4884 Orbital Interactions in Metal Dimer Complexes
P. Jeffrey Hay, Jack C. Thibeault, and Roald Hoffmann* Contribution from the Department of Chemistry and Materials Science Center, Cornell University, Ithaca. New York 14853. Received January 9, 1975
Abstract: A molecular orbital analysis shows that the antiferromagnetic contributions to magnetic coupling, favoring a low- spin ground state for a dimer containing two weakly interacting metal centers, can be analyzed in terms of pairwise interac- tions of dimeric molecular orbitals, with the square of the splitting in energy between the members of a pair being a measure of the stabilization of the low-spin state. The effect of geometrical distortions, electronegativity, and variation of substituents on the magnetic interaction in dimeric systems is examined in detail for singly bridged L,M-X-ML, (n = 3,4, 5); Cu~C16~- and other doubly bridged species where the bridging ligands are halogens, OR, pyridine N-oxides, oxalate, squarate; and the acetate bridged dimers Cu~(RC00)4.The emphasis is on d9 Cu(I1) dimers, but other transition metal systems are also ana- lyzed.
Transition metal complexes containing more than one mentslv'O,'iwhich seek to extend such analyses to the cases metal atom with unpaired electrons can generally be cate- involving molecular, rather than atomic bridging species, gorized according to their magnetic behavior into three with special interest in molecular dimers. Within this latter main groups depending on the strength of the metal-metal context this paper will attempt to provide a broader theoret- interaction. In the noninteracting type the magnetic proper- ical framework for the analysis of superexchange interac- ties of the dimer (or polymer) are essentially unchanged tions. The scheme developed here seems capable of giving from the paramagnetic monomer. In the strongly interact- semiquantitative information about the effects on the or- ing type formation of relatively strong metal-metal bonds dering of spin states of geometrical distortions and of sub- occurs, and the molecule will display simple diamagnetic stituent changes for the general case of a molecular-bridged behavior (for even numbers of electrons). dimer. In this paper the properties of weakly interacting metal Primarily we shall attempt to show that (a) the antifer- ions will be investigated. In such compounds this weak cou- romagnetic contributions to superexchange, which are usu- pling between the electrons of the two metal ions leads to ally the more important and more sensitive to changes in low-lying excited states of different spin which can be popu- the system, can be analyzed in terms of pairwise interac- lated at thermal energies (SI000 cm-I). The resulting tions of dimeric MO's, 4i and 4,; (b) the square of the split- magnetic behavior will be antiferromagnetic or ferromag- ting in energy between these orbitals, It; - ',I2, may be netic, depending on whether the low spin (spins paired) or used as a measure of stabilization of the low-spin molecular high spin (spins parallel) state is the ground state, respec- state; and (c) the energy and symmetry of the orbitals of tively. These interactions-often termed superexchange be- the bridging group are crucial determinants of the level cause of the large distances involved (3-5 A) between the splitting pattern. The last point, to be illustrated by the metal ions-have been observed in a wide variety of com- analysis of several Cu(I1) systems, will establish an obvious pounds. I -5 connection between antiferromagnetically coupled metal In experimental studies the magnetic interaction between centers and the now well-established phenomenon of spins SA and Sg for atoms A and B is usually written in a through-bond coupling of lone pairs or r electron systems in form suggested originally by Heisenberg, Dirac, and Van organic moIecuIes.I2 Vleck6 We begin by a discussion of the relationship between mo- H = -255,*sB lecular orbital energies and magnetic exchange parameters. of where the coupling constant J is positive if the spins are Theory of the Electronic States Weakly Interacting parallel and negative if they are paired. (In this paper an Metal Centers unsubscripted J refers to the above expression, while a sub- In this section we shall discuss the electronic structure of scripted Ji refers to a two-electron Coulomb integral.) If two weakly interacting metal ions from two distinct, but /SA/ = ISB( = SA molecular states with total spin S = 0, 1, equivalent, viewpoints: a molecular orbital description and a . . . , SA are possible, and the energy difference between localized orbital description. After an analysis of the case of two states with spin S and S - 1 is given by one unpaired electron on each metal atom (e.g., the d9 case) the general d" case will be treated. E(S) - E(S - 1) = -2JS (21 Molecular Orbital Basis. In 1 we show a schematic inter- r----1 In the most common case discussed here, SA = and the 'h, I +2 I triplet-singlet splitting, E( 1) - E(O),equals -25. The theoretical interpretation of superexchange interac- xcy2 X2- y2 tions has traditionally been based on ideas developed for in- finite solid lattices.'.* Since it has been realized empirically that the bridging atoms between the metal ions determine the sign and magnitude of the exchange interaction, these qualitative treatments focus on the various types of overlap interactions between the ligand atomic orbitals and the metal d orbitals. A number of quantitative implementations of a configuration interaction computational scheme have Metal A Dimer Metal B appeared .9 More recently there have been theoretical treat- 1
Journal of the American Chemical Society / 97:17 / August 20, 1975 4885 action diagram for the predominantly d-like orbitals of two ba = +(dl + 6,) (5) weakly interacting square planar d9 complexes, bridged by 12 one or more atoms. In the absence of strong metal-metal 1 Cbb = $bl - 62) (6,lbJ = 0 bonding due to direct overlap of the d orbitals, the molecu- lar orbital levels of the dimer will closely resemble the lig- will contain both metal and ligand character but will be and field levels of the monomer, but the pairs of monomer essentially a d orbital on metal A, and &,will be the mirror levels will each be split slightly by the perturbation of the image localized on metal B. In terms of these orbitals we other metal atom. have the following identities: For the d9 case, where the unpaired electron occupies a Jil = l/?(Jaa+ 'Jab) + Kab + d,2-y~ orbital, we need focus only on the two highest levels 2(aalab) formed from the two linear combinations of these (predomi- J?,' = I/(Jaa+ Jab) A Kab - 2(aa ab) nantly metal-like) orbitals, since the lower orbitals are all J12 = "?(Jaa + Jad - Kab filled. K12 = I'?(J= - Jab) b1 dax?-r2 + dbx2,,? - where the dominant terms are the one-center and two-cen- d, - dax?-,? - dbx2-,z ter coulomb repulsion integrals J,, and Jab. respectively. The following many-electron configurations arise from When the splitting between hl and h2 is small compared to these orbitals: K12 ( = l/2( 10 - 5) eV = 2.5 eV), eq 4 becomes 4- +c +% 4-44- + 4, where we have neglected JII - J22 and terms of order (1 / K1 2)2. Finally we wish to make the correspondence between T SI s, s3 hl and h2 and orbital energies €1 and €2. Since we have seen that neither SI nor S2 is an adequate description of the sin- T: 141.. 424 glet state, we consider the Hartree-Fock operator for the SI: I41a 414 triplet state orbitals €1 I/* + Jl, - Ki? s2: I42a 424 €2 112 + J,2 - K1; s3: +5(I41.424 -I41P424) and hence
In this and succeeding discussions the MO's themselves are 72, - I/? = €1 - €2 presumed to have been obtained from an SCF calculation and on the high-spin (triplet) state. The lowest singlet state of the system $s will be an ap- proximately equal mixture of SIand S2 4, = X,i,, + X2illS2 (7) while the lowest triplet state is well represented by $T. In For the degenerate case et = ~2,the triplet state is the the limit of noninteracting metal ions 1x11 = 1x21, while in ground state the opposite extreme 1x11 >> 1x4 for strong metal-metal E, - E, = 25 = 2Kab (Kab > 0) bonding. (When ~$1 and 42 are of different symmetry, S3 will be of different symmetry from SI and S2, and in any while a significant splitting between the molecular orbitals case S3 will correspond to an excited state much higher in 41 and 42 will yield a singlet ground state. Equation 7 energy.) The respective energies of the triplet and singlet suggests that we can focus on the difference of orbital ener- states are as follows, after diagonalizing the 2 X 2 matrix gies, €1 - €2, as a measure of the singlet-triplet energy split- involving SIand S2. ting. Such a relationship was also apparent from eq 3 with- out the simplifying assumptions leading to (7). It should ET = + 112 + Jl? - Ki2 (3 1 also be noted here that expression 7 is not novel, with simi- E, = 111 + 112 + '/z(J11 + J??) - lar forms having been derived by others.l3.I4 The superex- change problem in inorganic chemistry is very much akin to !'2[(212i + Jll- 2/12 - J.?)' + 4~,,~]"~the diradical problem in organic chemistry where more than where one configuration is needed for a proper description of a sin- glet ground state. Discussions similar to ours have been hi = sbi*(l)h(l)bi(l)dv, given concerning the singlet-triplet splitting and the state 1 Jij = Jdi*(l)bj*(Z)rbi(1)Qj(2) dvldv? energies. ' 12 The preceding MO analysis becomes unwieldy for the general case of more than one unpaired electron on each metal atom. For example, for a dimeric Ni2+ (d8) complex and h represents the core operator consisting of the kinetic with local octahedral symmetry about the metal ions the energy, nuclear attraction, and all other electron-repulsion high-spin (S = 2) molecular state of the two weakly inter- terms. acting S = I ions can be written (apart from the doubly oc- The quantity of interest, the singlet-triplet splitting, then cupied orbitals) becomes iJ(S = 2) = /@[CY CbZQ@)ICY(i)$(Y' E, - E, = -25 = 512 - K12 - :(z(J,, + 522) + b1 - dAx?-,?+ dB,!-,Z 1!2[(2121+ J,, - 212? - 522)' + ~KI,~]~'~(4) Q2 - dAI?-Y2- dB,?-v? It will be useful to define orthogonal localized molecular or- @j - dAZ?+ dBzi bitals (LMO's), & and &,, as follows: $1 dAzl - dBz>
