Generation and Structural Characterization of the Cationic Iron

Feb 28, 1995 - in the 3da orbital (doubly occupied in the 4 state and singly occupied in the 4 " analog) to account for the energetic differences betw...
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J. Phys. Chem. 1995, 99, 11405-11411

11405

Generation and Structural Characterization of the Cationic Iron-Dinitrogen Complex Fe(N#? Joseph Schwarz, Christoph Heinemann, and Helmut Schwarz* Institut jiir Organische Chemie der Technischen Universitat Berlin, Strasse des I7 Juni 135, 0-10623 Berlin, Germany Received: February 28, 1995; In Final Form: May 15, 1995@

Gas-phase experiments in conjunction with CCSD(T) calculations were used to characterize the Fe(N2)+ complex in terms of electronic structure and binding energy. Theory clearly indicates a clear preference for an end-on structure of the N2 ligand to the transition-metal cation, resulting in a 42- state. At the highest level of theory, including estimated corrections, the binding energy amounts to 11.9 f 2.3 kcaYmol. From ligand exchange reactions, equilibration measurements, and theoretical considerations we further conclude NZ is at least 1 kcal/mol more strongly bound to Fe+ than C02 and 1.7 f 1.5 kcaYmol more strongly bound that Xe. Entropy drives the replacement of N2 by Xe in the Fe(N2)+ complex at 300 K.

Introduction The interest in direct nitrogen fixation, a long-standing challenge in chemistry, started in the early 1960s, when bacterial nitrogenase, a metalloenzyme complex containing molybdenum and iron as part of its reaction center, was isolated in its active form.' The preparation of the first stable and well-characterized dinitrogen complex, [Ru(NH&N2I2+, in 19652 and the immediately following discoveries of other stable dinitrogen complexes gave new impetus to this topic. From the chemical point of view the ability to synthesize complexes containing the dinitrogen group, especially those accompanied by a considerable altemation of the electronic structure of the usually inert dinitrogen molecule, may open up the possibility of the direct fixation of dinitrogen from the atmosphere. However, although the in vitro nitrogen fixation via stable or intermediate dinitrogen complexes, which can be reduced under certain conditions to release ammonia or hydrazine, slowly fills the gap between the chemistry of biological nitrogen fixation and that of N2 reactions in model system^,^ until now there has been no single large-scale procedure that can compete economically with the Haber-Bosch process. In the area of the dinitrogen complexes involving transitionmetal elements, most of the experimental work is confined to the liquid and solid phases; relatively little is known about the gas-phase properties of these species. In 1991, the cationic Cr(N2)+ complex was spectroscopically characterized by means of photodissociation ~pectroscopy,~ and the adiabatic binding energy between the ground state Cr+ (%, 3d5) cation and the dinitrogen molecule was determined to be 14.1 f 0.9 kcal/mol. This experiment prompted several quantum chemical investigations of N2-coordination to metal cation^.^ It was found that the ground state geometries of M(N2)+ (M = Na, Mg, Cr, Co) species correspond to linear C,, symmetry, which is favored over a T-shaped C2, arrangement due to the directional properties of the permanent quadrupole moment of Nz. Quite recently, Brucat and co-workers6 reported photodissociation experiments on Co(N2)+; interestingly and in contrast to all previous assignments, the data were interpreted to mean that the ground state of this molecule (deriving from the 3F, 4s03d8 state of Co+) adopts a T-shaped geometry, while an excited Dedicated to Professor Paul von RaguC Schleyer on the occasion of his 65th birthday. Abstract published in Advance ACS Absrracts, July 1, 1995 @

0022-365419512099-11405$09.0010

state, correlating with an excited 4s13d7configuration of Co+, was found to be linear. To our knowledge, no further information, either experimental or theoretical, is available on isolated transition-metddinitrogen complexes. However, many other weakly bound metalfligand systems have received growing attention, since they can be understood as the simplest solvation model for a single main group or transition metal ion.7 Detailed information has been obtained on the cationic argon-dinitrogen cluster Ar(Nz)+,*which is, however, electronically quite different than metal-dinitrogen systems due to the very similar ionization energies of Ar and N2. In the present article we first describe the experimental generation and characterization of the hitherto unknown Fe(N2)+ cluster. Accurate theoretical calculations on the geometry and the electronic structure of this species are presented. Finally, we compare the interaction energies between the Fe+ cation and the ligands L = N2, Xe, and C02, combining ligand exchange reactions in a Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometer, and theoretical result^.^

Experimental and Theoretical Methods The experiments were performed in a Spectrospin CMS-47X FT-ICR instrument equipped with an extemal ion source. The apparatus and its operation have been described in detail previously.'0 Briefly, the Fe+ ion is formed via laser desorption/ ionization" by focusing the beam of a Nd:YAG laser (Spectron Systems, fundamental frequency 1064 nm) onto a stainless steel target that was affixed in the extemal ion source.12 The ions are extracted from the source and transferred into the analyzer cell by a system of electrostatic potentials and lenses. The ion source, the transfer system, and the ICR cell are differentially pumped by three turbomolecular pumps (Balzers TP330 for the source and the cell and Balzers TPU 50 in the middle of the transfer system). After deceleration the Fe+ ions were trapped in the field of a superconducting magnet (Oxford Instruments), which has a maximum field strength of 7.05 T. The isolation of the metal's most abundant isotope (56Fe+)and all subsequent isolations were performed by using FERETS,I3 a computercontrolled ion ejection protocol that combines frequency sweeps and single-frequency pulses to optimize ion isolation. For the generation of the Fe(COZ)+ ion, atomic Fe+ was allowed to react for 3.5 s with B-butyrolactone, which was present at a static pressure of 1.4 x mbar. For collisional cooling of excited 0 1995 American Chemical Society

11406 J. Phys. Chem., Vol. 99, No. 29, 1995

Schwarz et al.

