Relative Strengths of Axial and Equatorial Bonds and Site Preferences

7/27/2019 Relative Strengths of Axial and Equatorial Bonds and Site Preferences

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2648 Inorganic Chemistry, Vol. 17 , N o. 9, 1978 Evgeny Shustorovichformed upon repeated recrystallization from methanol or acetone whichdiffered in elemental composition from the green product. The brownproduct forms in both the presence and absence of oxygen from a solutionof the green product.(31) R. L. Carlin and F. A . Walker, Jr., J . Am . Chem. Soc., 87, 2128 (1965).(32) B. N. Figgis and J. Lewis, in Modern Coordination Chemistry, J. Lewisand R. G. W ilkins, Ed., Interscience, New York, N.Y., 1960, p 403.(33) J . P. Chandler, Program 66, Quantum Chemistry Program Exchange,Indiana University, Bloomington, Ind., 1973.(34) J . A . Pople and D. L. Beveridge, Approximate Molecular OrbitalTheory, McGraw-Hill, New York, N.Y., 1970.( 3 5 ) B. Bleaney and K. D. Bowers, Proc. R. SOC.ondon, Ser. A , 214,451(1952).(36) B. J . Hathaway and D. E. Billing, Coord. Chem. Rev., 5, 143 (1970).(37) P. C. Jain and E . C. Lingafelter, J . A m . Chem. Soc., 89, 6131 (1967).(38) J. A. Fee, Struct. Bonding (Berlin),23, 1 (1975), and references therein;E. Frieden and H. S. Hsieh, Adu. Enzym ol. Relat. Areas Mol. Biol. ,44, 187 (1976), and references therein.(39) B. E. Myers, L. Berger, and S. A . Friedberg, J . Appl . Phys . , 40, 1149(1969).(40) M. W . Van Tol, K. M . Diederix, and N . J. Poulis, Physica (Utrecht),64, 363 (1973).(41) S. N. Bhatia, C. J. OConnor, R. L. Carlin, H . A . Algra, and L . J .DeJongh, Chem. Phys . Lett. , 50 , 35 3 (1977).(42) B. Morosin, Acta Crystallogr. , Sect. E, 6, 1203 (1970).(43) B. Morosin, Acta Crystallogr. , Sect. E, 2, 1237 (1976).(44) F. A. Walker, R. L. Carlin, and P. H. Rieger, J . Chem.Phys., 45, 4181(1966).

B. A. Goodman and J . B. Raynor, Adv. Inorg. Chem. Radiochem., 13,235 (1970).B. C. Saunders, in Inorganic Biochemistry, Vol. 2, G. L. Eichhorn,Elsevier, 1973, Chapter 28, and references therein.For example,see C. Heitner-Wirguin and J. Selbin,J . Inorg. Nucl. Chem.,30, 3181 (1968).P. J. Hay, J . C. Thibeault, and R . Hoffmann, J . A m . Chem. SOC. , 7,4884 (1975).E. F. Hasty, T. J. Co lburn, and D. N . Hendrickson, Inorg. Chem., 12 ,2414 (1973).A . P. Ginsberg, Inorg. Chim. Acta, Rec. , 5, 45 (1971).W. H eisenberg, Z. Phys., 49, 619 (1928).P. A. M. Dirac, Proc. R. SOC.ondon, Ser. A , 123, 714 (1929).P. A. M. Dirac, The P rinciples of Quantum Mechanics, 3rd ed, OxfordUniversity Press, London, -1947, Chapter 9.D. Kivelson, J . Chem. Phys . , 33, 1094 (1960).J. D. Currin, Phys. Reu., 126, 1995 (1962).J. H . Freed, J . Chem. Phys., 45, 3452 (1966).C. S. Johnson, Mol. Phys., 12, 25 (1967).M . P. Eastman, R . G. Kooser, M. R . Das, and J. H . Freed, J . Chem.Phys., 51,2690 (1969); J. H. Freed, J . Phys . Chem. , 71, 38 (1967); M .P. Eastman, G. V. Brunoand J . H . Freed, J. Chem. Phys., 52,321 (1970).W. L . Reynolds and R . M. Lumry, Mechanisms of Electron Transfer ,Ronald Press, New York, N.Y., 1966.R . A . Marcus, Annu. Rec. Phys. Chem., 15, 155 (1964).J. Halpern, Q. Rev., Chem. Soc., 15, 207 (1961).H . Taube, Adu. Chem. Ser . , No. 162, 127-144 (1977).R. T. M . Fraser, J . A m . C h e m. SOC., 3, 4920 (1961).

Cont r ibu t ion f rom the D epar tm ent of C hemis t ry ,Cornel1 Universi ty, Ithac a, New Yor k 14853

Relative Strengths of Axial and Equatorial Bonds and Site Preferences for LigandSubstitution in a-Bonded Trigonal- and Pentagonal-Bipyramidal ComplexesE V G E N Y S H U S T O R O V I C H Received February 14 , 1978

For bipyramidal t rigonal (TB) EL5 D3,,and pent agonal (PB ) EL7 D Sh omplexes (E is a transition metal M or main-groupelement A) two problems have been considered: ( 1 ) the relat ive st rengths of axial (ax) and equatoria l (eq) bonds and (2 )the si te preferences (SP) of st ronger donor (or acceptor) subs t i t uen ts L. An analyt ical approach has been developed inthe f ramework of canonica l LCAO M O theory. Rat ios of overlap populat ions T = N , / N a X were est imated for ns , np ,a n d (n - )d cont r i bu t ions pro dwin 8 va lues of 1 < FS),< FP) 1.15, = 1.5, and Fd*) 0.3 for TB complexesand fl)< 1,O.g < FP) 1, and fid 4) 1 .2 fo r PB complexes. The contribut ions al l reinforce to make equatorial bondsrelat ively st ronge r than axial bonds, eq > ax , i n AL 5 and M L5 (do-d4) complexes whi le t h e pd8)ont r i bu t ion dominat esin M L5 (d) complexes to make ax 2 eq. The perturbing influence of ( n - l )d lo shells in AL 5 complexes wa s also examinedand found capabl e of making ax > eq under cer tain condi t ions. The opposing contribut ions of s, p, and d in M L7 (do-d4)complexes equal ize axial and e quatorial bonds whi le s and p contribu t ions predom inate in AL, complexes resul ting in ax> eq. SP for substituents were examined using perturbation theory with the finding that a stronger donor ligand will substituteequator i a l ly i n A LS and ML 5 (do-d4) complexes and ax i al l y i n M LS (d8) and AL , complexes. Quant i tat ive detai ls mustbe considered in ML 5 (dO) and M L7 (do-d4) cases. Th e relationship between bond energy and bond polari ty cri teria fo rSP (equivalent in some instances) was ex amined for al l cases. The resul ts obtained a gree wi th the avai lable experimentaland computa t i ona l da t a and permi t a number of predict ions to be made.

IntroductionBy tradition most studies on the electronic and geometricstructu res of coord ination compou nds are devoted to the s quareor tetrah edral EL4 and octahedral EL, complexes (E is atransition metal M or a main-group element atom A). In thesepolyhedra with very high symmetry all the ligands are geo-metrically equivalent, permitting sy mmetry argum ents to beused most effectively. Th at, in turn , makes reliable manyresults obtained from a variety of approxim ate models. Inparticul ar, the theory of the mutu al influence of ligands (M IL )has been developed only for square and o ctahedral complexeswhere all valence angles are equ al to 90 or 180 reducing theMIL to the trans-cisIn recent years one can observe the sharply increasinginterest in E L5 and EL 7 polyhedra w here all ligand positionscan not be equivalent. Most effort has been directed to theproblem of the relative stability of different possible polyhedra

for a given composition EL, and the barriers to their inter-conversion.18 Th e present work will not address this problembut consider only bipyramidal structures, trigonal (TB) EL5and pentagonal (PB) EL7. The difference between axial,E-La,, and equ ator ial, E-L,, bonds gen erate s th ree specificproblems of structure for these compounds (as compared withsquare and octahedral ones): (1 ) the relative strengths of th eE-La, and E-L, bonds in unsubstituted complexes EL,; (2 )the site preference of a given substituent L for an axial orequatorial position under substitution EL, - L,-,L; (3 )differences in th e influence of t he ligand L, in a substitutedEL,-lL complex, on th e strength of the initial axial andequatorial bonds.Sufficient experimental data exist for a discussion of somefundam ental regularities in the stru cture of these complexes,especially EL5. Moreover, quantitative quantum chemicalcalculations have been performed on specific EL5839,15-18nd

0020-1669/78/1317-2648$01.00/0 0 1978 American Chemical S o c i e t y


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Axial and Eq uatorial Bonds in TB and PB ComplexesTable I. Orbital Basis Functions Forming u Bonds in Bipyramidal EL, Com plexes

Inorganic Chemistry, Vol. 17, No. 9, 1978 2649

irreduciblecomplex representation AOs of E group ligand orbitalsA , A ,

A1E,TlU

AI A ,El

E

PY2n 4n 6n

5 5(2/5)/ (u4 sin3 u5 sin- u6 sin- u, sin-4n 8n 12n(2/5)/(u, + u4 co s- u5 co s- u6 os- u , co s-5 5 5

