Filling a Gap: The Coordinatively Saturated Group 4 Carbonyl Complexes TM(CO)8 (TM=Zr, Hf) and Ti(CO)7

Abstract Homoleptic Group 4 metal carbonyl cation and neutral complexes were prepared in the gas phase and/or in solid neon matrix. Infrared spectroscopy studies reveal that both zirconium and hafnium form eight‐coordinate carbonyl neutral and cation complexes. In contrast, titanium forms only the six‐coordinate Ti(CO)6 + and seven‐coordinate Ti(CO)7. Titanium octacarbonyl Ti(CO)8 is unstable as a result of steric repulsion between the CO ligands. The 20‐electron Zr(CO)8 and Hf(CO)8 complexes represent the first experimentally observed homoleptic octacarbonyl neutral complexes of transition metals. The molecules still fulfill the 18‐electron rule, because one doubly occupied valence orbital does not mix with any of the metal valence atomic orbitals. Zr(CO)8 and Hf(CO)8 are stable against the loss of one CO because the CO ligands encounter less steric repulsion than Zr(CO)7 and Hf(CO)7. The heptacarbonyl complexes have shorter metal−CO bonds than that of the octacarbonyl complexes due to stronger electrostatic and covalent bonding, but the significantly smaller repulsive Pauli term makes the octacarbonyl complexes stable.


Introduction
It has long been knownt hat molecules possess ap articular stabilityw hen their atoms have ac ertain number of electrons in as hell structure in whicht he outermost shell is wholly or partially connected to other atoms. This was formulated by Langmuir followingt he electron-pair modelo fL ewis [1] nearly a century ago, when he wrote:" The electrons in atoms tend to surround the nucleusi ns uccessive layers containing 2,8,8,18,18, and 32 electrons, respectively." [2] The counting of electrons is the basis of the octet, 18-electron and 32-electron rules, which are still used to explaint he stability of molecules. With the advent of quantum theory,t he physical basis of the electron-counting rules was later laid when the valence shell of atomsw as described in terms of s, p, d, andfatomic orbitals (AOs). Main group atoms employ their s/p valence shell forc ovalentb onding [3] and obey the octet rule, transition metals use their s/p/d valence AOs in many stable complexes that are subject to the 18-electronr ule, and the 32-electron rule is often av alid devise for the lanthanides and actinides possessing as /p/d/f valence shell.
There are exceptions to the electron-counting rules,w hich have been mysterious to chemists for some time, and which could only be explained when the quantum chemical nature of covalent bonds was understood. [4] The most persistent problem wast he so-called hypervalent main-group compounds, which apparently violate the octet rule. Prominent examples are pentavalent phosphorus molecules like PF 5 and hexavalent sulfur molecules like SF 6 . [5,6] Af ormal electron count gives 10 valence electrons at phosphorous and 12 electrons at sulfur in the two species. However,t he covalentb onds come from the interference of the electronic wave function, and the symmetry of the resulting molecular orbitals (MOs) shows that some valence electrons occupy MOs that have zero or negligible coefficients at the central atom. This was independently proposed by Rundle [7] and Pimentel [8] as ab ondingm odel for molecules that appear to violate the octet rule. It is now known as the three-center four-electron bondingm odel, which was adapted by Coulson to the valence-bond (VB) theory. [9] The conclusion is that fort he electron-counting rules, only those electrons should be counted that actuallyo ccupy the valence AOs of the given atom. The octet rule is then valid for main group atoms having as /p valence shell also in "hypervalent" molecules, which are better termed" hypercoordinated" compounds.
The present work deals with as imilar situation for the 18electronr ule for transition-metal complexes. Homoleptic transition-metal (TM) carbonyl complexes are archetypical examples for demonstratingt he metal-ligand bondinga nd the 18-electron rule. [10] Mononuclear transition-metal carbonyl complexes of groups 10, 8, and 6, such as Ni(CO) 4 ,F e(CO) 5 and Cr(CO) 6 , are well-known stable homoleptic carbonyl complexes that follow the 18-electronr ule. The metalÀCO bonds can be straightforwardly explained with the Dewar-Chatt-Duncanson (DCD) bonding model. [11] The early transition metals with fewer valence electrons need to bind with more than six carbonyl ligands to accomplish the 18-electron configuration; however, high coordination may causes teric repulsion between the ligands.T herefore, the 18-electron rule was considered to be less strict fore arly transition metals.V (CO) 6 with 17 valence electrons is ah ighly reactiveb ut isolable homoleptic metal carbonyl complex. [12] The seven-coordinate carbonyl complexes of Group 4a toms TM(CO) 7 (TM = Ti,Z r, Hf) formally satisfyt he 18electron rule and were theoretically predicted to be stable species by Luo et al. [13] Earlierm atrix isolation spectroscopics tudies suggest that the 16-electron TM(CO) 6 complexes,r ather than the 18-electron TM(CO) 7 complexes, are formed in solid matrices. [14,15] The finding is in agreement with the idea that transition-metalc omplexes TM(CO) n with higher coordination number than n = 6a re not stable, at least not for neutral species.