SCHEME 1 states possibly formed by the generation process, argon was present as a buffer gas as well as a collision gas at a static Fe(C02)+ + Kr -$%Fe(Kr)+ + COP pressure of ca. 1 x mbar. The pressures of p-butyrolactone and of the various other compounds were measured with an SCHEME 2 (uncalibrated) ionization gauge (Balzers IMG 070) and corrected Fe(C02)* + N2 Fe(N2)+ + COP for the reactant gas efficiency.I4 For the collision-induced decompositi~n'~ and ligand displacement experiments,I6argon and the other compounds were introduced through either correlation is found to increase this result such that, for example, pulsedI7 or leak valves. High-resolution and double-resonance a multireference configuration interaction treatment (six active experiments were performed as described elsewhere?s'0-'8 and electrons in six active orbitals as reference) yields a result of great care was applied to avoid any off-resonance excitation of 1.15 au,27close to the experimental value of 1.09 & 0.07 au?* the ions of interest, while ejecting unwanted signals.I9 All liquid All reported geometries have been optimized pointwise by compounds were subjected to multiple freeze-pump-thaw treating Fe(N2)+ as a quasi-diatomic molecule with the N-N cycles to remove uncondensable gases. I3CO2 was on-line distance fixed at the experimental equilibrium intemuclear synthesized by gently warming a mixture of Bai3C03 (98%, distance of 2.068 b ~ h r The .~~ N-N29 and Fef-(N2) stretching from Sigma Chemical Co.) and H2SO4. The rate constants of frequencies were obtained by fitting an analytical representation (cubic splines) to the computed total energies and solving the the ligand exchange reactions of Fe(Nz)+ with Xe (kxe)and FeSchrodinger equation for nuclear motion in this potential.27For (Xe)+ with N2 ( ~ N Jwere determined by applying a doublethe computation of binding energies, the magnitude of the basis resonance pulse to eject Fe(C02)+, which can be formed in a set superposition error was estimated using the standard secondary reaction of Fe(X)+ (X = Xe, N2) with the stationary counterpoise c o r r e ~ t i o n . All ~ ~ calculations were carried out P-butyrolactone. The absolute rate constants have estimated using the MOLPR094 software3' on a CRAY-YMP computer errors of f30%. To avoid mass discrimination effects, the of the Konrad-Zuse Zentrum fur Informationstechnik Berlin. intensity for Fe(Xe)+ was determined by multiplying the signal intensity of the most abundant Fe(Xe)+ isotopomer, Le., FeResults and Discussion (132Xe)+(natural abundance 132Xe: 26.9%), with the scaling factor 3.72 to account for the remaining isotopomeric Fe(Xe)+ As described earlier, the Fe(C02)+ cluster ion is easily ions. II-I each experiment an appropriate number of spectra were accessible when bare Fe+ is reacted in the gas phase with accumulated until the noise was below 10% (ca. 1000-1500 P-butyr~lactone.~' The bond dissociation energy (BDE) of Fe+scans). All functions of the instrument were controlled by a (C02) was determined by ligand exchange reactions with neutral Bruker Aspect 3000 minicomputer. compounds whose BDEs had been previously measured or The theoretical investigations of the Fe+-N2 complex were calculated. The lower limit of the BDE(Fe(C02)+) was carried out within the restricted open-shell coupled-cluster estimated from the nonoccurrence of the exchange process with approximation.20 To generate a zeroth-order wave function, a argon. In this case the calculated DOvalue for the 4A state of restricted open-shell Hartree-Fock (ROW) calculation was Fe(Ar)+ (7.4 kcdmol) from ref 5d was used. This is the correct carried out. The subsequent coupled-cluster treatment included procedure provided the ligand exchange reaction occurs under all single and double excitations from this reference function spin conservation on a quartet potential energy surface. How(CCSD), and the effects of triple contributions were evaluated ever, Fe(C02)+ could also be formed in a sextet state, which in a noniterative, perturbative way, denoted CCSD(T). The requires the sextet ground state bond energy of Fe(Ar)+ (6A, employed one-particle basis sets were of the atomic natural 4.3 kcaVmol from ref 5a) to derive the lower limit for BDEorbital (ANO) type?' have been designed to give an accurate (Fe(CO2)+). To refine this result, we performed an additional description of atomic ionization energies, electron affinities, and ligand exchange experiment and found that trapping the isolated polarizabilities, and should thus be well suited for the present Fe(C02)+ complex in Kr did not give rise to the formation of purpose. For iron, we chose the 8s7p6d4f2g contraction of a Fe(Kr)+. (See Scheme 1.) 21s15plOd4f2g primitive set according to Widmark et a1.,22 Additionally, we have recently initiated theoretical calculawhich has recently been successfully employed for the descriptions on Fe(L)+ clusters (L = noble gas), from which a lower tion of weakly and strongly bound cationic iron c ~ m p l e x e s . ~ J . ~ ~limit for the adiabatic BDE of Fe(Kr)+ (4CD molecular ground The AN0 contraction for the nitrogen atoms was of the type state to 6D and 'S atomic ground states, respectively) was ( 17s12~5d4f)/[7~6p4d3fl. predicted as 7.3 k ~ a l / m o l .Together ~~ with the upper limit for The following calculations were performed to calibrate the the experimental BDE for Fe(Xe)+ (11 k ~ a l / m o l the ~ ~ )BDE of performance of the employed basis sets and methods for the the Fe(C02)+ cluster is determined to be 9 f 2 kcaymol. Due treatment of electron correlation: (i) The excitation energy to this extraordinarily small bond dissociation energy, the Febetween the 6D(4s'3d6) ground state and the 4F(4s03d7)first (CO# species represents an ideal precursor for the generation excited state of the atomic Fe+ cation amounts to 0.197 eV of other interesting cluster ions like F ~ ( O Z ) + .Although ~J Fe(CCSD(T) result), compared to an experimental value (j-level ( 0 2 ) + can also be formed in a different manner, e.g., electron averaged) of 0.248 eV.24 A detailed discussion of this result impact ionization of a Fe(C0)5+/02 mixture, a similar procedure in light of remaining theoretical deficiencies and their systematic fails for the generation of Fe(N2)+. However, as shown in improvement can be found in our recent study of Fe+/noble Scheme 2, ligand displacement of Fe(C02)+ with N2 is a gas interaction^.^^ (ii) For the N2 molecule, using the expericonvenient method for producing Fe(Nz)+. mental intemuclear distance of 2.068 b ~ h r one , ~ obtains ~ good Due to the very high bond dissociation energy (BDE) of the agreement between the calculated (azz= 14.79 au; an = a,, dinitrogen triple bond (DO= 228.4 kcaVm01~~) and the genera= 10.20 au, CCSD(T) results using a finite electric field tion process of the Fe(N2)+ ion, we did not expect the insertion perturbation) and the experimental (azz= 14.98 au; a, = a,, of the transition-metal ion into the NN triple bond to generate NFeN+. In fact, when Fe(N2)+ is mass selected and subjected = 10.39 au26)components of the dipole polarizability tensor. to collisional activation with argon, over the entire energy regime The employed basis set yields a quadrupole moment of 0.94 au applied (the center-of-mass energies cover the range 0-50 eV), at the Hartree-Fock level of theory. As stated earlier,saelectron

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J. Phys. Chem., Vol. 99, No. 29, 1995 11407

Cationic Iron-Dinitrogen Complex Fe(N2)+

TABLE 1: Theoretical Result9 for Electronic States of Fe(W

Re(bohr)b w e (cm-l)c

Do (kcal BDE (kcal mol-!)’ TO(kcal mol-’)f

4x-

4A

6rI

6A

3.693 318 18.1 13.6

3.990 267 15.3 10.8 2.89

4.567 152 8.1 8.1 5.5

4.550

0.0

157 8.8 8.8 4.8

a From CCSD(T) calculations. Equilibrium distance between the Fe+ cation and the nearest nitrogen atom with the N-N distance fixed at 2.068 bohr. Stretching frequency between Fe+ and N2. Binding energy with respect to the metal asymptote of the same spin, corrected for the zero-point energy of the Fe+-N2 stretching frequency. e Bond dissociation energy of Fe(N2)+ to Fe+ (6D) and N2 (’X,+),corrected for the zero-point energy of the Fe+-N2 stretching frequency. Correction for basis set superposition reduces the quartet state BDEs to 12.8 (42-)and 10.1 (4A) kcaymol, respectively. /Adiabatic excitation energy, corrected for zero-point energies of the Fe+-N2 stretching frequency. 9 The fine-structure splitting of the 4A state can be estimated as 1.1 kcaVmol (Lefkbvre-Brion, H.; Field, R. W. Perturbations in the spectra of diatomic molecules; Academic Press: Orlando, 1986). Thus, spin-orbit coupling is unlikely to interchange the relative order of the lowest 4A and 4X- states (see also the discussion in ref 23).