4n 8 n 12 n+ u 5 sin- u6 sin- U, sin-5 5xyThese explicit expressions can be obtained from the relevant general relationships: (17) for r = 3 .h 18 ) fo r r = 3. h (1 1) or (14)(16) for r = 2 (the equatorial axis in a square).h (h See explanations in the tex t.or r = 4 .h e (12) or (15) for r = 4 .h ? ( 1 6 ) fo r r = 4 . hEL710919omplexes which permit explanation of regularities,such as th e site preferences for donor (acceptor) substituentsin TB AL?O or the influence of the metal d configuration onrelative bond streng ths of axial and equatorial bonds in TBML,.9 Som e regularities have been rationalized in theframeworks of oth er approaches, in particular the VS EPRmodels: Bartells primary-se condary effect s appr oach , th eangu lar overlap model,12 and the M O W alsh-type ap-proach.13J4 But, to our knowledge, there is no formalismembracin g all of these problems explicitly in the fram eworkof the LC AO M O theory, the most general language fordescribing electronic effects in chem ical compounds.Formulation of the ObjectiveTh e purpose of the present work is to develop such a g eneralM O approach . Most of the problems of axial and equatorialnonequivalency will be considered as manifestations of theMIL in bipyramidal polyhedra EL, for m = 5 (TB, D 3 J an dm = 7 (PB, D5h) with the octahedron, m = 6 (oh),nteringas the p articular case when axial and equatorial positions areequivalent. In this sense we continue our earlier work on th eM IL in sq uare EL 4 and octahedral EL6 complexes21,22 herewe found that some regularities for main-group element AL,complexes may be both similar to and different from those fort ra ns it io n- me ta l M L, c ~ m p l e x e s . ~ ~ * ~ ~ * ~eedless to say, anymodel is formu lated in relatively simple terms and one m ustaccept some drastic approximations to obtain explicit inter-relations among the parameters. At the same time quantitativecomputations may be based on a quite different, often muchmore sophisticated m athematical formalism taking into ac-count m any facto rs which have been neglected in the modelor introduced in a nonexplicit form. Therefore, comparisonof compu tational results with those from the model is usuallynot a trivial procedure and rather often these two groups ofresults should be compared with experimental data quiteindependently.Due to computational difficulties, most calculations havebeen on simple systems such as PH 5 or PF5which have beencalculated m any times and by man y methods including theab initio (PH5,15PF518),CND0/2 (PF517a), IVN AP and

AR C ANA (PH5,17bF517b), nd EH M (PH5,8 F516)methods.Calculations on other complexes are rare and h ave been usuallyperformed by means of simple semiempirical methods, es-pecially of the EHM type (for example, PC15,16a sF5,17orIF719), o that the a b initio calculations like those on VF, an dVF5-43a re really unique.The most interesting thing for a chemist is to predictregularities along the series EL, when we replace either E orL, for instance, in the horizontal series from CdC153- o SbC15,in the vertical series from P F5 to B iF5, or alon g th e series PF,,P(OPh)S,PCl,, PP h5, etc. At present reliable calculations onentire series like these ar e impossible, so that any prediction,based on even very accurate calculations on the simplestcompounds of the PH 5 or PF, type, is an extrapo lation withoutwell boundary conditions. In a situation like this the modelpredictions may not only be more digestible for a chemistbut m ore informative as well. Th e model has adv antages inthat it can focus on the essential features and probe theirimportance one by one.The present work will consider the first two problemsmentioned above for E L5 and EL 7 complexes, namely, therelative strength of axial and equatorial bonds and the sitepreferences for a more donor (acceptor) substituent. Th e thirdproblem, the M IL in substituted complexes ELm-kLk,will beconsidered in a subsequent paper.24Results and Discussion1. Composition and Energies of the Group Ligand Orbitals.Let us consider polyhedra EL, where there are two axialligands (1 an d 2 ) on the z axis and r equatorial ligands (3 ,4, ... r + 2) occupy vertices of a regular r polygon in th e x yplane, the ligand 3 being on th e x axis (Figure 1). Nowcompare the o rbital basis sets forming u bonds in these bi-pyramidal complexes (Table I). In the EL6 0, case s, p, andd orbitals belong to different irreducible representations. Onlythen is there no mixing of the cen tral atom orbitals in therelevant canonical MOs of the E L,,, complexes making t hes, p, and d contributions to the relative stren gth of axial andequatorial bonds independent of each other, each axial con-tribution being equal to t he corresponding equatorial one. In


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2650 Inorganic Chemistry, Vol. 17 , No. 9, 1978( 2 )

I I I I

Evgeny Shustorovich

( I ) (I i) (iii) ( I V )Figure 1. General scheme for bipyramidal complexes EL, (i) andenumeration of ligands in TBEL5 (ii), Uh EL6 (iii), and PB EL, (iv).In the case (i) th e coordinate axes and the valence angles are shownas well.the D3h EL5 and D S hEL , cases the s, p, and d contributionsto the axial bond strength a re unequal to the equatorial onesand must be considered separately. It is necessary also to takeinto accou nt sdz2 mixing in bo th M L5 D3h and ML7 D5has wellas pxdx ~,,2 p,d,) mix ing in ML5 D3h complexes, thoughcertainly we c an neglect these mixings in main group elementcomplexes AL, for which th e hypervalent structurez5withoutvacant nd orbitals is usually a rather good approximation.z6Let us begin wit h sdz2 mixing. Tab le I lists four orbitals(s , dZ2,uax, nd ueq)within the totally symmetric irreduciblerepresentation A I where

and1uq = ((73 +a, + ...+ u,+2)(r(1 + 2S,4 + . . . ) ) 1 / 2

are reduced to the usual forms (see Table I)(3 )

and1

r/2ueq = -(u3 + u4 + .., + ur+J (4 )if we neglect all the overlap integrals S, = (uJu,), i # j .Th e fourth-order secular equation can b e reduced by usinglinear combinations of uax nd uq (eq 5 and 6), where pl and

PI = C l l g a x + ~ l ~ u e q ( 5 )4% = C 2 1 0 a x - C ~ ~ f f e q (6 )

cpz are orthogonal to each other, p1 s orth ogo nal t o d,2, an dpz s orthogonal to s, i.e.

((PlIVZ) = 0 (7 )(cplld2) = 0 (8 )(cpzls) = 0 (9)

c11 = c22, c 1 2= czl, cl12+ c 1 2 = 1 for S, = o ( i + j ) (10)Though strict fulfillment of both conditions 8 and 9 is possibleonly in the EL6 Oh case (where s and dZ2belong to differentirreducible representatio ns), for the EL5and EL , cases thesetwo orthogonalization schemes give us a possibility of esti-mating separately the s and dZ2 contributions t o the relativebond strength (see below).T h e s contribution will be entirely isotropic if we neglectinterligand interactions. In fact, neglecting all the overlapintegrals S,] ( i # j ) , we have for condition 9 the mutuallyorthogonal group orbitals (1 1) and (12). Because of the form$91 = ( + 2qcr1u2 + ... + ur+J (11)

of (1 1) the s contribution to th e streng th of all the bonds-bothaxia l and equatorial-is th e sam e. So the only way to takeinto account the real anisotropy of the s contribution is toinclude somehow interligand interactions (see below).If we use the second orthogonalization scheme (8) a nd ta keinto account [cf . ( loo )]

we obtain mutually orthogonal group orbitals (14) and (15).

p i = ( + 8qz(gluz) -It is obvious that cpl (1 1) coincides with cpl (14) and cpz (12)with cp; (15) Only in the EL 6 o h case where r = 4 (see Tab le1) The forms of relevant equatorial ligand MOs pk dependupon whether or not there is a ligand trans to ligand 3. Letting6 = w , 2w, ..., where w = 2 7 / r stands for the valence anglebetween ligands 3 and 4 (see Figure 1 and Tab le I) , we havethe following:(a ) For a nondegenerate level when there exists a transpositionpk = (1/r)I2(u3 + u4el8+ u s e z t 8+ ...+ u r + z e ( r l ) r o ) (16)(b ) For a doubly degenerate level where there is no transposition, bu t th ere a re pairs of equivalent quasi-cis ligands

u5 cos 28 + ... + ur+2cos (r - l )6 ) (17)pk()= (2/r)12(a3+ 0 4 co s 6 +The second MO pk()will be, obviously,

( p k ( 2 ) = (2/r)1/z(u4 sin 6 +u5 sin 26 +...+ a,+z si n ( r - l)6) (18)

There is a clear analogy in the forms of MOs (16)-(18)and the Hiickel T MOs of cyclic polyenes C,H, where theforms of T MOs depend on whether the number r is even orFurth er, one should emphasize tha t by symmetry th eequatorial px,py orbitals intera ct with th e group ligand orbitalscorresponding to 6 = w while t he equatorial dx2~y2,dxyrbitalsinteract with t he group ligand orbitals corresponding to 0 =2w. Only in D3, (TB), where w = 2~ - 2w, cos w = cos 2w= cos 4w, and sin w = -sin 2w = si n 4w, do the two sets oforbitals belong to the same irreducible representation, e.Though neglecting Sl j i # j ) , we shall not neglect resonanceintegrals p ij = (a l l f lu ,) , i # 6 , so tha t the energies of thedifferent grou p ligand orbitals ( 1 1)-( 12) and (14)-( 18) willbe different. The significance of such energy splittings isdemonstrated in t he photoelectron spectrum of SF, where theenergy splittings a, -tl, and alg-eg between the relevant gro upF 2s orbitals have te e n found to be equal to 2.7 and 4.9 eV ,respectively.28


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Axial and Equatorial Bonds in TB and PB Complexest