Hay, Thibeault, Hoffmann / Orbital Interactions in Metal Dimer Complexes 4886 The low spin (S = 0) state, however, will require major con- where the second sum is over the distinct pairs of MO’s. tributions from five configurations: (41)2(43)1(44)’, The specific example of two high spin d8 monomers is (4d2(43)‘(44)’, (41)‘(42)’(43)27 (41 )‘(d~2)’(44)~, and worked out in detail in Appendix 1. The result and an analysis would have to deal (41)’(42)’(4~)’(44)’, 2J= -E(S = 1) + E(S = 0) = ‘,/[-E(S = 2) + with the 5 X 5 interaction matrix. Localized Orbital Basis. In terms of the localized orbitals E(S = 111 = ”z(Kac + K,, + K, t K,) - defined in eq 5, the d9 case can be solved by perturbation ?i(€,- €212 - :’d(€3 - €,)2 theory in terms of the configurations Jaa - Jac Jbb - Jbd s14: /fi(1 4aa $bd - I $a@ $bd where 41and 42 are the MO’s involving the x2 - ,u2 orbit- als and @cB) and 43 and 44 involve the z2 orbitals (4bA S’5a: I4aa 4ad and 4dB), shows that the antiferromagnetic terms can be S’5b: I4ba $bd traced to the separate contributions of the (x2 - y2)-like and z2-like orbitals, respectively. T’: I dJaa 4b.1 Nonorthogonal Orbital Basis. In the two preceding where S’4 is the “covalent” state and S’sa and S’5b are frameworks the inclusion of configuration interaction was “ionic” states. needed: in the former case by mixing the doubly excited E,,! = ha + kb + Jab 4- Kab state $z2 with 412,and in the latter case by including ionic states. It is possible to retain a one-electron single-configu- ET, = /la + hb + Jab - Kab ration representation by using nonorthogonal orbitals. The singlet wave function in terms of LMO’s = E,.S, = 212, + J, (ha = hd I(ab - %)I/& + X(laZl + lb6l) Without admixture of the ionic states the singlet state will can be rewritten as be very slightly above the triplet state E,, - E,,$ = -2Kab < 0 la’b’ -a’b’I/& if one defines Configuration mixing will preferentially lower the singlet, since no ionic triplet states are possible bat = da + HIS,)’ - (sibI HI s,)? E, 2 E, - Eia - E, - (2h,, + 2(aa lab))‘ = E, + 2Kab - Jaa - Jab - Kab If 4a’ and $b’ are chosen to be atomic orbitals, the wave (2ka,)2 E, - E, = -2Kab + function corresponds to the Heitler-London type. 4a’ and Jaa - Jab $b’ can be optimized self-consistently as in the GVBI6 and where we have ignored the smaller two-electron integrals as spin-projected unrestricted Hartree-Fock methods,!’ which before. This is the identical result obtained above in (3-4) can be extended to n electrons per metal ion. They would using MO’s since also correspond approximately to the “oligomer MO’s” of Dance.]’ 2hab = (b, + d,!h!bl 62) = 12, - h‘ = €1 - €2 - Superexchange and the Extended Huckel Framework. (9) The preceding analysis, if perhaps somewhat belabored, has The preceding derivation is similar to Anderson’s treat- attempted to establish the link between antiferromagnetic ment of superexchange in insulators, which was based on an exchange interactions and the difference in energies be- unrestricted Hartree-Fock formalism.’ The ferromagnetic tween otherwise degenerate MO’s. The orbital energies in term -2K,b favoring the triplet corresponds to “potential this paper areobtained from extended Huckelcalculations’8- exchange” in the Anderson model, and hat, in the antifer- the simplest all valence-electron model. Details of the pro- romagnetic term favoring the singlet corresponds to the cedures we used are given in Appendix 2. Although these “transfer integral” in “kinetic exchange”. calculations do not explicitly include two-electron interac- For the dn case with m unpaired electrons on each metal tions, the behavior of the levels is expected to reflect what atom one can usually group the MO’s involving the un- one would observe in more sophisticated calculations. To paired electrons into m distinct pairs I(@,, 42), (43, 44), the extent that the qualitative changes in these orbital ener- , . . ,] of closely related orbitals from which localized orbit- gies as a function of structure and substituents are repro- als can then be formed [(&I, &I), (4a2, 4b2), . . . .]. A per- duced by extended Huckel theory, one would expect this turbation analysis of the energy differences of the spin simple one-electron model to treat the AF part of the ex- states of the dimer (S = 0, 1, . . . , 2sA) for monomers with change interaction. Since two-electron interactions are not spin SAyields the familiar result (eq 2) explicitly included in the theory, actual singlet-triplet ener- gy differences cannot be computed. In the two-electron E(S) - E(S - 1) = -2SJ case, where consistent with the Heisenberg Hamiltonian, where J can be decomposed into orbital contributions. As in the above case with one unpaired electron, there will be ferromagnetic (JF)and antiferromagnetic (JAF)contributions we would focus on the quantity (tl - €2) since the denomi- nator should be a fairly slowly varying quantity as a func- tion of distortions or substituent effects for closely related compounds. The same considerations should apply to Kat,, which is usually small (-1-50 cm-] experimentally) and dominated by the second term. The reader should note the terminological bind we are in.
Journal of the American Chemical Society / 97:17 / August 20, 1975 4887
The study of magnetic interactions in metal complexes is traditionally tied to a spin Hamiltonian, with experimental results uniformly expressed in terms of the above mentioned coupling constant J. Words such as “ferromagnetic” and “superexchange”, when taken literally, relate to the spin formalism. On the other hand we have shown a relationship between the singlet-triplet gap and the splitting of pairs of one-electron energy levels. We will examine the effect of ge- -1st I ometry and substituents on the low-spin high-spin energy difference through the perturbations of these levels. Our t problem is in comparing our theoretical inferences, ex- pressed in terms of diminished or increased energy gaps, with experimental results phrased in the spin formalism, ex- pressed in terms of “superexchange”, “significant antifer- romagnetic (AF) coupling”, or “large negative J”. We will often opt for any of these terms, but our meaning should be 90 120 150 180 clear. e”-- Influence of Bridging Angle on Spin State Figure 1. Energies of metal orbitals of CU~CI~~-as a function of bend- The effect of the metal-ligand-metal bridge angle on the ing at the bridging chlorine. exchange interaction has been studied extensively, and a CuC14 fragment is kept planar as the Cu atoms move in a qualitative justification has been provided by the Goode- plane perpendicular to the original molecular plane. The or- nough-Kanamori rules8 and the Anderson model.’ Such bital energies as a function of Cu-CI-Cu angle % are shown considerations lead one to expect a large AF coupling for a in Figure 1. For % = 180’ @A is higher in energy than &, 1 80’ bond angle when the metal orbitals can interact with a and as 0 decreases the energy difference becomes smaller ligand orbital of the same symmetry, and a weak F coupling until at 0 = 90’ the two are practically degenerate. Accord- for a 90’ bond angle when the metal orbitals are interacting ing to our previous discussion the factor (t~- t~)~ favoring through orthogonal ligand orbitals. a singlet state would have its maximum value at 0 = 180°, Although our analysis will yield the same qualitative pre- while a triplet ground state would be expected near 90’ dictions as to the effect of bond angles, we shall use these when 6s = t~. results to show the consistency of the MO approach with This behavior may be understood from the interactions of previous interpretations and to justify its application later the d orbitals with the lower-lying filled orbitals of the to more complex systems. bridging atom. The local square planar environment about A comprehensive discussion of the structural and mag- each metal orients the highest molecular orbital into a local netic evidence for the angular dependence of metal-metal L6x2 - y2” orbital pointing along the M-L bonds. For the interactions of Cu(I1) and Cr(II1) systems has been pre- linear case, the symmetric combination (4s) of d orbitals sented by Hodgson.I9 He provides a perceptive theoretical can interact with the 3s orbital of the bridging CI, and the discussion which has many parallels to our qualitative anal- antisymmetric combination (@A) can interact with the 3p, ysis. orbital. This was shown in 2. Since the metal 3d (-14.0 eV) Dimers with Single Bridging Atoms. Consider first the is much closer in energy to the CI 3p (- 15.6) than the 3s hypothetical case of CU~CI~~-,two square planar CUCI~~- (-27.1), the d-p interaction is much stronger and +A is complexes joined by a single atom. In the d9 monomer the shifted upward more than 4s. unpaired electron occupies an x2 - y2 orbital oriented As the molecule is bent, the overlap of the d, - db combi- along the bond axes.2o (Throughout this paper we will use nation with px decreases, since the d orbitals’ local field the abbreviated notation for p and d orbitals, x2 - y2stand- constrains them to point approximately along the bond di- ing for dX2-,,2, z for pz, etc.) The highest occupied orbitals rections. This is shown in 3. The antibonding character in of the dimer are the symmetric (4s) and antisymmetric (+A) combinations of the monomer x2 - y2 orbitals, shown in 2. We proceed to bend the dimer in such a way that each
,/cl x i’y I‘ ,CI c I -c 6’- CI -Cd- c I / / CI CI
‘I I
3 f is reduced, and the orbital energy consequently de- creases with bending. Although the d, + db interaction with the 3s orbital is unaffected, in bent geometries it begins to interact with the much higher-lying 3p2 CI orbital-leading to an increase in antibonding character and a rise in ener- gy. At 90° the d-p, and d-p, overlaps are identical, and one would thus expect Comparable orbital energies. apart 2 from the small d-3s interactions.
