Article pubs.acs.org/JPCA

A Combined Experimental and Theoretical Study of the Ti2 + N2O Reaction A. Marzouk,†,‡ H. Bolvin,§ P. Reinhardt,∥,⊥ L. Manceron,†,‡,# J. P. Perchard,†,‡ B. Tremblay,*,†,‡ and M. E. Alikhani*,†,‡ †

Sorbonne Universités, UPMC Univ. Paris 06, UMR 7075, LADIR (MONARIS, UMR 8233), Université Pierre et Marie Curie, 4 Place Jussieu, case courrier 49, F-75252 Paris Cedex 05, France ‡ CNRS, UMR 7075, LADIR (MONARIS, UMR 8233), Universite Pierre et Marie Curie, 4 Place Jussieu, case courrier 49, F-75252 Paris Cedex 05, France § Laboratoire de Chimie et Physique Quantiques, IRSAMC, 118 route de Narbonne, 31062 Toulouse Cedex, France ∥ UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique (LCT), Sorbonne Universités, 4 place Jussieu, case courrier 137, F-75252 Paris Cedex 05, France ⊥ CNRS, Laboratoire de Chimie Théorique (LCT, UMR7616), Université Pierre et Marie Curie, 4 place Jussieu, case courrier 137, F-75252 Paris Cedex 05, France S Supporting Information *

ABSTRACT: The reactivity of diatomic titanium with nitrous oxide has been studied in solid neon. Two molecules with the same Ti2−N2O stoichiometry are identified from concentration, temperature, and irradiation effects. The more stable one is characterized by five fundamental vibrational transitions located below 1000 cm−1, the high frequency one at 946 cm−1 corresponding to a pure TiO stretching mode. Its structure, a rhombus OTiNTiN with the extra O atom fixed on one Ti, is confirmed by quantum chemical calculations, at the CCSD(T) level, which predict a Cs structure in the singlet state with a Ti−O bond length close to 1.66 Å, two nonequivalent Ti−N distances close to 1.94 and 1.75 Å, and a OTiTi angle of 119.2°. The second Ti2−N2O molecule, only observed after annealing, is easily converted into the first one upon irradiation above 12 000 cm−1 and its kinetics of photoconversion allows vibrational transitions to be identified. The strongest one located at 2123.4 cm−1 characterizes an N−N stretching mode. Corresponding ab initio calculations complete this picture with details on the electronic structure and allow us to identify a most adequate density functional to describe the spectroscopic properties of the studied species in a simpler broken-symmetry open-shell DFT context. The theoretical results predict the existence of a metastable product OTi2N2 and correctly account for the observed spectra of the various isotopic varieties.

I. INTRODUCTION The gas phase chemistry of transition metal (TM) atoms with small di- or triatomic ligands have been widely studied, with special attention paid to the influence of their ground and lowlying excited electronic states. In contrast, for the technical problem of sublimating TM diatoms, these is no corresponding studies about the reactivity of (TM)2 in the gas phase. All our knowledge stems from matrix isolation, which allows us to stabilize highly reactive products, some of them involving di- or tri-TM atoms randomly aggregated during matrix deposition, identified through their vibrational and, sometimes, by their vibronic spectra. The identification of rhombic (TM)2N2 species was first reported by Andrews and co-workers1−4 in 1998, but the proposed reaction mechanism does not involve (TM)2, proceeding in two steps: formation of (TM)N2 followed by fixation of a second TM atom. Since then, new systems were examined with N2, CO, and O2 as ligands (L), leading to the conclusion that transition metal diatoms (TM)2 were responsible for the formation of rhombic (TM)2L2 © XXXX American Chemical Society

structures, with complete cleavage of the intramolecular L bond. Zhou’s and Xu’s groups first considered CO interactivity with Sc2,5 Ce2,6 Gd2,7 and then O2 interacting with Mn2,8 Ti2, Zr2, Hf2,9 and N2 with Gd2.10 In three cases with CO as ligand an intermediate state was identified in which CO is tied either sideon to Sc25 and Ti211 or end-on to Ag2.12 In parallel, Manceron and co-workers13,14 performed a thorough study of the Ti2N2 molecule formed in spontaneous reaction at 9 K, extending the absorption spectrum of this molecule from the near UV to the far-infrared. They also examined the Ti2−CO system15 and confirmed the existence of reaction intermediate easily converted in the more stable OTi2C oxycarbide form. Finally the most recent study in this field concerns the rhombic Th2O2 molecule.16 The purpose of the present work is to extend the study of the reactivity of the TM diatoms with respect to a triatomic Received: July 1, 2013 Revised: December 20, 2013

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molecule. The system Ti2−N2O has been chosen for two reasons: the possibility of controlling the Ti2 abundance through its vibronic spectrum in the near-infrared17 and the fact that the reactivity of the Ti−N2O or TiO−N2 systems have been examined in an Ar or Ne matrix,18−20 giving a first approach to the spectral analysis. Note, however, that in none of these works was the presence of Ti2 and of subsequent Ti2− N2O complexes reported. In parallel, we perform a systematic and critical study of the functional density approach in comparison with data obtained at a very high level of calculation (CCS(T) and CASPT2). Electronic and vibrational analyses of the experimentally observed species were then undertaken using the most adequate density functional.

II. EXPERIMENTAL AND COMPUTATIONAL METHODS 1. Experimental Details. The experimental technique has been described in detail in our previous work on the Ti−N2O pair.21 The matrix deposition and spectral data acquisition remain strictly unchanged as the data for Ti−N2O and Ti2− N2O are obtained from the same spectra. Also irradiations were carried out using the same band-pass filters and irradiation sources. 2. Computational Details. All DFT calculations were performed with Gaussian 0922 using several functionals in the Generalized Gradient Approximation (GGA) and metaGeneralized Gradient Approximation (mGGA) families. The chosen functionals include the most popular ones such as B/LYP,23,24 B/B95,25 B/P86,26 B/PW91,27,28 mPW/PW91,29 PW91/PW91,27,28 O/B95,25,30,31 O/PBE,30−33 PBE/PBE,32,33 TPSS/TPSS,34 and M06L.35 The 6-311+G(2d) triple-ζ quality extended basis set of Pople,36 labeled as Pop(2d) in this paper, was used for with all the functionals. All the multireference calculations (CASSCF and CASPT2) have been performed with the MOLCAS suite of programs,37 version 7.6, employing Atomic Natural Orbital basis sets (ANO-RCC, relativistic with core correlation) of triple-ζ quality including polarization functions.38,39 Using the ANO-RCC basis sets includes automatically the calculation of the scalar relativistic effect on the one-electron integrals. The active space consists of six electrons in 12 orbitals, namely the (remaining) 3d and 4s of the two Ti+ ions, allowing occupation of the corresponding atomic orbitals. First, a CASSCF (Complete Active Space Self Consistent Field) calculation is performed with 6 roots in each spin symmetry,40 then dynamical correlation is calculated by the CASPT2 (Complete Active Space Perturbation Theory at the second order) method.41 The geometry of the final product, which is a monoreference system has also been optimized at the CCSD(T) level of theory using the Def2-TZVPPD basis set.42,43 The nature of chemical bonding has been investigated in the framework of the AIM (“Atoms In Molecule” of Bader44) topological approach with help of the “AIMAll (Version 12.09.23)”45 code.