>.aWzWa

(1,111 (I ) ( I l lELCI(D3h) E L 6 (Oh ) EL 7 ( D S h )

Figure 2. Relative energies of the group ligand u orbitals in EL5 (fJ3h),ELs (oh), nd EL , (D5*)omplexes. For the al M O s tw o cases areshown: (i ) for th e s orthog onaliz ation and ( ii) for the d,2 or thogo -nal izat ion. I n the EL7complexes for the case (i ) the energies of theM O s az/ and 2al may be interchangeable; for the case (ii) the energyof 2al may be h igher or l ower t han aL.The dot ted l ines connectorbi tals of the sam e type. See the text for designations of th e MOs.Th e energies of the MOs (1 1)-( 12) an d (14)-( 18 ) are asfollows (OIL = a):

a(lal) = a + )/5(12PCls 6P, + 2P1,)4 h ) = a + 3/31(24PciS+ 16P, + 3PtJ

EL 5 D3h[the (11) type1 (19)[ the (14) type1 (20)[the (12) type1 (21)[ the ( 1 5 ) type1 (22)

(23)(24)

(25)(26)(27)

a(2al) = a - f/s(12Pcls 4Peq - 3PtJa(2al) = a - YlI(24Pcis- 6Peq - 8P t J

a(a?) = cy - Pt,a(e) = a - Peq

4a ig>= a + 4Pc1s+ P Ir4 t lU) = cy - PI ,

.(e,) = a - 2PClS + PI ,

EL6 Dh

EL7 D5ha ( l a l ) = a + j/7(10@eq(o) 10fle,(20)+

20PClS + 2PtJ [the ( 1 1) type1 (28)a(lal) = a + f/13(16@eq(0) 16P q 2w ) +

4OPcIs+ S P t J Ithe (14) type1 (29)a(2al) = cy + Y7(4p,(4 + 4Peq 2 w ) -20Pcls+ W t J [the (12) type1 (30)a(2al) = a + 1/13(10Peq(w)+ -[the (15) type1 (31)

(32)40Pc1s+ 8PtJ

a ( a / ) = a - Pt ,a(el) = a + 0.618Pe,()- 1.618Pe,(2) (33)cy(ei) = a - 1.618Peq(w) 0.618Peq(2) (34)

for the relevant internuclear distances R 12= 2R, R13 = 1.41R,Ru = 1.73R (EL5) or 1.17R (EL7), and R 3 5= 1.90R (EL7)if all the bond lengths E-L are equal to R (see Figure 1 ) .He r e Pa x = Pt r = P12, PCIS P13, Peq(w)= P349 an d Peq(2w)= 8 3 5

Inorganic Chemistry, Vol. 17, No. 9, I978 2651T o estimate th e relative energies of these MOs we shouldtake into account the short-range characte r of Pi j interactions(cf. Appendix, Table V I), namely

for EL s and EL6 I Pc is l >> IPeql > lPtrl (35)and

for EL7 IPq(o)l >> lPclsl >> IPeq(2w)I> IPtrI (36)For example, estimating PEis nd Ptr for group ligand F 2sorbitals of th e type (25)-(27) from the experimental d ata forSF628we obtain &is = -1.0 eV and Pt, = 0.All th is easily defines the relative order of th e MOs cy(la,),a(2al), a ( a F ) , a(el), and Ly(ei) which is shown in Figure2. Th e fine point is the relative order of the al MOs obtainedby the s and dzz orthogonalization s, i.e., (19) vs. (20) an d (28)vs. (29). As the dominant Pi j value is Pcis or ELS and & ( w )for EL7 , we have to compare the magnitude s of th e coefficients[see ( l l ) , (1 2) and (14), (15)] in (37) and (38), which is

L I- < - for ELS (P = 3)r + 8 r + 21L


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2652 Inorganic Chemistry, Vol. 17 , No. 9, 1978 Evgeny Shustorovichtype, IF7,has been reliably identifiedS3Th e latter is easilyunderstood, as t he hypervalent central atom A using only nsand np orbitals can hardly hold seven ligands.253. Relative Strengths of Axial and Equatorial Bonds. Asa criterion of th e E-L bond stren gth, we choose th e overlappopulation32

(53)wN( E-L) = 4 C C ~ , C ~ L S ~ Li mor

occN(E-L) = )&(E-L) = CCC~~C~LS~L54)i mMere cim and ciLstan d for coefficients in th e canonical CT M O+i

+i = C C i m X m + CciLcL ( 5 5 )m Lreferring to a given irreducible representation, the xm re A O son the central a tom E, and Sm L (x,,(uL).In cases when, within a given irreducible representation, th enumber of unoccupied MOs qj s less than th at of occupiedMOs + i , it is more convenient to use th e right part of theidentity (see below)

OCC unocci iC C i m C i L = - C CjmCjL (56)

W e shall consider separately t he s, p, and d contributionsto the strength s of E-Lax and E-L,, bonds. W e shall beginwith the p contribution because it is of greatest importancein hypervalent complexes AL, and ties in directly with th eprevious discussion of the energy splitting of the ligand gr ouporbitals.(a) The p Contribution. In all the complexes EL m he porbital contribution to the overlap populations are [cf. (48)]Nq(P) = ef(2/r)1/2Sp, (57)

N,,(P) = cd(Y2)1/2Spo ( 58 )and [cf. (47)]

In th e 0, case 2J r = ] I 2 , o axial and equatorial bonds ar eequivalent and th e MOs e(x), e(y), a nd a2/(z) ar e degen -erate. The ratio l i p ) of these overlap populations may bewritten as in (59), which identically equals 1 in the EL6 Oh

(47)+ ( P J = ep, +

f( : ) 1 2 [ ~ 3 + u4 cos w + ...+ C T ~ + ~os (r - l)w (48)

( q 2 ( q( r + 2) + ff 4 + ..*+ r + 2 ) ] (49)or

(T3 + ff 4 + ... + T , + 2 ) ] (49)$(dx2~y2)= ld,2~~2 m ( )12[CT3 + u$cos 2w + ... +

ur+2 os 2(r - l ) ~ ]50)Her e (46), (46) and (49), (49) refer to ( l l ) , (14) and (12),(15) , respectively; for (48) an d (50) there exist the relevantcounterparts of these doubly degenerate sets [+(py) and +(dxy),respectively]; and for all these M O s (46)-(50) we accept therelations (39)-(45). As the A O s d,, and dyzare n ot involvedin the formation of u bonds in an y bipyramid al complex EL,,the results obtained below will be t he s ame for do-d4 ML,cases.Th e only serious deviation from this M O scheme (46)-(50)arises in the TB D3* ML 5 case wh ere some d istinct pxd,z- 2(p,d,) mixi ng can exis t. S o, instead o ff ou r MOs +(p,$,$*(p,), $(dx2-p), $ * (d ,2 ~ ~ ~ )(48) and (50) and their anti-bonding counterparts], we have three MOs of the type+,(Px*dx2-y2)= CZP + gldX2-yZ +

ht( 5)12(cr3 - Y2u4- 1/g5) (51.i)where th e coefficients c,, g,, h , (i = 1, 2, 3) a re defined bysome variation procedure. For the d0-d4 M L, or AL5 cases,only M O qI (p x, +2) (51.1) will be filled. Because the majorcontribution to bonding is provided by th e ( n- l)d orbita lsin transition-metal complexes or the np orbitals in main-groupcom plexes, we can rep lace $ l(px, dG-y2) (51.1 ) by +(d2-y2) (50)in M L5 and by $(p,) (48) in AL5 (see below). In the dS-dM L 5 cases we have to fill +2(px, dX292) (51.2) also, SO thepopulation q2 of the ligand group orbital e

9 2 = h12 + h2/2 = 1 - h32 ( 5 2 )will be less than 1 and the magnitude of h i 2 = 1 - q2 > 0 maybe of impo rtanc e for a numbe r of consequences (see below).T h e TB EL5 D3h complexes are very common for bothmain-group elements A an d transition-metal atom s M. TheD3 hdo-d1ML , complexes exist only in the gas phase.30 In th esolid sta te the do-di M L, complexes dimerize or polymerizeto reach hexa (or higher) coordination around th e central atom,so T B d XM L5 D3,, complexes are more common for 7 I I10 (see references in ref 9 ).The PB EL7 D5hcomplexes are most typical of (n - 1) d o d 4transition m etalsi0 and only one nontransition complex of this

(59)case (efand EL7 cases.cd , r = 4) bu t requires some analysis for the EL ,Using (44 ), (47), and (48), we find

112 > 1 for TB ( I = 3)


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Axial and Equatorial Bonds in TB and P B Complexes= 1 for Oh ( r = 4 ) ( 6 5 )< 1 for PB ( r = 5 ) ( 6 6 )

where pp0= ( p z l ~ u l ) ( p x l ~ u 3 ) .etting ap- ai(P)= Aai(P)and introducing the parameteryi = Aa, * ) / p , , ( 67 )

we have

or

From the energies (20 ) , (24 ) an d (32 ) , (33 ) and the relations( 6 4 ) , ( 6 6 ) we havefor TB (aax(p)I (aq(p)I, ap- aax(p)> ap- ae9(p) ( 7 0 )

IPaxpI > IPeq(p)I ( 7 1 )IPax(P)I< IPeq(p)I ( 7 3 )

for PB laax(P)l< I a q (P)J , ap- yax(!) < ap- e q ( p ) ( 7 2 )So there is a tendency for fa, and skg to be approxim ately equalto each other, and therefore for qualitative estimates (seeSection 4 and especially the subsequent paper24)we shall usethe relations

c x , d =f, cd = ef ( 7 4 )Iaax(P) C Y p I l e q for PB ( 7 7 )

