and N2O - Semantic Scholar
Energetic and Topological Analyses of the Oxidation Reaction between Mon (n ⴝ 1, 2) and N2O MARIA DEL CARMEN MICHELINI,1 NINO RUSSO,1 MOHAMMAD ESMAI¨L ALIKHANI,2 BERNARD SILVI3 1
Dipartimento di Chimica and Centro di Calcolo ad Alte Prestazioni per Elaborazioni Parallele e Distribuite-Centro d’Eccellenza MURST, Universita` della Calabria, I-87030 Arcavacata di Rende, Italy 2 Laboratoire de Dynamique, Interactions et Re´activite´ (UMR 7075), Universite´ P. et M. Curie, Boıˆte 49, baˆtiment F74, 4 Place Jussieu 75252 Paris Cedex 05, France 3 Laboratoire de Chimie The´orique (UMR 7616), Universite´ P. et M. Curie, Boıˆte 137, Tour 2223, 4 Place Jussieu 75252 Paris Cedex 05, France Received 19 November 2004; Accepted 9 March 2005 DOI 10.1002/jcc.20269 Published online in Wiley InterScience (www.interscience.wiley.com).
Abstract: The interaction between molybdenum, atom, and dimer, with nitrous oxide has been investigated using density functional theory. The analysis of the potential energy surfaces for both reactions has revealed that a single molybdenum atom can activate the N—O bond of N2O requiring a small activation energy. However, the presence of several intersystem crossings between three different spin states, namely, septet, quintet and triplet states, seems to be the major constraint to the Mo ⫹ N2O reaction. Contrarily, the low-lying excited states (triplet and quintet) do not participate in the reaction between the molybdenum dimer and N2O. The latter reaction fully evolves on the singlet spin surface. Three different regions have been distinguished along the pathway: formation of an adduct complex, formation of an inserted compound, and the N2 detachment. The connection between the two first regions has been characterized by the formation of a special complex in which the N—O bond is so weakened that it could be considered as a first step in the insertion process. It has been shown that the topological changes along the pathways provide a clear explanation for the geometrical changes that occur along the reaction pathway. In summary, the detachment of the N2 molecule is found to be kinetically an effective process for both reactions, owing to the high exothermicity and consequently to the high internal energy of the insertion intermediates. However, in the case of Mo atom, the reaction should be a slow process due to the presence of spin-forbidden transitions. These results fully agree with previous experimental works. © 2005 Wiley Periodicals, Inc.
J Comput Chem 26: 1284 –1293, 2005
Key words: electronic structure; reaction pathways; mono- and di-molybdenum oxidation; nitrous oxide reduction;
bonding description; AIM and ELF topological analyses
Introduction The reaction of gas-phase metal atoms with N2O have been previously studied both theoretically1–7 and experimentally,8 –10 due to its importance in many fields, such as oxidation of transition metals, catalytic activation of the N—O bond, and earth’s atmosphere. Nitrous oxide, other than a well-known catalytic oxidant, is one of the greenhouse gases, and is also involved in the depletion of stratospheric ozone. Although there are many known natural and anthropogenic sources, emissions of nitrous oxide have been difficult to quantify on a global scale, primarily because it has been one of the least studied greenhouse gases to date. In contrast to carbon dioxide and methane, nitrous oxide is released in small
quantities from anthropogenic sources. The largest source of emissions is energy use, which includes mobile source combustion (i.e., emissions from motor vehicles) and stationary source combustion from residential, industrial, and electric utility energy use. The second-largest source of nitrous oxide emissions is agriculture, primarily fertilizer application and a small amount released from the burning of crop residues. Nitrous oxide emission arise during
Correspondence to: N. Russo; e-mail: [email protected] Contract/grant sponsor: CNRS; contract/grant number: 041730 Contract/grant sponsor: Universita` degli Studi della Calabria Contract/grant sponsor: MUIR
© 2005 Wiley Periodicals, Inc.