The first report of as even-coordinate homoleptic carbonyl was on the heptacarbonyl cation Ti(CO) 7 + ,which was observed and investigated by using guided ion beam mass spectrometry in the gas phase. [16] Although the bond dissociation energy of the 17-electron Ti(CO) 7 + complex is relatively small ((0.54 AE 0.07) eV),i ti ss tronger than expected for al igand in the second coordination shell. Recent infrared photodissociation spectroscopic studies in the gas phase revealed that the 15electron TM(CO) 6 + complexes, rather than the 17-electron TM(CO) 7 + complexes, should be characterized to be the fully coordinated complexes for TM = Ti,Z r, Hf. [17] In the cases of group 3a nd group 5m etals, the heavierm etal cations form the expected 18-electron complexes TM(CO) 7 + (TM = Nb, Ta ) and TM(CO) 8 + (TM = Y, La), but the lighter Sc + and V + ions form only the 16-electron complexes Sc(CO) 7 + and V(CO) 6 + ,r espectively. [18] The 18-electron complexes Sc(CO) 8 + and V(CO) 7 + were predicted to be stable, and higher-temperature experiments gave the expected 18-electronc omplex V(CO) 7 + for vanadium. [19] Very recently,t he 17-electron Cr(CO) 6 + cation was isolateda sas table salt compound. [20] The situation for negatively charged metal carbonyl complexes is different. Very recently,w er eported the observation of the anionsT M(CO) 8 À (TM = Sc, Y, La), whicha re isoelectronic with the neutral Group 4c omplexes TM(CO) 8 TM = Ti,Z r, Hf. [21] Given that the valence shell of the anions has al arger radius than that of the neutrals pecies, we were hopingt hat ah igher coordination number than six could be achieved. Our expectation was approved, buts urprisingly we observed the octacarbonyl complexes TM(CO) 8 À (TM = Sc, Y, La) as coordinatively saturatedc omplexes. The latter systemsa re formally 20-electron systemsw hen all valence electrons of the metalÀCO bonds are counted. Our theoretical analysiss howed that the complexes possess cubic (O h )symmetry,inwhich one of the metalÀCO valence MOs with a 2u symmetry has no AO coefficient at the metal. [21] The remaining nine MOs have AO coefficients at the metal;t hey can be easily associated with the TM ! CO s donation and TM!CO p back-donation with the latter being the dominant term. Thus, the octacarbonyl complexes TM(CO) 8 À (TM = Sc, Y, La) fulfill the 18-electron rule suggested by Langmuir if only those valence electrons are counted that by symmetry bind to the metal.
Av ery surprising result was the recent observation by us that the heavy alkaline-earthe lements calcium,s trontium, and barium can also bind eight CO ligandsf orming the eight-coordinate neutral complexes M(CO) 8 (M = Ca,S r, Ba) in low-temperatures olid neon matrix. [22] At heoretical study showedt hat the latter species also have cubic (O h )s ymmetrya nd that the metalÀCO bonding exhibits the same pattern as the transitionmetal carbonyl complexes. Very recently,w ee ven reported the observation of the isoelectronic dinitrogen complexes M(N 2 ) 8 . [23] The analysis of the bonding situationin M(CO) 8 (M = Ca, Sr,B a) revealed that it can be understoodw ith the DCD model in terms of the M ! CO s donation and M!CO p backdonation, for which the metal AOs of the latter term come from the valence dA Os. [21] The heavy alkaline-earthe lements Ca, Sr,a nd Ba bind like transition metals in the octacarbonyl complexesM (CO) 8 .T he complexes are formally1 8-electron systems, but the occupied valence a 2u MO of the cubic (O h )s tructures has an ode at the metal atom,a nd thus, the complexes are actually 16-electron systems. The degenerate e g HOMO is only doubly occupied, and therefore, the complexes M(CO) 8 (M = Ca, Sr,Ba) have at riplet ground state. [21] With the above knowledge, we re-investigated the question of the stability of the coordinatively saturated Group 4c arbonyl complexes, which may be realized in octacarbonyl complexes TM(CO) 8 rather than heptacarbonyl complexes TM(CO) 7 (TM = Ti,Z r, Hf). Here we report ac ombined infrared spectroscopic and theoretical study on coordinatively saturated Group 4m etal carbonyl complexes prepared in the gas phase and/or solid neon matrix. With respect to coordinatives aturation of transition metals,w er efer to the 18-electron rule. The results show that although titanium only forms the Ti(CO) 6 Experimental Section

Experimental methods
The Group 4m etal carbonyl cation complexes were generated in the gas phase by using ap ulsedl aser vaporization/supersonic-expansion source and were studied by infrared photodissociation spectroscopy. [24] The 1064 nm fundamental of a Nd:YAG laser was used to vaporize ar otating metal target. The metal carbonyl cation complexes were produced from the laser vaporization process in expansions of helium seededw ith 5-10 %C Ob yu sing ap ulsed valve (General Valve, Series 9) at 0.6-1.0 MPa backing pressure. After free expansion and cooling, the cations were skimmed into as econd chamber and were pulse-extracted anda nalyzed by using at ime-of-flight mass spectrometer (TOFMS). Cations of as pecific mass were mass-selected by their flight time and decelerated. The ions were subsequently excited by at unable IR laser in the extraction regiono fasecond collinear TOFMS. The infrared source was generated by aK TP/KTA/AgGaSe2 opticalp arametric oscillator/amplifier system (OPO/OPA, Laser Vision) pumped by a Continuum SureliteEXNd:YAGlaser,providing tunable infrared light about 1.0-2.0 mJ pulse À1 in the range of 1500-2200 cm À1 . The wavenumber of the OPO laser was calibrated by using the CO absorptions. When the infrared laser was on resonance with av ibrationalf undamental of the ion complex,a bsorption took place, which resulted in the dissociation of the complex. The fragment andparent ions were reaccelerated and mass analyzed by the second TOFMS. The photodissociation spectrum was obtained by monitoring the yield of the fragment ion as a functiono ft he dissociation IR laser wavelength and normalizing to the parenti on signal. Typical spectra were recorded by scanning the dissociation laser in steps of 2cm À1 and averaging over 300 laser shots at each wavelength.