Figure 1. Spectral changes for a Ti/14N2O/Ne = 0.2/0.5/1000 sample in selected regions of absorptions of OTi2N2 (2130−2110 cm−1) and OTiNTiN (955−940 cm−1). Spectra recorded at 3 K after deposition (a), after annealing at 11 K (b), and after 15 min irradiation in the range 830−710 nm following the annealing step (c).

A noticeable evolution occurs upon annealing because a very strong new band appears around 2123 cm−1 (Figure 1b) for 14 N2O; so as the N2O/Ne molar ratio is kept below 1/1000, the absorption near 946 cm−1 becomes sharper but keeps the same integrated intensity. The appearance of this band was concomitant with the decrease of the Ti2 bands above 4000 cm−1. The species responsible for this band, referred to as an intermediate product, is revealed to be highly sensitive to irradiations at wavelengths less than 1 μm. Figure 1c displays the effect of irradiation in the range 0.8−0.7 μm, which causes the full photolysis of this species correlated, as seen below, to the appearance of five bands: four in the mid-infrared and one in the far-infrared. These bands keep a constant intensity ratio whatever the experimental conditions and thus belong to the same species. The geometries and the stoichiometry of these two species will be examined below. 1. Intermediate Product: OTi2N2. The spectrum of the intermediate product, dominated by one absorption assignable to a N−N stretching mode at 2123.4 cm−1 for 14N2O (Figure 2a) is easily identified by very specific properties, namely the complete absence after sample deposition, strong intensity after annealing at 11 K for samples with low N2O and high Ti contents. The presence of only one N2 molecule stems from the observation of a unique signal between 2300 and 1700 cm−1, split into two components close to 2123 and 2054 cm−1 for mixed 14N2O/15N2O samples (Figure 2d). On the other hand, a 2.4 cm−1 splitting of the main component for 14N15NO (Figure 2b) due to a nonequivalence of the N atoms in the complex is the proof of an end-on position of this molecule. Also, much weaker absorptions can be correlated with this N−N absorption at 4183.1, 755.2, 263.8, and 211.6 cm−1 (Table 1). The 755 cm−1 band is almost insensitive to the 14N/15N isotopic substitution and gives the primary evidence for the presence of two Ti atoms in the observed Ti isotopic fine structure as displayed in Figure 2. A band fitting taking into account the existence of three trapping sites shows that for the main site the relative

III. EXPERIMENTAL RESULTS About 20 matrix samples were prepared in various Ti/N2O/Ne doping conditions. At low titanium concentration and relatively high N2O content (typically 1000 ppm) the absorptions assigned by Zhou et al.20 to OTi(N2)n, n = 1−4, predominate. When the Ti concentration is increased, the bands assigned to electronic transitions of Ti2 above 4000 cm−1 increase in intensity and a very weak absorption is detected at around 946 cm−1 (Figure 1a). B

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Table 2. Observed Absorptions (cm−1) for the Final Product OTiNTiN Trapped in Ne at 3 Ka 14

N14NO

946.0 890.3 779.5 713.4 349.7

(78) (24) (51) (100) (27)

14

N15NO 945.9 880.0 769.1 703.2 346.1

15

N15NO 945.6 867.6 759.7 693.3 341.8

mode (assignment) ν1 ν2 ν3 ν4 ν5

(TiO stretch) (TiN sym stretch) (TiN asym stretch) (TiN sym stretch) (TiNTiN bending)

The IR intensities relative to the strongest fundamental ν4 (Iν4 = 100) are in parentheses.

a

Figure 2. Isotopic shifts for OTi2N2 in three spectral regions. Spectra recorded at 3 K after annealing at 11 K: (a) Ti/14N2O/Ne = 0.2/0.5/ 1000; (b) Ti/14N15NO/Ne = 0.2/0.5/1000; (c)Ti/15N2O/Ne = 0.2/ 0.5/1000; (d)Ti/14N2O/15N2O/Ne = 0.2/0.25/0.25/1000. The bands around 755 cm−1 are masked by the Ti215N2 bands in traces c and d.

Table 1. Observed Absorptions (cm−1) for the Intermediate Product OTi2N2 Trapped in Ne at 3 Ka 14

N14NO

4183.1 2123.4 755.2 263.8 211.6

(1) (100) (3) (2) (3)

14

N15NO

n.o.b 2090.0, 2087.6 754.6 262.5,d 260.7d 209.1

15

N15NO

4048.0 2053.7 c 259.6 207

mode (assignment) 2ν1 ν1 (NN stretch) ν2 (TiO stretch) ν3 (bending) ν4 (bending)

Figure 3. Five fundamental transitions of OTiNTiN observed for a Ti/14N2O/Ne = 0.2/0.5/1000 sample annealed at 11 K and then irradiated in the range 830−710 nm for 63 min. When observable, the Ti isotopic fine structures are reported. ν3 frame: obtained after subtraction of the absorptions of Ti2N2 due to the presence of N2 as impurity trace.

The IR intensities relative to the strongest fundamental ν1 (Iν1 = 100) are in parentheses. bNot observed (n.o.). cMasked by the Ti215N2 band. dValues deduced from a fit. a

To simplify the discussion, we use from now the assignment which will be given later by the calculations (Table 2). ν1: This band is quite insensitive to the 14N/15N isotopic substitution and thus can be assigned to the Ti−O stretching mode. In spite of the existence of two main trapping sites that render the analysis more intricate, a typical pattern of isotopic titanium is observed for each site with spacings between the successive components, between 46Ti and 48Ti, 48Ti and 49Ti, and 49Ti and 50Ti, of 5.3/2.5/2.4 cm−1, corresponding to the values found for the TiO molecule trapped in Ne. Note that the 47Ti component perfectly overlaps the main component of the second site at 948.6 cm−1, which renders the intensity and position measurements impossible. On the other hand, the intensity ratio between the components 46Ti/48Ti/49Ti/50Ti, 0.11/1/0.088/0.079, is close to that expected for only one Ti atom involved in the vibration, isotopic Ti abundance being in the ratio 0.11/1/0.07/0.07. ν2: A large amplitude motion of nitrogen atoms is deduced from large frequency shifts, 10.3 and 22.7 cm−1 when going from 14N2O to 14N15NO and 15N2O, respectively. The corresponding bands display an isotopic Ti fine structure, as shown

intensities for four of the five isotopic components at 757.4, 756.2, 755.2, and 753.2 cm−1 are 0.23, 0.22, 1, and 0.15, close to the ratios expected when two Ti atoms are involved in the vibration (calculated relative intensities of 0.22, 0.20, 1, and 0.14 for respectively 46Ti48Ti/47Ti48Ti/48Ti48Ti/50Ti48Ti, the isotopic site 49Ti48Ti is found to be under a secondary site). Finally, in the far-infrared the two observed bands have almost the same 14N/15N isotopic shift (Figure 2). It was shown that upon irradiation, this species is very sensitive to the photochemistry process and its conversion to the final reaction product requires at least a wavelength between 830 and 710 nm (Figure 1). 2. Final Product: OTiNTiN. The assignment of the five bands in the mid- and far-infrared to a common species (Table 2) is based on their constant intensity whatever the experimental conditions. However, they behave differently in 14N/15N isotopic substitution and also when considering the Ti isotopic fine structures. Figure 3 displays the five main absorbance bands of the final product. C