Oxidation Reaction between Mon (n ⴝ 1, 2) and N2O
the oxidation of NH3 in the nitric acid production, which is a key ingredient in nitrogen-based fertilizer industry. Therefore, it becomes fundamental for the development of theoretical studies to obtain a detailed description of catalytic processes involving N2O. On the other hand, due to its importance as one of the essential elements in biology as well as because of its applications in heterogeneous catalysis, it is of great interest to the study the gas-phase chemistry of molybdenum. Previous experimental8 and theoretical works11,12 indicate that transition metal atoms and dimers show remarkable differences in reactivity with respect to adduct formation reactions depending on the electron acceptor/donor capabilities of the ligand. In the case of Lewis base ligands, an increase of reactivity in going from the atom to the dimer has been observed, whereas for -acceptor ligands the opposite behavior has been manifested. Experimental studies have shown that molybdenum atoms and dimers show differences in reactivity with respect to N2O. In particular, Lian et al.8 have reported flow tube kinetic measurements that indicate that nitrous oxide reacts with Mo2, leading to the N—O bond activation, but the Mo ⫹ N2O assembly is a nonreactive process at room temperature. On the other hand, McLean et al.9 have presented experimental data of depletion kinetics of Mo(a7S3, a5S2, a5DJ ) by several small molecules, including N2O. In that work it has been determined that ground state Mo is unreactive toward N2O at room temperatures; however, observable reaction rates were measured for Mo(a7S3) ⫹ N2O as the temperature was increased. The authors have suggested that the inefficiency of the reaction could be attributed to the production of spin-forbidden states. On the theoretical side, DFT calculations for the oxygen abstraction from N2O by the ground state of the first row transition metal (TM) atoms have been recently reported.1,3,6 The main finding of these works is that the reactions with Sc, Ti, and V proceed almost without energy barriers, and that the 3d n⫹1 4s 1 configuration gives rise to a higher reactivity than the 3d n 4s 2 configuration. The N—O cleavage has been mostly explained as an electron transfer model (electron transfer from the metal to the N2O molecule via initially 3d, then 4s ⫺ 3d hybrid orbitals) against a direct oxygen abstraction one. In a recent work,13 we have presented an energetic and topological study of the adduct formation process for the interaction of Mo and Mo2 with different small ligands, namely NH3, C2H2, and C2H4. We have shown that Mo and Mo2 essentially interact with C2H2 and C2H4 via an electron pair transfer from the metalliccenter to the ligand, forming a chemical bond with the carbon atoms, while the interaction between Mo (or Mo2) and NH3 has mostly an electrostatic character. In the present work, our main interest is the investigation of the whole oxygen-transfer process and the complete analysis of the potential energy profiles corresponding to the interaction of N2O with Mo atom and dimer. To gain insight into the reaction mechanisms of the N—O bond activation we report a complete analysis of the reaction pathways for the ground and low-lying excited states of Mo and Mo2. The chemical bonding evolution along the effective reaction pathways has been also investigated from a topological point of view.