the complex exclusively decomposes to Fe+ and N2. This is precisely expected to occur for a weakly bound ion-quadrupole1 charge-induced dipole complex and serves to exclude the formation of any covalent iron-nitrogen bond in the Fe(N2)+ ion produced according to Scheme 2. However, the problem of the exact coordination of N:! to Fe’ side-on (C2”)versus endon (C-”) cannot be solved experimentally with the methods presently available to us. To this end, ab initio calculations on the Fe(N:!)+ complex have been performed. Let us first consider the linear end-on coordination. As discussed earlier in a related one expects seven lowlying electronic states for a linear Fe+-N2 system in the AS coupling scheme: 42-,41-1, 4A, and 4@ with quartet multiplicity, correlating with the first excited 4F(4s03d7)atomic state of the iron cation, and %+, 611,and 6A in the sextet regime, which is connected with the atomic ground state 6D(4s’3d6)for Fe+. We will present explicit results for four of these states, two from the quartet (42-and 4A, the lowest and highest quartet states in cationic irodnoble-gas complexes23)and two from the sextet (611and 6A, which were the lowest sextet state in cationic iron/ noble-gas systemsz3)manifolds, respectively. The remaining states should be energetically as well as geometrically close to those of the same multiplicity calculated here, since the overall ligand field splitting in weakly bound metal-ligand systems has been found to be rather The theoretical results are summarized in Table 1. The molecular properties of the two sextet states appear to be very similar. A comparison of the quartet and sextet states reveals that the two molecular quartets are characterized by shorter Fe+-N2 distances, higher Fe+-N2 stretching frequencies, and larger binding energies with respect to the metal asymptote of the same spin. As discussed ea~dier,~~,’~,g differences between the two spin states can be understood from the additional repulsion that arises in the sextet states due to the single electron in the spatially diffuse 4s orbital of the metal cation. In terms of their spectroscopic properties, the two quartet states are found to be more distinct from each other than their sextet analogs. In the one-electron picture, this may be rationalized from the synergetic donor/acceptor ability of the Nz ligand: in the 42-state the dominant electron configuration is of the 3da’3dd3dd2type on the Fe+ cation, whereas for the 4A state the corresponding occupation pattem is 3da23djt23dd3. In a quartet electronic state for Fe(NZ)+, the N2 molecule can act as a weak a-donor and n-acceptor ligand, transferring

electron density from the nonbonding “lone-pair“ in the “empty” 4s orbital of Fe+ with concomitant back-donation from the occupied 3dn orbitals of Fe+ into the n* orbitals of the N-N triple bond. This is qualitatively apparent for both states from the Mulliken population analyses applied for the Fe+ cation in the Hartree-Fock (ROHF) wave functions (42-: q(Fe) = f0.92; s(Fe), 6.10e; p(Fe), 12.04e; d(Fe), 6.92e; f(Fe), 0.01e. 4A: q(Fe) = +0.92; s(Fe), 6.10e; p(Fe), 12.04e; d(Fe), 6.92e; f(Fe), 0.01e, both at the equilibrium distances). On the contrary, electron release from the ligand into the 4s orbital and backdonation of 3d electrons is not apparent as such in the sextet molecular states (6A: q(Fe) = f0.92; s(Fe), 6.97e; p(Fe), 12.0%; d(Fe), 6.01e; f(Fe), 0.01e. 61-1: q(Fe) = $0.93; s(Fe), 6.98e; p(Fe), 12.06e; d(Fe), 6.01e; f(Fe), 0.01e). Still, the Mulliken analyses applied to the ROHF wave functions of the quartet states do not explain the shorter bond distance, the higher Fe+-N2 stretching frequency, and the larger bond energy of the 42- as compared to the 4A state. Note, however, that on the Hartree-Fock level of theory, the 42-state is energetically disfavored with respect to the 4A (e.g. by 4.4 kcaVmol at an Fe+-N2 distance of 3.9 bohr), and it is only upon inclusion of electron correlation that is relative energy is lowered: within the CCSD model, which does not incorporate the perturbative estimate for the connected triple excitations, the two quartet states are energetically almost degenerate (the adiabatic 4A to 42-excitation energy amounts to 0.4 kcdmol). Finally, at the highest level of computation applied in this work (CCSD(T)), the adiabatic excitation energy from 42- to 4A amounts to 2.8 kcaVmo1, and it is expected that higher levels of n-particle space treatment will enlarge this energy gap even further. Part of the pronounced correlation effect stems from the necessity of including a second valence configuration (occupation pattem on the Fe+ center: 3da’3djt23dd4)in the total molecular wave function of 42- symmetry, whereas the 4A state has only one important valence configuration (3d02-‘ 3dn23dd3). Moreover, if there is a higher degree of n backdonation in the 4Z- as compared to the 4A state (which is suggested from the d-orbital occupation patterns; see above), it would only be apparent from an explicitly correlated wave function, since the Hartree-Fock populations of the two quartet states are essentially identical. The same conclusion was reached in a recent case study of the cationic Fe(CO)+ species,33 which is formally isoelectronic to Fe(N2)+. On the other hand, one could simply invoke the repulsion between metal electrons in the 3d, orbital (doubly occupied in the 4A state and singly occupied in the 42- analog) to account for the energetic differences between the two quartet states. As expected from the electrostatic properties of N2, the theoretical investigations clearly reveal the preference for endon versus side-on coordination to the Fe+ cation. For reasons of computationalconvenience, this comparison has been carried out at the CCSD level of theory. Since the relative stability of a linear Fe+-N2 coordination is energetically in the same order as the calculated overall binding energies, it is not expected that inclusion of the perturbative treatment of triple excitations (CCSD(T)) will render a side-on structure more favorable. Rather, a higher degree of electron correlation treatment will lower the relative energy of the linear 42- state, as discussed above. In Figure 1 we give the optimized CCSD geometries as well as total CCSD binding energies relative to the ground state of Fe+ for the side-on and end-on approaches of dinitrogen to the transition-metalcation in both relevant spin multiplicities. The occupation patterns in the Hartree-Fock reference functions for the side-on approaches were 4s’3da‘3djt23dd3 (6A2) and 3du23d.7z23dd3(4A2),re~pectively.~~ It is found that formation

Schwarz et al.