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in Figure 3 for 14N2O. The main quintet is measured at 894.5/ 892.4/890.3/888.3/886.3 cm−1, i.e., with splitting of 2.1/2.1/ 2.0/2.0 cm−1 from 46Ti to 50Ti, smaller than those measured for ν1 (Table 2). As for the relative intensities, they are found in the ratio 0.11/0.10/1/0.07/0.06, which means that only one Ti atom is involved in this vibration. ν3: It is characterized by a shift comparable to that for ν2 upon isotopic nitrogen substitution (10.4 and 19.8 cm−1, respectively, with 14N15NO and 15N2O). For 14N2O its position, close to the strong bands of Ti214N2 at 782 and 775 cm−1 (Figure 3, after subtraction of the Ti2N2 spectrum).13,14 But for 14 15 N NO, the ν3 vibration is well separated from the two absorptions of Ti214N15N and its Ti isotopic structure is clearly identified with splitting close to 1.6 cm−1 between successive components, in good agreement with the pattern observed after subtraction of the Ti2N2 spectrum (Figure 3). Also, the intensity ratios of the isotopic pattern are in agreement with the ratios expected when two Ti atoms are involved in the vibration. They are found to be 0.26/1/0.14/0.12 for respectively 47Ti48Ti /48Ti48Ti/ 49Ti48Ti /50Ti48Ti; the isotopic site 46Ti48Ti is found to be under the Ti2N2 vibrational bands. These ratios are close to the expected ones, 0.22/0.20/1/ 0.15/0.14. ν4: The 14N/15N isotopic shifts are close to those measured for the two last ones. With 14N2O (Figure 3), a quintet is measured at 715.4/714.4/713.4/712.5/711.4 cm−1 from 46Ti to 50Ti, corresponding to splitting of approximately 1 cm−1 between successive components. As for the intensity ratios, they are comparable to those measured for ν1 and ν2, which means that only one titanium atom is involved in the vibration. ν5: The fifth fundamental transition is observed close to 350 cm−1 (Figure 3) on the basis of a behavior upon annealing and irradiation similar to that observed for the previous ones. No titanium isotopic structure can be observed for this band, and a relatively large amplitude motion of nitrogen atoms is deduced from the frequency shifts, 3.6 and 7.9 cm−1 when going from 14N2O to 14N15NO and 15N2O, respectively. To confirm the interconversion between OTi2N2 and OTiNTiN, presented in the Experimental Results, we have done several kinetic studies at selected frequencies. The results are displayed in Figure 4 for a sample exposed to the irradiation in the range 830−710 nm for more than 1 h. We have measured the time development of the intensities It of the bands at 2123 and 946 cm−1. The absolute value |ΔIt| = |(It − I0)| are considered, ΔIt being negative for OTi2N2 (decreasing of the 2123 cm−1 band) and positive for OTiNTiN (increasing of the 946 cm−1). In this last case the observed values have been multiplied by a factor 8 which takes into account the difference of the absorption coefficients of the two bands under scrutiny. The OTi2N2 → OTiNTiN interconversion is confirmed, but the growth rate of the bonds of the OTiNTiN molecule is not totally identical to the disappearance rate of the OTi2N2 complex. The depletion of the intermediate compound is complete after 15 min exposure with a half-time of about 2 min, whereas OTiNTiN continues growing after even 1 h. However, the total depletion of OTi2N2 corresponds to 90% of the final amount of OTiNTiN. Note that the interconversion occurs also for other wavelengths of irradiation (514 and 365 nm), but with different half-time. 3. Formation and Structure of the Species from the Experimental Results. Two new molecules have been formed by two routes: (i) the first one, the adduct complex OTi2N2, characterized by a very intense band at 2123.4 cm−1, invisible

Figure 4. Time development of the areas (cm) of the bands of OTi2N2 around 2123 cm−1 (□) and of OTiNTiN around 946 cm−1 (◆) versus the irradiation duration at 830−710 nm. Ti/14N2O/Ne = 0.2/0.5/ 1000 and samples annealed at 11 K.

after deposition, appears only with an increasing of the temperature up to 11 K, and (ii) the second one, the OTiNTiN molecule, characterized by a weak band at 946 cm−1 after deposition, increases typically by 1 order of magnitude following irradiation at least in near-IR (λirr < 830 nm). To understand the observation immediately after deposition, it is important to recall that during the deposition process, which lasts about 1 h, the sample is submitted to the irradiation from the Ti/Mo filament heated to ∼1800 K, which emits significantly in the very near-infrared. In these conditions, all the OTi2N2 formed during deposition is converted into OTiNTiN. Upon annealing to 11 K, the very strong band of OTi2N2 appears, in the absence of any molecular excitation, and this appearance is concomitant with the decrease of the Ti2 bands above 4000 cm−1. This observation evidences that the Ti2 + N2O → OTi2N2 reaction is spontaneous. This sensitivity of OTi2N2 to the irradiation in the very near-infrared explains why it is not observed after deposition. Also, at this point, experimental data alone have already given some general picture for the molecular shape of these species: 3.1. OTi2N2. • This species possesses one strong NN bond in end-on coordination: the proof is that the band at 2123 cm−1 gives two bands at 2090.0 and 2087.6 cm−1 with 14N15NO . • The band at 755 cm−1 shows an isotopic structure in agreement with two Ti atoms involved in the vibration. Because this band is insensitive to the 14N/15N isotopic substitution, we can assign this band to a O−Ti2 vibration. Finally, from all these experimental observations, the intermediate complex OTi2N2 could be considered like a Ti2O molecule with N2 coordinated to one Ti atom as a OTi2-(η1-NN) structure. 3.2. OTiNTiN. • A confirmation of the interconversion between OTi2N2 and OTiNTiN is obtained through the kinetics studies. D

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• This species possesses one TiO bond: the band at 946 cm−1 is insensitive to the 14N/15N isotopic substitution and the observed Ti isotopic structure is in agreement with only one Ti atom. • The band at 779 cm−1 shows an isotopic structure in agreement with two Ti atoms involved in the vibration, but the Ti isotopic structure of the bands at 890 and 713 cm−1 implies only one Ti atom. • The three bands at 779, 890, and 713 cm−1 show large frequency shifts with the 14N/15N isotopic substitution, and the shifts are close to those observed in the Ti2N2 molecule.13,14 From these observations, we can assume that the final product has a cyclic Ti2N2 structure with an oxygen atom coordinated to one Ti atom.