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Computational Details All calculations have been performed with the Gaussian 2003 quantum chemical package14 using the density functional (DFT) method. The DFT calculations have been carried out with the Perdew and Wang (1991) density gradient correction to the exchange and correlation functionals (denoted hereafter as PW91PW91).15–19 The singlet state optimization has been done within the restricted Kohn–Sham formalism, while the open-shell structures have been investigated using the unrestricted Kohn– Sham formalism. In the latter case, the spin-contamination has been found as always negligible (⬍5%). The LANL2DZ effective core potential20 has been employed for the molybdenum atom. In LANL2DZ, the 14 electrons of the valence shell are represented explicitly using a double zeta basis. The 6-311G⫹⫹(2d,2p) extended basis set21–23 has been employed for the other atoms. The TopMod package24 has been used to analyze the chemical bonding of the studied species from a topological point of view. Topological analysis of the one-electron density function (known as the Atoms in Molecules Theory25: AIM), and of the electron localization function (ELF)26,27 represent for the chemical bonding description an alternative to the standard molecular orbital approaches. They rely upon the gradient field analysis of the corresponding local functions. Their common aim is “to provide a mathematical bridge between chemical intuition and Quantum Mechanics.”28 Because both Lewis and Gillespie’s phenomenological29 models describe the bonding within a molecule in the usual three-dimensional space, the mathematical model makes a partition of this space into regions related to chemical properties. According to the AIM topology, positive values of the electron density Laplacian (ⵜ2 ⬎ 0) at bond critical points (BCP: points for which ⵜ ⫽ 0) are associated with closed-shell interactions (ionic bonds, hydrogen bonds, and van der Waals interactions), while ⵜ2 ⬍ 0 indicates shared interactions (covalent bonds). Also, the partitioning of the molecular space allows the definition of atomic volumes in the molecules and by integrating any property density function over an atomic basin, it is possible to estimate the corresponding atomic property.30 For instance, the integration of the electron density function over an atomic basin gives the atomic electron population, and consequently, the net atomic charge. The topological description of the chemical bond proposed by Silvi and Savin27 is based on the gradient field analysis of the electron localization function (ELF) of Becke and Edgecombe.26 In a region of space dominated by an antiparallel spin pair, the Pauli repulsion is weak, and therefore, the value of the ELF function (labeled as ) is close to 1. Near the boundary between two such regions, where same spin electrons necessarily come close together, they exert a significant Pauli repulsion that decreases the value of ELF function to low values. In particular, ⫽ 0.5 corresponds to the homogeneous electron gas case. Therefore, the topological analysis of the ELF function provides a partition scheme of the molecular space into basins of attractors that have a clear chemical meaning. These basins are either core basins [labeled as C(A)] surrounding nuclei or valence basins, V(A, . . . ), belonging to the outermost shell and characterized by their coordination number with core basins, which is called the synaptic order. The basin population are evaluated by integration of the one-electron density over the volume of the basin. In addition, a
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measure of the delocalization is provided by considering the fluctuations of the basin populations.31 Within the framework provided by the ELF analysis, a chemical reaction is viewed as a series of topological changes occurring along the reaction path. The parameters defining the reaction pathway, such as the nuclear coordinates and the electronic states, constitute the control space. Therefore, the topological behavior of the gradient field can be studied by using Thom’s catastrophe theory.32 This type of analysis is the so-called bonding evolution theory (BET).33 There are two important indicators in using this technique: the morphic number, that is, the number of basins, and the before-mentioned synaptic order of valence basins. Each structure is only possible for values of the control parameters belonging to definite ranges called structural stability domains. For any two points of the control space belonging to a given structural stability domain, there is the same number of critical points of each type in the ELF gradient field. This technique shows how the bonds are formed and broken, and also emphasizes the importance of the geometrical constraints in a chemical reaction. Moreover, the identification of the elementary catastrophe and, therefore, the knowledge of its universal unfolding yield the dimension of the active control space governing the reaction. In addition, from a quantitative viewpoint, the evolution of the total and spin basin populations along the path provides keys to understand the role played by the different chemical interactions. Chemical processes are then classified into three groups: the