Hay, Thibeault, Hoffmann / Orbital Interactions in Metal Dimer Complexes 4888
1 T
0
','YZS LXZS
levels XYS'XY,
Journal of the American Chemical Society / 97:17 / August 20, 1975 4889
0.041
,.,,I 80 90 100 It0 8"- I1 80 90 IO0 I10 Figure 5. Energies of highest metal orbitals in Cuz(OH)zCI4*- as a 8'- function of bridge angle. The solid es line is for an oxygen 2s Slater ex- ponent of 2.275, the dashed es line for a higher exponent of 2.7. The t~ Figure 4. Variation of metal-ligand overlap S in a dibridged dimer ge- line does not depend on the oxygen 2s exponent. ometry.
(93') were fixed as 6 was varied while maintaining D2h Table I. Experimental Cu-OH-Cu Bridging Angles (0) and symmetry. Hiickel parameters were taken from a model Singlet-Triplet Energy Differences (W= ES-ET)(values are taken [CUCI~(OH)~]~-calculation (see Appendix 2). For this d9 from ref 27) system we need again focus only on the two highest d-like Compound e 21(cm-') Mo's-4~ and $s, shown in 6 and 7. In this coordinate sys- [Cu(tmen)OH],Br, 104.4 -509 [Cu(teen)OH]z(CIOJ, 103.0 -410 p-[Cu(DMAEP)(OH) ] ,(C10 J 100.4 -201 [Cu(EAEP)OH] ,(C10J2 99 -130 [Cu(bipy)OH] ,(SO,).SH,O 97 +48 6 [Cu(bipy)OH 1 ,(NO,), 95.6 +172
Y 4 Since favorable AF coupling depends only on the abso- LX lute value and not the sign of e~ - €A, a ground state singlet should also occur for smaller values of 8 below the cross- over point. For bridging angles smaller than 90°, the M-M direct overlap begins to be appreciable, and direct interac- 7 tion can also lead to a ground state singlet. We do not wish to ascribe much significance to the actual computed bond angles where the cross-over from a triplet to singlet ground state occurs, since the value is dependent on tem the metal orbitals will remain xy for all M-L-M the choice of exponents. Nevertheless, these results are in bridge angles since these are the only d orbitals of bl, and very reasonable accord with the experimental results of bzu symmetry. (There is an unimportant admixture of 4p, Hatfield, Hodgson, and coworker^:^ who have carefully component into the metal orbitals.) On the bridging atoms characterized a series of OH-bridged Cu dimers with re- there is one symmetry adapted combination of p orbitals (jl gard to their crystal structures and magnetic properties (see + y2) which interacts with 4s and another combination (XI Table I). In th'ese complexes the terminal groups are amine - x2) which interacts with @A; the 2s oxygen orbitals can derivatives and in most cases there is a fifth group weakly interact with 4s but not with 4~. coordinated to the Cu in an axial position. The Cu ions still The relative order of t~ and t~ as a function of 6 will be have pseudo-square planar symmetry in this series, and the determined by the metal-bridging ligand overlap, especially spin state is determined by the bridging ligands, so that the the 2p orbitals since they lie much higher in energy (-15.6 results of our simple model calculations can still be com- eV) than the 2s (-32.2 eV). For 6 = 90' (Figure 4) since pared. The experimental results show J > 0 (triplet below the (xylx) and (xyly) overlaps are equal, one should ex- singlet) for 8 < 98' and J < 0 and growing in magnitude pect es to equal t~ and a ferromagnetic coupling to occur. for larger 6. This suggests that our latter choice of parame- As 8 increases, the overlap-and hence the antibonding ters is in better agreement with experiment. Although no character of the predominantly metal-like orbitals-with complexes have been reported with 0 < 95O. it would be of x~Aincreases and the overlap with xys decreases. This interest to observe whether the singlet state would eventual- would in turn lead to an increase in t~ and a decrease in es ly become the ground state again as indicated by our calcu- for 8 > 90'. Thus a larger AF coupling would be expected lations. as the quantity t~ - ts increases. In Figure 5 the calculated This analysis has focused on the numerator Its - t*lZ of results do indeed show t~ rising and cs falling as 6 increases, the AF contribution (eq 8). since the denominator is slowly but that the crossing occurs not at 90' but somewhat later varying. Actually J,, - Jab will be decreasing slightly as 0 (e - 1070). increases since Jab - 1 /R-resulting in enhancement of the The preceding analysis ignored the effect of the 2s bridge singlet-triplet gap. We also note at this point that the sym- orbitals, however, which also have an antibonding interac- metry of the bridging group orbitals as a significant factor tion with 4s. This interaction would shift t~ to higher ener- in determining the magnetic properties of dimers has been gy and thus displace the crossing point to larger 6. In Figure stressed by Bertrand.28 5 we illustrate the effect of a reduced (xy12s) interaction where we have increased the 2s orbital exponent from 2.275 The Role of Other Geometrical Distortions to 2.7. The net result is a downward shift in e~ and the The Twisting Mode in Cu2CI6*-. A related series of com- crossing occurs for 6 = 96O. pound~,~~-~~all containing the Cu$21h2- entity, has been
Hay, Thibeault, Hoffmann / Orbital Interactions in Metal Dinier C'oniplexes 4890
Table 11. Experimental Exchange Parameters and Structural Information for Dimers Containing the ICu,CI,12- Unit Bond angle@
Compound CU-Clb-cU Clt-CLl-Clb Clt -CU-Clt R(Cu-Cu)(A) W(cm-') Ref LiCuC1;2H20b 95.1 180 93 3.47 KO) 30 KCuCl,b 95.9 174.5 93.2 3.44 -39 31 (CH,),NH,CuCl,b 95.6 166 92.3 3.42 -3 32 P h,A sC uC1, 93.6 145 100.3 3.39 +4 6 29 Ph.PC uC I, 93.3 144 100.9 3.36 C 33 aKey: clb = bridging C1, Clt = terminal C1. Clt-CU-Clb refers to the larger of two such angles. Where a range of angles was observed, the average is given in the table. bThese compounds show varying degrees of association of the dimers to infinite network structures. cNot known.
