Experimental and theoretical characterization of the Zn - Zn bond in [Zn2(η5-C5Me5)2]

esea ch pape s 862 doi:10.1107/S0108768107045880 Ac a C ys . (2007). B63, 862–868 Ac a C ys allog aphica Sec ion B S uc u al Science ISSN 0108-7681 Expe imen al and heo e ical cha ac e iza ion o he Zn—Zn bond in [Zn 2 (g 5 -C 5 Me 5 ) 2 ] Juan F. Van de Maelen, a * En ique Gu ie ´ ez-Puebla, b A ´ngeles Monge, b San iago Ga cı ´a-G anda, a I ene Resa, c E nes o Ca mona, c Ma ı ´a Te esa Fe na ´ndez-Dı ´az, d Ga y J. McIn y e, d Philip Pa ison e and Hans-Pe e Webe a Depa amen o Quı ´mica Fı ´sica y Analı ´ ica, Facul ad de Quı ´mica, A da. Julia ´n Cla e ı ´a8, Uni e si y o O iedo, E-33006 O iedo, Spain, b Ins i u o de Ciencia de Ma e iales, Consejo Supe io de In es igaciones Cien ı ´ icas, So Juana Ine ´s de la C uz 3, E-28049 Mad id, Spain, c Ins i u o de In es igaciones Quı ´micas, Consejo Supe io de In es igaciones Cien ı ´ icas, Ame ´ ico Vespucio 49, E-41092 Se illa, Spain, d Ins i u Laue–Lange in, A . des Ma y s BP 156, F- 38042 G enoble CEDEX, F ance, e Swiss- No wegian Beam Lines, Eu opean Synch o on Radia ion Facili y, Jules Ho owi z 6, BP 220, F-38043 G enoble CEDEX, F ance, and Labo a o y o C ys allog aphy, Swiss Fede al Ins i u e o Technology, CH-1015 Lausanne, Swi ze land Co espondence e-mail: [email p o ec ed] #2007 In e na ional Union o C ys allog aphy P in ed in Singapo e – all igh s ese ed The exis ence and cha ac e iza ion o a bond be ween he Zn a oms in he ecen ly syn hesized complex [Zn 2 ( 5 -C 5 Me 5 ) 2 ], as well as be ween Zn and ligand C a oms is i mly based on neu on di ac ion and low- empe a u e X- ay synch o on di ac ion expe imen s. The mul ipola analysis o he expe imen al elec on densi y and i s opological analysis by means o he ‘A oms in Molecules’ (AIM) app oach e eals de ails o he Zn—Zn bond, such as i s open-shell in e - media e cha ac e ( he esul s a e consis en wi h a ypical me al–me al single bond), as well as many o he opological p ope ies o he compound. Expe imen al esul s a e also compa ed wi h heo e ical ab ini io calcula ions o he DFT (densi y unc ional heo y) and MP2 (Mølle -Plesse pe u - ba ion heo y) elec on densi ies, gi ing a cohe en iew o he bonding in he complex. Fo ins ance, cha ges calcula ed om he AIM app oach applied o he a omic basin o each Zn a om a e, on a e age, +0.72 e om bo h he expe imen al and he heo e ical elec on densi y, showing a mode a e cha ge ans e om he me al, con i med by he calcula ed opological indexes. Recei ed 23 May 2007 Accep ed 18 Sep embe 2007 1. In oduc ion Recen ly, we epo ed (Resa e al., 2004) he i s s able molecula compound o zinc wi h a me al–me al bond, bis[1,2( 5 )-pen ame hylcyclopen adienyl]dizinc(II)(Zn—Zn), [Zn 2 ( 5 -C 5 Me 5 ) 2 ] (1), which a ac ed g ea in e es in he scien i ic communi y, and consequen ly h ee new species ha e been ecen ly s udied (Wang e al., 2005; Zhu e al., 2006; G i ane e al., 2007). These compounds ha e been cha - ac e ized by a numbe o echniques (including NMR, IR and Raman spec oscopies, and con en ional X- ay single-c ys al di ac ion) in o de o demons a e, among o he hings, he absence o any b idging H a om be ween he Zn a oms. The appea ance o such an elusi e me al–me al bond, in spi e o he ac ha o ganozinc compounds ha e been well known since he ea ly days o o ganome allic chemis y, mo ed us o s udy synch o on X- ay di ac ion da a, and also he heo- e ical opological p ope ies o he Zn—Zn bond. Se e al heo e ical calcula ions dedica ed o (1) and ela ed compounds ha e been published o da e (Del Rı ´oe al., 2005; Xie, Schae e III & Jemmis, 2005; Xie, Schae e III & King, 2005; Timoshkin & Schae