11408 J. Phys. Chem., Vol. 99, No. 29, 1995

BDE=84

BDE=-O

BDE-IO

BDE = .6 8

Figure 1. Optimized CCSD geometries (N-N bond length fixed at 2.068 bohr) and total interaction energies for the side-on and end-on approach of N2 to Fe+ in sextet and quartet multiplicity. Bond lengths are given in bohr, and total interaction energies (kcaYmo1) are with respect to Fe+ (6D) and N2 (]E,+).For comparison, the corresponding results for the linear geometries within the CCSD(T) approximation are (a) bond lengths 4.550 bohr (6A), 3.693 bohr (42-);(b) total using the Fe+ interaction energy 9.0 k c d m o l (6A), 11.7 kcal/mol (4E-, 4F-6D separation from the CCSD calculations).

of a linear Fef-N2 complex is energetically much more favorable as compared to the side-on mode of coordination. For example, the side-on approach in the considered quartet state is not bound at all with respect to the sextet asymptote. Similar to linear coordination, the overall interaction energy (Le., the binding energy with respect to the metal asymptote of the same spin) in the side-on approach of N2 to Fe+ is much smaller in the sextet as compared to the quartet spin state. The preference of end-on versus side-on coordination of N2 to a transitionmetal cation has been theoretically evidenced for Co(N2)+ and Cr(N2)+ before.5a Along with the results from the present investigation it appears that it is the quadrupole moment of N2 that controls the geometries of these species. Simply speaking, this molecule will preferentially orient itself so that a region of negative charge concentration points toward the positively charged center of the Coulombic field generated by the transition-metal cations. Among all attractive electrostatic and inductive contributions to the Fe+-N2 potential, the chargequadrupole interaction Vcs has the longest range behavior (Vcs = r-3). Against this background, the recently derived6T-shaped geometry for Co(N2)+ appears somewhat surprising. For an explanation, the authors employed a purely electrostatic model in which the repulsive part was a hard wall potential, which, despite the preference for linear coordination due to the quadrupole moment and the polarizability, results in a lower energy for the side-on approach due to the geometric anisotropy of the dinitrogen molecule. The conflicting experimental6 and t h e ~ r e t i c a lresults ~ ~ concerning the structure of this molecule obviously call for further clarification from both sides. We note in passing that in the neutral Fe(N2) and Fe2(N)2 clusters, however, the side-on approach may well be preferred, since in the absence of a charge the degree of 3d(Fe) n*(N2) electron donation will become a crucial factor with respect to the ground state geometry of these species.5c As exemplified in a recent investigation employing semiempirical molecular orbital methods,35 the question of end-on versus side-on coordination of dinitrogen to transition-metal atoms and clusters can become rather complicated if the corresponding complexes incorporate additional ligands. For a prediction of the true ground state multiplicity, as well as the ground state binding energy of the Fe(N2)+ complex, one has to correct the theoretical results so that the method of calculation correctly describes the asymptotic 6D(4s’3d6)/4F(4s03d7) energy separation in the Fe+ cation. The latter is underestimated by 1.2 kcal/mol within the chosen CCSD(T) model, which is considerably smaller compared to the calculated excitation energy from the lowest quartet (42-)to the lowest +

sextet (6A) state (4.8 kcaumol, Table 1). Furthermore, we have recently d e m ~ n s t r a t e dthat ~ ~ explicit consideration of deficiencies in the present CCSD(T) calculations (incomplete treatment of one- and n-particle space, core correlation, relativistic effects) would lower the quartet states with respect to their sextet counterparts. It is thus a straightforward conclusion that the ground state of Fe(N2)’ is of quartet multiplicity. Next, we derive a theoretical estimate for the adiabatic (molecular ground state to fragment ground states) bond dissociation energy of Fe(N2)+, After correcting for the description of the asymptotic dissociation limit and adding the zero-point vibrational energies for the remaining vibrations (0.8 k c a l / m 0 1 ~ ~one - ~ ~arrives ) at a directly computed 0 K bond dissociation energy of 11.6 kcaV mol for the 42-state of this species. To account for remaining errors, we add the counterpoise correction for basis set superposition (-0.8 kcal/mol), adopt estimates for the effects of higher one- and n-particle space treatment, relativistic effects, and core correlation from our recent study on Fe’hoble-gas systems ( f l . 1 kcal/m01~~), and add the same estimated uncertainty of k2.3 kcal/mol as in the earlier study. The theoretical prediction, on equal footing with our previous results for Fe+/ noble-gas systems, for the ground state interaction energy between Fe+ and N2 amounts to 11.9 41 2.3 kcal/mol. Note, however, that the assumption that the corrections for higher levels of computation are numerically identical for the Fe+/ noble-gas and Fe(N2)+ systems is rather crude and may lead to an underestimation of the true Fe+-N2 bond strength.38 Finally, the electronic properties of the Fe(N# complex are briefly compared to the formally isoelectronic Fe(C0) species. Both molecules39are predicted to exhibit linear geometries and 4Z- electronic ground states. Within the CCSD(T) approximation the calculated distances between the Fe+ cation and the closed-shell ligand appear to be very similar (Fe(Nz)+, 3.693 bohr; Fe(CO)+, 3.61 133). However, the bond strength between Fe+ and N2 is less than half that of the Fe+(CO) couple (experimental,3 1.4 & 1.8 kcal/mol; calculated within the CCSD(T) approximation, 28.8 kcal/moP3). Concomitantly, excited electronic states of both spin multiplicities are energetically less disfavored in Fe(N2)+: the molecular quartet-sextet excitation energies within the CCSD(T) approximation amount to 12.3 kcal/mol for Fe(C0)+33and less than 5 kcal/mol for Fe(N2)+. A higher degree of the a-donor, n-acceptor character of the neutral ligand (see above) is apparent when the metal’s 4s and 3d orbital populations in the two 4C- electronic ground states are compared (Fe(N2)+: 4s(Fe), 0.10e; 3d(Fe), 6.92e, present work. Fe(CO)+: 4s(Fe), 0.26e; 3d(Fe), 6.77e, ref 39). In summary, these data confirm a well-known rule of inorganic coordination chemistry: within the “spectrochemical row” carbon monoxide is a much better ligand than the isoelectronic dinitrogen molecule.40 Without referring to molecular orbital arguments, this result is already borne out from elementary electrostatic considerations: in contrast to N2, by way of symmetry, CO has both a nonvanishing dipole moment and dipole moment derivative. Moreover, the quadrupole moment of CO is 60% larger than that of N2,27and its average electric dipole polarizability is about 10% largefl’ than for the homonuclear isoelectronic counterpart. Let us now compare the theoretical findings with the experimental results. By employing ligand exchange experiments, we have tried to bracket the BDE of Fe+-(N2). As depicted in Scheme 3, ligands L (with L = C2H6,7eCH4,7fand Xe7d)that were introduced via a pulsed valve replace N2 from the thermalized Fe(N2)+ complex, while in the reaction of Fe(N2)+ with Ar and Kr (also pulsed-in) no displacement is observed. According to the generation process of Fe-(Nz)+,

J. Phys. Chem., Vol. 99, No. 29, 1995 11409

Cationic Iron-Dinitrogen Complex Fe(NZ)+

SCHEME 3 Fe(N2)+ + L-

Fe(L)+

+

N2

+

N2

L = C2Hs,CHI, Xe Fe(N2)+

+ L+

Fe(L)+

+

L = Ar. Kr

TABLE 2: Bond Dissociation Energies (BDEs) of FeLf Complexes BDE (Fe+-L) (experimental) (kcaymol)

ligand (L)

BDE (Fe+-L) (theoretical) (kcaVmol)

15.3 f 1.8“ 13.7 f 0.8b 9.0 f 2.0‘

C2H6

CH4 Xe

14.2 f 2.3d 9.6 f 2.3d 5.6 f 2.3d

Kr

Ar

Reference 7e. Reference 7f. Reference 7d. Reference 23.