t E (eV)
-12.6
80 90 100 110 82
Figure 6. Energies of highest metal orbitals of CU~CI~~-as a function 0 30 60 90 of bridge angle. ~wlstangle +' a found to display both singlet and triplet ground states de- Figure 7. Energies of metal orbitals of CUCI~~-as a function of dihe- pending upon the geometry when various counterions are dral twist angle. used (see Table 11). The bridging Cu-CI-Cu angles are all rather similar (8 = 95'), although the one compound with the triplet ground state has a slightly smaller angle (93.6') D2d) for 4 = 90'. The xy orbital containing the unpaired than the rest. In addition the central CI atoms in the latter electron, while widely separated from the others for 4 = Oo, compound are twisted out of the molecular plane, 8, with becomes essentially degenerate with the xz orbital in the perpendicular geometry. Only the region 0' I 4 I50' will concern us since the known compounds fall into this area. For intermediate values of 4, xy and xz both have b sym- metry, and the xy orbital incorporates xz character to lie in the plane midway between the Clt-Cu-Clt and Clb-CU-clb planes, 9. 6 resulting Clb-cU-cI, angles far from We have investigated the effects of the bending and twisting modes on superexchange in the cu2c162- species, with parameters obtained from model CUCI~~-calculations 9 described in Appendix 2. The level ordering of the two high- In the dimer (Figure 8) the xy orbitals are split into 4s est metal orbitals (xy-like), shown in Figure 6, is essentially and 4~,with 4,.~,higher in energy for planar cU2c1b2-, as the same as the OH-bridged series-a larger AF coupling we would expect for a bridge angle of 95' from our previous expected as 8 increases from 90'. The antisymmetric orbit- discussion. As the molecule is twisted, a level crossing oc- al, $A, lies higher in energy than 4s for 8 > 90' because of curs near = 35' where a ferromagnetic coupling would the greater interaction of xy with the 3px orbital relative to arise. This is in agreement with the observation that the the 3p, orbital of chlorine.34 An earlier MO description of dimer with a substantial twist angle (48' between dihedral cu2c162-, given by Willett and Lile~,~~is in qualitative planes) has a triplet ground state. agreement with our analysis. The origin of this crossing can be traced as follows. In the In our study of the twisting mode the plane containing MO $A (10) the xy-x overlap is decreasing as the bridge the Cu atoms and the bridging chlorines was rotated by an atom is lifted out of the molecular plane (12). The formerly angle, 4, relative to the plane of the terminal ligands. The "pure" xy orbital no longer points directly at the bridge following structural parameters were used: R(Cu-Clb) = atoms but now lies midway between the original plane and 2.3, R(Cu-CI,) = 2.26, clb-cu-clb angle = 85', Clt-Cu- the Clb-CU-clb plane. (The coordinate system in 12 has CI, angle = 93', and 0 5 6 I90'. To understand what been rotated to show this effect more clearly.) In the 4s happens in the dimer it is best to consider the effect of a MO, 11 - 13, the situation is similar since the xy-y over- similar distortion on a CuCL2- monomer with similar lap is also decreasing, but in the twisted geometry it can structural parameters. This is done in Figure 7. The mole- also interact with z to compensate partially for this loss and cule is transformed from CzL'symmetry (very nearly D4h) to account for the smaller slope of cs as a function of 4. Fi- for 4 = Oo, through C2. to Ci, symmetry again (very nearly nally we note that at the special perpendicular D2h geome-
Journal of the American Chemical Society / 97:17 / August 20, I975 489 I
n +=o"
10 11
Figure 8. Energies of selected orbitals in Cu3C16*- as a function of di- hedral twist angle of bridging atoms. d = goo
14 15 try (compared with C2h for intermediate points) 4.4 has no bridge atom component (14) while 4s retains z character (15) and is pushed to higher energy. In summary both an increase in twist angle and decrease in bridge angle 8 would lead to smaller exchange couplings. Before leaving the subject of doubly bridged dimers we should direct the reader to two elegant discussions of the factors influencing the bridging ar~gle.~~.~' Dimeric Structures with Pentacoordinate Metal Centers. There are a number of stru~tural~*-~~and magneti~~~,~~ studies of pentacoordinate Cu(I1) dimers. These show a va- riety of structures in which the local geometry about each Cu is square pyramidal (SP) or trigona:l bipyramidal (TBP).44 Species have been found with one or two bridging groups. We shall focus here on but one possible distortion of a dimer with a single group bridging two pentacoordinate t j Cu atoms.
16 Figure 9. CuCls3- levels: top, square pyramidal distortion. maintaining Examples of such species include a CI-bridged and a CN- C4" symmetry; bottom, distortion toward trigonal bipyramid CA~(8 =
bridged Cu dimer where the terminal ligands in both cases 90') -+ CzV+ Djh (0 = 120'). are amine derivatives3' Our model for this study is the hy- pothetical [(CI~CU)-CI-(CUCI~)]~-molecule where all In the CUCI~~-fragment, as the four basal ligands are Cu-CI bond lengths are taken to be 2.3 A, and the angles bent back, the highest orbital remains x2 - y2 (bz). This is between the bridging CI and terminal Cl's in the respective if CdVsymmetry is maintained, as in mode (b). If only two y and x planes are 01 and 82. Two possible distortions are ligands are bent back, in the resulting C?,.symmetry the z2
considered. (a) 82 = go', 01 varied from 90 to 130'. This and x2 - y2 orbitals will mix. The x2 - ~9~ orbital acquires transforms the SP dimer (01 = 90') through the TBP dimer components along the z axis and eventually becomes the (01 = 120'). (b) 01 = 82, 81 varied from 90 to 130'. This "x2" orbital (al') of the D3h TBP. The z? orbital in turn be- changes the axial-metal-basal angle of a SP dimer. comes the lower-lying "$ - z2" member of the el' pair. The CI-bridged example mentioned above corresponds to In the case of the dimer with el = 82 = 90' there are no (a) with 01 = 121, 124' and the CN-bridged example corre- bridging orbitals on the ligand which have the proper sym- sponds to (b) with 01 = 113'. In addition the axes of the metry to interact with either of the symmetric (4s) or (4~) TBPs are rotated 90' relative to each other, but the results x2 - y2 orbitals (bl, and bl, in D4h symmetry). Hence no of our model should still pertain. Our calculations are illus- AF coupling would arise due to through bond coupling since trated in Figures 9 and 10. ts = €A. The situation remains the same in case b where
Hay, Thibeault, Hoffmann / Orbital Interactions in Metal Dinier Conipleses 4892 amplitude Cor of the orbital xo nearest the metals so as to c I increase the metal-ligand interaction. In the cases with which this analysis is concerned, the amplitudes in 41will not be changing appreciably, but the total charge on the bridging ligand will be changing and will affect primarily the denominator of the expression. In the self-consistent charge process (or in any other -11.5 method using a self-consistent field approach), removal of electron density from an atom reduces the electron-electron 'IL--LLL repulsion and lowers the atomic orbital levels of that atom. 120 90 120 This in turn will lead to lower orbital energies in MO's SP-I-TBP e which contain substantial character of the atom involved. Consider what happens when the ligands involved in the Figure 10. Monobridged C14CuCICuC14 dimer showing distortions of important ligand orbitals @ls and @lA are made more posi- fragments toward SP and TBP. tive and their orbital energies tis and €1~are lowered to 61s - A and €1~- A, respectively (A > 0). The metal orbit- local C4" symmetry is maintained, so that there should be als now differ in energy by an amount essentially no superexchange interaction for such geome- tries. To the extent that z2 is admixed in the Czc case, how- ever, interactions are possible with the filled 3p2 and 3s CI orbitals. Since the higher-lying p orbitals interact more strongly with the d orbitals, 4~ increases in energy relative to 4s as tI2 increases and a singlet should be stabilized (Fig- Since the quantity in brackets is positive, ts' - t~'< ure 10). ts - t~ and the antiferromagnetic interaction decreases as This accounts for the large coupling (-144 cm-I) ob- electron density is removed from the bridging atoms. Con- served for the CI-bridged case, where 0 = 12 1 ' and no in- versely, an increase in electron density raises the ligand lev- teraction would have been expected for 0 = 90'. Unfortu- els and enhances the AF coupling. This conclusion was also nately the small interaction in the CN bridged (-5 cm-I) reached by Hodgson, Hatfield, and their coworkers.45 cannot be traced solely to the fact that the d orbital is pure- TO illustrate this effect the model complex 17 has been ly x2 - y2. CI- had the property that the orbitals capable X of interacting with the S and A d combinations were very x\px different in energy and thus effective in splitting the d-like of MO's. The two highest lone pair orbitals CN- are much cI\ /"\/cl closer in energy and would be less effective in producing an es - energy gap. CI /c\o/c"\cl
Influence of Substituents on Superexchange Interactions XAXX In the preceding discussion we were attempting to ana- lyze how geometrical distortions of a particular dimer af- fected the order and spacing of the highest occupied MO's 17 containing the unpaired electrons. Here we shall focus on studied as the electronegativity of X is varied. In one case X these same metal orbitals for a fixed geometry as a function has been chosen as a hydrogen whose orbital energy has of the changes in the bridging ligands. been steadily decreased from - 13.6 to - 17.6 eV, to simu- Electronegativity Effects. From second-order perturba- late an increase in electronegativity. The substituent tion theory the quantity of interest cs - CA is given by -CH2CI has also been used to replace -CH3 by a more elec- tron-withdrawing group. The parameters for the dimer were obtained from calculations on the square planar [CI~CUOCX~]~-species with RC"-CI= 2.26, Rcu-o = 1.94 The labels I and d stand for bridging ligand and metal d or- A. Separate calculations were also performed on the isolat- bitals, respectively. In the above expression it is assumed ed ligand X3CO- in the presence of a + 1 point change. that there is only one important ligand orbital of each sym- In both series of calculations the resulting orbital levels metry (A and S). Furthermore H;; of the oxygen 2s and 2p orbitals become lower in energy as X is made more electronegative. In the calculation on the = (b,,i ~;b,~)= c~,~(~~,SIH~X~)Cu monomer, the 3d levels also shift downward, but there is i an overall increase in the gap between metal and ligand lev- where the x; are the atomic orbitals comprising the ligand els. The increased energy gap as electron density is with- orbital. Usually the M-L interaction will be dominated by drawn from the bridging ligands is reflected in the decreas- the interactions with the orbital(s) of the atom nearest the ing EA - es splitting in the xy-like metal orbitals. The elec- metal, xo tronic structure of the bridge is essentially identical with the OH-bridged series discussed earlier, since the 2p, and HI: 2 ColSH,,S 2p, lone pair orbitals of the 0 in the methoxy group differ which leads to the following expression little from the OH species. For an assumed Cu-0-Cu bridge angle of 90°, lies slightly higher in energy than (C (H, ,"I - (C A ) * (HodA)' Es - E* = ' ' &, and the splitting decreases from 0.104 to 0.067 eV as f& - E1S 'dA - €1, the "dummy" atom is made more electronegative; a similar One way in which substituents on the bridging ligand can reduction (of 0.01 1 eV) is observed when H is replaced by affect the coupling between metal ions is to increase the CI.