TPSSh/Pop(2d) level for the spin-contaminated singlet state) whereas the ∠(TiOTi) angle was varied from 60° to 180°, keeping the C2v symmetry. In a multireference CASSCF calculation, the spin functions are correctly constructed without contamination, and a further perturbational treatment by CASPT2 adds missing correlation contributions to the total energy. Correlation depends on the considered spin state and mainly on the number of paired electrons. Figure 5 shows the energies of all the states as the function of the angle θ, the energy reference being the ground state at

IV. THEORETICAL RESULTS To describe the spectroscopic properties of the experimentally observed species from the reaction between Ti2 and N2O, we discuss in a first step the electronic structure and chemical bonding nature of the Ti2O (an intermediate of reaction), which could be of a particular character because of the presence of two metallic centers. Following this study, we will determine the most appropriate functional to investigate the experimentally detected compounds. 1. Electronic Study of Ti2O (C2v Symmetry). In Table 3 are reported some preliminary results of geometry optimizations Table 3. Data on the Singlet State of Ti2O at the DFT/ Pop(2d) Levela r(Ti−O) ∠(TiOTi) ⟨S2⟩

TPSSTPSS

TPSSh

B3LYP

PBE1PBE

1.846 69.6 0.685

1.838 91.2 2.203

1.841 95.2 2.288

1.848 99.3 2.524

a Distances are in angströms, angles in degrees. ⟨S2⟩ stands for the expectation value of the total spin operator of the open-shell DFT wavefunction.

of the two independent parameters of the Ti2O compound in C2v symmetry with four popular functionals TPSSTPSS, TPSSh, B3LYP, and PBE1PBE. The Sz component is fixed to zero, aiming at a (broken-symmetry open-shell) singlet state. Even if the unrestricted wave functions are not an eigenfunction of the spin operator but only of the Sz component, we will refer to the the MS = 0 function as “singlet”, the MS = 1 function as “triplet”, and the MS = 2 function as “quintet”. From the results shown in Table 3, we note that the expected value of the total spin squared operator, ⟨S2⟩, is actually different from its theoretical value (zero), indicating the presence of RHF/UHF instability of the SCF wave function. One may easily notice that the TPSSTPSS functional results in ⟨S2⟩ ≤ 1 and the other ones to highly contaminated solutions with ⟨S2⟩ ≥ 2. The bond angle, ∠(TiOTi), is calculated to be about 70° for the former and larger than 90° for the hybrid functional. However, the Ti−O bond length is found to be similar (around 1.84 Å) in all cases. Lacking experimental data for the Ti2O molecule, the only strategy to assess the reliability of a functional is the comparison with high-level theoretical reference data. 1.1. CASSCF-CASPT2 Results. CASSCF/CASPT2 calculations were thus carried out at a fixed value of the Ti−O bond of 1.838 Å (the distance of the optimized geometry at the

Figure 5. Relative energies (kJ/mol) as a function of the ∠TiOTi angle: (a) CASSCF; (b) CASPT2.

θ = 72°. At the CASSCF level (Figure 5a), including the essential static correlation to describe coherently the different spin configurations, all states find an energy minimum for the linear setup. However, when dynamical correlation via the CASPT2 level is added (Figure 5b), the energy rises first when the molecule is bent but suddenly decreases for the singlet, triplet, and quintet states, leading to a local minimum for the last, but a global minimum for the first ones. The global minimum is found to be a singlet state at around θ = 72° and lies about 36 kJ/mol lower than the linear setup. At that bond angle, the two Ti atoms come sufficiently close to sharing electrons, forming even a triple bond (bonding orbitals are depicted in Figure 6): the σ and π bonds have bonding indices of 0.75, 0.74, and 0.92, respectively. Bonding indices are calculated as (nb − nab)/2 where nb (nab) is the population of the considered bonding (antibonding) orbital. E

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and septet) with different amounts (0, 2, 10, and 25%) of the HF exchange added to the TPSS functional, and also using two other popular hybrid functionals, B3LYP and PBE1PBE, which include already an exact-exchange contribution by 20% and 25%, respectively. The energetic ordering of the four lowestlying states is displayed in Figure 7. We should underline that Figure 6. Orbitals involved in the triple bond at θ = 72°.

It is interesting to note that the strength of the σ orbital is lower than the π∥ because the latter is stabilized by the bonding interaction with the oxygen atom. The two first excited states at θ = 72° lie at 6 and 7.5 kJ/mol above the ground state and are spin triplet states. They correspond to π⊥ → δ and σ → δ single-electron excitations respectively, confirming that the π⊥ is the least bonding orbital, followed by the σ orbital. The formation of a multiple bond is only possible in the singlet state, less possible in the triplet state, and not possible in the septet state, having necessarily six open shells as the dominating configuration. The wave function in the singlet ground state is mainly borne by the closed shell determinant with a weight of 70%. The introduction of dynamical correlation by the CASPT2 calculation favors the bend configuration because a triple bond is highly correlated. To confirm the validity of the DFT geometry optimization, we optimized independently the geometry for each spin state (following the energy of the lowest CASPT2 state of the 20 RASSCF roots). Indeed, for the singlet state we obtain a bond length of 1.834 Å with a Ti−O−Ti bond angle of 71.8°. The triplet yields a slightly longer bond length (1.835 Å) and a slightly changed bond angle (71.7°). The energy difference between the individually optimized singlet and triplet is 1.5 mH or 4 kJ/mol. 1.2. DFT Results. Some of the most important conclusions evidenced in the CASSCF/CASPT2 study may be summarized as follows: • The ground electronic state is actually a singlet state with a triple bond between the Ti atoms with a bent C2v geometry, • The lowest-lying state corresponds to a bent C2v structure in the triplet state and is situated by 4 kJ/mol above the ground electronic state. • The ∠TiOTi bond angle is calculated to be about 72° for both the singlet and triplet states. • The bound quintet and septet states are of linear geometry (D∞h framework), and they lie energetically above the singlet and triplet bent structure at least by around of 44 kJ/mol. On the ground of these considerations, we have undertaken a more systematic DFT study on the bent structure for both the “singlet” and “triplet” spin states using several exchange− correlation functionals. We emphasize that the benchmarking validation especially consists of the reproduction of the energetic and geometrical properties of the bent structure. Furthermore, to take into account the strong multireference character of the “singlet” wave function, we checked for each functional the stability of the optimized wave function. We mixed the frontier molecular orbitals using the “Guess=Mix” and stabilized the wave function using “Stable = Opt” keywords, as implemented in the Gaussian 09 package. To assess the nonlocal HF exchange effect on the performance of density functional, we optimized the Ti2O geometry for four spin states (“singlet”, “triplet”, “quintet”,