SCHEME 4 Fe(Xe)+

+ N2 (pulsed-in)

-

Fe(N2)+ + Xe

SCHEME 5 Fe(N2)+

kxe + Xe = Fe(Xe)+ + N2 kN2

BDE(Fe-(N2)+) should be larger than BDE(Fe-(C02)+). From the data given in Table 2 and the occurrence versus nonoccurrence of ligand exchange, we arrive at BDE(Fe-(Nz)+) = 9 f 2 kcdmol. The very small range of BDEs for Fe+-(X) (X = C02, N2, Xe) and the possibility of observing slightly endothermic reactions when reactants were introduced via pulsed valves$2 however, prompted us to perform further experiments to establish the BDE of Fe+-(Nz). To check the upper limit for BDE(Fe+-(Nz)), isolated Fe(Xe)+ (generated from Fe(C02)+ and pulsed-in Xe) was reacted with N2 in a pulse experiment. As depicted in Scheme 4,formation of Fe(N# is observed. The occurrence of the exchange reaction Fe(N2)+ Xe Fe(Xe)+ N2 in both directions implies (i) the BDEs of Fe(Nz)+ and Fe(Xe)+ are very similar and (ii) bracketing the upper limit for BDE(Fe+-(NZ)) by isolating Fe(N2)+ and pulsing-in Xe is not the method of choice. Rather, equilibrium measurements should be performed. However, the presence of P-butyrolactone, which also reacts with either Fe(Nz)+ or Fe(Xe)+, complicates this procedure and causes, in addition, serious intensity problems. In view of these obstacles we have chosen a more indirect method43for the determination of the relative BDEs of Fe+-(NZ) and Fe+-(Xe). The rate constants of the reaction of Fe(N2)+ with Xe(kxe) and of Fe(Xe)+ with N2 (kNz) were determined independently and then converted into the equilibrium constant Keq. For the exchange process Fe(N2)+ with Xe, the rate constant amounts to kxe = 1.6 x lo-’’ cm3 molecule-’ s-l. In the analogous reaction of Fe(Xe)+ with N2, we determined a rate constant of kN2 = 1.0 x lo-’’ cm3 molecule-’ s-l. From these two rate constants, one obtains the equilibrium constant Keq = kxe/kN, = 1.6 f 0.4 for the reaction depicted in Scheme 5 , with the assumption of 10% errors in the relative rate constants. The standard free enthalpy AG for this process, AG = AH - TAS, can be obtained from the measured equilibrium constant via the Gibbs-Helmholtz equation, AG = -RT ln(Keq). Accordingly, we conclude that under the conditions of the experimental setup (for which we assume a temperature of 300 K) substitution of Fe+-coordinated Xe by molecular NZis endoergic by 0.3 0.1 kcdmol. Furthermore, if Fe(C02)+ is reacted with a 1: 1 mixture of N2 and Xe for 2 s,

+

+

*

Few# and Fe(Xe)+ are formed in a ratio of 1:2,also indicating that Xe is preferentially coordinated to the “bare” Fe+ cation as compared with Nz. It is usually assumed that in ligand exchange reactions (MA+ B MB+ A) under low-pressure conditions the entropic term TAS is negligible. We have found, rather, that in such experiments the occurrence versus nonoccurrence of a ligand substitution process will be governed by the associated enthalpy change AH, which directly relates to the bond dissociation energies of the two ligands A and B in the sense that a more strongly bound ligand will substitute a more weakly bound one but not vice versa (“bracketing”). According to this argument, in general, a reaction, although exothermic, may be hampered due to activation barriers. In the present case of weakly bound ligands, however, the existence of activation energies in the classical sense, i.e., energy maxima along a reaction pathway associated with the simultaneous cleavage and formation of chemical bonds, is unlikely since the metal-iodligand interactions are mainly electrostatic in nature. Nevertheless, one might argue that a possible change of spin state may prevent a ligand substitution reaction at the Fe+ cation from proceeding along the adiabatic pathway, Le., from ground state reactants to ground state products. Against this argument, we note theoretical predictions that both Fe(Xe)+ and Fe(N2)+ are ground state quartet molecules; kinetic restrictions due to spin change might thus appear only if Fe(COz)+ was of a sextet spin multiplicity. Since one does in fact observe ligand exchange from Fe(C02)+ to both Fe(Xe)+ and Fe(NZ)+ energy barriers for the reverse processes, it must, if it exists at all, be smaller than the reaction enthalpy in the forward direction and thus will not influence the derivation of relative bond energies from the observation and nonobservation of ligand substitution reactions. Now, we address the TAS term. To this end, the total entropies (translational, rotational, and vibrational contributions) of Fe(Xe)+, Fe(Nz)+, N2, and Xe at 300 K have been calculated using the theoretically determined geometries and frequencies for Fe(Xe)+ (R = 4.994 bohr; Y = 159 cm-’ 23) and Fe(N2)+ (R(Fe-N) = 3.693 bohr; R(N-N) = 2.068 bohr; vo = 318 cm-I; vn = 275 cm-’ 36) as well as a N-N bond distance of 2.068 bohr for the free N2 molecule.32 The analysis reveals that the considered ligand displacement reaction Fe(Nz)+ Xe Fe(Xe)+ N2 is driven by the favorable change in entropy upon substitution of the Fe+-coordinated dinitrogen molecule by the atomic xenon ligand. More specifically, the extra rotational degrees of freedom on the product side (characteristic temperature of rotation for N2: 2.8 K) are not compensated by the additional intemal degrees of freedom in the Fe(N2)’ system, i.e., the Fe+-(N*) rocking motions with corresponding characteristic vibrational temperatures of 396 K. Moreover, the Fe(Xe)+/N2 couple is entropically favored due to the lower vibrational temperature for the metal-ligand stretching mode of Fe(Xe)+ (229 K) as compared to Fe(N2)+ (458 K). In summary, the total entropy change AS (Fe(N2)+ Xe Fe(Xe)+ N2) amounts to +7.2 caY(mol.K), thus contributing a TAS term of -2.46 kcdmol to the overall free enthalpy change of the ligand substitution reaction. We point out that this relatively large entropic contribution to a ligand substitution reaction (commonly, much smaller effects in the range of 0.1 k c d m o l are encounteredg) arises from the particular situation that a light molecular ligand is displaced by a heavy atom of comparable binding affinity to the transition-metal cation. Furthermore, the calculated frequencies allow for an estimate of the thermal contribution to the reaction enthalpy A ( W = AH(300K) - AH(0K). It is found (Table 3) that the additional rotational energy on the product side (two linear molecules

-

-

+

+

+

+

+

-

11410 J. Phys. Chem., Vol. 99, No. 29, 1995

Schwarz et al.