Journal of the American Chemical Society / 97.1 7 / August 20, 1975 4893 Acetate-Bridged Dimers. Historically antiferromagnetic n coupling in a dimer compound was first observed in the ace- tate-bridged molecule CU~(CH~COO)~~H~O,~~*~~and a
18 variety of related dimers have been reported which possess the common 0-CR-0 triatomic molecular b~-idge.~,~~Al- though the nature of the electronic structure has been a matter of considerable controver~y,~~]~~~~~~~it is now evident that the unpaired electron on each Cu occupies a x2 - y2- like orbital oriented toward the four 0 atoms in the very nearly square-planar environment about the metal.50 For a Cu-Cu distance of 2.64 8, the small 6-6 overlap would pre- Figure 11. Selected metal and ligand lone pair orbitals in clude any direct interaction. The symmetric and antisym- Cu*(HC00)4 interacting. metric x2 - y2 orbitals, ds and dA (Figure ll), can inter- act, however, with the symmetry adapted combinations of Table 111. Effect of Electronegativity Changes in the 0-CX-0 lone pair acetate orbitals, IS and 1~.In the SCC-EHT cal- Bridged Cu Dimer Series (X = H, CH,, and CCI,) culations on CH3COO- the highest occupied MO’s are the CH, a1 (Is),b2(1~) and a2(s) orbitals shown below. Hii(M15.6 = 17.6 CC1, H 13.6
Hii(2po) -16.64 -16.59 -16.89 -17.12 -17.30 do) -0.699 -0.727 -0.721 -0.715- -0.724 e3 pV) -12.733 -12.711 -12.737 -12.755 -12.754 EA (eV) -12.843 -12.836 -12.853 -12.864 -12.869 e-f~(eV) 0.110 0.125 0.116 0.109 0.115 19 Is 20 IA 21 k 2.l (~rn-’)’~ -485 - 305 1.39 1.77 Despite the favorable through-space interaction in 1s it is kff @Bl3 PKa(L) 3.75 4.75 0.70 pushed higher in energy than IA, presumably because of the antibonding interaction with the C-C bonding orbital.12 If both orbitals have nearly equal overlaps with the x2 - y2 K is only 0.007 A shorter than at 300 K. 53a orbitals, the higher-lying S orbital would be expected to The effect of electron-withdrawing groups on the Cu-Cu produce the ordering 4s > $A for the metal orbitals of the interaction in the acetate series was probed by calculations dimer. In Figure 11, which shows the results for the formate on (0-CX-0)- bridged compounds where X = H, CH3 bridged dimer, the ordering (x2 - y2)s (-12.73) > (x2 - (with the IP of H variously set at 13.6, 15.6, and 17.6 eV). y2)~(-12.84) is found and this order is retained in the ace- and X = CCI3. tate series to be discussed below.51 That differential interac- The results (Table 111) again show a reduced Cu-Cu in- tion with the acetate groups will produce a splitting of the teraction as the H is made more electronegative or is re- Cu orbitals has been previously pointed out by Goodgame, placed by CI, in agreement with the experimental observa- Skapski, and coworkers.52 tion that replacement of CH3 by CC13 reduces J and in- If our calculations are correct, not only is there no 6 bond creases the effective magnetic moment from 1.39 to 1.77 in the copper carboxylate dimers but there may be some- MU^.^*^^^ Formate is somewhat anomalous since the calcula- what of a 6 antibond. What we mean by this is the fol- tions show a reduced 0 charge and a reduced Cu-Cu inter- lowing. The singlet ground state of the system will be a mix- action (consistent with the greater acidity of formate) com- ture of the two configurations $ = CS(S)~+ c~(A)~ where S pared to acetate. The experimental coupling5* is actually = (x2 - y2)s,A = (x2 - y’)~.With A and S close in ener- greater in formate (2J = -485 cm-I) than in acetate gy cs and CA will be comparable size. To the extent that A (-305 cm-I). Although these calculations are only to be is below S in energy the net effect will be slight metal- semiquantitative at best, a possible explanation may lie with metal antibonding. Of course at very short Cu-Cu separa- the shorter Cu-0 bond lengths (1.983 A) in the formate tions the direct interaction will begin to dominate, bringing dimer than in the acetate dimer (2.03 A). (These structural S to lower energy, but in the distance range in question the and magnetic data relate to the [(Me4N)J[Cu(X- indirect coupling is greater. No direct proportionality be- CO2)2(NCS)2]2 molecules.52 In our calculations the basic tween the magnitude of AF coupling and Cu-Cu distance is structure was taken from a recent neutron-diffraction to be expected. The experimental facts are that the coupling of [Cu(CH3C00)2(H20)]2, and standard bond in the formate dimer is greater than in the acetate, despite a lengths were assumed for ligand substituents.) We should shorter Cu-Cu separation in the latter.52. In Cu2- bring to the reader’s attention a recent structural and mag- (CH3C02)4(pyrazine) the copper atoms are 2.58 A netic study of a copper trifluoroacetate quinoline apart53a and yet the coupling is, for copper carboxylates, The magnitude of the Cu-Cu interaction in the trifluo- moderate.53bIn this complex the Cu-Cu separation at 100 roacetate derivative (25 = -310 cm-I) is very similar to
Hay, Thibeault, Hoffmann /’ Orbital Interactions in Metal Dimer Conrp1e.re.s 4894 that in the acetate. This brings into question the correlation was borne out by the calculations. between the substituent electron withdrawing power and The experimentally observed splittings in the py0 series the metal-metal coupling. (-1000 cm-I) are among the largest observed in any dimer Though we have not carried out any relevant calcula- and yet still small enough to have a triplet population de- tions, we should mention at this point two interesting sys- tectable by standard techniques. It would appear that a pri- tems related to the copper acetates. The first of these are mary factor in the coupling is the large Cu-0-Cu bond the triazenido (RNNNR-) complexes of Cu and Ni, exem- angle, since a coupling of -500 cm-' was observed in the plified by Cu2( Ph2N3)4. These possess a geometry similar OH-bridged series with a smaller (105') angle. An assess- to the acetates, but with a much shorter metal-metal dis- ment of the effects of substituents would be aided by fur- tan~e.~~~There is a corresponding strong antiferromagnetic ther systematic studies on the structures of these dimers. coupling.55bThe other set of molecules are the strongly cou- pled d4-d4 systems of the type Mz(RC02)4, M = Cr or Mo.~~In these compounds the question of thermal popula- Metal-Metal Interactions in Oxalate and Squarate Dimers tion of a high spin state does not arise-indeed the short One final class of dimeric compounds will be treated, M-M bond distance is indicative of metal-metal multiple which strikingly shows how superexchange interactions can bonding. be decomposed into pairs of MO contributions. In the oxa- The orbital interaction diagrams discussed so far have al- late-bridged compounds a pseudo-octahedral metal ion is ways dealt with stabilization of a low-spin ground state as bridged by an oxalate moiety which serves as two bidentate caused by destabilization of metal orbitals by filled ligand ligands. Structures and magnetic susceptibility measure- orbitals. The pyridine N-oxides, discussed in the next sec- ments have been reported for the Cu(I1) and Ni(I1) com- tion, may provide a situation where stabilization by low- pounds, as well as for a squarate, 24, bridged Ni dimer.61-63 lying virtual orbitals influences the quantity ts - EA. Pyridine N-Oxide Dimers. The pyridine N-oxide (py0) Y bridged Cu dimers have been studied extensively with re- gard to magnetic proper tie^.