Figure 7. Relative stability of the spin states with respect to the “singlet” state energy calculated with hybrid density functionals.

all states were optimized for a bent C2v geometry; however, the optimized geometry at septet state becomes linear. The relative energies are calculated using the “singlet” state energy as a reference for each theoretical model. One can easily note that none of the four functionals reported in Figure 7 reproduces both the energetic ordering and the energetic gap obtained with the CASPT2 method. Furthermore, the ∠(TiOTi) bond angle at the “singlet” state is significantly larger than the CASPT2 optimization (≅72°) for all four functionals (91.2, 99.0, 95.2, and 99.3°, respectively). Consequently, we exclude the use of hybrid functional in this study. This statement is in line with previous studies on openshell “singlet” states.15,46−52 Similarly, geometry optimizations have been performed using eleven pure GGA and meta-GGA functionals. In all the studied cases, the “quintet” and “septet” states were found energetically to be above the “singlet” and “triplet” ones. The optimized “singlet” state for all tested pure DFT functionals presents an expectation value of ⟨S2⟩ in the range 0.5−0.75, always smaller than 1 (Table S-1 in Supporting Information). For clarity of the discussion, we display in Figure 8 the energetic results only for the two lowest states: “singlet” and “triplet” ones. In light of these results, functionals could be grouped into two categories: • Functionals for which the “triplet” state is more stable than the “singlet” one (TPSSTPSS, BPW91, mPWPW91, PW91PW91, OB95, OPBE, and PBEPBE). We exclude these functionals because the obtained energetic ordering is in contradiction with the CASPT2 result. • Family containing four functionals (M06L, BB95, BLYP, and BP86), which give the same energetic ordering as the CASPT2 method. The “singlet”/“triplet” gap was calculated to be 6, 1.5, 1, and 0 kJ/mol, for the M06L, BB95, BLYP, and BP86 functionals, respectively. Compared to the CASPT2 singlet/triplet gap (≅4 kJ/mol), we retain only the M06L functional for this study. Following F

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Laplacian at the bond critical point are associated with closedshell interactions (ionic bonds, hydrogen bonds, and van der Waals interactions), whereas, ∇2ρ < 0, indicates shared interactions (covalent bonds). As has been proposed by Cremer and Kraka,55−57 the sign and magnitude of the total electronic energy density at the BCP, H(r), could be used as another criterion to evaluate the importance of sharing of electrons (when H(r) < 0). The local properties, such as the charge density ρ(r) (e/Å3), the Laplacian of the electron density Δρ (e/Å5), the energy density denoted as H(X,Y) (Hartree/Å3) (X = Ti and Y = Ti or O), and the ellipticity (ε), which provides a quantitative measurement of the anisotropy of the electron density at the BCP, constitute an accurate and unique quantum chemical fingerprint of any particular BCP, and hence any bond can be represented in terms of the properties at its BCP. These parameters are reported in Table 4. Table 4. Topological Information (ρ, Δρ, H(X,Y), and ε) of the BCPs (X, Y) and the RCP (O, Ti, Ti) Obtained within AIM Analysis, Calculated at the M06L/Pop(2d) Level of Theory (X = Ti, Y = Ti, O)

Figure 8. Comparison of the energetic stability of the two lower spin states of Ti2O between different pure density functionals using the Pop(2d) basis set. The “singlet” state was taken as a reference.

3

Ti2

the suggestion of Himmel et al.,14 we used a modified molecular term (1)Λ to represent a contaminated “singlet” state in which the multiplicity is set in parentheses to indicate only state with Sz = 0. Consequently, the ground electronic state of the free Ti2O molecule is denoted as (1)A1. To provide a deeper analysis of the contaminated “singlet” wave function obtained at the M06L/Pop(2d) level, we calculated the natural orbital occupation numbers (NOON), as implemented in Gaussian 09. We found that, in addition to the 25 doubly occupied orbitals, we observe two partially occupied orbitals (26th and 27th) with 1.55 and 0.45 electrons, respectively. Both orbitals are of bonding nature. With two singly occupied orbitals (and otherwise orbitals completely filled with two electrons) the unrestricted “singlet” wave function (ΨS=0 UDFT‑BS) may be considered as a linear combination of two “pure” components: a “triplet” and a “singlet” state48,53,54 like

BCP(Ti,Ti) BCP(Ti,O) RCP(Ti,Ti,O) atomic charges

ρ, ∇ ρ H, ε ρ, ∇2ρ H, ε ρ, ∇2ρ H, ε Q(Ti)/Q(O) 2

3

TiO

0.13, 1.04 −0.04, 0.00 0.26, 0.91 −0.17, 0.00

22/−

21.1/8.9

(1)

[Ti2O]

0.12, 0.33 −0.05, 0.62 0.14, 0.66 −0.04, 0.28 0.09, 0.37 −0.02, − 21.4/9.2

Figure 9a displays the Laplacian contour maps for the Ti2O molecule with all the critical points calculated with the M06L local function. Three BCPs and one RCP have been investigated: one BCP between the two Ti atoms, two equivalent BCP for two (Ti, O) pairs, and one tricentric RCP (Ti, Ti, O). In the Ti2O system, the Laplacian at all the BCPs is positive, which is associated with closed-shell interactions. Nevertheless, the negative values of H(r) indicate the partially covalent character of the bonds. From the ellipticity values reported in Table 4, we note an important electron delocalization at the Ti−Ti BCP, suggesting the presence of an off-axis bond. This consideration is in agreement with the presence of Ti−Ti π bonds with the CASSCF/CASPT2 calculations. For the two Ti−O bonds, the delocalization is quite small. Finally, we emphasize that the chemical bonding analysis is an a posteriori analysis with respect to the wave function calculation. As it has been shown above, we obtain two different types of wave function for the bent structure at the “singlet” state according to the functional used. We expect therefore to obtain two different bonding schemes for the Ti2O grand electronic state. As depicted in Figure 9b, the BCP(Ti,Ti) and RCP(Ti,O,Ti) indeed disappear when using a hybrid functional. Naturally, it explains two geometrical changes: the opening of the ∠TiOTi bond angle and the increase of the Ti−Ti bond length in the Figure 9b with respect to Figure 9a. Furthermore, discrepancy appears on the vibrational analysis obtained from an inadequate functional (such as TPSSh for instance) and a suitable functional (M06L). Indeed, the Ti−Ti stretching frequency is calculated to be 135 and 400 cm−1 with the TPSSh and M06L functional, respectively. Compared to the experimental Ti−Ti