The Group 4m etal carbonyl neutralc omplexes were prepared by the reactions of metal atoms and carbon monoxide in solid neon and were investigated by using Fouriert ransform infrared absorption spectroscopy as described in detail previously. [25] The metal atoms were prepared by pulsed laser evaporation of ar otating metal target andw ere co-deposited with ad ilute carbon monoxide-neon mixture (0.1-10 %C O/Ne on the basis of volume) onto ac ryogenic CsI window maintained at 4K by means of ac losed-cycle helium refrigerator.T he 1064 nm fundamental of aN d:YAGl aser (Continuum, Minilite II, 10 Hz repetition rate) was used for evaporation.A fter 30 min of deposition, infrared spectra of the resulting samples were recorded in the transmission mode between 4000 and 450 cm À1 by using aB ruker Vertex 80 Vs pectrometer at 0.5 cm À1 resolution. Al iquid-nitrogen-cooled broad-band HgCdTe( MCT) detector was used. Barew indow backgrounds, recorded prior to sample deposition, were used as references in processing the sample spectra.A fter the infrared spectrum of the initial deposition had been recorded, the samples were warmed up to the desired temperature andq uicklyr e-cooled and more spectra were taken.A lternatively,f or somee xperiments,b road-band photoexcitation was performed by using a high-pressure mercury arc lamp with glass filters.T he CO/Ne mixturew as prepared in as tainless-steel vacuum line by using standard manometric techniques. CO (Shanghai BOC, > 99.5 %) and isotopically labelled 13 C 16 O( ISOTEC, 99 %) and 12 C 18 O (ISOTEC,99%)w ere used without further purification.

Theoretical methods
The quantum chemical calculations using density functional theory (DFT) werec arried out with the M06 functional developed by Truhlar and Zhao [26] in combinationw ith the def2-TZVPP [27] basis set. Comparative calculations with other functionals gave very similarr esults, with M06 showing the best agreement with experimental results. This level was also coupled with the D3 correction proposed by Grimmee tal. [28] This basis set uses quasirelativistic effective core potentials for 28 and 60 core electrons for Zr and Hf atoms, respectively.A ll these computations were carried out by using the Gaussian 16 program package. [29] Superfine integration grid was used for the computations. Unless otherwisem entioned, all the geometries that are reportedh ere are minima on the potential energy surfaces.
The DE elstat term represents the quasiclassical electrostatic interaction between the unperturbed charge distributions of the prepared fragments. The Pauli repulsion DE Pauli is the energy change associated with the transformation from the superposition of the unperturbed electron densitieso ft he isolated fragmentst ot he wave function, which properly obeys the Pauli principle throughe xplicit antisymmetrization and re-normalization of the product wave function. The term DE orb is originated from the mixing of orbitals, charget ransfer,a nd polarization between the isolated fragments. Considering that we used a metahybrid functional for EDA-NOCV,i tg ives an additional metahybrid correction DE hybrid .T his comes from the use of Hartree-Fock exchange in the functional, which cannotb eb roken up, separated, andassigned to the three energy terms in Equation (1).
The combination of EDA with the NOCV method allowsu s to partitiont he total DE orb term into pairwise contributions of the orbital interactions.T he electron density deformation D1 k (r), whichi so riginated from the mixing of the orbital pairs y k (r)a nd y Àk (r)o ft he interacting fragments in the complex, represents the amounta nd the shape of the charge flow due to the pairwise orbital interactions [Eq. (2)],w hereasthe associated orbital energy term reflects the strength of such orbital interactions [Eq. (3)].T he eigenvalues u k provide aq uantitative amount of the chargem igration that is associated with each orbitalinteraction.
n k ½Ày 2 Àk r ðÞþy 2 k r ðÞ ð2Þ Therefore, both qualitative (D1 orb )a nd quantitative (DE orb )i nformation of the strength of individual pairs of orbital interactions can be obtained from an EDA-NOCV analysis. For further details on the EDA-NOCV method and its application to the analysiso ft he chemicalb ond, some recent reviews are recommended. [36] Results and Discussion

Experimental results
The mass spectra of carbonyl cation complexes of titanium, zirconium, and hafnium are shown in Figure 1. The spectra were recorded under the experimental conditions that favor the formation of coordinatively saturated mononuclear carbonyl complexes with relatively high thermal stability. The spectrum of titanium is dominated by the Ti(CO) 6 + peak. The Ti(CO) n + complexes of n > 6w ereb arely observed. Besides the n = 6c omplexes,t he TM(CO) n + (TM = Zr,H f; n = 7, 8) complexes were also observedt oh ave appreciable intensities in the mass spectra of zirconium and hafnium.