^^-^^ One of the typical dimeric units resembles the OH-bridged dimers,60 e.g., 22, with a 0 B 23 24 The Cu oxalate structure is considerably distorted from oc- tahedral symmetry, with N3 replaced by an 0 ligand with much longer bond length and with significant lengthening I N of the Cu-01 bond as well. In the above coordinate system the unpaired Ni electrons will occupy the z2 and xy orbitals, while for Cu the stronger 22 N-ligands of the idealized structure would be expected to 0 orient the unpaired electron along the NI-N~axis in the z2 Cu-0-Cu bridging angle of 108O. The pyridine rings, near- orbital. AF exchange is observed in the Ni compounds (-17 ly perpendicular to the Cu202 plane, are twisted 70' about cm-l in C~04~-and -1 cm-I in C40d2-) while none is ob- the N-0 bond out of that plane, and the terminal CI ions served for Cu. are also somewhat puckered out of the ring plane. An ideal- Our analysis in the theoretical section and in Appendix 1 ized structure was adapted from the experimental geometry showed that in such a case with two unpaired electrons on so that all atoms bonded to the Cu are kept in the same each metal atom, the superexchange could be decomposed plane and the pyridine rings are rotated perpendicular to into a sum of two contributions-one proportional to the this plane. splitting [t(z2s) - t(Z2A)l2 and another proportional to Charge iterative calculations on the py0 molecule itself [t(xys) - €(XyA)]*, where the symmetry adapted combina- showed the highest filled orbitals to be localized primarily tions of metal orbitals are sketched in Figure 12. The four on the oxygen lone pair orbitals of C~04~-are also shown and are labeled -/I 23 -I/ 42 -13 49 as lZ2,, lZ2,,, I,,, and I,, to denote with which particular metal orbital combination each can interact. The qualitative level ordering of the oxalate orbitals64 follows the expected trend from nodal structure with X~A> xys, but the orbital with best 0-0 overlap (z2s)lies above the Z~Aorbital. This is apparently a result of through bond coupling,I2 since the former orbital will be shifted to higher energy by virtue of its antibonding interaction with the C-C b2 b, 7T Q! bonding orbital. When the plane of the ring is perpendicular, the bl and a1 The ordering of the pairs of metal orbitals of the dimer orbitals can interact with the A and S combinations of the follows the ordering of ligand levels: z2s (- 11.82) > z2~ xy metal orbitals, respectively. The situation is strongly (-1 1.85) and XYA (-12.04) > xys (-12.17). (The relative reminiscent of the OH-bridged series since the A and S lig- ordering of the z2 and xy pairs is determined by the ligand and orbitals are essentially x and y oxygen orbitals. The field about the metal.) The smaller z2 splitting (0.03 eV) large bridging angle would lead to a strong preference for compared to xy (0.13 eV) can be attributed to the much an ordering EA > t~ based on our earlier overlap analysis. more favorable xy-ligand overlap, since the z2 orbitals are The location of the ligand S orbital below the ligand A or- oriented along the perpendicular axis. This is also conso- bital would reinforce this tendency, and in fact this ordering nant with the stronger AF coupling in the Ni dimer than in
Journal of the American Chemical Society / 97.1 7 / August 20, I975 4895 the Cu dimer where the xy orbitals are filled and cannot nn contribute to superexchange. The analysis of the squarate system-where the same H;; parameters and bond distances are used as in the oxalate system-is quite similar except that the ligand orbitals, shown in 25 - 28, now have the ordering z2s > z2~and 25 26
xyA (1,2& (1xy's -13 '3 -13 89
Figure 12. Interaction diagram for selected metal and ligand lone pair orbitals in the oxalate bridged Cu dimer. 27 28 A A N 3,I' NO wN
29 30 31 xys > X~A.The ligand z2s orbital has a strong antibonding interaction with the highest C-C bonding orbital of the cy- splittings has a strong conformational dependence, in the clobutane system,65 and X~Ais markedly stabilized by an prototype 29 being relatively insensitive to rotation around interaction with the lowest u* orbital of the C-C system. the central (2-3) u bond, but very sensitive to torsion This ordering is again reflected in the final metal orbitals' around the side (1-2, 3-4) bonds. Metal centers coordinat- energies, with a z2 energy difference of 0.05 eV and a dif- ed to such systems should respond to the energy splitting by ference of 0.12 eV for xy. That the squarate interaction is showing a sizable antiferromagnetic coupling. observed to be extremely small (ca. -1 cm-*) experimen- The kind of molecule we have in mind is shown in 32 or tally is presumably due to the fact that the self-consistent 33. These appear to be unrealistic, but we would encourage orbitals of the larger C4042- system would be lower in en- ergy and interact more weakly with the metal orbitals, as our previous electronegativity studies would argue. The A1 main points of these arguments-the occupancy of z2 vs. - cu - xy, better xy-ligand overlap, and weaker squarate-metal I "wN-?- interaction-were initially forwarded by Duggan and Hen- dri~kson~~and their suggestions have apparently found some support from these calculations. Since the structure 32 33 for the squarate dimer has not yet been determined, the experimental investigation of this general type of complex. small interaction may be due to distortions from the as- Ethylenediamines generally prefer to act as bidentate lig- sumed geometry. ands toward one metal center rather than bridging two metal atoms. A unique structure, CurEDTA-4HrO has the Metal-Metal Interactions and through Bond Coupling EDTA molecule bridging in an extended fashion two In the realm of organic chemistry photoelectron spectros- Cu(I1) atom^.^^.^' A preliminary study shows very little de- copy has provided abundant evidence for the splitting of crease at low temperatures in the magnetic moment from lone pair and T levels as a consequence of interaction with its 1.92 p~ value at 295°K.68 This unfortunately is consis- occupied and empty (T levels.'* The discussion of the previ- tent with the solid state geometry, the N-Cu directions. ous sections is much along the same lines-the bridging when viewed along an N-C bond, forming an angle of 72O group provides orbitals of a certain symmetry type, and this with the crucial coupling CC bond. in turn effects a certain well-defined splitting of the metal Several DABCO-copper( 11) complexes are known: Cu- orbitals. (a~etate)*-O.SDABC0,~~~CUCI~-DABCO,~~~~~ CuC12. An interesting point is that among these metal-metal 0.5DABC0.69CIn the acetate complex, which presumably coupled systems that have been carefully studied there are retains the basic Cuz(acetate)4 structure, adding in the few examples of the coupling unit which has proven most solid state bridging DABCO units, the unpaired electron is spectacular in organic systems-two lone pairs separated by in an orbital which does not have the correct symmetry to three u bonds. The unit is exemplified by 1,2-diami- interact with the through-bond coupled DABCO lone pairs. noethane 29, pyrazine 30, and diazahicyclo[2.2.2]octane The CuClr DABCO complexes show normal magnetic be- (DABCO) 31. The through bond coupling of the N lone ha~ior.~~~Their structures are unknown and would he of pairs in these molecules is large, producing splittings be- considerable interest. tween symmetric and antisymmetric lone pair combinations Pyrazine has been utilized as a bridging ligand in several of 1-2.5 eV. The interaction which leads to these large instances. The 1 : 1 copper nitrate:pyra7ine complex shows
Hay. Thibeault. Hoffmann / Orbital Interactions in Metal Dimer Complexes 4896 antiferromagnetic coupling between the Cu(I1) ions sepa- Table IV. Parameters for the SelfConsistent Charge Calculations. All Quantities Are in eV rated by 6.7 A.70 The crystal structure contains infinite ~~ chains of Cu(N03)~alternating with pyra~ine.~’The ni- Atom C B A Y trate groups are asymmetrically bonded, so that the local c 2s 19.50 12.07 1.54 10.201 symmetry at the copper atoms is low. It is difficult to deter- 2P 10.66 12.07 1.54 10.201 mine the precise orientation of the orbital holding the un- N 2s 25.50 13.64 2.01 11.052 paired ele~tron.’~It should have considerable u character 2P 13.14 13.64 2.01 11.052 (along the Cu-pyrazine axis) and thus this may be the kind 0 2s 32.40 15.00 1.72 13.625 of system where the through-bond coupling capability of 2P 15.87 15.00 1.72 13.625 c1 3s 25.3 10.84 0.69 10.292 the pyrazine is exhibited. The magnetic properties of sever- 3P 13.8 10.84 0.69 10.292 al other pyrazine bridged copper, nickel, and cobalt systems H 1Sa 13.6 6.44 -12.9 12.848 have been e~arnined.