.~ Thus for a typical X-band spectrometer frequency of 9.4 GHz a = 0.65 for 63Cuand a = 0.70 for 65Cu as indicated in the figure and only the transitions given by y (n.m.r.) and y(-*) are observed. Fig. 2 shows the e.s.1.spectrum observed from an argon matrix in which Cu and 63CuMg +I $. ' 1 4 P- I I I I I I 0 1 2 3 4 5 6 kG FIG.2.-E.s.r. spectrum of an argon matrix containing Cu and Mg atoms. Mg atoms were cocondensed. The signals indicated by the arrows are those of isolated Cu atoms. Two sets of quartets were recognized among the remaining E.S.R. OF INTERMETALLIC MOLECULES signals. They were unique to matrices containing Cu and Mg atoms and hence were assigned to (j3CuMg and TuMg as indicated. The overall spread the line shape and their positions indicate that the coupling tensors to the Cu nuclei of these species are nearly isotropic and correspond to the situation C( = 0.28 in fig. l(b). The molecular symmetry of CUM (or AuM) dictates that their e.s.r.spectra be compatible with an axially symmetric spin Hamiltonian [eqn (4)] 2-F = g,,PHzSz + glP(KSx + HYSY) + AllIz& + AI(IxSx + IySy) (4) where A,,and Al represent the hyperfine coupling tensor to the Cu (or Au) nucleus. When the hyperfine interaction is of such magnitude as that encountered here the usual second-order solution of the matrix cannot be used to determine the relevant parameters in eqn (4). However it can be shown that when the magnetic field is parallel to the symmetry axis the secular determinant derived from eqn (4) is tri- diagonal and hence can be expanded exactly using a continuous fraction technique.* From the eigenvalues expressed in the continuous fraction form the following " con-tinued expressions " were obtained for the resonance positions of the parallel com- ponents.(5) where hV and a If /A,,-All < gPH a condition which is surely met in the present case the secular determinant derived from eqn (4) can be treated as being tridiagonal when the mag- netic field is perpendicular to the symmetry axis also. It is thus possible to derive the following " continued expressions " for the perpendicular components of the resonance signals Hl(MI) = HY -MIA; -Fl -GI (6) where Q:[I(I + 1) -MI(MI+ 111 F_i = HdMI) + (MI + %)A; + F_L and P. H. KASAI AND D. MCLEOD JR A close examination of the CuMg spectrum observed in an expanded scale clearly resolved the pattern expected from an axially symmetric system. The measured parallel and perpendicular positions of each hyperfine component of 63C~Mg are listed in table 1.From the observed parallel and perpendicular resonance positions TABLE1 .-OBSERVED (G) RESONANCE POSITIONS OF 63C~M 1740 480 465 250 (n.m.r.) 273 (n.m.r.) ++{& 2392 971 940 986 965 -4{& 3335 2538 2520 3346 2570 2578 4587 5188 5203 5483 4603 5234 5306 5795 v/GHz 9.4255 9.4256 9.4237 9.4213 of the MI = 3-components and eqn (5) and (6) the consistent set of g and hyperfine coupling tensors can be readily determined through a computer-assisted iteration process. The g tensor and the hyperfine coupling tensor to the Cu nucleus thus deter- mined for 63C~Mg are given in table 2. 2.-sPIN HAMILTONIAN TABLE PARAMETERS OF 63C~M ~ ~ Mg 2.0031 (7) 1.9984 (7) 2.609 (2) 2.618 (2) Zn Cd Hg 2.0049 (7) 2.0001 (7) 1.996 (1) 1.9895 (7) 1.9659 (7) 1.890 (1) 4.186 (2) 4.200 (2) 4.968 (3) 4.195 (2) 4.218 (2) 4.976 (3) 2.34 (10) 2.83 (10) free Cu 1.9994 (2) 6.151 (1) a Coupling to "'Cd or 199Hg.Fig. 3-5 show respectively the e.s.r. spectra observed from argon matrices in which Cu and Zn Cu and Cd and Cu and Hg atoms had been cocondensed. In each trace the signals due to isolated Cu atoms are marked by solid straight arrows. The two sets of quartets readily recognized in fig. 3 and 4 were assigned to CuZn and CuCd. The overall spread of the quartets indicates that the hyperfine coupling constants to the Cu nuclei in these molecules correspond to the case a E0.45 in fig. l(b). In the case of CuHg (fig.5) the normal quartet signals were no longer observed; only the n.m.r. transition and the highest-field component of the e.s.r. transitions were recog- and 65C~Hg nized for both 63C~Hg as indicated. The spectral pattern of CuHg is that expected for a zz0.53 in fig. l(b). The measured parallel and perpendicular positions of each observed transition of 63CuZn (j3CuCd and 63C~Hg are listed in table 1. The g tensors and the hyper- fine coupling tensors to the 63Cu nuclei of these molecules determined from the parallel and perpendicular positions of the Mi = &-$ components (the n.m.r. and MI = -3 component in the case of WuHg) resorting to the iteration process described earlier are compiled in table 2. Comparison of the spectra seen in fig.2-5 shows that the E.S.R. OF INTERMETALLIC MOLECULES 65C"Z" 1 2 3 4 5 6 kG FIG.3.