e III, 2005; Xie & Fang, 2005; K ess, 2005; Kang, 2005; Philpo & Kawazoe, 2006a,b; Pa hak e al., 2006). These s udies, based on he molecula o bi al (MO) app oach, ha e ound he minima in he po en ial ene gy su ace o (1), wi h geome ies ha closely esemble he p e iously published expe imen al geome y. They ha e also shown ha he Zn—Zn bond is compa able in s abili y o o he me al–me al bonds, wi h dissocia ion ene gies calcula ed be ween 259.58 and 309.82 kJ mol 1 depending on he heo- e ical model used (Xie & Fang, 2005; G i ane e al., 2007). As a as we know, no s udies ela ed o he opological p ope ies o he Zn—Zn bond, ei he om a heo e ical o an expe i- men al poin o iew, ha e been published so a , al hough some au ho s ha e men ioned he u gen need o such s udies (Philpo & Kawazoe, 2006a). Ou heo e ical app oach o his p oblem is based on he Quan um Theo y o A oms in Molecules (QTAM o AIM; Bade , 1990) and cen ed no only on he Zn—Zn bond, bu also co e ing he Zn–ligand bonds. This ea men is complemen a y o he abo e-men ioned s udies gi ing a ully cohe en and mo e comple e iew o he bonding in (1) when combined wi h he MO calcula ions while, on he o he hand, ha ing he addi ional ad an age o being equally applicable o bo h expe imen al and heo e ical elec on densi ies. 2. Expe imen al and compu a ional de ails 2.1. Neu on di ac ion expe imen A pla e-like single c ys al wi h maximum dimensions 2 1 0.3 mm 3 was plucked om a pool o poly lo ine he oil using a s anda d 1 mm diame e anadium pin, and placed quickly in he p e-cooled helium- low c yos a o he new Ve y- In ense Ve ical-Axis Laue Di ac - ome e (VIVALDI) a he Ins i u Laue Lange in (ILL) in G enoble (F ance) o he neu on di ac ion expe imen . VIVALDI uses he Laue di ac ion echnique on an unmono- ch oma ed he mal-neu on beam and wi h a la ge solid-angle (8 s e ad) cylind ical image-pla e de ec o (Wilkinson e al., 2002) o inc ease he de ec ed di ac ed in ensi y by one- o- wo o de s o magni ude compa ed wi h a con en ional monoch oma ic expe imen . The e we e 17 Laue di ac ion pa e ns, each accumu- la ed o e 2.5 h, collec ed a 170 K ypically in 10in e als du ing he o a ion o he c ys al pe pendicula o he inciden neu on beam. The pa e ns we e indexed using he p og am LAUEGEN o he Da es- bu y Labo a o y Laue Sui e (Camp- bell, 1995; Campbell e al., 1998) and he e lec ions in eg a ed using he local p og am ARGONNE_BOXES, which uses a wo-dimensional e sion o he (I)/Ialgo i hm (Wilkinson e al., 1988). No co ec ion o abso p- ion was deemed necessa y in iew o he small c ys al dimensions. The in eg a ed e lec ions we e no malized o a common inciden wa eleng h, using a cu e de i ed by compa ing equi alen e lec ions and mul iple obse a ions, ia he p og am LAUENORM (Campbell e al., 1986). Re lec ions we e obse ed wi h wa eleng hs be ween 0.85 and 3.56 A ˚, bu only e lec ions wi h wa eleng hs less han 3.0 A ˚we e accep ed o scaling, as e lec ions a longe wa eleng h had oo ew equi alen s o be able o de e mine he no maliza ion cu e wi h con idence. In all, 12 265 e lec ions we e obse ed, o which 8553 we e single well- esol ed e lec ions wi h wa eleng hs be ween 0.85 and 3.0 A ˚, which yielded 1665 unique e lec ions, co esponding o 73.7% o he possible unique e lec ions o dspacings > 0.96 A ˚, he minimum dspacing obse ed. The con en ional X- ay single- c ys al pa ame e s o non-H a oms (Resa e al., 2004) we e used as he ini ial model. The H a oms we e all loca ed om di e ence-Fou ie maps. Re inemen s we e ca ied ou using esea ch pape s Ac a C ys . (2007). B63, 862–868 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond 863 Table 1 Expe imen al de ails. X- ay