-

TABLE 3: Calculated Reaction Entropy and Thermal Contributions to Reaction Enthalpy for Fe(Nz)+ Xe Fe(Xe)+ NZat T = 300 K

+

+

TAS(lJb

AS(? translation rotation vibration total

-2.2 +11.3 -1.9 17.2

-0.66

$3.40 -0.58 +2.16

4

AH(lJ - AH(T=O)b 0 +0.60 -0.43 +0.17

I

Fe(C0,)'

4 I 1 I

In caU(mo1-K). In kcaUmol.

compared to only one linear molecule on the educt side) is almost compensated for by the thermal energy in the low-energy rocking modes of Fe(Nz)+ (A(AH) = f 0 . 1 7 kcaymol). Thus, our result for the free enthalpy change of -0.3 f 0.1 kcdmol in the reaction Fe(NZ)+ Xe Fe(Xe)+ f NZ corresponds mainly to the sum of the zero-Kelvin enthalpy change (+1.7 kcaYmo1) and the entropy contribution at 300 K (-2.2 k c d mol) with only a small contribution from the thermal enthalpy term ( f 0 . 2 kcaymol). Estimating errors of 0.5 kcdmol for the deduced A ( W value and 1 kcdmol for the TAS term, we arrive at the conclusion that at T = 0 K N2 is more strongly bound to Fe+ than Xe by 1.7 f 1.5 kcallmol. Another point to be considered is the relative BDEs of Fe(Nz)+ and Fe(C02)' since in both cases the experiments (see above) gave the same "bracketing" result (9 f 2 kcdmol) for the bond dissociation energy. Therefore, we have reacted thermalized Fe(N2)' cations with stationary present I3CO2 for 1 s, applying again a double-resonancepulse at Fe(I2C02)+(see the Experimental and Theoretical Methods section). In this experiment, no Fe(I3C02)+could be detected. For the process, Fe(N2)+ C02 Fe(C02)+ N2, it is reasonable to assume that both A ( W and TAS are, in fact, smaller than for the Nz/ Xe exchange discussed above, since one is looking at the displacement of one linear molecule by another linear molecule, in contrast to the molecule/atom exchange. According to the prevailing reaction conditions, COz should be at least 1 kcaY mol more weakly bound (in the sense of 0 K bond dissociation energies) to Fe+ than N2.44 Moreover, COz should be bound more strongly to Fe+ than a Kr atom by ca. 2.0 kcdmol (1 kcdmol from the nonobservation of the exchange reaction (see above) and an assumed TAS term of 1.0 kcdmol, in analogy to the Nz/Xe case). For an estimate of absolute bond energies, one might be tempted to take the lower (calculated) limit for BDE(Fe+-Kr) = 7.3 kcdmol (Table 2) to arrive at the following results: BDE(Fe+-COz) > 9.3 kcdmol; BDE(Fe+-N2) > 10.3 kcdmol. On the other hand, one could also use the experimental BDE for Fe(Xe)+ (9.0 f 2.0 kcdm01'~) to derive absolute binding energies, which would be slightly smaller. However, we would like to point out that both the experimental and the theoretical uncertainties for relative and absolute bond energies in the present set of data are in the order of the accuracy that is required for weakly bound ligands such as noble-gas atoms, Nz, and CO2. However, in view of the intemal consistency the relative bond strengths to Fe+ for the couples Kr/C02, COzNz, and NzKe as derived from the present experiments should be all right (see Figure 2). Moreover, we note that the absolute bond energy for Fe(N2)+ deduced from the theoretical calculation discussed above (1 1.9 C! 2.3 kcal/mol) fits well to the absolute Fe+-N2 bond strengths that can be derived from the various anchor points. Nevertheless, the relative order of calculated bond lengths for Fe(Xe)+ (14.2 f 2.3 k c d m 0 1 ~ and ~ ) Fe(NZ)+ (1 1.9 f 2.3 kcallmol) appears contrary to the experimental result that Xe is less strongly bound to Fe+ as compared to N2. In conclusion, we have presented a convenient method for the generation of the Fe(N2)+ ion. This weakly bound species

+

+

-

*

> 1 kcaliinol

I

'

I I

'

ca. I .7kcal/mol

I

Fe(Xe)+

> I .S kcaliinol

I

Fe(Kr)+ -

+

+

Figure 2. Relative bond dissociation energies (BDEs) derived from the present study. is characterized as a complex between the "bare" Fe cation and an intact dinitrogen moiety. Theoretical calculations indicate a clear preference for end-on coordination of the N2 ligand to the transition-metal cation. Combining ligand exchange reactions, equilibrium measurements, and theoretical considerations, we have established that (i) N2 is at least 1 kcaYmol more strongly bound to Fe+ than C02; (ii) NZis more strongly bound to Fe+ than Xe by 1.7 f 1.5 kcdmol. The fact that NZ is a better ligand to a transition-metal cation (Fe+ in the present case study, Co+ in refs 5a, 6 and 7g) than COz is indeed astonishing, as, from a purely electrostatic approximation (see above), the reverse order of bond strengths would be expected. Obviously, more detailed experimental and theoretical work on these interesting cluster species is indicated.

Acknowledgment. The authors would like to thank Dip1.Chem. Hans Comehl, Dip1.-Chem Andreas Fiedler, DipLChem. Max Holthausen, Dr. Detlef Schroder, and Dr. Detlef Stockigt for stimulating discussions and helpful comments. Computing resources and technical assistance (Dr. Thomas Steinke) were generously provided by the Konrad-Zuse Zentrum fur Informationstechnik Berlin. The financial support of our work by the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie, and the Volkswagen-Stiftung is gratefully acknowledged. References and Notes (1) Camahan, J. E.; Mortensen, L. E.; Mown, H. F.; Castle, J. E. Biochem. Biophys. Acta 1960, 38, 188. (2) Allen, A. D.; Senoff, C. V . Chem. Commun. 1965, 621. ( 3 ) (a) Bemo, P.; Hao, S . ; Minhas, R.; Gambarotta, S . J . Am. Chem. Soc. 1994,116,7418. (b) Shilov, A. E. Pure Appl. Chem. 1992,64, 1409. (c) Shilov, A. E. J . Mol. Catal. 1987, 41, 221. (d) Chatt, J.; Dilworth, J. R.; Richards, R. L. Chem. Rev. 1978, 78, 589. (4) Lessen, D. E.; Asher, R. L.; Brucat, P. J. Chem. Phys. Lett. 1991, 177, 380. ( 5 ) (a) Bauschlicher, C. W., Jr.; Partridge, H.; Langhoff, S . R. J . Phys. Chem. 1992, 96, 2475. (b) For a further discussion of Mg(NZ)', see: Sodupe, M.; Bauschlicher, C. W., Jr.; Partridge, H. Chem. Phys. Lett. 1992, 192, 185. (c) For a study of neutral Fe(N2). see: Bauschlicher, C. W., Jr.; Pettersson, L. G. M.; Siegbahn, P. E. M. J . Chem. Phys. 1987, 87, 2129. For studies of M'hoble-gas interactions of the same research group, see: (d) Bauschlicher, C. W., Jr.; Partridge, H.; Langhoff, S . R. J . Phys. Chem. 1992, 96, 5351. (e) Bauschlicher, C. W., Jr.; Partridge, H. J . Phys. Chem. 1994, 98, 2301. (6) Asher, R. L.; Bellert, D.; Buthelezi, T.; Brucat, P. J. J . Phys. Chem. 1995, 99, 1068. (7) More recent work from representative laboratories include the following: (a) von Helden, G.; Kemper, P. R.; Hsu, M.-T.; Bowers, M. T. J . Chem. Phys. 1992, 96,5350. (b) Kemper, P. R.; Bushnell, J.; von Helden, G.; Bowers, M. T. J . Phys. Chem. 1993, 97, 5 2 . (c) von Helden, G.; Kemper, P. R.; Bushnell, J.; van Koppen, P. A. M.; Bowers, M. T. J.Phys. Chem. 1993, 97, 1810. (d) Schultz, R. H.; Crellin, K. C.; Armentrout, P. B. J . Am. Chem. Soc. 1991, 113, 8590. (e) Schultz, R. H.; Armentrout, P.