All these carbonyl cation complexes can dissociate by losing one CO ligand under loosely focused IR laser irradiation in the carbonyl stretchingf requency region. The infrared photodissociation spectra of the Zr(CO) n + cation complexes with n = 6-8 are shown in Figure2.T he spectra of Ti(CO) 6 + and Hf(CO) n + (n = 6-8) are shown in FiguresS1a nd S2 (SupportingI nformation). The spectra of the n = 6c omplexes each exhibits as ingle band centered at 2114 cm À1 for Ti,a t2 096 cm À1 for Zr and at 2076 cm À1 for Hf, in full accord with previous reports. [17] Theinfrared spectra of Zr(CO) 7 + and Hf(CO) 7 + are very similar,s how-ing am ajor peak at 2071 cm À1 for Zr and at 2059 cm À1 for Hf, together with ap artially resolved shoulder peak at around 2098 cm À1 for Zr and at 2081 cm À1 for Hf. The spectrao ft he n = 8c omplexes of zirconium and hafnium feature as ingle sharp band at 2085 cm À1 for Zr and at 2074 cm À1 for Hf. The observation of only one sharpb and in the carbonyl stretching frequency region indicates that these n = 8c ation complexes have high symmetry. The mass spectrometric and infraredp hotodissociation spectroscopic resultsi mply that the n = 6c omplex is the saturatecoordinate complex for titanium, whereas both the seven-and eight-coordinate complexesa re formed for zirconium and hafnium. The observation of only the 6-fold coordinate complex for titanium is in accord with the work of Duncan and Brathwaite. [17a] However, previous gas phase studies of Armentrout and Meyer found as table Ti(CO) 7 + complex. [16] The seventh CO binding energy was determined to be (0.54 AE 0.07) eV.T he discrepancy was suggested to be due to the differencesi ni on production methods employed. [17a] In the Armentrout experiment,i ons are thermalized by many room-temperature collisions in af low tube, andt hus only the thermally stable ions can survivet ob es tudied. The ions in both Duncan and coworkers' experiments andi no ur experiments are produced by pulsedl aser evaporation/supersonic-expansion source.T he kinetics is the key factor that governs the formation mechanism. The Ti(CO) 6 + complex has aq uartetspin ground state, whereas the seven-coordinateT i(CO) 7 + complex was predicted to have ad oublet ground state. [17a] As pin change is therefore needed to form the seven-coordinate complex from Ti(CO) 6 + .A sh as been discussed, the spin-changing ligand addition reactions involve barriers, and the reaction rates are much slower than the spin-conserving reactions. [37] Both the n = 7a nd n = 8c ation complexeso fz irconium and hafnium are formed in our experiments,w hich are in apparent disagreementw ith the previouse xperiments of Duncan and co-workers. [17a] In that study,t hey did not observe the sevenand eight-coordinate complexes.This discrepancy is due to differenti on production sources employed by the two laboratories. In our experiments,aSmalley-type laser vaporization/su-  personic-expansioni on source is used. [24] The source involves a growth channel, which can keep the laser-ablated metal vapor and reactantg as mixtures confined to allow more condensation reactions beyondt he laser vaporizationp oint. This type of source is good for growing larger thermally stable clusters as has been demonstrated for the production of C 60 + . [38] On the other hand, Duncan employed as o-called "cutaway"l aser vaporization ions ource, [39] which eliminates the growth channel beyondt he laser vaporization point. The gas flow from the nozzle picks up the ablated metal and electrons forming cold metal complexes. There is no further confinemento ft he gas after laser vaporization. [38] The supersonic expansion conditions make very cold ions, which may limit the production of the seven-coordinate complex as ar esult of the existence of a small barrier.
Besidest he gas phase infrared photodissociation spectroscopic studies of the cation complexes,aseries of matrix isolation experimentswere performed to preparethe saturate-coordinate Group 4m etal carbonyl complexes in solidn eon matrix. The speciesf ormed were detected by using IR absorption spectroscopy.E xperimentsw ere performed by using aw ide range of CO concentrationsr anging from 0.1 to 10 %. The infrared spectra are summarized in Figures 3a nd 4a nd Figures S3-S6 (Supporting Information). The spectra from the experiments with relatively low CO concentrations (see Figure S3, Supporting Information, for hafnium)a re about the same as those in previous reports. [15] Mononuclear low-coordinate carbonyl complexesT M(CO) n of n = 1-6 were formed either on sample deposition and/or on sample annealing. The relative intensities of the lower coordinated complexes decrease, whereas the relative intensities of the higher coordinated complexes increasew ith increasingC Oc oncentrations ( Figure 3f or Hf, Figures S4 and S5, Supporting Information, for Zr and Ti,r espectively). Only two obvious bands at 1979.1 and2 066.2 cm À1 for zirconium ( Figure S6, Supporting Information) and at 1972.5 and 2056.3 cm À1 for hafnium ( Figure 4) were observed in the zirconium and hafnium experiments using high CO concentrations( > 2%). Both bands increaseo na nnealing. The upper band is much weaker and is totally destroyed under UVvisible light irradiation and cannot be recovered on subsequent annealing ( Figure 4). The low band is the dominate product band presented in the spectra,w hichd ecreases on UV-visible light irradiation and is partially recovered on subsequent annealing.I nt he case of titanium, multiple bands are observed to exist in the highest CO concentration experiments ( Figure S5, Supporting Information). Experiments were also performed by using the isotopic-substituted 13 CO and C 18 O samples. The isotopics hifts are appropriate for terminal CO stretching vibrations.