But in principle lax rq and as we usually havethe typical relations will be

By the way, using the expressions (41) and (42) an d ( 6 2 )and( 6 3 ) , we can predict t hat in A Lj and AL-, complexes thebonding (filled) M O s a and e must be very close in energyand even interchangeable. Actually, in the ab initio calcu-lations on PH5ISasbhe M O e lies slightly lower than the M Oa c , but the two are inverted in the E HM calculationson PHs,8the ene rgy difference being 0.4-0.7 eV. The same inversionwith the same energy difference takes place for the ab initio18and EH M calculations on PF5. Moreover, in the samemulti-STO-Huckel calculations on PF , and P C1s33 lies 0.1e V low er tha n a in PF5but 0.6 eV higher in PCls. Accordingto the E HM calculations, el lies 0.5 eV lower than a in IF7.19In the PE spectra of PFj and PC15,33 he only exp erimen talresults available, the energies of a; and e are not distin-guishable.If we neglect the difference aax(P) aqQ(P)s compared withap- alL, Le., we accept34AaaX(P) = Aaeq(P)= A d ) = (ap aL(

Ya x = Y e q = Y(75)( 7 8 )

we immediately obtain1

2 y 2 / 4 + 4cd = ( ( 7 9 )

Inorganic Chemistry, Vol. 17 , No. 9, 978 2653cd > ef , c > e , d f for PB ( 8 2 )

for TB ( r = 3 ) ( 8 3 )= 1 fo r 0, r = 4) (84)= ( 1 -&y2 for PB ( r = 5 ) (85)

As y2> 0, we have [cf. (81), ( 8 2 ) ,an d ( 5 9 ) ] the followingmain inequalities:1 < f l p ) < 4 / 3 ) / 2 = 1.15 for TB ( 8 6 )0.89 = (YS) l2< T(p)< 1 for PB ( 8 7 )

Thus, the p-orbital contribution will cause the relativestrengthening of equatorial bonds in the TB case and axialbonds in th e PB c ase in the ranges defined by the inequalities( 8 6 ) and ( 8 7 ) . 3 4It is obvious from th e st ructu re of y ( 6 7 ) and the relations(83) and ( 8 5 ) hat this inequivalence of axial an d equatorialbonds will rapidly disappear with an increase in Aa(P) ( 7 5 9 ,Le., an increa se in the elec tronegativity difference of th e cent ralatom and ligand. We can expect the equalization of all E-Lbonds, i.e., the decrease of the relevant ratios A R I R , alongthe series SbC15> SnCL- > (InC152-)> CdClS3- r PPh5 >PC15> P( O Ph ) j > PF, in agreement with experiment (Table11). We shall discuss them in more detail a fter considerationof the s contribution to relative bond strengths.(b ) The s Contribution. In order to est imate the s con-tribution we can first neglect sd,z mixing, especially for hy-pervalent AL, complexes. An accu rate solution of the relevantsecular equation for the A l representation would produce th eMOs in (88), where k = 1, 2 , an d 3 and the normalizing$k(kal) = aks + -(al + o2+ ... + u , +~ )+LNhcoefficients ak, bk, ck, Nb, Nc,ax,nd Nc.mare defined by somevariational procedure. Depending on-th e sign of the su m P[cf. (5611

P = a l f c l f+ a2/c2/ = -a3/c3 ( 8 9 )the axial bonds will be stabilized if P > 0 or destabilized ifP < 0 (all the products akbkgivean isotropic contribution).We shall simulate the structure of $k(kal) [88] by per-turbing the initial set

(a1 + ~2 + ... + ~ , + 2 ) (46)( r + 2 ) / *q l ( 1 a l f )= as +

a( r + 2) / 2$3 (3a l ) = bs - ( U I + ~2 + ... + ur+2) ( 9 0 )

the set correspond ing to the isotropic s contribution which wasobtained by neglecting all the overlap integrals Si (u i ( o j ) ,i # j , n the interaction of the s orbital with the ligand group


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% - e (r + 2)2p, O( r + 2)12p, ~ ( 1 ) H d$i j>0 HdPij) a(2)-

Evgeny Shustorovich

= 0

where a an d b are taken from (46) and (so), E23 s the excitingenergy from the M O $2 (12) to $3 (90), and

= 2pcis + b t r - P t r - 2Pcis fo r EL6 Oh (93)= 3P,i, ptr - 2pe,(w)- 2p,,(zw) for EL-, D5h (94)

ln t he EL6 Oh case we obtain th e trivial result H I 2E 0. Inother cases the sign of H I 2 depends, in principle, on themagnitudes of pip But, as we have already said, Pcisdominatesin EL5 while does in EL7. Thus H 1 2< 0 in the TBcomplexes, but H12> 0 in the PB ones. This conclusion isconfirmed by numerical estimations of H 1 2 f we approximatepij as Pi j = -(const JRij see Appendix, Table VI). As r , ab,and E 23 re positive, the sign of P coincides with t he sign ofH12.W e are led to the conclusion that the s contribution willcause the axial bonds to be relatively weakened in t he E L5 casebut s trengthened in the EL7 case. Therefore the ratios T()will beN (S) > 1 for T B EL 5 (92)SI = eqNax(S)

1 fo r Oh EL6 (93)< 1 for PB EL7 (94)which qualitatively are the same as for the p contribution [cf.(83)-(87)1.It is easy to show that the MOs &(2a,) obtain ed fro m

[here E 1 2> 0 is the excitation energy from the M O (46) tothe MO (12 )]. Th us the nodal structur es of $(2al) will be(97)

(98)

$(2al) = s - uax+ ueq for TB EL 5$(2al) = s + u,, - ueq for PB EL-,but

which is confirmed by the results of quantitative calculationson AL58915,18ndThe perturbation ap proach may be applied to nny three-orbit al, four-electron case,23 n particu lar, to th e analysis ofthe MOs in any thre e-atom molecules or fragments L-E-L

*I$ 1 *I

A AL, L, A AL, L A AL, L,( i ) ( i ) ( i i i )

Figure 3. Energy splitting of the a, MOs in the TB AL 5complexes.It is shown why EZ3 ecreases as the difference in energy as aLdecreases. The cases (i), (ii), an d (iii) correspond to typical situationsin HgClS3-, FS,and PCI5, espectively. See the text for designationsof the MOs.where every atom h as one valence orbital (of u or T type). Bydefinition the first M O has no nodes and thus is entirelybonding

$1 = XE + XL + X Lwhile the second MO must have one node. However, th eproblem is where this node is located, in the E-L or E-Lregion, which correspond respectively to the MOs

$2() = XE - XL + X L (97)$2(2) = X E + XL - X L (98)

This nodal distribution determines the relative strength of theE-L and E-L bonds and is on e of the decisive factors in t hetheory of the mutual influence of ligands.2,22Th e perturbationapp toa ch permits the nodal distribution (97) an d (98) to befound qu ite reliably.23 It is of imp ortance because until nowthe relationships like (97) an d (98) have not been explainedqualitatively in an unequivocal way. For example, it istempting to explain the energetic preference of the nodalstructure (97) over (98) in T B AL5 complexes by th e fact th at(97) corresponds to three bonding (equ atorial) vs. tw o anti-bonding (axial) interactions . However, from (12)

I . I(99)

so that in the A L5 case ~ c a , / c e q ~3 / 2 [cf. Appendix, (142)]which exactly compensates the above ratio of the numbers ofbonding and antibonding interactions. Th e main weakness ofthe above argument is that it would lead to the incorrectconclusion tha t the same nodal structure (97) occurs in th ePB AL7 case.The usefulness of the relation (91) is that it permits therelative changes in the s overlap populations an d s charactersof A-Lax and A-Le, bonds to be predicted. Th e numericalvalue of the parameter a b / E z 3 n (91) will increase as abincreases and the energy gap E23 decreases. As seen fromFigure 3, this ga p will be less th e lower the energy of th e sorbital relative to the grou p ligand orbitals. Thoug h theproduct ab may be cha nged in a nonmonoton ical way whileth e s orbi tal energy decreased along th e series (i)-(ii)-(iii) inFigure 3, these changes in ab are insignificant compared withchanges in E23.This consequence of (91) is confirmed by the EHM cal-culations on PF, and PC15.16 Th e employed para meters (ap3,= -20.20, aFZp -20.86, = -15.3 eV) correspond to th ecases (ii) and (iii) in Figure 3, and the s chara cters of P-Laxand P-Le, bonds have been found to be 19. 4 and 20.4% forPF5and 11.7 and 25.5% for PCl,. Th e drastic increase in theP 3s character in equatorial as compared w ith axial bonds is


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Axial and Equatorial B onds in TB and PB ComplexesTable 11. Bond Lengths (A ) of Some TB AL, a nd ML,(n - )d lo Complexes

phys R(E- R(E- AR(ax-complex state La&" Le&" eq) ARIR,, refPF, g 1.58 1.53 0.04 0.03 aP(OPh), c 1.66 1.60 0.06 0.04 bPP h, c 1.99 1.85 0.14 0.07 dAsF, g 1.71 1.65 0.06 0.03 eSbCl, c 2.34 2.29 0.05 0.02 fSnC1,- c 2.38 2.36 0.02 0.01 gHgCl, 3- c 252 2.64 -0.12 -0.05 i

a K.W. Hansen and L. S. Bartell , Znorg. Chem., 4, 775 (1965).R. Sarma, F. Ramirez, B. McKeever, J. F. Marecek, and S. Lee,.lm. Chem. Soc., 98 , 581 (1976).Bartell , J . Mol. Struct., 8, 23 (1971). P. . Wheat ley, J . Chem.Soc., 2206 (1964). e F.B. Clippard, Jr., and L. S. Bartell , Inorg.a e m . , 9, 805 (1970). S.M. Ohlberg, J. Am. g e m . Soc., 81,811 (1959). g Reference 35. Reference 36. Reference 37.