J. Phys. Chem., Vol. 99, No. 29, 1995 11411

Cationic Iron-Dinitrogen Complex Fe(NZ)+ B. J . Phys. Chem. 1992, 96, 1662. (f) Schultz, R. H.; Armentrout, P. B. J . Phys. Chem. 1993, 97, 596. (8) Asher, R. L.; Bellert, D.; Buthelezi, T.; Brucat, P. J. Chem. Phys. Lett. 1994, 227, 623. (h) Asher, R. L.; Bellert, D.; Buthelezi, T.; Weeraskera, G.; Brucat, P. J. Chem. Phys. Lett. 1994, 228, 390. (i) Schwarz, J.; Schwarz, H. Organometallics 1994, 13, 1518. (i)Schroder, D.; Fiedler, A.; Schwarz, J.; Schwarz, H. Inorg. Chem. 1994, 33, 5094. (k) Yeh, C. S.; Pilgrim, J. S.; Willey, K. F.; Robbins, D. L.; Duncan, M. A. Znt. Rev. Phys. Chem. 1994, 13, 231. (1) Robbins, D. L.; Brock, L. R.; Pilgrim, J. S.; Duncan, M. A. J. Chem. Phys. 1995, 102, 1481. (8) (a) Stephan, K.; Miirk, T. D. Chem. Phys. Lett. 1982,87, 226. (b) Illies, A. J.; Bowers, M. T. Org. Mass Spectrom. 1983, 18, 553. (c) Ding, A.; Futrell, J. H.; Cassidy, R. A.; Cordis, L.; Hesslich, J. Surf. Sei. 1984, 156, 282. (d) Nagata, T.; Kondow, T. Z. Phys. D.1986,4, 89. (e) Frecer, F.; Jain, D. C.; Sapse, A,-M. J . Phys. Chem. 1991, 95,9263. (f) Magnera, T. F.; Michl, J. Chem. Phys. Lett. 1993, 192, 192. (8) Mihnert, J.; Baumgiirtel, H.; Weitzel, K.-M. J . Chem. Phys. 1995, 102, 180. (9) For a similar study on A u f L systems, see: Schroder, D.; HruHAk, J.: Hertwig. R. H.; Koch, W.; Schwerdtfeger, - P.; Schwarz, H. Omanometallies 1993, 14, 312. (10) (a) Eller, K.; Schwarz, H. Int. J . Mass Spectrom. Ion Processes 1989, 93, 243. (b) Eller, K.; Zummack, W.; Schwarz, H. J . Am. Chem. Soc. 1990, 112, 621. (c) Eller, K. Ph.D. Thesis, Technische Universitat Berlin, D83, 1991. (1 1) (a) Freiser, B. S. Talanta 1985, 32, 697. (b) Freiser, B. S.Anal. Chim. Acta 1985, 178, 137. (12) Kofel, P.; Alemann, M.; Kellerhans, Hp. Int. J . Mass Spectrom. Ion Processes 1985, 65, 97. (13) Forbes, R. B.; Laukien, F. M.; Wronka, J. Int. J . Mass Spectrom. Ion Processes 1988, 83, 23. (14) Bartmess, J. E.; Georgiadis, R. M. Vacuum 1983, 333, 149. (15) (a) Cody, R. B.; Bumier, R. C.; Freiser, B. S. Int. J. Mass Spectrom. Ion Phys. 1982, 41, 193. (b) Bumier, R. C.; Cody, R. B.; Freiser, B. S. Anal. Chem. 1982, 54, 96. (c) Bumier, R. C.; Cody, R. B.; Freiser, B. S. J . Am. Chem. Soc. 1982, 104, 7436. (16) Halle, L. F.; Houriet, R.; Kappes, M.; Staley, R. H.; Beauchamp, J. L. J. Am. Chem. Soc. 1982, 104, 6293. (17) (a) Carlin, T. J.; Freiser, B. S. Anal. Chem. 1983, 55, 571. (b) Jacobson, D. B.; Freiser, B. S. J . Am. Chem. Soc. 1985, 107, 5876. (18) Comisarow, M. B.; Grassi, V.; Parisod, G. Chem. Phys. Lett. 1978, 57, 413. (19) (a) Beauchamp, J. L. Annu. Rev. Phys. Chem. 1971,22, 257. (b) Heck, A. J. R.; de Koening, L. J.; Pinske, F. A,; Nibbering, N. M. M. Rapid Commun. Mass Spectrom. 1991, 57, 413. (20) For recent reviews on the coupled-cluster method, see: (a) Bartlett, R. J. J. Phys. Chem. 1989, 93, 1697. (b) Bartlett, R. J.; Stanton, J. F. In Reviews in Computational Chemistry; Lipkowitz, K. B., Ed.; VCH: New York, 1994; Vol. 5. (c) The employed program computes the triples contributions according to the following: Watts, J. D.; Gauss, J.; Bartlett, R. J. J . Chem. Phys. fi93, 98, 8718. (21) Almlof, J.: Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (22) (a) Widmark, P.-0.; Perrson, B. J.; Roos, B. 0. Theor. Chim. Acta 1991, 79,419. (b) Pou-Amerigo, R.; Merchan, M.; Widmark, P.-0.; Roos, B. 0. Manuscript in preparation. (23) Heinemann, C.; Schwarz, J.; Koch, W.; Schwarz, H. J . Chem. Phys., in press. (24) Moore, C. E. Atomic Energy Levels; National Standard Reference Data Series; National Bureau of Standards, NSRDS-NBS 35: Washington, DC, 1971. (25) Herzberg, G. Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules; Krieger (reprint edition): Malabar, FL, 1989. (26) Botticher, C. J. F.; Bordewijk, P. Theory of Electric Polarization; Elsevier Scientific Publishing: Amsterdam, 1978. (27) These calculations were performed using the corresponding modules of the MOLCAS-2 program system: Anderson, K.; Blomberg, M. R. A.; Fiilscher, M. P.; Kello, V.; Lindh, R.; Malmqvist, P.-A.; Noga, J.; Olsen, J.; Roos, B. 0.;Sadlej, A. J.; Siegbahn, P. E. M.; Urban, M.; Widmark, P.-0. University of Lund, Sweden, 1991. (28) Buckingham, A. D.; Graham, C.; William, J. H. Mol. Phys. 1983, 49, 703. (29) The CCSD(T) equilibrium internuclear distance for the free N2 molecule is 2.081 bohr with the employed basis set. The corresponding frequency amounts to 2354 cm-' (exptl 2360 cm-], ref 25). Varying the nitrogen-nitrogen bond length while holding the optimized distance (see Table 1) between Fe+ and the bond midpoint of N2 constant yields a minimum N-N distance of 2.083 bohr for the linear 4X- state of Fe(N2)+ at the CCSD(T) level of theory. In the latter potential, the N-N stretching frequency amounts to 2331 cm-I. Despite the fact that there is a small contribution of Fe+ displacement in the N-N stretching mode within the Fe(N2)+ complex, the computed stretching frequencies for free Nz and NZ attached to Fe+ indicate that this intemal mode is only weakly affected by