The band at 1979.1 cm À1 forz irconium and at 1972.5 cm À1 for hafnium were observed to be the end-product absorptions upon progressivea nnealing of the samples to temperatures of 10 to 12 Ku nder relatively high CO concentrations. These absorptions are the dominant features in the spectraw ith the highest CO concentration (Figure 4a nd Figure S6, Supporting Information), suggesting the assignment to the coordinatively saturateZ r(CO) 8 and Hf(CO) 8 complexesi ns olid neon matrix following the observation of the octacarbonylc ation complexesi nt he gas phase. The isotopic splittings in the experimentsw ith the 12 CO+ + 13 CO mixture cannot be resolved because of band overlap.T wo broad bands slightly shiftedf rom those of the pure isotopicc ounterparts are observed with the 12 CO+ + 13 CO mixed sample ( Figure S7, Supporting Information).
The much weakerb and at 2066.2 cm À1 for zirconium and at 2056.3 cm À1 for hafnium can be assigned to the octacarbonyl cation complexes in solid neon. These bands are respectively 18.8 and 17.7 cm À1 red-shifted from the gas phase values. These values of gas phase-to-matrix shift are typical for cation species. [40] The spectra of titanium are completely different from those of zirconium and hafnium.F our bands at 1990. 8, 1966.4, 1953.3, and 1942.0 cm À1 are observed to be the end-product absorptions with high CO concentrations, which can be assignedt ot he seven-coordinate Ti(CO) 7 neutral complex. The  bands at 1856.5 and 2098.2 cm À1 are photosensitive and are assigned to the Ti(CO) 6 À and Ti(CO) 6 + charged complexes, respectively,both of which are characterizedtob ec oordinatively saturated complexes with absorptions at 1856 and 2114 cm À1 , respectively,i nt he gas phase. The experimentally observed CÀOs tretching frequencies in neon matrix and in the gas phase and the calculated DFT values of the neutrala nd positively charged TM(CO) n q (n = 8, 7, 6; q = 0, + 1) species are shown in Ta ble 1.
Theoretical results and bonding analysis Information,f or other isomers). [21] AllG roup 4o ctacarbonyl complexes are minima on the potential energy surface, but the titanium complex Ti(CO) 8 is thermodynamically unstable for the loss of one CO ligand.T he dissociation reaction TM(CO) 8 ! TM(CO) 7 + +CO is calculated to be exothermic for TM = Ti,w hereas it is endothermic for TM = Zr,H f( Figure 5). This explains why Zr(CO) 8 and Hf(CO) 8 could be observed but Ti(CO) 8 could not. The neutralG roup 4h eptacarbonyl complexes TM(CO) 7 have C 3v symmetry and as inglet ( 1 A 1 )e lectronic ground state like the isoelectronic group 3a nionsT M(CO) 7 À (TM = Sc, Y, La) (see Figure S9, Supporting Information, for other isomers). [21] All Group 4h eptacarbonyl complexes TM(CO) 7 are stable with respect to CO loss yielding the hexacarbonyl complexes TM(CO) 6 ,w hich have D 3d symmetry and at riplet ( 3 A 1g )g round state (Figure 5a nd Figure S10, Supporting Information). The heptacarbonyl complexT i(CO) 7 is calculated as the highest-coordinate neutral titanium carbonyl complex that is thermodynamically stable. Our calculated geometries of TM(CO) 7 agree quite well with the values reported by Luo et al. for the capped octahedron (C 3v )s tructures. [13] The authors also calculated TM(CO) 7 structures with pentagonal bipyramidal (D 5h ) and face-capped trigonal prismatic (C 2v )g eometries,w hich were found to be saddle points on the potential energy surface. As econd energy minimum structure with one side-on-bondedC Ol igand and C s symmetry lies 17-22 kcal mol À1 above the C 3v structures. [13] Ac omparison of the geometries of the octacarbonyl complexes with that of the heptacarbonyl complexes shows that the TM(CO) 8 complexes have significantly longer TMÀCO bonds than that of the TM(CO) 7 adducts. This is in agreementw ith the calculated bond dissociatione nergy (BDE) for the loss of one CO ligand, which is alwaysl arger for TM(CO) 7 than for TM(CO) 8 ( Figure 5).   (Figure 5a nd Figure S12, Supporting Information). All heptacarbonyl cationsT M(CO) 7 + ,w hich have C s symmetry and a 2 A' electronic ground state for TM = Ti,Z r and C 2v symmetry and a 2 A 1 electronic ground state for TM = Hf, are energy minima. The hexacarbonyl Ti(CO) 6 + is calculated as the highest-coordinate cationic titanium carbonyl complex that is thermodynamically stable. The cations TM(CO) 6 + have octahedral (O h )s ymmetry and aq uartet ( 4 A 1g )e lectronic ground state (Figure 5a nd Figure S13, Supporting Information).
Ta ble 1a lso shows the calculatedC ÀOs tretching modes and IR intensities of the experimentallyo bserved neutrala nd positively charged carbonyl complexes with coordination numbers 6, 7, and 8. The complete list of the calculated vibrational frequencies and IR intensities of all computed species is given in Ta ble S1 (Supporting Information). The theoreticalv alues are scaled by 0.958,w hichi st he ratio of the experimental value of free CO (2143 cm À1 )a nd the calculated value at M06-D3/def2-TZVPP (2237 cm À1 ). Table 1a lso gives the frequency shifts with respect to free CO and the isotope shifts of the 13 C 16 Oa nd 12 C 18 Oi sotopomers.