PCI, g 2.12 2.02 0.10 0.05 c

CdCl, 3- c 2.53 2.56 -0.03 -0.01 h

W. J. Adams and L. S .

the main reason for the increase of the total ratio N e S/ N a xwhich (with out 3d orbitals of the P ato m) has been found tobe 1.08 for PF, and 1.55 for PCl,.Finally , the relatio nship (91) perm its the influence of stericeffects to be included. As P s a function of @!j which rapidlydecreases (in absolute value) with increasing interliganddistances , one can expect tha t, other conditions being equal,the relative equatorial strengthening will be larger the smallerthe bond length R(A-L).Qualitativ e similarity of the s and p contributions permitsthe ARIR,, regularities in AL, complexes to be explained.Th e simplest regularity con cerns AL5 complexes when we fixan atom A, its s orbital being at the same energy as the aorbital of some initial ligand L. In the AL; series where donorability of the ligand L' increases (and bond lengths do notchange greatly) both s and p contributions t o the relativeequato rial streng thenin g will increase monotonically, increasingARIR,,. Th e series PL, where L = F, O Ph, C1, and Ph is justsuch a case (see Table 11).

If L is fixed as A varies along a g roup of the periodic table,values of ARIR should decrea se (by the inverse of t he previousargument), but possible nonmonotonic changes in the s an dp contributions may complicate the trend in question. Twopairs of com plexes PF, and AsF5 and PC15 and SbC15 (seeTable 11) are good illustrations. In the form er case the valuesof ARIR are practically the same; in the latter case thedecrease of A Rl R is quite obvious.However complicated the regularities of AR /R prove to be,the s and p contributions can result only in a relative weakeningof axial bonds, though for strong donor central atoms thisweakening must be very small as, for example, in S r ~ C l y . ~ ~Two TB AL, complexes, CdC153-36 nd HgC153-,37re knownat p resent where axial bonds are shorter than equatorial ones,so we have to look for the source of this reversal.In PB AL 7 complexes we can predict the relativestrengthening of axial bonds with similar regularities to theTB AL, case (but of opposite sign). Unfortunately, reliablestructural d ata are known only for IF7 where indeed the I-Faxlength is much sh orter than the I-F one (AR -0.072 A3I) .(c ) T h e d Contribution. (i) T h e T n - l )dIo Case. On th ebasis of E H M calculations Hoffmann, Muetterties, et aL9J0have done an excellent analysis of relative bond strength s andsite preferences in transitio n-met alcomplexes ML Z and ML7I0as a function of dx electronic configuration of the cen tral atom.We shall show that our model leads to the same qualitativeresults, but first we want to examine a special subclass ofcomplexes, ( n - l)d Io ML5 , which previously9 has beenconsidered exactly the same as the AL 5 case. As in theformally isoelectronic AL, case, to a first approximation, the

Inorganic Chemistry, Vol. 17, No. 9, 1978 2655hypervalent s chemez5 can be adopted for ( n - l ) d I o M L5complexes with ns and np orbitals responsible for bonding. Incontras t to AL 5, however, the ax ial bonds are sh orter, e.g., AR= -0.03 in CdC153-36 nd -0.12 A in HgC153-.37 To ourknowledge, no theoretical model or calculation has explainedthis ~ h o r t e n i n g . ~ ~s shown above, the s and p contributionscan lead only to relative strengthening of axial bonds in anyTB comp lex, though in the cases of the CdClS3- nd HgC1,3-this strengthening must be minimal.

Le t us try to estima te the influence of filled ( n- )dl o shells.In neutral AL, complexes with A belonging to the end groupsof the periodic table, the central ato m has either no (n- ) dorbitals at all (Si, P, S , etc.) -or very de eply ly ing ( n - l )dIoorbitals (As, Sb, Sn, Sb, et^.).^^ It is another story for thebeginning group elements, especially for such 2B elements asCd or Hg. For example, the energy difference between 6s and5d atomic orbitals in gaseous Hg equals only ca. 5 eV.40Certainly this difference will be smaller in anionic complexeslike HgC153-.Let us consider the perturbation interaction of filled (n -1)d or bitals of al'(d2,2) and e'(d2X2-y2,d2,) sym met ries with therelevant MO's $(SI, $*(s) and $(P,), $*(P,) [see (39 ), (401,(46), and (48)]; AE,, I E, corresponds to the excitationenergies from ( n - l)d2,2 to $*(s) and from ( n - l)d2x2-y2 o$*(px), respectively. As we consider only a bonds A-L, allthe relevant matrix elements should be expressed in terms of@do = .-lconstlSd,. Th is can be perform ed by using theexpansions41 omitting non-a omponents) of (100) and (101),

dZ2= d,,z(cos2 w - v2sin2 w) + ... (100)3112d,2~~2 dZ,2- sin2 w + .,. (101)2

where w is the angle between axis z an d z' (in the x z plane)and the z' axis is the axis of the A-L a bond.After the relevant transformations, we obtain , as a first-orderperturbation, the ( n - l)d lo orbital contribution to N(A-L,,)and N(A-L,)(1 02)S2 d c a2AN(A-La,) = Jconstl- -0 AE,,AN(A-Le,) = Iconst\-2du( -5c 2 --.) (103)20 AEeq

The first (positive) term in (103) is defined by the dZxZ-contribution. a an d c = e (74) are the coefficients from theMO's (46) and (48). Since AE,, 5 AE, (see above), we find,as a condition for relative axial strengthening, AN(A-La,) >AN(A-L,,), that

contribution and the second (negative) term by the di2

a > 5 I l 2 c (104)Let us emphasize that the inequality (104) reflects the ( n- l)d Io contribution to the bond strength via the algebraiccoeffici ents of s an d p orbitals in the relevant M O of an AL,complex. For strongly donor atoms like Cd and Hg wherevalence p orbitals lie rather high (they ar e even vacant in theneutral atom ground state), the condition (104) looks rea-sonable?2 For th e usual electronegativeatoms A, where AEaxand AE are large, the relative axial strengthening due to th e

(103)] and can not overcome the relative equatorialstrengthening due to the ns an d np contributions.So it is worthw hile to distingu ish the ( n - l)d lo ML, casesfrom the ndo AL, cases. We shall includ e in the former classatoms M of the beginning groups of the periodic table (CUI,Hg", Cd", etc.) and in the latter class atom s A of the middle

( n- )d fb contrib ution must be extremely small [cf. (102) and


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2656 Inorganic Chemistry, Vol. 17, No. 9, I978and end groups (SnV (Sn-), Pv, IV", etc.).In the AL7D5 hPB case the contribution of ( n- l )d loshellsincludes only the ( n - l)d2,z contribution because (n - 1)d2x 2_~ d2, nteract with t he filled ligand group orbitals withinthe irreducib le representation e2/ (remember th at th e influenceof ( n - l)d2,2_y~d2xyrbitals in the AL 5 D3hT B case is definedby the presence of vacant antibonding orbitals within the e'representation to which px, d+,2, py, and d, belong). Afterthe relevant transformations we obtain

Evgeny ShustorovichTable 111. Bond Lengths (A ) in Some PB AL,and ML, Comple xes

phys R(E- R(E- A R ( ~ x -complex dX s t a te Lax)av Leq)av eq) refIF7 ndo g 1.78, 1.85, -0.07 QZ r F ,3 - ( n - l ) d o c 2.00 2.03 -0.03 dV(CI\T),,' (n - l ) d 2 c 2.14, 2.14, -0.0 eReference 31. Reference 45. ' nly the mean Re-F dis-ReF, ( n - l )d o g -0.06' b

tance is given (1.835 k 0.001 A). The uncertainty in the equatori -al -axial di fference is o n the order of 0.02 A .J. C. Taylor, Ac ta Crystal logr. , Sect. B, 26, 17, 2136 (1970).e R. A. Levenson and R. L. R. Towns, Inorg. Chem., 13 , 1 0 5(1974).