=0 sin g ΨSUDFT (S=0) + bΨ trip(S=1) ‐BS = a Ψ

with a2 + b2 = 1

One can easily write the expectation value of S2̂ : 2

S ̂ = a 2⟨ψS|S2|ψS⟩+b2⟨ψT |S2|ψT ⟩+2ab⟨ψS|S2|ψ T⟩ = 2b2

as ⟨ψS|S2|ψT⟩ = 0, ⟨ψS|S2|ψS⟩ = 0, and ⟨ψT|S2|ψT⟩ = 2 for the respective spin eigenfunctions. Thus b = (⟨Ŝ2⟩/2)1/2 and a = [(1 − b2)]1/2. For instance, we find a = 0.803 and b = 0.595 from the above-mentioned M06L results. 1.3. Topological Analysis. The topology of the charge density, ρ(r), leads to a partitioning scheme which defines atoms inside a molecule or a molecular complex via the gradient vector field, ∇ρ. Critical points (CP) are found where ∇ρ = 0. Bond critical point (BCP), found between two nuclei of a compound in equilibrium geometry, indicates the existence of a chemical bonding between them. We can also find the ring critical point (RCP), a point found in the middle of several bonds forming a ring. The Laplacian of ρ, ∇2ρ, at the critical point measures to what extent the electron density is locally concentrated if ∇2ρ < 0, or depleted if ∇2ρ > 0. According to the topological theory of AIM, the positive values of the G

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Figure 9. Laplacian contour maps of the Ti2O structure, from M06L and TPSSh wfn for the contaminated “singlet” state. Solid lines (blue) stand for ∇2ρ < 0 and dashed ones (red) for ∇2ρ > 0. The green circles represent BCPs, and the black one represents the RCP.

vibrational frequency in the titanium dimer (407 cm−1),17 the Ti−Ti stretching frequency in Ti2O strongly weakens with a hybrid functional versus a very small weakness with the M06L functional. This result is in agreement with the presence of a TiTi triple bonds as predicted at CASPT2 level. 2. Reactivity of Ti2O with N2: Encounter Complex and Product Species. 2.1. Energetic and Structural Considerations. As shown in the Experimental Results, the diatomic Ti2 reacts spontaneously with N2O at low temperature (11 K) in solid neon without any significant activation barrier to break up the NO bond leading to an encounter complex containing two molecular species: OTi2 and N2. The total conversion of the intermediate complex to the final product occurred only after irradiation process. Owing to the singlet ground state of the Ti2O and N2 moieties, we studied the two structures stemming from the Ti2O + N2 reaction as well as singlet states. Because, as noted above, the Ti2O molecule exhibits a relatively strong multireference character, we present at first the CASPT2 results on the two experimentally observed structures. The CASPT2 optimized geometrical parameters, using a CAS(4,4), are reported in Figure 10. Concerning the encounter complex, called also end-on adduct complex, it is worth to note: 1. The Ti2O moiety is no longer symmetric (two different Ti−O bond lengths). However, the ∠TiOTi angle is nearly the same in two compounds (72.3° vs 71.7°). 2. The Ti−Ti bond length increases by 0.01 Å when going from free Ti2O to the end-on adduct complex. The Ti− Ti bond lengthening could be considered as the first step toward to the bond activation. 3. The N2 molecule is out-of-plane with respect to Ti2O. The dihedral angle between the NTiTi and TiTiO planes is either 112° or 110° depending upon the considered nitrogen atom. The other structure, the final product, is characterized by a nearly planar TiNTiN cycle (dihedral angle = 3°) with the oxygen atom bonded to one of the titanium atoms. The OTiTi plane is actually the bisector plane of the ∠NTiN angle. The final product was found to be more stable by 285 kJ/mol than the end-on adduct complex. Concerning the wave function, the CASSCF treatment shows, for the final product, a closed-shell reference with a weight above 0.95, which means that a simple optimization of a Hartree−Fock state with single-reference Møller−Plesset

Figure 10. DFT and CASPT2 optimized structures of two experimentally observed species. Distances are in angstroms and angles in degrees. Note that two TiNTi triangles are equivalent in the 1 S2 structure.

perturbation theory would have led to the same optimum geometry. Consequently, we optimized this structure at the CCSD(T) level using the Def2-TZVPPD basis set. As shown in Figure 10, geometrical data obtained at CASPT2 and CCSD(T) are very similar to each other. In contrast, for the end-on adduct complex the weight of the fundamental closed-shell configuration is only 75% in the CASSCF singlet state, as it is in the Ti2O molecule. The bonding scheme between the two Ti atoms is the same in these two molecules with an elongated triple bond. H

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In accordance with the aforementioned discussion on Ti2O, we optimized both structures using the M06L functional and two basis sets (Pop-2d and Def2-TZVPPD) at the singlet state within the broken-symmetry formalism. Selected geometrical parameters are reported in Figure 10. In the case of the final product, the single-determinant DFT wave function has been found to be stable with respect to relaxing various constraints. Accordingly, the electronic state actually corresponds to a singlet state with MS = 0 and ⟨S2⟩ = 0. Contrarily, the DFT wave function of the end-on adduct complex presents a RHF/UHF instability. Broken symmetry DFT geometry optimization converges to an open shell singlet state presenting a significant spin contamination (S2 = 0.849) for the MS = 0 setting. The NOON analysis of the open-shell “singlet” state (labeled as (1)S1 in Figure 10), at the M06L/ Pop(2d) level, reveals the presence of two partially occupied orbitals (1.42 and 0.58 |e|), in agreement with the CASSCF natural populations (two bonding orbitals with occupation 1.7 and the corresponding antibonding ones with 0.3 |e|). These numbers clearly indicate that the (1)S1 wave function is indeed contaminated by higher spin component with Smax = 1, the “triplet” state. It is noticeable that the DFT geometrical parameters are almost in good agreement with the CASPT2 and CCSD(T) results (Figure 10). The energetic gap calculated between the two structures, (1) S1 and 1S2, is 285 kJ/mol by CASPT2 and 295 kJ/mol by M06L/Pop(2d). The good reproduction of the CASPT2 geometric and energetic parameters by the M06L functional shows again the performance of the symmetry broken single determinant approach. For the (1)S1 complex, we observe small geometrical changes with respect to the free N2 and Ti2O moieties. The N−N and Ti−Ti bond lengthening are about +2.4% and +3.2%, respectively. The OTi2 subunit loses its C2v symmetry upon complexation resulting in two nonequivalent Ti−O bond lengths: 1.837 Å (−0.4%) and 1.853 Å (0.5%). The Ti−N bond distance (2.099 Å) is slightly less than the bulk Ti−N bond length (2.12 Å). Concerning the 1S2 structure, one can easily note three important structural changes: the NN bond breaking, the Ti−Ti bond lengthening by 25% with respect to that in the Ti2O, and the presence of a unique TiO bond with R(TiO) = 1.649 Å, close to the CCSD(T) value (Figure 10), significantly shorter than that of Ti2O and slightly perturbed with respect to that of titanium monoxide (1.620 Å experimental value,58 and 1.619 and 1.615 Å calculated values at respectively this work and C-RCCSD(T) + DKH2 level).59 Finally, it is interesting to compare the structural parameters of the OTi2N2 ground state to those of Ti2N2 compound studied previously.13,14 It has been shown that the Ti2N2 has a cyclic structure within the D2h symmetry, whereas OTi2N2 belongs to the Cs group in which the cyclic Ti2N2 moiety no longer planar within the final product. Both the Ti−Ti and N−N bond lengths increase when we compare the Ti2N2 cyclic compound to the 1S2 structure: 2.552/2.631 and 2.483/ 2.520 Å for the Ti−Ti and N−N distances, respectively. We cannot leave this section without commenting on the reaction pathway. Even though the Ti2O + N2 interaction proceeds entirely on the “singlet” state, we cannot determine the full reaction path by DFT due to presence of “contaminated transition states”.