The calculated CÀOs tretching modes are alwayss lightly larger than the experimental values, but the trends and the [a] The BDE with respect to Ti(CO) 8 + (D 4h , 2 A 1g )!Ti(CO) 6 ···CO + (C 3v , 4 A 1 )+ +CO. frequency shifts support the assignment of the recorded modes in the gas phase and in the matrix. The neutral octacarbonyl complexes Zr(CO) 8 and Hf(CO) 8 have (as expected) as ignificantly larger red-shift than the cationsZ r(CO) 8 + and Hf(CO) 8 + .T he calculations suggest one IR-activem ode for the neutral O h complexes but two IR-active modes for the D 4h cations;a lthough the splitting of the latter modes is too small to be resolved with our equipment. The calculated isotope shifts of all octacarbonylc omplexes are in excellent agreementw ith the experimental shifts. The experimental assignment of two frequencies for Zr(CO) 7 + and Hf(CO) 7 + indicates thep eaks to be the rather broad signals,w hicha re observed (Figure 2a nd Figure S2, SupportingI nformation). The experimental spectrum agrees very well with the calculated strongly IR-activeC O stretching modes of the heptacarbonyl cations. Thet heoretical data suggest six frequenciesf or the C s structure of Zr(CO) 7 + and five frequencies for the C 2v structure of Hf(CO) 7 + within a rather narrow range of approximately 35 cm À1 ,which conforms with the recorded signals.
Ta ble 1a lso shows that the calculated IR-activeC Os tretching modeso ft he highest-coordinate neutrala nd positively chargedt itanium carbonyl complexes Ti(CO) 7 and Ti(CO) 6 + agree quite well with the experimental spectra.F our frequencies within ar ange of approximately 49 cm À1 are calculated and experimentally observed for the C 3v structure of Ti(CO) 7 , whereas only one is found for the octahedral cation Ti(CO) 6 + . The differences of the four IR-activesignals for Ti(CO) 7 between theory and experiment may be partly due to dynamic effects of the fluctuate structure. Overall, the calculated IR signals and the isotope frequency shifts provide strong evidencef or the assignments of the recorded spectra to the molecular species.
We analyzed the metalÀCO interactions in the neutral and chargedc omplexes with the EDA-NOCV method, whichh as been proventogive deep insight into the nature of the chemical bonds in metal carbonyl complexes [21,22,41] and other compounds. [42,43] Ap articularly interesting topic concerns the question why the heavierG roup 4m etals form stable octacarbonyl complexes,w hich are formally 20-electron species, as highest-coordinate complexes;a lthough the heptacarbonyl complexes satisfy the electron demando ft he metalsi nt he 18-electron complexes TM(CO) 7 .F igure 6s hows the correlation diagram of the (n)s,( nÀ1)d, and (n)p valence orbitals of aG roup 4t ransition metal TM with four valence electrons in the electronicr eferences tate in the cubic field (O h )o fe ight CO ligandsa nd the interactions with the 5s and 2p*v alenceM Os of (CO) 8 .T he occupied 5s MOs of (CO) 8 donate electronic chargei nto the vacant (n)s (a 1g ), (nÀ1)d (t 2g ), and (n)p (t 1u )A Os of the metal, and the p back-donation from the occupiedm etal (nÀ1)d (e g ) AOs takes place into the vacant 2p*(e g )M Os of (CO) 8 .T he occupied a 2u MO of (CO) 8    strongesti nteractions due to relativistic effects, whereas the second-row element Zr has the weakest interactions. It is interesting to note that the isoelectronic anionsT M(CO) 8 À (TM = Sc, Y, La) show am ore regulart rend for the DE int values (Sc À > Y À > La À )i nw hich the heaviest metal anion La À has the weakest bonds. [21] The reason for this remainst ob es tudied. The breakdown of the orbitalt erm DE orb ,w hich provides about two-thirds oft he total TMÀ(CO) 8 attraction in the Group 4o ctacarbonylc omplexes, into the pairwise orbitali nteractions shows that the major contributionc omesf rom the [TM(d)]! (CO) 8 p back-donation followed by [TM(d)] ! (CO) 8 s donation ( Table 2). The two orbitalt erms afford > 87 %o ft he covalent TMÀ(CO) 8 bonding. The EDA-NOCV resultss uggest that the most important valence orbitals of the metal atoms for the covalent bonds are the (nÀ1)d AOs. Figure 7s hows the deformation densities D1 (1) -D1 (5) of Zr(CO) 8 ,w hich are associated with the most important pairwise orbitali nteractions DE orb(1) -DE orb (5) given in Table 2, which nicely illustrate the chargef low that accompanies the orbitalt erms. The deformation densities D1 (1) -D1 (5) of Ti(CO) 8 and Hf(CO) 8 look very similara nd are shown in Figures S14a nd S15 (Supporting Information). The color code of the charge migration is red!blue. Onlyo ne component of the degenerate orbitali nteractions is shown. The shape of D1 (5) shows that the stabilizing polarizationo ft he (CO) 8 cage involves ac harge migration from oxygen to carbon. Figure 8s hows the orbitalc orrelation diagram betweent he valence orbitals of aG roup 4t ransition metal TM in the capped octahedron (C 3v )f ield of seven CO ligands in TM(CO) 7 and the interactions with the occupied s andv acant p*v alence MOs of (CO) 7 .C onsideringt he lower symmetry of the heptacarbonyl complex, all of the occupied s valence MOs of (CO) 7 can donate electronic charge to the metal, satisfyingt he 18-electron rule in TM(CO) 7 .T he shape of the occupied valence orbitals of Ti(CO) 7 displayed in Figure 8i ndicates that all metal AOs are involved in the occupied molecular orbitals. In principle, the metal valence( n)s, (nÀ1)d, and (n)p AOs, which split into a 1 and eo rbitals in the C 3v field could mix into all occupied a 1 and ev alence orbitalso ft he complex.I nspection of the metal AO coefficients suggest that the 1a 1 MO of the complex has mainly contributions from the (n)s AO, the 2a 1 MO has mainly contributionsf rom the (n)p AO, and the 3a 1 MO has mainly contributionsf rom the (nÀ1)d AO. The 1e MO of the complex has mainly contributions from the (n)p AO, the 2e MO has mainly contributionsf rom the (nÀ1)d AO, and the 3e MO has contributions from the (nÀ1)d and (n)p AOs. The latter AOs serve as polarization of the occupied( nÀ1)d AOs.