H. J. Hurs t and2 d o u2ANax= -Iconst/--- -4 AE,,A N , = Iconstl- __28 AE, ,S 2 d a U 2Le., contrary to th e ALS D3hTB case, (n- )d2,2 will destabilizeaxial bonds and stabilize equatorial ones. Thu s the ns , np, an d( n- 1)d'O contributions ar e always of opposite sign. Again,for atoms in the last groups of the periodic table, LEaxs very!arge, so it is not surprising that in IF7axial bonds prove tobe distinctly shorter th an eq uatorial ones (as discussed above).A t the sa me time we might predict tha t in anionic complexesof the AL7"- type (if such can be made) t he ( n - l)dl o con-tribution may become remarkable and AR will be smaller inabsolute value, perhaps changing sign as compared with ARin IF7 (cf. SnC15- and HgC153-).(ii) The ( n - l ) d x Case. Now we turn to the ( n - l ) dcontribution in transition-metal complexes M L5 an d ML,. Ourarguments will be rather similar to those used earlier to es-timate the p contribution. The only substantial complicationis that the dZ2orbital contributes to both axial and equatorialbonds [a fact already used to obtain the relations (102) and(103) and (105) and (1 06)l. Further, we can use two formsof MO's including the dZzorbitals, namely (49) or (49'), thelatt er being preferable. Takin g into account (16 ), (49'). ( 5 0 ) ,(l oo ), and (101) an d introducing the obvious designations, weobtain

Table IV. x Cont r ibu t ion t o f i x ) n Complexes EL,

Im( $)1'2)S'dc for M L5 and ML, (108)

= ( g h ( &)'" + lm ( $ ) 1 ' 2 ) s d ofor. M L6 Oh ( 1 09)

for M L5 a nd M L7 (1 10 )= j / d + - ( - l h r )m 3(r + 8 ) l" = 1

gh

(In th e Oh case ( 1 13) becomes (3''*/2)pd,, so that ( r + 8)'i2/2

complex T ( S ) T(P) f i s+p ) a $d) re fT B E L , D3h >1 1.0-1.15 >1 -1.5 this work1.14 1 .13 1 .13 b1.12 1 .04 C1.06 d1.08 e1.16 1.79, f1 . 1 7 g

1.22 h1.23 i1.25 i1.37" k1 . 5 P 1P B E L , D ,h


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Axial and Eq uatorial Bonds in TB and PB Complexes

= 1.56 for TB ( r = 3) (115)= 1.32 for PB ( r = 5) (116)

so tha tI m / g h < 1 (117)and, from (1 lo),

N (4eqf i d ) =- 1.42 for TB ( r = 3) (118)Na,(d) < 1.24 for PB ( r = 5) (119)Using (49) instead of (49) leads, in the same way, to

an dN (d)eqf l d ) =- 1.62 for TB (I = 3) (118)

< 1.16 for PB ( r = 5) (119)From Figure 2 and discussion above it appears that Im and

N*,(d)

gh will be close, especially in the ML, case, Le.g = I, h = m, Im i= gh (74)

which is similar to the relations (74) [see also ref 34bl.So , neglecting the complications connected with the sdZ2mixing (in particular, the M O cpl (1 1) gives some additionalcontribution to Fd) f the opposite signs for ML 5 and ML 7),we obtain the following approximate ranges:

for TB ML 5 do-d4 fld)= 1.5 (1 20)for PB ML 7 do-d4 fid)= 1.2 (121)

Thu s, in the M L5 do-d4 complexes the d contribution is of thesame sign as that of the s and p contribution, so axial bondsmust be weaker tha n equato rial ones.Unfortunately, the known stru ctura l (electron diffraction)data30 are not accur ate enough to determi ne the difference inaxial and eq uato rial bonds, though this difference can reach0.1 a rath er large value even compared to the AL 5 D3hcomplexes (cf. Table 11). But our conclusion agrees with theresults of quantitative calculation^^^^^^^^^^^ (cf. also Table IV).In the ML5 D3h d8 cases the vacant hybrid orbital (51.3)is entirely antibonding, the coefficient c3before the px orbitalbeing much larger than g3before the dXz+ orbitals9 Thus thedX2_y2d,) contrib ution to fld)may be neglected, but f l p )changes insignificantly. So, taking into account only the ( n- )d,2 contribution to fid), e obtain, from (1 10) and (1 lo),the approximate range

for TB ML5 d8 7fd)= 0.25-0.33 (120)This drastic decrease in Fd) an result in the relativestrengthening of axial bonds.52 Actually, in all of th e knownTB ML 5 d8 complexes, axial bonds are either th e sam e [e.g.,Pt(SnC13)53-] or sho rter (see ref 9 and references therein).

Inorganic Chemistry, Vol. 17 , No . 9, 1978 2657On the contrary, in ML 7DSh B complexes (the d0-d 4case)the d contribution is of the opposite sign as tha t of the s andp contribution, so we can expect, as a rule, substantialequalizing of all the bonds. Actually, in all known M L7 D5hcomplexes the differences in bond lengths are insignificant(Table 111).Th e opposing contributions a re clearly reflected in calcu-lations on a typical complex do-d4 ML 7 Dshlowhere overlappopulations of the M-Lax and M-L, bonds differ hard ly at

all (0.55 and 0.52, respectively). Th e small differences in totalenergies of different polyh edra ML710and a suggestion of thed-orbital contribution of R e atom as th e main reason for asubstantial difference in the hard ness of D5hpolyhedra ReF,vs. also agree with our results.Our estimates for the fix) ranges a re summarized in TableIV and compared with published calculations. Agreemen tamong them is quite satisfactory.34b4. Relative Stability of Axial and Equatorial Isomers.Nonequivalency of axial and equ atori al positions in EL 5 TBand EL7 PB complexes raises the question of which positionsshould be preferable upon substitution of a ligand L by a givenligan d L. For clarity let us accept that L is a stronger donorligand than L, i.e.( u L J I H ~ u L ~ ) (aLIHlaL) = 6a > 0 (122)and consider this change in the diagonal m atrix element asa perturbation. To determine which isomer-axial orequatorial-should be more stabl e we have to find the dif-ference in total energies of the two isomers

occ OCCAEax-eq = E B x - Eeq = 2(Eel,ax - CE1,eq) (123)

I 1

Thus, AEBx-eq> 0 ( 0 (122), E> 0 ( > f > (127)and we can neglect small nd admixtures, simply assuming h= 1 an d g = 0. In AL, cases there is no sd,z mixing and t hes contribution will be considered to be isotropic.In transition-metal complexes the situation is more com-plicated. First, in the inequality

f > > b > h (128)we can neglect no coefficients. Second, sdZ2mixing forces usto check the results of both orthogonalization schemes for theal group ligand orbitals. Thus, for ML, complexes we shall


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2658 Inorganic Chemistry, Vol. 17, No. 9, 1978give two values of E (12 6), for MOs ( l l ) , (12) and (14), (15),which we shall name E(s) an d E(d,z), respectively. Th ird ,in t he ML 5 TB case we have to take into acco unt pXdXz_,z(p,d.+,) mixin g, Le., to consi der th e MO s (51.1) and therelationship (52) where

hi < h (1 29 )h < f < q < l (130)

but

Wi th all this w e obtain t he following expressions for E.(a) The TB EL5 Case.(1 ) AL5 ndo

E = y3(l -f2) e 2 /3 > 0 (131)This result illustrates the well-known Muetterties rule20concerning the preference for equatorial substitution bystron ger donor ligands. Moreover, from (1 3 1) and (1 26) wecan predict that this preference will increase as the differencein electronegativities of L a nd L increases (ba increases) an dth e difference in electronegativities of A an d L decreases (eincreases); i.e., for a given L th e donor ability of A decreases.Unfortun ately, there is no relevant experimental data .

(2) ML5 ( n - l)do-d4E(s) = 2 - h2 > 0 (1 32)

E(d,z) = f 2 - 7/33b2- 26/33h2> 0 (132)Equatorial substitution is always preferable which reflects thefact that a ll the p) 1.(3 ) M L j ( n - l)d*

E(s) = f 2 + y3h2 - y33a2 < 0 (133)(133)(d,z) = f 2 - 7/33b2+ 6/11h2-4/3v2 < 0

Axial substitution is always preferable.(4 ) M L j (n - 1)d

E(s) =f + y3- y3q2< or > O (134)E(d,z) = f2 Yl1 - Y3q2< or > 0 (134)

This uncertainty in the signs of E reflects the fact thatequatorial bonds may be stronger or weaker than axial bondsdepending upon the values of the coefficientsf an d 7 [cf. theinequality (104)] .(b ) The Oh EL6 Case. For any d configuration and anycentral atom (A or M ) we have the trivial identityE(s) = E(dZz) = 0 (135)

For example, in th e M L6 do case

Evgeny ShustorovichE(dZz) = f 2 / 5 -b 9/130b2- )/65h2< or > 0 (137)

This case is t he only one where t he site preference dependson t he details of sdzz mixing because fl)< 1 and 0.9 < PP)< 1 (87), but Pd) 1.2 (121).All the above results are summarized in Table V.Th e site preference expressed in terms of the bond or totalenergy differences E (126) exactly corresponds to th at in termsof bond polarities. In an unsubstituted complex EL, theeffective charges of the axial ligand L, ( 4 ) and equatorialligand L3 (q3) will be

occq1 = 1 - 2CC2ilq3 = 1 - 2C c 2 , 3

(138)(139)

iW C

iwhere Ci k stands for the coefficient of the C7k orbital in theoccupied LCAO MO There fore the difference in effectivecharges of the axial L, a nd equatorial L3 igands will be equ alto th e negative of E (126), namely

(c) The PB EL7 Case.(1) A L7 ndo

E = y5U2 1) = -e2/5 < 0 (136)This result is quite opposite to that in the AL 5 case (131). Th erelevant interpretation is analagous to that given for the AL 5series (see above) if we replace the word donor byacceptor.(2 ) M L ~n - i)do-d4

E ( s ) = f 2 / 5 - h2/5 > 0 (137)