Neu on C ys al da a Chemical o mula C 20 H 30 Zn 2 C 20 H 30 Zn 2 M 401.18 401.18 Cell se ing, space g oup T iclinic, P 11 T iclinic, P 11 Tempe a u e (K) 100 (1) 170 (2) a,b,c(A ˚) 6.9115 (6), 10.889 (1), 13.893 (1) 6.9329 (3), 10.8831 (5), 13.8384 (7) ,,() 109.91 (1), 101.551 (8), 93.905 (9) 109.777 (1), 101.603 (1), 94.201 (1) V(A ˚ 3 ) 952.6 (2) 951.09 (8) Z22 D x (Mg m 3 ) 1.399 1.452 Radia ion ype Synch o on Whi e beam (mm 1 )2.51 – C ys al o m, colo Pla e, colo less P isma ic, colo less C ys al size (mm) 0.70 0.70 0.05 2.0 1.0 0.3 Da a collec ion Di ac ome e CCD a ea de ec o VIVALDI Da a collec ion me hod ’and !scans Laue Abso p ion co ec ion Mul i-scan (based on symme y- ela ed measu emen s) None T min 0.272 – T max 0.881 – No. o measu ed, independen and obse ed e lec ions 57 003, 13 873, 12 354 8553, 1665, 985 C i e ion o obse ed e lec ions I>2(I)I>2(I) R in 0.054 0.364  max () 43.5 21.8 Re inemen Re inemen on FF 2 R[F 2 >2(F 2 )], wR(F 2 ), S0.036, 0.040, 1.09 0.105, 0.264, 1.08 No. o e lec ions 11 249 1665 No. o pa ame e s 782 469 H-a om ea men Mix u e o independen and cons ained e inemen Mix u e o independen and cons ained e inemen Weigh ing scheme w= 1/[ 2 (F o )] w= 1/[ 2 (F2 o) + (0.1322P) 2 ], whe e P=(F2 o+2F2 c)/3 (/) max 0.047 0.032  max , min (e A ˚ –3 ) 0.59, 0.48 0.67, 0.60 Compu e p og ams used: C ysAlis CCD and C ysAlis RED (Ox o d Di ac ion, 2004), SORTAV (Blessing, 1989), SHELXL97 (Sheld ick, 1997), XD2006 (Volko e al., 2006). SHELXL97 (Sheld ick, 1997) by ull-ma ix leas -squa es analysis wi h aniso opic displacemen pa ame e s o all a oms, including H a oms, wi h he la e conside ed as iding on hei me hyl g oups. No diso de ea men was applied he e o he me hyl g oups. Fu he de ails a e gi en in Table 1 and he molecula geome y ob ained is shown in Fig. 1. As may be clea ly seen in Fig. 1, no b idging H a oms we e ound be ween he Zn a oms. This esul was he main pu pose o he neu on di ac ion expe imen , i.e. o elimina e he emo e possibili y o ha ing missed b idging hyd ide ligands in he p io expe imen al s udies, as ce ainly happened in he well known p oposed cobal compound [Co 2 ( 5 - C 5 Me 5 ) 2 ], i s ly epo ed as ha ing a Co—Co bond bu which, in ac , is a hyd ide (Ke s en e al., 1992). Fo he expe imen al cha ge- densi y s udy he esul s we e ob ained om he synch o on X- ay expe imen wi hou he use o neu on da a. 2.2. Synch o on X- ay di ac ion expe imen In o de o ob ain be e da a o he mul ipola e inemen han he da a collec ed p e iously om con en ional X- ay di ac ion, a synch o on di ac ion expe imen was pe o med. A lamina colo less single c ys al o 0.70 0.70 0.05 mm 3 was selec ed. Measu emen s we e ca ied ou a he BM01A (Swiss–No wegian Beam Line) o he Eu opean Synch o on Radia ion Facili y (ESRF) in G enoble (F ance). Da a collec ion was ia a KUMA KM6- CH (equipped wi h a CCD de ec o ) six-ci cle single-c ys al di ac ome e , u ilized as a s anda d ou -ci cle ins umen . The da a collec ion empe a u e, con olled by an Ox o d c yos eam cooling sys em, was 100 (1) K, and he wa eleng h o he adia ion used was 0.71 A ˚. 1 The expe imen al s a egy was as ollows: (i) a good di ac ing c ys al was selec ed ( he c ys al was moun ed on he di ac ome e and a couple o ames we e obse ed p io o s a ing he comple e da a collec ion); (ii) a ound 20 ames we e hen collec ed o indexing pu poses; (iii) a un o ca 2 h o da a collec ion was hen used o y and sol e he s uc u e; (i ) inally he ull da ase was collec ed. In ac , h ee di e en da ase s we e collec ed a his s age: a high-angle da ase , using no il e , was collec ed i s ; hen a low-angle da ase was collec ed using a 50 mm Cu il e ; inally a e y low-angle da a collec ion was pe o med wi h a 100 mm Cu il e . A o al o 57 003 e lec ions we e measu ed [(sin /) max =1.08A ˚ 1 ], co e ing 90.3% o all possible e lec ions om = 2.01 o  max . Da a educ ion was hen applied using he SORTAV p og am (Blessing, 1989), gi ing a o al o 13 873 unique e lec ions (R in = 0.054), and an abso p ion co ec ion was also applied using SADABS (Sheld ick, 2003; Blessing, 1995). Solu ion and s anda d (sphe ical a oms) e inemen we e made using he WinGX p og am package (Fa ugia, 2005). Some diso de in he me hyl g oups was obse ed du ing he e inemen and he e o e some we e spli in o wo componen s in o de o p e en hem om being non-posi i e de ini e using he usual cons ain s (Van de Maelen U ı ´a & Sheld ick, 1996; Van de Maelen U ı ´a, 1999). Fu he de ails o his expe imen a e gi en in Table 1. 2 A selec ion o he molecula geome y da a, compa ed wi h he esul s om neu on di ac ion, is shown esea ch pape s 864 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond Ac a C ys . (2007). B63, 862–868 Table 2 Selec ed molecula geome y da a (A ˚,) o (1). Bond dis ance o angle Con en ional X- ay† Neu on di ac ion‡ Mul ipole X- ay‡ Zn—Zn 2.305 (3) 2.292 (1) 2.3186 (3) Zn—C§ 2.268 (2)–2.306 (2) 2.272 (4)–2.326 (3) 2.2756 (12)–2.3132 (9) Zn—Zn—C§ 145.72 (6)–150.52 (6) 145.2 (4)–150.2 (4) 145.12 (6)–150.65 (4) † Da a om Resa e al. (2004). ‡ This wo k. § Lowes and highes alues; indi idual alues may be ound in he supplemen a y ma e ial (Tables S1 and S2). Figu e 1 Displacemen ellipsoid plo o (1) om he neu on di ac ion expe imen , d awn a he 80% p obabili y le el, showing he a omic labelling scheme (labels o H a oms a e omi ed o cla i y). 1 In ou p oposal o he expe imen , di e en expe imen al condi ions we e asked o : a wa eleng h o 0.5 A ˚and a empe a u e o 10 K, bu only a mo e s anda d se -up was made a ailable. 2 Supplemen a y da a o his pape a e a ailable om he IUC elec onic a chi es (Re e ence: BS5050). Se ices o accessing hese da a a e desc ibed a he back o he jou nal. in Table 2. All in all, due mainly o a g ea e edundancy o he da a collec ed, a be e p ecision han in he con en ional X- ay di ac ion expe imen was achie ed, as e lec ed in he lowe s anda d de ia ions (see x3 o mo e de ailed commen s). 2.3. Mul ipole e inemen The mul ipole e inemen was ca ied ou by means o he p og am XD2006 (Volko e al., 2006), which uses he Hansen–Coppens o malism o he asphe ical a omic densi y expansion (Hansen & Coppens, 1978). Se e al models we e ied, bu he bes esul s we e ob ained wi h a ea men ha p oceeded as ollows. Hexadecapole ep esen a ion was used o he Zn and C a oms, while he H a oms we e ea ed as o ien ed dipoles, wi h hei coo dina es ixed, du ing he ea ly s ages o he mul ipole e inemen p ocess, a he posi ions ound in he sphe ical-a om e inemen . An a e age dis ance o 1.0495 A ˚, ob ained om he neu on di ac ion expe i- men , was used la e as a cons ain o all he C—H bond dis ances. Radial pa s o co e, sphe ical- alence and de o - ma ion- alence densi ies we e all cons uc ed using ela i is ic Di ac–Fock a omic wa e unc ions expanded o e Sla e - ype basis se s o he Zn a oms (Su & Coppens, 1998), while o C and H a oms he adial pa s o he de o ma ion alence densi ies we e single-Sla e - ype unc ions. Fu he cons ain s we e used o keep he e ined pa ame e s o all he H a oms wi hin each me hyl g oup equal. Radial scaling pa ame e s o he sphe ical and de o ma ion pa s o he alence densi y (and 0 l;l= 0–4) we e independen ly e ined o bo h Zn a oms, while o he C a oms only and 0 0we e independen ly e ined, using he cons ain 0 l=0 0(l= 1–4) o he o he scaling pa ame e s. Fo he H a