Ta ble 3s hows the numericalr esults of the EDA-NOCV calculations for TM(CO) 7 ,w hich provide aq uantitative account of the orbitali nteractions that are qualitativelys ketchedi n Figure 8. It becomes obvious that the covalentb ondingc omes mainly from the [TM(d)]!(CO) 7 p back-donationf ollowed by [TM(d)] ! (CO) 7 s donation, which has two (2e and 3a 1 )c omponents. The overall metal-ligandbonding situation in the heptacarbonyl complexes is thusv ery similar to those in the octacar- Figure 7. Shape of the deformationdensities D1 (1)- (5) ,w hich are associated with the orbital interactions DE orb(1)- (5) in Zr(CO) 8 and eigenvalues j n n j of the charge flow.T he isosurface valuesare 0.002f or D1 (1)- (2) and 0.0008 for D1 (3)- (5) .O nly one component of the degenerate orbitalinteractions is shown. The color code of the chargef low is red!blue. bonyl complexes.H owever,w hy is then TM(CO) 8 favored over TM(CO) 7 ?Acomparison of the EDA-NOCV results for the two sets of complexes in Ta bles 2a nd 3g ives as omewhat surprising answer.T he intrinsic TMÀ(CO) n attraction DE int of the octacarbonyl complexesi s( as expected) stronger than that in the heptacarbonyl complexes.H owever,t he attractive components DE elstat and DE orb in TM(CO) 7 are much stronger than that in TM(CO) 8 .T he covalent bondinga nd the electrostatic attraction in the octacarbonyl complexes are weakert han that in the heptacarbonyl complexes,w hich agrees with the shorterT M À CO bonds in the latter,b ut the octacarbonyl complexes are yet the energetically more favored complexes.T his is because the destabilizing component of the repulsiveP auli term DE Pauli is much higher in TM(CO) 7 than in TM(CO) 8 (Tables 2a nd 3). There is strongers teric repulsion between the CO ligandsi n the C 3v structures of TM(CO) 7 as ar esult of the shorter TMÀ (CO) 7 bonds, which overcompensates the stronger attraction compared with TM(CO) 8 .The role of Pauli repulsion is often ne- Figure 8. Splitting of the (n)s, (nÀ1)d, and (n)p valence orbitals of aGroup4transition metal TM (TM = Ti,Z r, Hf) in the capped octahedron field (C 3v )ofs even CO ligands and interactions with the 5s and 2p*v alenceM Os of (CO) 7 .The shape of the occupied valenceMOs of Ti(CO) 7 is also shown.
[a] The valuesi np arentheses give the percentagec ontribution to the total attractivei nteractions DE elstat + +DE orb . [ b] The valuesi np arentheses give the percentagec ontributiont ot he total orbital interactions DE orb .
glected in the discussion about bond strength, whichu sually only considers covalenta nd electrostatic (ionic) attraction. It has been shown that Pauli repulsion prevents the maximum overlap of the bondingo rbitals at the equilibrium bond distance [44] and that the weaker Pauli repulsion is why CO has a higher BDE than N 2 . [45] The deformationd ensities D1 (1)- (6) , which are associated with the pairwise orbital interactions DE orb(1)- (6) in TM(CO) 7 ,a re shown in Figure 9( for Zr(CO) 7 )a nd in Figures S16a nd S17 (Supporting Information) (for Ti(CO) 7 and Hf(CO) 7 ).