-E.s.r. spectrum of an argon matrix containing Cu and Zn atoms. 65CuCd 1 63CuCd I I kG FIG.4.-E.s.r. spectrum of an argon matrix containing Cu and Cd atoms. anisotropy (the separation between the parallel and perpendicular positions within each hyperfine component) of CUM (M = Mg Zn Cd Hg) increases with the in- creasing atomic number of M. The spin Hamiltonian parameters determined and given in table 2 reveal that the hyperfine coupling tensor to the Cu nucleus is essentially isotropic in each case and the noted increase in the anisotropy is due entirely to in- crease in the anisotropy of the g tensor. The parallel and perpendicular resonance positions of all the components of 63C~M and TuM computed based upon the para- meters given in the table the known ratio of the magnetic moments of 63Cu and Vu and the iteration process based upon eqn (5) and (6) were found to be in excellent agreement with the observed values.The representative result obtained for CuCd is shown in table 5. There are two magnetic Cd nuclei of significant abundance lllCd (natural abund- P. H. KASAI AND D. MCLEOD JR 65CuHg(nmr) 6sCu Hg n I,! 63CuHg (nmr) 63CuHg n T-O 1 kG FIG.5.-E.s.r. spectrum of an argon matrix containing Cu and Hg atoms. ance = 13% I = 4,p = -0.5922pN) and 'I3Cd (natural abundance = 12% I = 3 p = -0.6195PN) and two magnetic Hg nuclei of significant abundance 199Hg (natural abundance = 17% I = 3 p = 0.4979 pN)and "'Hg (natural abundance = 13% Z = $ p = -0.5513pN).The curved arrows in fig. 4 indicate the signals that were .recognized as the perpendicular components of the "'Cd and 'I3Cd satellites of the MI = -3 component of 63C~Cd. The curved arrows in fig. 5 indicate the per- pendicular components of the 199Hg satellites of the MI = -$ component of 63C~Hg. The parallel components of these satellites and in the case of CuHg the satellites due to 201Hg were too weak to be detected. Because of the coexistence of extremely large coupling interactions with two nuclei the coupling tensors to the magnetic Cd and Hg nuclei in CUM could not be determined completely from the resonance positions of the perpendicular components only.However in each case the peak-to-peak intensity ratio of the satellite to the main peak is close to that expected from the natural abundance of the isotopes involved. It thus appears that the coupling tensors to the magnetic Cd and Hg nuclei are nearly isotropic. The magnitudes of the coupling interactions with the "'Cd and 199Hg nuclei assessed from the resonance positions of the MI = -3 main peak and its satellites assuming an isotropic tensor are included in table 2. Fig. 6-9 show the e.s.r. spectra observed from argon matrices containing Au and Mg Au and Zn Au and Cd and Au and Hg atoms respectively. In each trace the quartet signals due to isolated Au atoms are indicated by solid straight arrows. The hyperfine coupling constant of Au atoms isolated in an argon matrix has been deter- mined to be 3.1379 GHz,~ and corresponds to the situation CL = 0.33 in fig.I@). The second set of quartets observed in each trace with substantially reduced spacings was unique to the matrix containing Au and the specific M(M = Mg Zn Cd and Hg) and was assigned to the diatomic species AuM. The parallel and perpendicular signals of all the hyperfine components of AuM are well resolved as indicated. The experimentally determined resonance positions of AuM are listed in table 3. The g tensors and the hyperfine coupling tensors to the 19'Au nucleus determined from the parallel and perpendicular positions of the MI = &-% components using eqn (5) and (6) are given in table 4. The resonance positions of all the components of 197A~M E.S.R.OF INTERMETALLIC MOLECULES 1 3 4 5 kG FIG6.-E.s.r. spectrum of an argon matrix containing Au and Mg atoms. / J I1 1I 1 2 3 4 5 kG FIG.7.-E.s.r. spectrum of an argon matrix containing Au and Zn atoms. P. H. KASAI AND D. MCLEOD JR Au Cd (I)Jl I 1 3 4 5 kG FIG.8.-E.s.r. spectrum of an argon matrix containing Au and Cd atoms. c4+ 1 I1 1 2 3 kG 4 5 FIG.9.