oms all hese pa ame e s we e le ixed o hei de aul alues. In addi ion, occupa ion ac o s o he wo componen s o he diso de ed me hyl g oups ha we e spli du ing he sphe ical a om e inemen we e le ixed a hei ea lie alues (P al pa a- me e s). A o al o 782 pa ame e s we e e ined agains he 11 249 ‘obse ed’ e lec ions [F>3(F)] included in he e inemen (N e /N pa = 14.4). The inal con en ional R ac o o e Fwas 0.036 o he ‘obse ed’ e lec ions and 0.043 o he whole se o unique e lec ions. Re inemen alues gi en in Table 1 a e o wha we conside o be he ‘bes ’ expe imen al model (BE model), in he sense ha i has he bes inal s a is ical indexes (R,S, max,min , di e ence Fou ie map, con e gence c i e ia e c.), bu we also used o he mul ipole models in he opological calcula ions in o de o u he check hei accu acy agains opological indexes (see below). 2.4. Expe imen al and heo e ical opological calcula ions The XDPROP module o he p og am XD2006 (Volko e al., 2006) was used o s udy he opological p ope ies o he expe imen al elec on densi y by means o he AIM app oach (Bade , 1990; Coppens, 1997). Bo h local (loca ion o c i ical poin s and bond-pa h analyses, among o he s) and in eg al p ope ies (a omic cha ges, olumes, dipole momen s e c.) we e calcula ed. Usually he calcula ions we e ca ied ou using he de aul alues gi en by he p og am o he di e en con ol pa ame e s; howe e , o he in eg al p ope ies se e al in eg a ion pa ame e s had o be es ed and modi ied in o de o inc ease he accu acy o he esul s. The be a- sphe e adii o he a oms we e aken, o he in eg a ions, as he dis ance be ween he a om nucleus and i s closes bond- c i ical poin (b.c.p.). S a ing om he ‘bes ’ expe imen al model ob ained in he mul ipola e inemen , as de ined abo e, he p ocedu e ollowed was able o ind all he b.c.p.s in he molecule, whe eas o he o he models se e al b.c.p.s we e ei he missing o loca ed a odd posi ions (e.g. be ween he H a oms o di e en me hyl g oups). Acco dingly, only he BE model was used o ob ain he compu a ionally leng hy in eg al p ope ies. On he o he hand, bo h molecula geome ies ob ained om neu on and X- ay di ac ion expe imen s we e used o he heo e ical elec onic s uc u e calcula ions pe o med using he GAUSSIAN03 p og am package (F isch e al., 2004). The elec onic s uc u e calcula ions we e pe o med on he expe imen al geome ies using bo h DFT and ab ini io pe u ba ion heo y me hods. The ollowing me hods we e used: he hyb ids B3LYP, B3P86 and B3PW91 Becke’s h ee- pa ame e exchange unc ional (Becke, 1993) wi h he non- local Lee-Yang-Pa (Lee e al., 1988), Pe dew (Pe dew, 1986) and Pe dew-Wang (Pe dew e al., 1996) co ela ion unc- ionals, espec i ely, and he Vosko–Wilk–Nusai local co e- la ion unc ional (Vosko e al., 1980), oge he wi h he Mølle –Plesse MP2 and MP3 me hods we e ied. All-elec- on s anda d basis se s 6-31G(d), 6-31G(d,p) and 6-311G(d,p) ha e been used o all a oms as is usual o o he calcula ions o o ganome allic compounds (Van de Maelen U ı ´ae al., 2003, 2005). The g ound-s a e elec onic wa e unc ions ob ained we e hen used o u he calcula ions on he opology o he heo e ical elec on densi y, including bo h local and in eg al p ope ies, pe o med wi h he aid o he p og am AIM2000 (Biegle -Ko ¨nig & Scho ¨nbohm, 2002). The accu acy o he in eg a ed p ope ies was inally se a 1.0  10 4 om he Laplacian o he in eg a ed elec on densi y, whe eas o he local p ope ies he accu acy was much g ea e (1.0 10 10 om he g adien o he elec on densi y a he b.c.p.s). Some heo e ical models (a combina ion o molecula geome y, me hod and basis se ) we e able o ind all he b.c.p.s ound om he ‘bes ’ expe imen al (BE) model, bu he bes esul s, in he sense ha heo e ical local p op- e ies we e close o he expe imen al ones, we e ob ained using he MP2/6-311G(d,p) model wi h he neu on di ac ion geome y (BT model). In ac , some calcula ions made on he X- ay di ac ion geome y we e e en unable o ind he Zn— Zn b.c.p. Consequen ly, in eg al p ope ies we e hen calcu- la ed using only he BT model, which we call he ‘bes ’ heo- e ical model. 