~~-’~ H Isb 13.6 0 0 12.848 A pyrazine molecule has been used to bridge two octahe- cu 4s 7.72 8.84 0.942 10.9 drally coordinated Ru or Os centers in varying oxidation 4P 3.98 6.64 1.05 10.9 states (2+, 2+; 3+, 2+; 3+, 3+) in the elegant studies of 3d 10.66 5.63 4.08 10.9 Taube and coworkers.80 In these systems the pyrazine acts aWhen -0.5 4 qH 4 0.5. bWhen 0.5 < qH < 1.0. as a weak coupling unit through its A system. We think its effectiveness for mediating interaction between metal cen- polyatomic ligands. It has been attempted to create such a ters should be greater when it operates through its u system, as in the d9-d9 systems. framework on which future quantitative developments may rest. Summary and Discussion Acknowledgment. Our work was generously supported by The preceding molecular orbital analysis has focused on the Advanced Research Projects Agency through the Mate- the splitting in energy between the highest two orbitals--( t~ rials Science Center at Cornell University and by the Na- - t~l2-as the dominant factor in antiferromagnetic inter- tional Science Foundation. We are grateful to a knowledge- actions of d9 metal dimer complexes (see eq 7). able referee for his comments and for providing us with use- ful additional references. Appendix 1 The computed changes in this quantity as a function of ge- Consider two interacting Ni(I1) ions with high spin (SA ometry have been found to reflect the experimental varia- = 1) ground states (t2g)6(eg)2.In the dimer there will be tions in J in hydroxo- and chloro-bridged Cu dimers. Al- four eg-like MO’s: 41, 42, 43, 44. From these four eg orbitals though our intent has been the analysis of qualitative one forms orthogonalized localized orbitals on each center changes in the orbital levels, the calculated splittings A and B (-0.1-0.2 eV) yield values for 23 (ca. -16 to -140 cm-1) of reasonable magnitude (assuming Ja, - Jab 5 eV). For d” systems the total superexchange interaction can be decomposed into contributions from disjoint sets of orbit- al pairs, 1 ti - t,l 2, and the various types of orbital interac- tions were reviewed for oxo-bridged metal dimers. Although only the magnitude 1 t~ - €4is important as far as superexchange is concerned, the actual relative ordering in most cases (with the possible exception of the acetate di- mers) can be inferred from the calculations and the known experimental information. Since the levels have real physi- The wave functions for the S = 2, 1, and 0 states of the cal significance, in the sense of observables, only for the dimer are high-spin state, which is usually not the ground state, exper- imental verification of the level scheme would be difficult. dzo = labcdX21 x2 = cyac~ff Information could possibly be obtained, however, from ESR (1,O = labcdx,~ x1 = (ap + FCY)CYLY- cia(afi + off) experiments on the dimers where an electron has been added or removed from the system in order to tell whether doo = abcdy,l yn = (00 + ga)(fffi+ Pff) - the S or A level lies higher in energy. 2affpp- 2&3cYa Substituents have also been found to influence the t~ - CA splitting-increasing it (and hence the AF coupling) as The compact notation for the Slater determinants differs electron density is added to bridging atoms, decreasing it as somewhat from that used previously but is self-evident. The electron density is removed. Model calculations demon- corresponding energies are strated the effect in methoxy- and acetate-bridged dimers. One of the more interesting features to emerge from this E,’ = Eo - K analysis has been a means to analyze metal-metal interac- tions when the intervening ligand is a “complicated” poly- E,n = Eo atomic molecule. At least in the case of acetate, oxalate, Eoo= En + \I7K and squarate dimers, inspection of the highest ligand orbit- als of the proper symmetry to interact with the d orbitals K = K,, + K,, + K, + K, > 0 has been sufficient to account for the ordering of the d lev- els in the dimer and their relative importance in superex- change. i >j Until recently there has been little theoretical foundation for analysis of superexchange in molecular dimers with The possible “ionic” configurations are
Journal of the American Chemical Society / 97:17 / August 20, 1975
4898
square planar [CI~CU(OCHO)]~-.Separate calculations towska, H. Kozlowski, T. Cukierda, and A. Ozarowski, J. Mol. Struct., 19, 663 (1973); B. Jezowska-Trzebiatowska and W. Wojciechowski were performed on the XCOO- ligand with two point TransirionMet. Chem., 6, l(l970). charges (q = +0.5) at the metal positions. Previous calcula- (24) J. Glerup, Acta Chem. Scand., 26, 3775 (1972). See also E. Larsen and tions on the OCH2X- series had shown this to be a reason- G. N. La Mar, J. Chem. Educ., 51, 633 (1974). (25) H. J. Schugar. G. R. Rossmann, and H. B. Gray, J. Am. Chem. SOC.,91, able assumption. The Hi; atomic levels of HCOO- were 4564 (1969). shifted to match the results from the Cu complex, and the (26) D. Baumann, H. Endres, H. J. Keller, and J. Weiss, J. Chem. Soc., Chem. Commun., 853 (1973). levels of the other XCOO- ligands were adjusted accord- (27) (a) K. T. McGregor, N. T. Watkins. D. L. Lewis, R. F. Drake, D. J. Hodg- ingly for the dimer. Finally the actual dimer considered was son, and W. E. Hatfield, lnorg. Nucl. Chem. Lett., 9, 423 (1973),and ref- Cuz(HCOO)*(XC00)2 where substituents were placed erences therein; (b) D. L. Lewis, W. E. Hatfield, and D. J. Hodgson, lnorg. Chem., 11, 2216 (1972): (c) D. L. Lewis, K. T. McGregor, W. E. only on two opposite carbon atoms. Hatfield. and D. J. Hodgson. ibid., 13, 1013 (1974): (d) E. D. Estes, W. E. For the pyridine N-oxide series, SCC calculations on the Hatfield, and D. J. Hodgson, ibid,, 13, 1654 (1974). ligand in the presence of a point charge (q = +1.0) 2.0 (26) J. A. Bertrand and C. E. Kirkwood, lnorg. Chim. Acta, 6, 248 (1972):J. A A. Bertrand, J. H. Smith, and P. G. Eller, horg. Chem., 13, 1649 (1974). from the 0 were used to determine the ligand levels. These (29) (a) R. D. Willett, J. Chem. SOC., Chem. Commun., 607 (1973);(b) R. D. were arbitrarily lowered 5 eV for the dimer calculation; Cu Wiilett and C. Chow, Acta CrystaNogr.. Sect. 8, 30,207 (1974); (c) C. Chow, R. Caputo. R. D. Willett, and B. C. Gerstein, J. Chem. Phys., 61, and CI values were taken from the Cu(OH)2C12 calcula- 271 (1974). tion. (30) (a) S. C. Abraham and H. J. Williams, J. Chem. Phys., 39, 2923 (1963); (b) P. H. Vossos, D. R. Fitzwater, and R. E. Rundle, Acta Crystallogr., The same technique was used for the oxalate dimer, with 16, 1045 (1963). two point charges (q = + 1 .O) located at the metal position. (31) (a) R. D. Willett. C. Dwiggins. Jr., R. T. Kruh, and R. E. Rundle, J. Chem. A constant shift of -3.5 eV was then added. When SCC Phys., 38, 2429 (1963);(b) G. J. Maass, B. C. Gerstein, and R. D. Willett, ibid., 46, 401 (1967). calculations of this type were attempted on Cu complexes of (32) (a) R. D. Willett, J. Chem. Phys., 44, 39 (1966);(b) B. C. Gerstein, F. D. ligands with extended 7 systems, the results usually showed Gehring, and R. D. Willett. J. Appl. Phys., 43, 1932 (1972). x* (33) M. Textor, E. Dubler, and H. R. Oswald, lnorg. Chem., 13, 1361 (1974). the lowest virtual level to lie below the highest occupied (34) In these calculations we again adopted an increased orbital exponent of d level. This perhaps arises from our choice of a single con- 2.7 for the CI 3%since the 3d (Cu)-3s (CI) interactions otherwise appar- stant in the formula for Hi,, while some investigators have ently are overestimated by the extended Huckei method. (35) R. D. Willett and 0. L. Liles, Jr., Inorg. Chem., 6, 1666 (1967). advocated different constants for u and x orbital^.^' (36) R. Mason and D. M. P. Mingos. J. Organomet. Chem., 50, 53 (1973). (37) B. K. Teo, M. E. Hall, R. F. Fenske, and L. F. Dahl, J. Organomet. References and Notes Chem., 70, 413 (1974). (36) D. M. Duggan, R. G. Jungst, K. R. Mann, G. D. Stucky, and D. N. Hen- (1) R. L. Martin in "New Pathways in Inorganic Chemistry", E. A. V. Eb- drickson, J. Am. Chem. SOC., 96, 3443 (1974). sworth, A. G. Maddock. and A. G. Sharpe, Ed., Cambridge University (39) J. A. Carrabine and M. Sundaralingam, J. Am. Chem. SOC., 92, 369 Press, London, 1968, Chapter 9. (1970); M. Sundaralingam and J. A. Carrabine, J. Mol. Biol., 61, 287 (2) P. W. Ball, Coord. Chem. Rev.. 4, 361 (1969);G. E. Kokoszka and R. W. (1971); J. P. Declercq. M. Debbaudt, and M. Van Meerssche, Bull. SOC. Duerst. ibid., 5, 209 (1970);E. Sinn, ibid., 5, 313 (1970). Chim. Belg., 80, 527 (1971).