-E.s.r. spectrum of an argon matrix containing Au and Hg atoms. E.S.R. OF INTERMETALLIC MOLECULES TABLE3.-oBSERVED RESONANCE POSITIONS OF AUM (G) 3003 2561 2535.5 2084 ++{$ 3033 2589 2578.9 2165 3220 2984 2968.2 2665 3255 3022 3025.9 2778 3452 3484 3483.4 3439 3492 3533 3556.6 3591 3703 4060 4081.9 4406 3748 41 21 4171.3 4602 v/GHz 9.4216 9.4228 9.42196 9.4238 TABLE4.-sPIN HAMILTONIAN PARAMETERS OF AUM MgZn Cd Hgfree Au 2.0003 (7) 1.9771 (7) 1.9996 (7) 1.9734 (7) 1.9983 (7) 1.9593 (7) 1.9932 (7) 1.9121 (7) 2.0012 (1) 0.650 (2) 0.658 (2) 1.390 (2) 1.403 (2) 1.433 (2) 1.447 (2) 2.132 (2) 2.146 (2) 3.1379 (2) 4.72 (10) 6.45 (10) Coupling to lilCd or 199Hg.TABLE5.-cOMPARISON OF OBSERVED AND CALCULATED RESONANCE POSITIONS OF CuCd AND AuCd (G) MI 63C~Cd 65C~Cd AuCd obs. calc. obs. calc. obs. calc. 465 465 191 193 2535.5 2535.5 187 2578.9 2578.9 940 943 (masked) 452 2968.2 2968.1 965 965 (masked) 470 3025.9 3026.0 2520 2522 21 57 2157 3483.4 3483.5 2578 2579 2214 221 3 3556.6 3556.8 5203 5203 (masked) 5308 4081.9 408 1.9 5306 5306 5414 5414 4171.3 4171.3 computed based upon the parameters given in the table and the iteration process based upon eqn (5) and (6) were in excellent agreement with the observed values.The representative result obtained for AuCd is shown in table 5. In the cases of AuCd (fig. 8) and AuHg (fig. 9) many minor signals are seen that are attributable to the satellites due to "'Cd and '13Cd and to I9'Hg and 201Hg respectively. The curved arrows in fig. 8 and 9 indicate the perpendicular components of the lllCd and 199Hg satellites of the main MI = -3 component of AuM. The parallel components of the satellites were not observed. Again because of the ex- treme magnitudes of the hyperfine interactions with two nuclei the coupling tensor to the magnetic Cd or Hg nucleus could not be determined completely from the resonance positions of the perpendicular components only.The magnitudes of the coupling P. H. KASAI AND D. MCLEOD JR interactions with the lllCd and 199Hg nuclei assessed from the resonance positions of the main MI = -3 peak and its satellites assuming an isotropic tensor are given in table 4. DISCUSSION As revealed in tables 2 and 4,the coupling tensors to the Cu and Au nuclei are essen- tially isotropic for all the CUM and AuM molecules examined in the present study. The electronic configurations of Cu and Au atoms are 38'4s' and 5d1°6s1 respectively and those of Mg Zn Cd and Hg are either ns2or (n -l)dl0ns2. The semi-filled orbital of CUM (or AuM) of the present series is thus expected to be given essentially by an antibonding combination of the valance s orbitals of Cu (or Au) and M atoms.Hence @ = aPcu(4s) -bPMW or The spin density at the Cu or Au atom is then given by p = a2 -abS where S here represents the overlap integral between the two valence s orbitals. The coefficients a and b in eqn (7) may be determined from the secular determinant 1%' -ESI = 0. The usual LCAO-MO calculations were carried out equating the Coulomb integrals Zrito the atomic ionization potentials of the respective atoms and approximating the resonance integrals Ziby the Wolfsberg and Helmholtz expres- sion~~ The spin densities p thus determined for the present series of CUM and AuM assum- ing the fixed values of K = 2.0 and Sij = 0.2 are compared with the experimental values in fig.10. The experimental values were given by A/Aowhere A and A. are respectively the observed coupling constants of the diatomic molecules and the isolated atoms. A reasonable agreement obtained here is a strong substantiation to the envisaged orbital interaction. As in the case of AgM a more accurate LCAO description of the semi-filled orbital of CUM or AuM would be of the following form 0= aPcu(4s)-bP&) -cPM(nPz)* (8) It reflects the fact that the valence state in which the unpaired electron resides on Cu is neutral while the valence state in which the unpaired electron resides on M is polarized c; . . . M++ cu . . . M. (-) (+I The coupling constants Ao(lllCd) or Ao(199Hg) expected from a unit spin density in the valence ns orbital of Cd or Hg are not known.They may be estimated from the known coupling constants of the Ag and Au atoms and the Goudsmit relation (9)" AisoK z(Eip)'(I/p) (9) where 2 Ei,and p represent the atomic number the ionization potential and the magnetic moment of the nucleus respectively. The resulting estimated values are A,("'Cd) = 12.5 and Ao(199Hg) = 40.0 GHz. Thus for CuCd CuHg AuCd and E.S.R. OF INTERMETALLIC MOLECULES I I I 1 1 I I ' ' 5 6 7 8 9 10 11 i.p./ eV FIG.10.