3. Resul s and discussion Neu on di ac ion expe imen s ca ied ou a he ILL (see x2) p o ided us bo h wi h expe imen al e idence o he absence o b idging H a oms be ween he Zn a oms in (1), and esea ch pape s Ac a C ys . (2007). B63, 862–868 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond 865 wi h he nuclea coo dina es o be used in he heo e ical elec onic s uc u e calcula ions, as explained ea lie . The molecula geome y, shown in Fig. 1, does no di e much om he p e ious esul s (Resa e al., 2004), gi ing he ypical sandwich s uc u e al eady p oposed. In Table 2 some ele an bond dis ances and angles ob ained om he neu on di ac ion da a and om he X- ay synch o on di ac ion da a a e compa ed wi h p e iously a ailable alues om con en ional X- ay di ac ion. As may be seen om he able, he Zn—Zn dis ance ob ained om he neu on di ac ion expe imen is sho e han he dis ances ound om bo h X- ay da a, whe eas he Zn—C dis ances a e only sligh ly longe and he main bond angles a e almos he same. The neu on Zn—Zn dis ance in (1) is e en sho e han he same dis ance in he bulk me al, so he e could be an ex a epulsion om he co e elec ons o he wo me al a oms ha would push hem away om he in e me allic egion, he e o e gi ing an X- ay dis ance la ge han he neu on alue. Published heo e ical calcula ions o he op imized geome y o (1) show Zn—Zn dis ances o e a wide ange, a ying om 2.287 o 2.339 A ˚, depending on he heo e ical model used (G i ane e al., 2007; K ess, 2005; Xie & Fang, 2005). On he o he hand, con en ional X- ay expe imen al da a ob ained o wo ecen ly syn hesized compounds, Zn 2 [{(2,6- i P 2 C 6 H 3 )- N(Me)C} 2 CH] 2 (Wang e al., 2005) and Zn 2 {C 6 H 3 -2,6-(C 6 H 3 - 2,6- i P 2 ) 2 } 2 (Zhu e al., 2006), ga e Zn—Zn dis ances o 2.3586 (7) and 2.3591 (9) A ˚, espec i ely. In o de o ob ain good quali y elec on densi ies sui able o an expe imen al opological analysis (Coppens, 1997; Ko i sanszky & Coppens, 2001; Coppens e al., 2005) we ca ied ou a mul ipola analysis o he expe imen al elec on densi y ob ained om he synch o on X- ay da a desc ibed in x2, ollowed by he applica ion o he AIM app oach (Bade , 1990). This analysis ga e a consis en iew o a ully connec ed molecule, including he comple e se o one b.c.p. be ween he Zn a oms, 10 b.c.p.s be ween Zn and C a oms, 20 b.c.p.s o he C—C bonds and 30 b.c.p.s o he C—H bonds, oge he wi h he 12 ing c i ical poin s ( .c.p.) and wo cage c i ical poin s (c.c.p.). In Fig. 2 a g adien ajec o y map o (1) is shown, whe e he c i ical poin and he bond pa h (b.p.) be ween he Zn a oms a e clea ly seen. Also shown a e he b.c.p.s and b.p.s ound be ween each o he Zn a oms, and he C-Me g oup in he ligand ing loca ed in he plane o he plo . Owing o he (nea ly) cylind ical symme y o he molecule, he image in Fig. 2 may be o a ed a ound he Zn—Zn axis o ob ain a comple e pic u e o he elec on-densi y g adien ield. In ac , e y simila plo s a e ound i di e en planes a e selec ed. Fu he mo e, ou heo e ical calcula ions made a he ab ini io le el show esul s ha closely esemble expe imen al calcu- la ions. Fo ins ance, cha ges calcula ed om he AIM app oach applied o he a omic basin o each Zn a om a e, on a e age, +0.720 e om he expe imen al elec on densi y and esea ch pape s 866 