Consequently, q < 0 (>O) means not only that the axial(equatorial) ligand is more electronegative but also that theequa torial (axial) bond is stronger. This relation easily explainswhy site preferences may be predicted in terms of bond polarityas is usually donee4Caution m ust be exercised, however. It is obvious that th eequation (140) can hold only as long as a bond strength isdefined by its covalency. Wi th significant Made lung cor-rections, as in the case of strongly polar hypervalent main-grou p complexes, the correspondence between bond p olarityand bond strength may not be clear a t all.48 In addition , wewant to stress that the two criteria only need coincide whenth e s, p, and d contributions to the relative bond stren gth ar eof the s ame sign, as in the T B ALs, ML 5 do-d4, or P B AL7cases. Otherwise the two criteria may lead to differentconclusions.A perfect ex amp le exists in the PB M L, do-d4 complexeswhere fi)< 1, PF) 1, but fld)> 1. Quantitative calcu-lations have shownO that less polar equatorial bonds havesmaller overlap population than more polar axial bonds.According to the bond strength criterion, a stronger donorligand L should prefer the axial position, but, according tothe bond polarity criterion, the equato rial position. In principlethe first criterion is more general because it reflects the relativetherm odyn amic stability of the isomers. Th e second criterionmay do minate in the kinetics of th e substitution reaction bu t,if there ar e no serious obstacles to interligand exchan ge, Le.,the interconversion b arrier is not very high, the more stabl eisomer must be formed. While in both known examples ofsubst i tu ted ML7 c ~ m p l e x e s - - - O s H ~ ( P R ~ ) ~ ~ ~nd hH5-(PR3)250-the stron ger don or ligand, hydrogen, occupiesequatorial positions (in agreement with the bond polaritycriterioni0) his may just be a result of steric repulsion of thebulky PR 3 igands. Futur e experimental and computationaldat a should answer this new question: which of the two criteriais more general?ConclusionW e see that ou r analytical LCAO M O approach allows theseparate s, p, and d contributions to relative bond strengthsto be obtained in explicit form. In particular, our approachis able to take into account th e anisotropy of th e s contributionan d to estima te som e effec ts of sdZz nd pxd,z-9 (p,d,,! mixing(which other qualitative models failed to do). Th e main resultsof our work ar e given in Tab les 1V and V. We see that the


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Axial and Equatorial Bonds in TB and PB ComplexesTable VI. Values of HlZa>

ncomolex 1 2 3

1.20 7 0.750 0.479-0 .134 -0.254 -0 .341EL,EL ,See t he express ion (92) for EL, and (94) f or EL,. All thevalues o f H , , h a v e to be mul t ipl ied b y [ ( r + 2)/ (2r)12]R-, whereR is the E-L bond length.

Table VII. Parameters Employed in EHM Calculationsatom orbi tal -Hii, eV Sla te r expon ent

A 3s 20.0 1.833P 11.0 1.83H 1s 13.6 1.30L 3s 15.0 1.30Table VIII. Overlap Populat ionsN,,(X) a n d N,,(x) in TB AL,

Y 3s 3a 3s + 30 (total )N,,(X) 0.134 0.220 0.3 54Na,(X) 0.117 0.195 0.312T ( X ) 1.14a 1 .13b 1 .13

a Cf. the inequal i ty (92). Cf. th e inequal i ty (86).ns and np contributions in T B E LS complexes are alwaysopposite to those in PB EL, complexes. Furth er, in th e TBML, case the (n - l) d contr ibution can greatly strengthenthose of ns and np, but in the PB M L7 case the (n - l ) dcont ribut ion always opposes those of ns and np. Ou r resultsagree with the known experimental and computational trends.Moreover, a number of results have been obtained for the firsttime, for instance the explanation of axial strength ening inCdClS3- nd HgClS3-, he prediction of possible axial weak-ening in AL,*- com plexes, and the prediction of the relativestability of isomers in the AL, series depending on the na tur eof A and L.

Acknowledgment. Th e auth or is most grateful to ProfessorR. Hoffm ann for numerous stimulating discussions and readingthe manuscript. Th e author would like to thank Professor E.L. Muetterties for valuable comments and for pointing out anum ber of key references. Professor P. Dobosh is greatlyacknowledged for editing of the manuscript and many illu-minating corrections. Finally, the author is grateful to E.Kronman for the typing and J. Scriber for the drawings. Thisresearch was generously supported by the National ScienceFoundation through Research G rant C H E 76-06099.AppendixTab le VI illustrates different signs of the s contributions tothe relative axial and equatorial bond strengths in EL, andEL 7 complexes.In order to illustrate some model conclusions we performedEHM49 alculations on TB complexes ALS and AL4H. T heparameters employed are given in Table VII.Th e central atom A is considered to be a typical atom ofthe third period; the ligand L som e 3s u igand of th e C1 type;for ligand H the standard parameters have been taken.9,s1Theinternuclear distances are R(A-La,) = R(A-L,) = 2.05 Aand R(A-H) = 1.35 A. For off-diagonal matrix elements therelationship Hll = 1.75S,l(H1,+ H,,) has been used.Th e overlap populations in AL, are given in Table VIII.The la l and 2a l MOs are found to be

$(lal) = 0.61s + 0.243(ul + u2)+ 0.23,(u3 + u4 + us)$(2al) = 0.02s - 0.58(ul + uz)+ 0.38(u3 + u4 + us)

i.e., in the la l all the coefficients before bk are approximately

(141)(1 42)

Inorganic Chemistry, Vol. 17, No. 9, 1978 2659the sam e [cf. the relationship (1 l) ], the no dal structure of the2al corresponds to s - u,, + uq [cf. the relationship ( 97 ) ] an dthe ratio of the axial and equatorial coefficients -0.58:0.38= -1.52 is almost equal to the unperturbed value -1.50 [cf.the relationship ( 99 ) ] . Finally, the difference in total energyEof axial (C3J and equatorial (C isomers AL4 H is positiveand equal to 0.45 eV [cf. the relationship (13 1) from whichAE= .17 eV]. Finally, the difference in total energy Eofaxial (C3) nd equatorial (C isomers AL4 H is positive andequal to 0.45 eV [cf. the relationship (131) from which AE = 0.17 eV].References and Notes

Formerly of the N. S. Kurnakov Institute of General and InorganicChemistry, Academy of Sciences of the US SR, Moscow B-71, 11 7071,USSR.T. G. Appleton, H . C. Clark, and L. E. Manzer, Coord. Chem. Rev.,10, 335-(1973).F. R. Hurtley, Chem. Soc. Reu., 2, 163 (1973).K. B. Yatzimirsky, Pure Appl. Chem., 38 , 341 (1974).E. M. Shustorovich. M. A. Porav-Koshits, and Yu. A . Buslaev. Coord.Chem. Reu., 17, 1 (1975).R. J. Gillespie, Molecular Geometry, Van Nostrand-Reinhold, NewYork, N.Y., 1972.R. G. Pearson. Svmmetrv Rules for Chemical Reactions: Orb italTopology and Elementary Processes, Wiley, New York, N .Y., 1976.R. Hoffmann, J. M . Howell, and E. L. Muetterties, J . A m . Chem. Soc.,94. 3047 (1972).A.R. Rosk and R. Hoffmann, Znorg. Chem., 14, 365 (1975).R. Hoffmann, B. F. Beier, E. L. Muetterties, and A. R . Rossi, Znorg.Chem., 16, 511 (1977).(a) C. J. Marsden and L. S . Bartell, Znorg. Chem., 15,30 04 (1976); (b)L. S. Bartell, F. B. Clippard, and E. J. Jacob, ib id . , 15, 3009 (1976),and references therein [see especially footnote 35 in ref llb].(a) J. K. Burdett, Struct. Bonding (Berlin), 31, 67 (1976); (b) J. K.Burdett, Znorg. Chem., 15,212 (1976).(a) B. M. Gimarc, J . Am. Chem.SOC.,00, 2346 (1978); (b) B. M.Gimarc, Qualitative M olecular Orbital Theory, Chapter 4, submittedfor pu blication.N. C. Baird, J . Am. Chem. SOC.,ubmitted for publication.(a) A. Rauk, L. C. Allen, and K. Mislow, J . A m . Chem.SOC.,4,3035(1972); (b) F. Keil and W. Kutzelnigg, ibid., 97, 3623 (1975); (c) J.A. Altmann, K. Yates, and I. G. Csizmadia, ibid., 98, 1450 (1976).(a) P. C. Voorn and R. S. Drago, J . Am. Chem.SOC.,8,3255 (1966);(b) R. S. Berry, M. Tamres, C . J. Ballhausen, and H. Johansen, ActaChem. Scand., 22, 231 (1968).(a) D. P. S antry and G. A. Segal, J . Chem. Phys., 47, 158 (1967); (b)J. B. Florey and L. C. Cusachs, J . A m . Chem.SOC.,4, 3040 (1972).(a) A. Strich and A. Veillard, J . Am. Chem.SOC.,5, 5574 (1973); (b)J. M. Howell, J. R . Van Wazer, and A . R. Rossi, Znorg. Chem., 13, 1747(1974).R. L. Oakland and G. H. Duffey, J . Chem. Phys., 46, 19 (1967).(a ) E. L. Muetterties, W. Mahler, and R. Schm utzler, Znorg. Chem.,2, 613 (1963); (b) E. L. Muetterties and R . A. Schunn, Q. Reu., Chem.Soc., 20, 245 (1966), and references therein.(a ) E. M. Shustorovich, M. A . Poray-Koshits, T. S. Khodasheva, andYu . A. Buslaev, Z h . Struct. Khim., 14, 706 (1973); (b) E. M. Shus-torovich, Yu. A. Buslaev, and Yu. V. Kokunov, ibid., 13, 11 1 (1972);(c) E. M. Shustorovich, ibid., 15, 123 (1974); (d) E. M. Shustorovich,ibid.. 15.977 (1974).