Figure 11. Laplacian contour maps of the (1)S1 and 1S2 structures, from the M06L/Pop(2d) wave function. Solid lines (blue) stand for ∇2ρ < 0 and dashed ones (red) for ∇2ρ > 0. The green circles represent BCPs, and the black ones represent the RCP.

2.2. Chemical Bonding Analysis. The QTAIM topological analysis of the bonding within these compounds is displayed in Figure 11. BCPs are represented by the green circles and RCP by the black one. Quantitative information are reported in Table 5. We remind readers that the numbers of critical points Table 5. Topological Information at the Critical Points within the (1)S1 and 1S2 Structures (1)

1

S1

ρ, ∇ ρ, H, ε 1: 2: 3: 4: 5: 6:

BCP BCP BCP BCP BCP RCP

0.13, 0.07, 0.63, 0.10, 0.14, 0.09,

+0.65, −0.04, 0.26 +0.38, 0.00, 0.48 −2.21, −1.07, 0.01 +0.26, −0.04, 0.42 +0.66, −0.04, 0.21 +0.32, −0.02, −

S2

ρ, ∇ ρ, H, ε

2

2

0.24, 0.13, 0.13, 0.21, 0.21, 0.06,

+0.89, +0.38, +0.38, +0.54, +0.54, +0.18,

−0.14, −0.05, −0.05, −0.12, −0.12, −0.01,

0.0 0.07 0.07 0.11 0.11 −

reported in Table 5 are just for clarification. We must pay attention to the fact that two critical points numbered with the same number do not necessarily describe the same situation. That said, we will now analyze the topological data. The BCP(Ti−N) in the (1)S1 structure clearly shows a weak interaction with the smallest charge density, a positive Laplacian, and the largest ellipticity. As a consequence, the encounter complex should be regarded as an association of two molecular units (Ti2O and N2) in weak interaction. Furthermore, topological changes occurring upon complexation within each partner are very small compared to free molecules (Ti2O and N2). Unlike the encounter complex, there is no topological link between two titanium atoms within the 1S2 structure. The Ti− O topological parameters are closer to those of free TiO than Ti2O. We observe two equivalent pairs of BCP(Ti,N): 2 and 3 on the one hand and 4 and 5 on the other hand. Even though the Laplacian at BCP(Ti,N) is positive, the total energy density is, however, negative. Following the total energy density values reported in Table 5, one can conclude a less covalent character for the BCPs numbered as 2 (and 3) than for the 4 (and 5) ones. This property is in line with the Ti−N bond lengths: 1.925 and 1.724 Å respectively. 2.3. Vibrational Analysis. This section is devoted to comparing the experimental vibrational frequencies to the theoretical ones. We note at first that theoretical vibrational I

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Table 6. Experimental Frequencies and Theoretical Harmonic Vibrational Data (cm−1) of the Two Observed Species with the Isotopic Shifts experiment modes (1)

1

S1

S2

Ti2O

a

ν4 ν3 ν2 ν1 ν5 ν4 ν3 ν2 ν1 νTiO as νTiTi νTiO s

14

N14NO

211.6 263.8 755.0 2123.4 349.7 713.4 779.5 890.3 946.0

14

N15NO

M06L/Pop(2d) 15

−2.5 −2 −0.6 −33.4; −35.7 −3.6 −10.2 −10.4 −10.3 −0.1

N15NO −4.6 −4.2

−69.7 −7.9 −20.1 −19.8 −22.7 −0.4

736.4a

14

N14NO b

242 [226 ] 298 [253b] 790 [781b] 2097 [2051b] 358 [351b] (350c) 731 [726b] (724c) 817 [794b] (785c) 950 [928b] (905c) 980 [971b] (957c) 400 416 807

14

N15NO

−2; −5 −2; −4 0 −35; −36 −4 −11 −11 −12 0

15

N15NO −7 −7 0 −71 −8 −22 −21 −25 0

b

Experimental data from ref 18. Vibrational frequencies corrected for the anharmonicity effect. cThe CCSD(T)/Def2-TZVPPD harmonic vibrational frequencies.

49/48 isotopes in ν2 and 1.003, 1001, and 0.999 for 46/48, 47/48, and 49/48 isotopes in ν4. All the evidence just mentioned is for the consistency of our vibrational analysis. Finally, we note that the dititanium oxide has been experimentally observed by the Andrews’ group in solid argon.18 They assigned the 736.4 cm−1 band to the asymmetric stretching of the bent molecule TiOTi. It was calculated to be at 807 cm−1. The calculated 16/18 ratio (1.047) is also very close to the experimental value (1.045).

analysis has been performed at the M06L/Pop(2d) level within the harmonic framework. For both structures, all vibrational frequencies are real. The harmonic vibrational frequency calculation has been also performed at the CCSD(T)/Def2-TZVPPD level of theory only for the final product because of its monoreference nature. The vibrational mode assignments have been done by a thorough detailed inspection of their eigenvectors. All the calculated and experimental frequencies as well as the nitrogen isotopic shifts are reported in Table 6. Anharmonic frequencies have been undertaken using the second-order perturbation theory (PT2) at the DFT level (Table 6). One can easily note that the CCSD(T) harmonic frequencies perfectly match the experimental results for the final product. DFT anharmonic values are very close to the experimental vibrational frequencies for both species and also in nice agreement with the CCSD(T) ones for the final product. It is interesting to note that the experimental frequency shifts due to the isotopic effect on the nitrogen atoms are well reproduced by harmonic DFT calculations, except for the two low frequencies of the adduct complex for the 15N15NO/ 14 14 N NO isotopic substitutions. As discussed in section II, in addition to the concentration and annealing effects, the experimental observation of isotopic titanium in our spectra allowed us to propose some stoichiometry and structure for chemical species formed from Ti2 + N2O trapped in the neon matrix. Of the first four vibrational modes of the final product (OTiNTiN, 1S2), for which a weak titanium isotopic effects have been experimentally observed, we compare the DFT results to the experimental ones. For ν1 mode (TiO stretch), with participation of only one of the two titanium in the vibration, the observed 46/48 and 49/48 ratios for the titanium isotopes, 1.006 and 0.997, are very close to the harmonic DFT values, 1.005 and 0.997. For ν3 mode (TiN asym stretch), where two Ti atoms are involved in the vibration, the observed 47/48 and 49/48 ratios for the titanium isotopes are exactly reproduced by the harmonic DFT values, 1.002 and 0.998. In the case of ν2 and ν4 modes (TiN sym stretch), characterized with participation of one of the two Ti atoms in the vibration, the harmonic DFT and experimental isotopic ratios are the same for two sets 1.002 and 0.998 for 47/48 and