plyomorphic one, in which an increase of the morphic number is observed (e.g., a covalent bond breaking); the tautomorphic diffeosynaptic process, in which the number of basins is conserved, but there is a variation of the synaptic order of at least one basin (e.g., a breaking of a dative bond); and the miomorphic process in which there is a decrease in the number of basins (e.g., covalent bond formation). Along the reactions there exist several domains of structural stability. Within a domain of structural stability, the topology of the ELF gradient field is not altered by the variation of the control space parameters, which belong to a definite range. Between two successive domains of structural stability the evolution is ruled by a bifurcation catastrophe. At this point, at least the type of catastrophe gives access to its unfolding and, therefore, to the minimal dimension of the control space enabling the modification of the topology. To account for the core electron effect in the topological study, the ELF calculations have been carried out on the global minima using an all-electron double- quality basis set (DGDZVP34,35) for the Mo atom. The other atoms are treated again using the 6-311⫹⫹G(2d,2p) basis set. For the reaction pathway analysis we have ensured that every transition structure has only one imaginary frequency, and that connects the reactants to the appropriate product species running IRC (Intrinsic Reaction Coordinate) calculations. In addition, we have paid much attention to two other points for the completion of the present calculations. 1. The size-consistency property has been checked when calculating the binding energies. In particular, we have checked the size-consistency for the Mo–ligand interaction by comparing the total calculated energy for a large distance with the sum of
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the two entities at the same spin state. It is an interesting feature, which clearly shows the reliability of the PW91PW91 functional at large interfragment distances. 2. Furthermore, because it is important to test the stability of restricted closed-shell structure calculated within Kohn–Sham formalism,36 the stability of the singlet states has been checked and no instability has been found. In a previous article,13 we have already checked the reliability of the level of theory employed in the present work by studying the bare molybdenum atom and dimer. For the energetic gap between the first excited state ( 5 S(d 5 s 1 )) and the ground state ( 7 S(d 5 s 1 )) of Mo, the PW91PW91/LANL2DZ level of theory is the one that better reproduce the measured value (1.38, 1.45, 1.42, and 1.33 eV, the PW91PW91,13 CI,37 BPW91,38 and experimental39 values, respectively). We have found a good agreement between the 3 ⫹ spectroscopic parameters of the two states of Mo2 ( 1 ⌺ ⫹ g and ⌺ u ) calculated at PW91PW91 level, with those obtained by means of highly correlated methods and with experimental data. See ref. 13 for details.
Mo ⴙ N2O Interaction Several approaches have been studied for the metal atom interaction with the nitrous oxide molecule: the “side-on” approach with respect to the N—O and N—N bonds, and “end-on” one, in which Mo interacts with the ending atoms (O or N) of N2O with a nearly linear arrangement. In the initial geometries for the geometrical optimization, we slightly displaced the atoms of N2O from the perfect collinear arrangement. Each geometrical approach has been studied for three low-lying electronic states of Mo: the septet ground state, and the quintet and triplet excited states. Structural and Energetic Analyses
The optimized geometrical parameters of all the Mo–N2O structures are displayed in Figure 1. All the structures have a C s symmetry, in which four atoms form a planar structure. The electronic states of the calculated Mo–N2O structures are A⬘ for all the three spin multiplicities, except in the case of the inserted compound in the septet spin state, which has a linear structure (II symmetry). In that figure the first column shows the adduct complexes formed between Mo and N2O, in which the metal atom interacts with the ending N atom of nitrous oxide. The second column shows the transition structures between the adduct complexes and the inserted compounds, which are shown in the third column. The adduct complex has a cis-structure (with respect to the N—N bond) in the septet state and a trans-structure in the quintet and triplet ones. The N—N and N—O bond lengths increase upon the complex formation between Mo and N2O. They also increase with the decrease of the spin multiplicity, whereas, the Mo–N distance shows the opposite trend. The transition state (TS) structures are of cis-shape geometry for all the three electronic states. Mo is found to be bound to the oxygen atom of N2O in the TS septet state, while it is N-bounded in the quintet and triplet TSs. In the septet and quintet TSs, the N–O distance is so large that we can assume that there is no bonding between O and
Oxidation Reaction between Mon (n ⴝ 1, 2) and N2O
Figure 1. Structural parameters of different electronic states of the adduct complexes (column 1), transition states (column 2), and insertion intermediates (column 3) of the Mo–N2O reaction. Distances are in Å, and angles in degrees.