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond Ac a C ys . (2007). B63, 862–868 Figu e 2 G adien ajec o ies mapped on a o al densi y plo (con ou le els a 0.1 e A ˚ 3 ) o he Zn2—Zn1—C1 plane o (1). B.c.p.s ( ed ci cles) and b.p.s (dashed lines) a e also shown. Figu e 3 Th ee-dimensional ep esen a ion o he molecula elec os a ic po en ial mapped on an elec on densi y isosu ace. Colo codes om +0.567 (da k blue) o 0.002 e A ˚ 1 (da k ed). Densi y con ou alue: 0.27 e A ˚ 3 . +0.725 e om he heo e ical elec on densi y. These alues a e sligh ly lowe han he o mal cha ge o +1 e empi ically pos ula ed o he Zn a oms in (1) and, compa ed wi h o he heo e ical alues ob ained om MO app oaches (Resa e al., 2004; Kang, 2005; K ess, 2005; G i ane e al., 2007), sugges he exis ence o a ce ain amoun o cha ge ans e om he ligands (see below). Acco dingly, a e age expe imen al and heo e ical cha ges o he en C a oms o he wo Cp * ings a e 0.39 and 0.27 e, espec i ely. Fig. 3 shows he expe i- men al elec os a ic po en ial mapped on an elec on densi y isosu ace. In Table 3 a summa y o he opological p ope ies calcu- la ed om bo h expe imen al and heo e ical elec on densi- ies is shown. As clea ly seen in he able, he expe imen al alue o he Zn—Zn bond leng h calcula ed om he bond pa h (see Fig. 2) ma ches almos pe ec ly he X- ay synch o on in e a omic dis ance (Table 2), hence showing no bending in he bond pa h. Al hough he heo e ical alue e lec s a sligh bending, gi ing a di e ence o only 0.15 A ˚ be ween he heo e ical bond-pa h leng h and he expe i- men al in e a omic dis ance, i is ai o conclude ha his is a nea ly pe ec bond, a esul which is con i med by he ex emely low ellip ici y calcula ed o his bond (0.001). This esul is in line wi h p e ious esul s, based on NBO and simila MO analyses (K ess, 2005; G i ane e al., 2007), which show ha he Zn—Zn bond is mainly o med by in e ac ion o he 4sme al o bi als, al hough wi h small con ibu ions om p  and d  o bi als (Philpo & Kawazoe, 2006a). Cu en bond classi ica ions based on he a omic alence shell o molecules in ol ing hea y a oms make use o bo h local (a he b.c.p.) and in eg al (o e he a omic basin) p ope ies (Macchi e al., 2002; Macchi & Si oni, 2003; Ge asio e al., 2004, 2005; Ga i, 2005). Among he o me , he elec on densi y ( b ), he Laplacian o he elec on densi y ( 2  b ), he o al ene gy densi y a io (H b / b ) and he kine ic-ene gy densi y a io (G b /  b ), wi h H( )=G( )+V( )and1 4 2 ( )=2G( )+V( )[V( )is he po en ial ene gy densi y], a e by a he mos common. F om he alues in Table 3 i is clea ha he Zn—Zn bond in (1) is a ypical open-shell me al–me al bond (e.g. Co—Co, Macchi e al., 2002; Macchi & Si oni, 2003; o Ru—Ru, S ash e al., 2005), which di e s om a pu e co alen bond (such as C—C in e hane). This esul is con i med by he in eg al p ope ies lis ed in Table 3, i.e. he delocaliza ion index,  (Zn—Zn), and he elec on densi y in eg a ed o e he whole Zn—Zn in e a omic su ace, HZn Zn ð Þ. The o me is indeed nea ly equal o he o mal bond o de o 1.0, showing ha he e is jus one elec on pai sha ed by he wo a oms, while he la e has a alue compa able in magni ude o ha o pu e co alen bonds (2.16 o he C—C bond in e hane; Ga i, 2005, and e e ences he ein), despi e he ac ha  b is one o de o magni ude lowe o (1). Some opological p ope ies o he Zn—Cp * in e ac ions a e also lis ed in Table 3. The e is mo e li e a u e on he opological p ope ies o me al–ligand bonds han o me al– me al bonds, bu hey a e mainly cen ed on me al–CO in e ac ions (Pille e al., 2003; S ash e al., 2005; Fa ugia e al., 2006). I is no unusual o ind jus one bond pa h be ween a me al and a -bound ligand simila o Cp * (e.g. he Z –indenyl in e ac ions; S ash e al., 2005). As men ioned abo e, a mos ema kable ea u e o he opological analysis o he Zn—C in e ac ions in (1) is ha some, al hough no all, o he models ied, bo h expe imen al and heo e ical, p o ided he en b.c.p.s and bond pa hs be ween he Zn and C a oms, a pai o which is shown in Fig. 2. The e o e, in his case i is ai o conclude ha we a e conce ned he e wi h eal bonds, no jus ‘in e ac ions’, in he sense ha eal bond pa hs ha e been ound be ween Zn and C a oms. The opological pa ame e s also e lec his ac ; o ins ance, he alue o he delocaliza- ion index lis ed in Table 3 o each o he i e Zn—C bonds is la ge enough o con i m he abo e asse ion and, in addi ion, sugges s han jus one elec on pai is sha ed be ween a Zn a om and i s bonded Cp * ing. The alues o he o he opological magni udes shown in he able a e e y simila o hose ound in o he me al—C bonds, no ably some Z — C(indenyl) (S ash e al., 2005) and Z —C(imine) (Pille e al., 2003) bonds. Acco ding o he classi ica ion o Macchi and Si oni (Macchi & Si oni, 2003), hey a e no pu ely ionic bonds bu hey may be labelled as dono –accep o bonds, wi h a mode a e cha ge ans e e ealed by he ela i ely modes alue o HZn Cð Þ. Mo eo e , since he a e age expe imen al bond pa h leng h o he Zn—C bond in (1) di e s only sligh ly om he a e age expe imen al in e a omic dis ance (0.03 A ˚), i can be said ha hese a e nea ly s aigh bonds and he e o e he e is a nea ly pu e ans e o app oxima ely one elec on om each me al a om o i s ligand. Finally, om he clea ly la ge alues ound o he expe imen al (3.21) and heo e ical (4.20) ellip ici ies, i mus be concluded ha he Zn—C bonds in (1) ha e a de ini e cha ac e , in ag eemen wi h p e ious heo e ical s udies based on MO heo y (Xie & Fang, 2005; Philpo & Kawazoe, 2006a,b). esea ch pape s Ac a C ys . (2007). B63, 862–868 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond 867 Table 3 Selec ed expe imen al ( i s ow) and heo e ical [second ow, MP2/6-3111G(d,p) le el] opological pa ame e s o (1). d A–B : bond pa h leng h;  b : elec on densi y a he b.c.p.; 2  b : Laplacian o he elec on densi y a he b.c.p.; H b / b : o al ene gy densi y a io a he b.c.p. (see ex ); G b / b : kine ic ene gy densi y a io a he b.c.p.; (A–B): delocaliza ion index (see ex ); HA B: in eg a ed elec on densi y (see ex ). Bond dis ance d A–B (A ˚) b (e A ˚ 3 ) 2  b (e A ˚ 5 )H b / b (h e 1 )G b / b (h e 1 )(A–B)HA B(e A ˚ 1 ) Zn—Zn 2.3206 (3) 0.348 (3) 1.824 (17) 2.1657 0.426 1.622 0.361 0.627 0.919 1.252 Zn—C† 2.2642 (12) 0.398 (8) 1.952 (20) 2.1699 0.332 3.922 0.160 1.118 0.225 0.254 † A e age alues. 4. Conclusions In summa y, he exis ence and cha ac e iza ion o a bond be ween he Zn a oms in he complex [Zn 2 ( 5 -C 5 Me 5 ) 2 ], as well as be ween he Zn and he Cp * C a oms, ha e been i mly based on neu on di ac ion and low- empe a u e X- ay synch o on di ac ion expe imen s, oge he wi h he mul i- pola analysis o he expe imen al elec on densi y and he opological analysis ia he AIM app oach o bo h he expe imen al and he heo e ical elec on densi y. Fu he s udies on his complex based on maps o he Laplacian o he elec on densi y, as well as o he p ope ies, including he opological analysis o he ligands hemsel es, a e in p og ess in ou labo a o y. Financial suppo om he Spanish Minis e io de Educa- cio ´n y Ciencia (MAT2006-01997 and ‘Fac o ı ´a de C is aliza- cio ´n’ Consolide -Ingenio 2010) is g a e ully acknowledged. We also like o hank he Co-edi o and he e e ees, whose help ul commen s and sugges ions much imp o ed he o iginal manusc ip . Re e ences Bade , R. F. W. (1990). 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