complexation to Fe+. Thus, we neglect its contribution to the zero-point energy correction for bond dissociation energies. The small geometry change in N2 is in accord with earlier results on linear M+-N2 species. See ref 5a. (30) (a) Boys, S. F.; Bemardi, F. Mol. Phys. 1970, 19, 553. (b) For a recent review of counterpoise calculations, see: van Duijneveldt, F. B.; van Duijneveldt-van de Rijdt, J. G. C. M.; van Lenthe, J. Chem. Rev. 1994, 94, 1873. (3 1) (a) MOLPRO is a package of ab initio programs written by Werner, H A . , and Knowles, P. J., with contributions from Almlof, J.; Amos, R. D.; Deegan, M. J. 0.;Elbert, S. T.; Hampel, C.; Meyer, W.; Peterson, K.; Pitzer, R.; Stone, A. J.; Taylor, P. R. (b) The open-shell coupled-cluster program is described in the following: Knowles, P. J.; Hampel, C.; Werner, H.-J. J . Chem. Phys. 1993, 93, 5219. (32) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; van Nostrand: New York, 1979. (33) Ricca, A,; Bauschlicher, C. W., Jr.; Rosi, M. J . Phys. Chem. 1994, 98, 9498. (34) Choosing the 3da13dd3dd2configuration at Fe+ for a 4A2 state leads to the following results: R(Fe+-N2) = 4.275 bohr; BDE = -5.1 kcaYmol (not bound with respect to the Fe+ ground state asymptote within the CCSD model). (35) Fryzuk, M. D.; Haddad, T. S.; Mylvaganam, M.; McConville, D. H.; Rettig, S. J. J . Am. Chem. SOC.1993, 115, 2782. (36) Complete frequency analyses for the 4X- state of Fe(Nz)+ were camed out at the UMP2 level of theory using GAUSSIAN92. Two calculations were performed: The first one (calculation a, numerical evaluation of frequencies) employed a 10-electron effective core potential and the corresponding (8~7p6d)/[6~5p3d] valence basis according to the following: Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J . Chem. Phys. 1987, 86, 866. The second (calculation b, analytical method for computation of frequencies) included an all-electron treatment for Fe using a Wachterstype basis of the form (14slOp6d)/[8sSd3d], as described in the following: Fiedler, A.; HruSAk, J.; Koch, W.; Schwarz, H. Chem. Phys. Lett. 1993, 211, 242. In both cases, nitrogen was described by a (lls7p2d)/[6~4p2d] basis (d-exponents: 0.58, 1.73), as proposed by Huzinaga, S.; Sakai, Y. J . Chem. Phys. 1969, SO, 1371. At the respective MP2 minimum geometries (a: R(Fe-N) = 3.744 bohr, R(N-N) = 2.076 bohr. b: R(Fe-N) = 3.798 bohr, R(N-N) = 2.078 bohr. Free N2: R(N-N) = 2.102 bohr) the Fe+Nz stretching (u) frequencies were obtained as 290 cm-' (a) and 274 cm-] ( b ) , similar to the all-electron CCSD(T) result of 318 cm-l. The results for the degenerate (n) rocking frequency (250 cm-I, a; 240 cm-I, b ) as well as the N-N stretching frequency in the ligand (3416 cm-I, a; 3353 cm-l, b; free N2, 2188 cm-I) were also quite similar in both calculations. Note, however, that with respect to the geometry change for Nz and the apparently unreasonable shift of the N2 stretching frequency29the MP2 results suffer probably from systematic errors (for pitfalls in the UMPn approach to transition-metal systems, see: Taylor, P. R. In Lecture Notes in Quantum Chemistry;Roos, B. O., Ed.; Springer: Berlin, 1992; Vol. 58). On the other hand, the rocking frequencies are within the expected range and quite similar to those of linear M(CO)+ complexes investigated earlier.39 For the entropy, enthalpy, and zero-point energies, these n frequencies as obtained from calculation a were scaled by 1.1, so that the Fe+-N2 stretching frequency matches the CCSD(T) result of 318 cm-] (Table 1). (37) Contributions of f 2 . 3 kcaYmol for inclusion of scalar relativistic effects (mass-velocity and Darwin terms), one- and n-particle space treatments, and -1.2 kcaYmol for the fact that the 42-state is not subject to spin-orbit coupling, in contrast to the free Fe+ cation. (38) For example, addition of a single h-function (exponent of 1.0) in the Fe basis increases the bond energy of Fe(N2)+ from the lowest molecular quartet state to the sextet atomic asymptote by + O S kcal/mol at the CCSD level, but only by +0.2 kcal/mol in the case of FeAr+.2S (39) Bames, L. A,; Rosi, M.; Bauschlicher, C. W., Jr. J . Chem. Phys. 1990, 93, 609. (40) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 5th ed.; Wiley: New York, 1988. (41) CRC Handbook of Chemistry and Physics, 68th ed.; Weast, R. C., Ed.; Chemical Rubber Co.: Boca Raton, FL, 1987. (42) The endothermic generation of CoCHj' from Co' and CH3I may serve as an example: (a) Fisher, E. R.; Sunderlin, L. S.; Armentrout, P. B. J . Chem. Phys. 1989, 93, 7375. (b) Van Koppen, P. M.; Kemper, P. R.; Bowers, M. T. J . Am. Chem. Soc. 1993, 115, 5616. (c) The formation of CoCHq+ from Co+ and CHd. which was introduced via a pulsed valve, is described in the following:- Jacobson, D. B.: Freiser, B. i.J . Am. Chem. Soc. 1984, 106, 3891. (43) Wolf, J. F.; Staley, R. H.; Koppel, I.; Taagepera, M.; McIver, R. T., Jr.; Beauchamp, J. L.{Taft, R. W . J . Am. Chem. Soc. 1977, 99, 5417. (44) Within the experimental accuracy, the abundance of Fe(I3C02) after trapping Fe(Nz)+ in I3CO2 for 1 s is less than 9%. Thus, AG = -RT ln(9/100) = 1.4 kcal/mol at T = 300 K, by applying Boltzmann's law. JP950566N