The final questionf or the neutral complexes concerns the finding that only Zr and Hf afford stable octacarbonyl complexes whereas Ti(CO) 8 is unstablef or the loss of one CO. EDA-NOCV calculations using TM(CO) 7 + +CO as interacting fragments provide an answer.T able4 gives the numerical results. The attractive terms DE elstat and DE orb in Ti(CO) 8 are strongert han that in their heavierh omologues. However,t he Pauli repulsion DE Pauli in the titaniumo ctacarbonyl is significantly larger,w hich makest he intrinsic interaction energy DE int in Ti(CO) 8 weaker than that in the heaviero ctacarbonylc omplexes, albeit it is Figure 9. Shape of the deformationdensities D1 (1)- (6) ,w hich are associated with the orbital interactions DE orb(1)- (6) in Zr(CO) 7 and eigenvalues j n n j of the charge flow.T he isosurface valuesare 0.004f or D1 (1) ,0 .001 for D1 (2)-(3) ,a nd 0.0008f or D1 (4)- (6) .O nly one component of the degenerate orbital interactions is shown. The colorc ode of the chargef low is red!blue.  still attractive. Whatm akesT i(CO) 8 energetically unstable for the loss of one CO is the assembling preparation energy DE prep , which is clearly larger than that for Zr(CO) 8 and Hf(CO) 8 (Table 4). Thus, Ti(CO) 8 is unstable for the loss of one CO because of repulsion between the CO ligands, which is stronger because of the shorter metalÀCO bonds than that in the heavier homologues. The BDE values D e in Ta ble 4a re slightly different from the data in Figure 5, because the former values were calculated with aSlater basis set of comparable quality. The bondinga nalysis of the neutralc omplexes is presented and discussed in detail to explain the peculiar observation that Ti(CO) 7 and TM(CO) 8 (TM = Zr,H f) appeara sc oordinatively sa-turatedG roup 4c arbonyl complexes. The EDA-NOCV resultso f the cations shall only be shortly discussed. Ta ble 5s hows the numerical results for the octacarbonyl cations TM(CO) 8 + using TM + and (CO) 8 as interacting fragments. The [TM(d)] + !(CO) 8 p back-donation has two components from orbitals having a 1g and b 2g symmetry as ar esult of the lower D 4h symmetry.T he contribution of the p back-donation in the cations is (as expected) smaller than that in the neutral species (Table 2) because of the positive charge of the metal and one lessdelectron, but it still provides 40 %-50 %o ft he total orbital interactions DE orb .T he [TM(d)] + ! (CO) 8 s donation also has two components (e g and b 1g ), which contribute 30 %-35 %t oDE orb .T he results for Zr(CO) 8 + must be taken with some caution because the self-consistent field (SCF) calculation of Zr + did not fully converge to the (n)s 0 (n)p 0 (nÀ1)d 3 valence electronic configuration but showed ah ybrid orbital of 70 %d z 2 and 30 %scharacter.T he EDA-NOCVresults for TM(CO) 6   [a] At M06/TZ2P-ZORA level, Zr + with (n)s 0 (n)p 0 (nÀ1)d 3 valencee lectronic configurationw as not fully converged even after several iterations. After numerous iterations, we used astate with (n)s 0 (n)p 0 (nÀ1)d 3 configuration in which the unpaired electronislocated in ahybrid orbitalof70% d z 2 and 30 %scharacter. [ b] Metahybridc orrection towards orbital interaction.
[c] The valuesw ithin the parentheses show the percentage contribution towardst he total attractivei nteraction DE elstat + +DE orb .
[ d] The values within the parenthesess how the percentage contribution towardst he total orbital interaction DE orb .

Conclusion
We report the first experimental observation of coordinatively saturated neutrala nd positively charged homoleptic Group 4 metal carbonyl complexes, which have been prepared in the gas phaseand/or in solid neon matrix. Combined infrared photodissociation spectroscopy and matrix isolation infrared absorptions pectroscopy studies revealt hat both zirconium and hafnium form eight-coordinate carbonyl neutrala nd cationic complexes.T he neutral octacarbonyl complexes TM(CO) 8 have cubic (O h )g eometries, whereas the cations TM(CO) 8 + have D 4h structures. In contrast, titanium only forms the stable six-coordinate cation complex Ti(CO) 6 + and seven-coordinate neutral complexT i(CO) 7 .T itanium octacarbonyl Ti(CO) 8 with O h symmetry is an energy minimum, but it is unstable with regard to loss of one CO ligand due to steric repulsion between the CO ligands. The Zr(CO) 8 and Hf(CO) 8 complexes represent the first experimentally observed homoleptic octacarbonyl neutral complexes of transition metals with 20 valencee lectrons. The molecules still fulfill the 18-electron rule, because one doubly occupied valenceo rbitalh as an ode at the metal atom, and thus, it does not mixw ith any of the metal valenceA Os. Ad etailed bonding analysis by using the sophisticated EDA-NOCV approachs uggests that the major contributiono ft he covalent metalÀCO bonding in the neutral complexes and in the cations comes from the [TM(d)]!(CO) 8 p back-donation. The most importantv alence orbitals of the metals are the do rbitals with the sa nd pf unctionsp laying an equally minor role. The bonding analysiss hows that Zr(CO) 8 and Hf(CO) 8 are stable for loss of one CO because the CO ligandse ncounter less steric repulsion than Zr(CO) 7 andH f(CO) 7 .T he heptacarbonyl complexes have shorterm etalÀCO bonds than that of the octacarbonyl complexes as ar esult of stronger electrostatic and covalent bonding, but the significantly smallerr epulsive Pauli term makes the octacarbonyl complexes lower in energy.
The described complexes of this work appear exotic and may not attractt he interest of chemists who are mainly interesting in "compounds in the bottle". It is indeed unlikely that the Group 4o ctacarbonyl complexes will find aw ide application in synthesis and chemicalt echnology.H owever,t hey increase our knowledgeo ft he most important bondingm odes of the Group 4m etal atoms and affect the 18-electron rule, which belongs to the arsenal of elementary rules of chemistry that are fundamental to chemical research. The dicationH e 2 2 + is irrelevantf or synthesis, but it is important to learn that the interference of the wave functions that give rise to covalent bondingc an overcome the immense Coulomb repulsion of 200 kcal mol À1 . [46] Likewise it is important to know the relevance of symmetry for the electron-counting rules in chemistry. According to the definition of coordinative saturation andu nsaturation, "a complexi ss aid to be coordinatively saturated if its electron count has attained the maximum permitted by bondingt heory.F or transition metals,t his is normally 18e." [47] We show in this work that the number 18 refers only to electrons that occupy orbitals, which have the right symmetry to mix with valence orbitals of the metal. The main relevance of the present study lies in its contribution to state the 18-electron rule more precisely.