1 (a) E. M. Shu storovich and Y u. A. Buslaev,Koord. Khim., 1,740 1975);(b) E. M. Shustorovich and Yu. A. Buslaev, ibid., 1, 1020 (1975); (c)E. M. Shustorovich and Yu. A. Buslaev,Znorg. Chem.,15,1142 (1976).(23) E. M. Shustorovich, J . Am. Chem. Soc., in press.(24) E. M. Shustorovich, J . A m . Chem. Soc., in press.(25) (a) J. I. Musher, Angew. Chem., Znt. Ed. Engl., 8, 54 (1969); (b) J.I. Musher, J . A m . Chem. SOC.,4, 1370 (1972); (c) J. I. Musher,Tetrahedron, 30, 1747 (1974).(26) The up-to-date calculations on complexes of Si, P, S, and Cl convincinglydemonstrate that the characteristic features of these complexes can beobtained regardless of 3d orbitals of the ce ntral atom. See for instance:(a ) Si04: J. A. Tossel, J . Am . Chem.Soc., 97,48 40 (1975). (b) PO4+,SO4*-, C104-: H. Johansen, Theor.Chim.Acta, 32, 273 (1974). ( c )PH,F>,,,: ref 15b . (d) SH 4, SH 6: G. M. Schwenzer and H. F. Schaeffer,111, J . Am. Chem. Soc., 97, 1393 (1975). and references therein. ( e )The same conclusion may be reached experimentally,e.g. from the X-rayphotoelectron data: W . L. Jolly, Coord. Chem. Rev., 13,68-70 (1974);W. B. Perry, T. F. Schaaf, and W. L. Jolly, J . Am . Chem.SOC.,7,4889(1975).(27) See, for instance, E. Heilbronner and H . Bock, The HM O-Model andits Applications. Basis and Man ipulation , Wiley, New York , N.Y.,1976: (a) p 138; (b) p 158.(28) (a) R. E. LaVilla, J . Chem. Phys., 57, 899 (1972); (b) U. Gelius, J .Electron Spectrosc., 5, 985 (1974).(29) See for instance: ( a) S. F. A. Kettle, Coord. Chem. Reu., 2, 9 (1967);(b) N. A. Pop v, Koord. Khim., 2,1 340 (1976), where there are formulasnecessary for obtaining the relationships (41)-(45).


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2660 Inorganic Chemistry, Vol. 17 , No. 9, 978(30) (a) VFS: G. . Romanov and V. P. Spiridonov, Zh. Struckt . Khim.,7,882 (1966). (b) NbBrS,TaBr5: V. P. Spiridonov and G. V. Romanov,Vestn. Mosk. Uniu., Khim., 21,109 (1966). (c) MoCI,: V. P. Spiridonovand G. V. Romanov, ibid., 22, 118 (1967). (d) NbF 5, TaF5: G. V.Romanov and V. P. Spiridonov, ibid., 23, 7 (1968). (e) N bCIS, TaCI,,WCl,: V. P. Spiridonov and G. V. Romanov, ibid., 23, 10 (1968).(31) W. J . Adams, H. B. Thompson, and L. S . Bartell, J . Chem. Phys., 53,4040 (1970).(32) For discussion of this criterion as the best measure of the covalent bondsee, for instance: ( a) E. M. Shustorovich,Koord. Khim., 2, 435 (1976);(b) ref 29b.(33) P.A. Cox, S. Evans, A. F. Or chard, N. V. Richardson, and P. . Roberts,Faraday Discuss Chem. Soc., No.54,26 (1972).(34) (a) It is obvious that the relationships (75)-(80) are more accu rate fortransition-metal as compared with main group elemen t complexes. (b)Remember that the relationships (74), (81), (82),etc. are obtained whenwe take into account only the u orbita l basis set and neglect all the overlapintegrals [cf. (1)-(7), (lo)]. At the same time the quantitative com-putatio ns on EL, complexes include both the extended basis sets (at leastthe u and a ones) and all the overlap integrals. Thus the comparisonof our model relationships among the LCAO MO coefficients withcomputed ones is not trivial (as already stressed in the Introdu ction) andrequ ires many corrections. Nevertheless, in all cases where the publishedfigures permit such corrections to be made (for instanc e, for the EHMcalculation on IF,I9) the results obtained agree with both the idea ofappr oxim ately equa l coef ficien ts for pz and p,(p,) orbita ls (74) nd theweak inequality (82). The same point sho uld be borne in mind for thed contribution.(35) R. F. Bryan, J . A m . Chem. Soc., 86, 33 (1964).(36) (a) T. V. Long, A. W. Herlinger, E. P. Epstein, and I. Bernal, Inorg.Chem. ,9, 59 (1970); (b ) E. . pstein and I. Bernal, J . Chem.Soc.

A , 3628 (1971).(37) W. Clegg, D. . Greenhalgh, and B. P. Straughan, cited in ref 12b.

Eric V. Dose and Lon J . Wilson(38) For this case the following has been written: It (the angular overlapmodel (E. SH.)) is not alone however in being unable to completelyrationalize the relative bond strengths in TB sys tems (ref 12b, 219).(39) C. E. Moore, Atomic Energy Levels, National Bureau of Stand ards ,Vol. 1-111, Wa shing ton, D.C ., 1949-1952.(40) S. Svensson, N . Martensson, E. Basilier, P. A. Malmqvist, U . Gelius,and K. Siegbahn, J . Electron Spectrosc. , 9, 1 (1976).(41) J. D. Dunitz and L. E. Orgel, J . Chem. Phys. , 23,954 (1955); . M.Shustorovich and M . E. Dyatkina, Zh . Struct. Khim., 1, 109 (1960).(42) There is some similarity between ou r explanation of axial shortening inTB HgCIs3-and th at for octahedra l complexes of Hg on the basis ofthe third-order Jahn-Teller effect [A. A. Levin and A. P. Klyagina,Koord.Khim., 3, 1154 (1977)l.(43) (a ) J. Demuynck, A. Strich, and A . Veillard, N o w . J . Chim., 1, 217(1977). b) The ab initio calculations on V F t 3 & ave given the followingoptim ized bond leng ths: V-F, = 1.76A, V-F, = 1.71 A. These maybe considered as more accurate than the experim ental values R V F

ratios N(V-F )/N(V-F,) were found to be 1.06 nd 1.12 or VFS (3d0)and VFs- (3d7, respect i~ely.4 ~~(44) J. K. Burdett, R. Hoffmann, andR . C. Fay, Inorg. Chem.,17,2553 (1978).(45) E. J. Jacob and L. S. Bartell, J . Chem. Phys. , 53, 2231 (1970).(46) The relation (124) s quite similar to that in the perturbation theory oforganic a systems (cf. ref 27b).(47) See, for instance, ref 8-10.(48) See, for instanc e, discussion in ref 22, 23, nd 32a.(49) D. W. art, T. F. Koetzle, and R . Bau, cited in ref 10.(50) R. Bau, personal communication to E. L. Muetterties.(51) R. Hoffmann, J . Chem. Phys. , 39, 1397 (1963).(52) All these predictions are confirmed by the E HM calcula tions on the modelTB ML5d8 complex FeHSS -where the values of 7), ),d),nd

were found to be 1.22, .36,0.21,nd 0.95,espectively: T . A. Albright,perqonal communication.

= R(V-F,) = 1.71A with a possible diffe renc e of0 0.1 A. -a Th e

Cont r ibu t ion f rom the D epar tm ent of Chemis t ry ,Wi l l i am Marsh Rice Univers i t y , Houston , Texas 77001

Synthesis and Electrochemical and Photoemission Properties of Mononuclear andBinuclear Ruthenium(I1) Complexes Containing 2,2-Bipyridine,2,9-Dimethyl-1,lO-phenanthroline, 2,2-Bipyrimidine, 2,2-Biimidazole, and2-Pyridinecarboxaldimine LigandsE R I C V . D O S E a n d L O N J. W I L S O N *R e c e i v e d D e c e m b e r 27, I977

Four new mononuclear ruthenium(I1) complexes, [Ru(PTP1),l2+ (PT PI = 2-p-tolylpyridinecarboxaldimine)nd [Ru(bpy),BI2+[B = 2,9-dimethyl- 1 lo-phenanthrol ine (2,9-Me2phen), 4,4-dimethyL2,2-bipyrirnidine (4,4-Me2bpyrm), and 2,2-biimidazole(bi imH,)], have been prepared as PF L salts and their electrochemical and photoemission properties investigated in solution.In addi t i on , t he l i gand-br idged b inuc l ear species [R~(bpy)~(B)Ru(bpy)~](PF,), B = bpyrm and 4 ,4-Mezbpyrm) havea l so been obt a ined as by-product s i n t he synthes i s of t he mononucl ear complexes and separa t ed f rom the i r mononucl earana logues by Sephadex chromatography. The m o n o n u c l e a r compound s al l exhibi t polarograms in acetoni t ri le consistentwi th quasi -reversible, one-elect ron [Ru (II) - u( II I)] oxidat ion processes wi th Ell2 oten ti a l s (SCE) ranging f rom 0 .93to 1 .29 V . T h e E,,, potent ials suggest an ordering in the B l igand ?r-acceptor abi l i ty of bi imH 2

Relative Strengths of Axial and Equatorial Bonds and Site Preferences

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