-Correlations between the observed spin densities (AIA,,)and the ionization potentials of the atom M for the CUM (solid circles) and AuM (open circles) series. The lines indicate the correla- tions predicted by the LCAO-MO calculations (see text).AuHg the spin densities (AIA,) in the valence s orbitals of both atoms were assessed as follows molecules vcu(4s) or VAuWI % v,M(ns)/ % CuCd 69 19 CuHg 81 7 AnCd 46 38 AuHg 68 16 We are thus led to surmise that the contribution of pM(np,)in eqn (8) is probably in the range 10-15 % for all CUM and AuM of the present series. It has been shown that for a paramagnetic molecule having a non-degenerate ground state the deviation of the g value along a principal axis " i" from that of a free electron (2.0023) can be given by l1 Agi = -2AC (OILi In>(nl Lilo> n+~ En -Eo where A is the spin-orbit coupling constant of the relevant atom Li is the usual angu- lar momentum operator and En -Eo is the energy separation between the ground P.H. KASAI AND D. MCLEOD JR state 10) and the excited state In). Thus for the ground state given by eqn (8) it follows immediately that Agl(=Ag,) = 0 and that Agl(=Ag = Agy) would be caused solely by the np part of M. One electron spin-orbit coupling constant of atom M may be assessed from the fine-structure intervals of the atom in its 3P(ns'np') 10 1 / A /cm" FIG.1 1.-Correlations between the observed Agi of CUM (solid circles) and AuM (open circles) and the one-electron spin-orbit coupling constant of the atom M. state.I2 Fig. 11 shows the values of Agi for CUM and AuM plotted against the spin- orbit coupling constant A of M. Linear dependencies were obtained for both the CUM and AuM series.As was the case with the AgM series studied earlier the straight line of the CUM series goes through the origin indicating the absence of the contribution of the Cu atom to Agl. The spin-orbit coupling constants of Cu and Au are 165 and 2544 cm-' respectively. The straight line of the AuM series inter- sects the ordinate at Agl x 100 = 2.3. We do not believe it represents the contribu- tion of Au to Agi. As discussed below if the semi-filled orbital of AuM contains the 6pz orbital of Au it is expected that A,,> Ai for the coupling tensor with the Au nucleus contrary to the observed result. The non-vanishing Agi at A = 0 for AuM may be ascribed to the increased interaction between the neighbouring Ar atoms and large valence orbitals of Au.'~'~ For the diatomic molecules CUM and AuM having the semi-filled orbitals of the form such as that given in eqn (8) the hyperfine coupling tensor to the Cu Au or M nucleus should be given by l4 All == Aiso + 2Adip Al= Aiso -Adip where Aiso is the isotropic coupling constant arising from the spin density in the valence s orbital and Adiprepresents the anisotropic part due to the spin density in the E.S.R.OF INTERMETALLIC MOLECULES valence p orbital of the nucleus under consideration. It thus follows that A, 2Al. For all the coupling tensors to the Cu and Au nuclei of CUM and AuM examined here A is slightly less than Al. It signifies the absence of the valencep orbital of Cu or Au in the semi-filled orbital and the presence of small negative spin density gener- ated through polarization in the p section of the filled bonding orbital.F. A. Cotton Accounts Chem. Res. 1969 2 240. * K. A. Gingerich J. Cryst. Growth 1971 9 31. W. A. Cooper G. A. Clarke and C. R. Hare J. Phys. Chem. 1972,76,2268. E. P. Kundig M. Moskovits and G. A. Ozin Angew. Chem. Int. Edn 1975 14 292. P. H. Kasai and D. McLeod Jr J. Phys. Chem. 1978 82 1554. ti P. H. Kasai E. B. Whipple and W. Weltner Jr J. Chem. Phys. 1966 44 2581. P. H. Kasai and D. McLeod Jr J. Chem. Phys. 1971 55 1566. See for example M. W. P. Strandberg Microwave Spectroscopy (Methuen London 1954) p. 11. M. Wolfsberg and L. Helmholz J. Chem. Phys. 1952 20 837. lo See for example H. Kopfermann Nuclear Moments (Academic Press New York 1958) pp.123-128. l1 M. H. L. Pryce Proc. Phys. Soc. A 1950 63 25. l2 C. E. Moore Nut. Bur. Stand. Circ. No. 467 1949 1; 1952,2; 1958,3. l3 F. J. Adrian J. Chem. Phys. 1960 32 972. l4 See for example P. W. Atkins and M. C. R. Symons The Structure of Inorganic Radicals (Elsevier Amsterdam 1967).