V. CONCLUSIONS In summary, it has been experimentally shown that the Ti2 dimer spontaneously reacts with N2O molecule leading to the formation of an adduct complex, OTi2N2. Irradiation in the near-infrared region results to the NN bond breaking and then to the formation of a new molecule, di(titanium nitride) oxide, OTiNTiN. The two compounds have been identified by their vibrational analysis, the isotopic effects and their interconversion under the photolysis process. Theoretical investigations have been performed to determine the most adequate density functional to describe systems with multireference electronic structure. First, high level studies on the Ti2O system provided valuable data to check the reliability of density functionals. The Ti2O molecule has actually a singlet ground state, due to electron correlation stabilization with respect to other spin states. The Ti2O molecule was used as a benchmark to assess the reliability of several DFT functionals. We showed that hybrid functionals fail to describe well the nature of either the ground state or the geometrical parameters. In contrast, pure functionals lead to the correct geometry, but some of them mismatch the energetic ordering of the “singlet” and “triplet” states. Second, calculations have been performed with CASPT2 and M06L functional on both end-on adduct complex and final product for the singlet ground state. It has been shown that the intermediate complex has a strong multireference character requiring simultaneously static and dynamic correlation processing, whereas the final product is almost a closed-shell monoreference system. For a correct description of the latter, including the essential physics, a monoreference treatment of the dynamical correlation is sufficient. A geometry optimization has thus been carried out at the CCSD(T) level. J

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(10) Zhou, M.; Jin, X.; Gong, Y.; Li, J. Remarkable Dinitrogen Activation and Cleavage by the Gd Dimer: From Dinitrogen Complexes to Ring and Cage Nitrides. Angew. Chem. Int. Ed 2007, 46, 2911−2914. (11) Xu, Q.; Jiang, L.; Tsumori, N. cyclo-Ti3[η2(μ2-C,O)]3: A Sideon-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character. Angew. Chem., Int. Ed. 2005, 44, 4338−4342. (12) Jiang, L.; Xu, Q. Infrared Spectra of the (AgCO)2 and AgnCO (n = 2−4) Molecules in Rare-Gas Matrices. J. Phys. Chem. A 2006, 110, 11488−11493. (13) Himmel, H.-J.; Hübner, O.; Klopper, W.; Manceron, L. Cleavage of the N2 Triple Bond by the Ti Dimer: A Route to Molecular Materials for Dinitrogen Activation? Angew. Chem., Int. Ed. 2006, 45, 2799−2802. (14) Himmel, H.-J.; Hübner, O.; Bischoff, F. A.; Klopper, W.; Manceron, L. Reactivity of Titanium Dimer and Molecular Nitrogen in Rare Gas Matrices. Vibrational and Electronic Spectra and Structure of Ti2N2. Phys. Chem. Chem. Phys. 2006, 8, 2000−2011. (15) Souvi, S. M.; Berkaïne, N.; Alikhani, M. E.; Manceron, L. Neonmatrix Spectroscopic and Theoretical Studies of the Reactivity of Titanium Dimer with Diatomic Ligands: Comparison of Reactions with Nitrogen and Carbon Monoxide. Phys. Chem. Chem. Phys. 2009, 11, 9831. (16) Andrews, L.; Gong, Y.; Liang, B.; Jackson, V. E.; Flamerich, R.; Li, S.; Dixon, D. A. Matrix Infrared Spectra and Theoretical Studies of Thorium Oxide Species: ThOx and Th2Oy. J. Phys. Chem. A 2011, 115, 14407−14416. (17) Hübner, O.; Himmel, H.-J.; Manceron, L.; Klopper, W. LowLying Electronic States of the Ti2 Dimer: Electronic Absorption Spectroscopy in Rare Gas Matrices in Concert with Quantum Chemical Calculations. J. Chem. Phys. 2004, 121, 7195−7206. (18) Chertihin, G. V.; Andrews, L. Reactions of Laser Ablated Titanium, Zirconium, and Hafnium Atoms with Oxygen Molecules in Condensing Argon. J. Phys. Chem. 1995, 99, 6356−6366. (19) Chen, M.; Wang, G.; Zhou, M. Formation of the End-On Bonded OTiNN Dinitrogen Complex and its Photoconversion to the Side-On Bonded OTi(N2) Molecule. Chem. Phy. Lett. 2005, 409, 70− 74. (20) Zhou, M.; Zhuang, J.; Zhou, Z.; Li, Z. H.; Zhao, Y.; Zheng, X.; Fan, K. Titanium Oxide Complexes with Dinitrogen. Formation and Characterization of the Side-On and End-On Bonded Titanium Oxide−Dinitrogen Complexes in Solid Neon. J. Phys. Chem. A 2011, 115, 6551−6558. (21) Marzouk, A.; Alikhani, M. E.; Madebène, B.; Tremblay, B.; Perchard, J.-P. Vibrational Spectra and Structures of Ti-N2O and OTiN2: A Combined IR Matrix Isolation and Theoretical Study. J. Phys. Chem. A 2013, 117, 1697−1705. (22) Frisch, M. J. ; Trucks, G. W. ; Schlegel, H. B. ; Scuseria, G. E. ; Robb, M. A. ; Cheeseman, J. R. ; Scalmani, G. ; Barone, V. ; Mennucci, B. ; Petersson, G. A.; et al. Gaussian 09, Revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (23) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098−3100. (24) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (25) Becke, A. D. Density-Functional Thermochemistry. IV. A New Dynamical Correlation Functional and Implications for ExactExchange Mixing. J. Chem. Phys. 1996, 104, 1040−1046. (26) Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B 1986, 33, 8822−8824. (27) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Phys. Rev. B 1992, 45, 13244−13249. (28) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Atoms, Molecules, Solids,

It has been evidenced that the M06L functional used in the framework of the broken symmetry approach is the most suitable in the case of studied compounds to reproduce well both the experimental results and those obtained from a high level ab initio method. In line with recent publications,60−63 we observe that the total energy obtained in the broken symmetry framework not only contains dynamic correlation in the effective way but also is capable of generating some extent static correlation effects.

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ASSOCIATED CONTENT

* Supporting Information S

Table of all the calculated geometric and energetic parameters of the Ti2O structure at singlet, triplet, quintet, and septet spin states. These calculated parameters are done by all the DFT functionals used in this manuscript and with the 6-311+G(2d) basis set. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Authors

*B. Tremblay: fax, 33-1-44273021; e-mail, [email protected]. *M. E. Alikhani: e-mail, [email protected]. # Also at: High Vacuum Group and Beamline AILES, Synchrotron SOLEIL, L’Orme des Merisiers, F-91192 Gifsur-Yvette, France. Notes

The authors declare no competing financial interest.

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REFERENCES

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