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Journal of the American Chemical Society / 97:17 / August 20, 1975 4899
A. Cotton and J. G. Norman, Jr., J. Coord. Chem., 1, 161 (1971). (c) M2 (71) A. Santoro, A. D. Mighell. and C. W. Reimann, Acta Crystallogr., Sect. = CrMo: C. D. Garner and R. G. Senior, J. Chem. SOC., Chem. Com- 8, 26, 979 (1970). mun., 580 (1974). (72) G. F. Kokoszka and C. W. Reimann, J. Inorg. Nucl. Chem., 32, 3229 (57) R. W. Jotham, S. F. A. Kettle, and J. A. Marks, J. Chem. SOC.. Datton (1970). Trans. 1133 (1972). (73) D. E. Billing, A. E. Underhill. D. M. Adams. and D. M. Morris, J. Chem. (58) Y. Muto. M. Kato, H. B. Jonassen, and L. C. Cusachs, BUN. Soc. Chim. SOC.A, 902 (1966). Jpn., 42, 417 (1969). (74) K. Hyde, G. F. Kokoszka, and G. Gordon, J. lnorg. Nucl. Chem., 31, (59) M. R. Kidd and W. H. Watson, Inorg. Chem., 8, 1886 (1969). 1993 (1969). (60) (a) H. L. Schafer, J. C. Morrow, and H. M. Smith, J. Chem. Phys., 42, (75) M. J. M. Campbell, R. Grzeskowiak. and F. 8. Taylor, J. Chem. Soc. A, 504 (1965); (b) R. S. Sager, R. J. Williams, and W. H. Watson, Inorg. 19 (1970). Chem., 6, 951 (1967); 8, 694 (1969): (c) W. H. Watson and D. R. John- (76) G. W. Inrnan. Jr.. J. A. Barnes, and W. E. Hatfield, lnorg. Chem., 11, 764 son, J. Coord:Chem., 1, 145 (1971). (1972); G. W. Inman. Jr., and W. E. Hatfield, ibid., 11, 3085 (1972); H. (61) N. F. Curtis, i. R. N. McCormick, and T. N. Waters, J. Chem. Soc., Dal- W. Richardson, W. E. Hatfield. H. J. Stoklosa. and J. R. Wasson. ibid., ton Trans., 1537 (1973). 12, 2051 (1973). (62) D. M. Duggan, E. K. Barefield, and D. N. Hendrickson, Inorg. Chem., 12, (77) R. W. Matthews and R. A. Walton, Inorg. Chem., 10, 1433 (1971). 985 (1973). (78) E. B. Fleischer and M. B. Lawson, Inorg. Chem., 11, 2772 (1972). (63) D. M. Duggan and D. H. Hendrickson. Inorg. Chem., 12, 2422 (1973). (79) P. W. Carreck, M. Goldstein, E. M. McPartlin, and W. D. Unsworth, (64) In the model dimer which we calculated, we replaced the terminal N- Chem. Commun.. 1634 (1971); M. Goldstein. F. B. Taylor, and W. D. Un- containing ligands by chlorines. The other structural parameters used sworth. J. Chem. SOC.,Dalton Trans., 418 (1972). were ~CU-CI) = 2.26 A, mcu-0) = 2.10 A, CI-cu-ci angle = 90". (80) (a) C. Creutz and H. Taube. J. Am. Chem. Soc.. 01, 3988 (1969); 05, and 0-C-C angle = 125". 1086 (1973); R. H. Magnuson and H. Taube, ibid., 04, 7213 (1972); S. S. (65) R. Hoffmann and R. B. Davidson, J. Am. Chem. SOC., 03,5699 (1971). lsied and H. Taube, /bid.. 05, 8198 (1973). (b) See also B. Mayoh and P. (66) T. N. Polynova, T. V. Filippova, M. A. Porai-Koshits, and L. I. Marmynen- Day, J. Am. Chem. SOC..04, 2885 (1972); E. 6. Fleischer and D. K. La- ko, Zh. Strukt. Khim., 11, 558 (1973). vallee, ibid.. 04, 2599 (1972): J. H. Elias and R. S. Drago. horg. Chem.. (67) A crystal structure of the O~MOEDTAMOO~~-ion shows the two octahe- 11, 415 (1972); S. A. Adeyemi. E. C. Johnson, F. J. Miller, and T. L. drally coordinated Mo(VI) centers bridged by a fully extended EDTA Meyer, ibid., 12, 2371 (1973), and references therein. chain: J. J. Park, M. D. Glick. and J. L. Hoard, J. Am. Chem. SOC..01, (81) The charge iterative calculations described here differ from many tradi- 301 (1969). Mo(V), d', complexes with two Mo centers and a single tional approaches by the inclusion of two-center Coulomb terms (See EDTA type ligand have been synthesized: R. L. Pecsok and D. T. Saw- text). A more complete discussion will be published separately by J. C. yer, J. Am. Chem. SOC.,78, 5496 (1956): L. V. Haines and D. T. Saw- Thibeault. yer, horg. Chem., 6, 2147 (1967). Crystal structures of two compounds (82) K. Ohno. Theor. Chim. Acta, 2, 219 (1964): G. Klopman. J. Am. Chem. in this series reveal a dioxo-bridged structure: R. M. Wing and K. P. Cal- Soc., 86, 1463 (1964). lahan, Inorg. Chem., 8, 2303 (1969). (83) M. A. Whitehead in "Sigma Molecular Orbital Theory", 0. Sinanoglu and (68) D. M. P. Mingos and I. Ghatak. Queen Mary College, private communi- K. Wiberg, Ed., Yale, 1970, p 50. cation. (84) C. J. Ballhausen and H. 6. Gray, "Molecular Orbital Theory", W. A. Ben- (69) (a) E. D. Stevens and J. T. Yoke, Inorg. Chim. Acfa, 4, 244 (1970); (b) G. jamin, New York, N.Y., 1964. J. Tennenhouse, Ph.D. Dissertation, University of Illinois, 1963; (c) H. M. (85) E. Clementi and D. L. Raimondi, J. Chem. Phys., 38, 2686 (1963). Hilliard, D. D. Axtell, M. M. Gilbert, and J. T. Yoke, J. Inorg. NucI. Chem., (86) J. W. Richardson, W. C. Nieuwpoort, R. R. Powell, and W. F. Edgell, J. 31, 2117 (1969). Chem. Phys., 38, 1057 (1962). (70) J. F. Villa and W. E. Hatfield, J. Am. Chem. SOC., 03, 4081 (1971). (87) L. c. Cusachs, J. Chem. Phys., 43, Si57 (1965).
An X-Ray Photoelectron Spectroscopic Study of Charge Distributions in Tetracovalent Compounds of Nitrogen and Phosphorus
Winfield B. Perry, Theodore F. Schaaf, and William L. Jolly* Contribution from the Department of Chemistry, University of California and the Inorganic Materials Research Division of the Lawrence Berkeley Laboratory. Berkeley, California 94720. Received November 25, I974
Abstract: Core electron binding energies for ten phosphorus and four nitrogen compounds have been measured by X-ray pho- toelectron spectroscopy in the gas phase. The chemical shifts have been correlated by the electrostatic potential equation using charge distributions from extended Hiickel theory and CND0/2 molecular orbital calculations. The data indicate that resonance structures of the type RAM+-X- (I) contribute significantly to the charge distributions in the tetracovalent com- pounds. The data for the phosphorus compounds can be fairly well rationalized without the inclusion of any pn - dn bond- ing between the central atom and the X ligand, but the effects of elctronic relaxation upon the core binding energy chemical shifts must be included.
The bonding in four-coordinate compounds of nitrogen bond resonance,',' I I. When the central atom is phosphorus, and phosphorus can be represented by I. However, because however, it is conceivable that the phosphorus 3d orbitals s R I I R-h+--S- K-W=X I R R- I1 1 may significantly participate in the bonding.? ' In his case. these compounds generally have short M-X bond lengths a resonance structure having no formal charges, such as 111. and high M-X stretching frequencies, multiple bond char- would be appropriate. The latter structure implies pn - dr acter has been postulated for the M-X bonds. Such multi- bonding between the central phosphorus atom and the pe- ple bonding can be explained by hyperconjugation, i.e., no- ripheral X ligand. Perry. Srhaaf, Jolly / Charge Distributions in Tetracoralent Compounds of .\ atid P