N. The Mo–N distance in all three inserted compounds is of around 2 Å. In these compounds, the N–N distance is larger than free N2 by at least 0.025 Å. In Figure 2 are shown the relative energies (in kcal/mol) of the nine studied structures as well as those of products (corresponding to the N2 detachment), with respect to the Mo( 7 S) ⫹ N2O(1⌺⫹) fragments. We note that the most stable adduct complex is of the quintet spin state, which correlates with the first excited state of the Mo atom. The quintet adduct complex is found to be slightly more stable than the septet one (ca. 4.1 kcal/mol). Indeed, the formation of the quintet adduct complex is assumed to occur through a crossing point between the two potential energy profiles (septet and quintet ones) at the entrance channel. For the inserted compounds, the septet structure is much less stable than the quintet and triplet ones. In fact, the triplet inserted structure is the ground state for the insertion intermediate, being slightly more stable than the quintet one (ca. 4.3 kcal/mol). As shown in Figure 2, the formation of the ground state of the inserted structure takes place through two intersystem crossings between three surfaces when going from the adduct complex to the inserted compound. First, the quintet adduct complex crosses the septet pathway allowing the evolution of the reaction via the septet TS, which requires a small activation energy (⬇13 kcal/mol). Second, the crossing between triplet and septet pathway leads to the formation of the triplet insertion intermediate. The energetic gain during the above-mentioned pathway is therefore around of 91.5 kcal/mol. Consequently, the formation of the ground-state insertion complex is energetic enough so that the exit channel leading to the formation of the N2 and MoO products could be kinetically reached. We note that the exit channel proceeds on the quintet surface via a new intersystem crossing between the triplet and quintet surfaces. The barrier height for the last part of the pathway, that is, the N2 detachment, is of about 22 kcal/mol.
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These considerations show that the N—O bond activation of the nitrous oxide by a single molybdenum atom is energetically favorable owing to the small barrier height in the septet surface, which starts from the ground state of the fragments. It is worthy to emphasize on the substantial role played by the ground state of the molybdenum atom leading to the formation of the molybdenum monoxide and N2. At this point we would like to compare our theoretical results on the reactivity of Mo with N2O with previous experimental results.8,9 As previously mentioned, flow tube kinetics studies on the reactivity of Mo and Mo2 with N2O have shown no reaction (second-order rate coefficient, k (2) , less than 5 10⫺15 cm3s⫺1) in the case of the Mo atom, whereas for the dimer it has been measured as a second-order rate coefficient of 4.4 10⫺12 cm3s⫺1 at 296 ⫾ 1 K.8 On the other side, on the basis of depletion kinetics data,9 experimental researchers concluded that the ground-state Mo is unreactive toward N2O at room temperature, whereas observable reaction rates were measured as the temperature was increased, attributing the inefficiency of the reaction to the production of spin-forbidden states. The calculated activation barrier for Mo(a 7 S) ⫹ N2O 3 MoO ⫹ N2 (13.2 kcal/mol) is in quite good agreement with the experimental data (9.8 kcal/mol),9 indicating the reliability of our theoretical work. Reaction Mechanism: ELF Analysis
From a qualitative point of view (the Chatt–Dewar–Duncanson scheme40,41), the reaction between Mo and N2O could be mainly understood as an interaction between the Mo 4d- and 5s-orbitals with the N2O HOMO and LUMO. The N2O HOMO is a -orbital, which
Figure 2. Energetic pathway for the Mo ⫹ N2O reaction from the initial fragments to the N2 detachment.
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Table 1. ELF Basin Populations (e) of the Mo ⴙ N2O Compounds.
Compounds N2( 1 ⌺ ⫹ g ) N2O(1⌺⫹) N2O⫺( 2 A⬘) Adduct Complex: Septet Quintet Triplet Transition state: Septet Quintet Triplet Insertion complex: Septet Quintet Triplet
C(Mo)[S z ]
V(Mo)[S z ]
V(N1,N2)
V(N,O)
V(N1)
V(N2)
3.34 3.78 2.45
3.26 4.31 4.41
3.26
1.98 1.13
2.58
5.60 6.18
1.42 1.45 1.38
4.45 4.71 4.93
2.04 2.72 3.05
5.70 5.75 5.71
1.15
3.65 4.28 4.68
3.21 3.47 3.12
6.70 5.88 5.91
3.43 3.50 3.70
3.57 3.68 3.85
5.60[0.5] 7.14[0.2] 6.22[0.1]
40.80[2.3] 40.70[1.8] 40.68[1.2]
0.69[0.3] 0.50[0.2] 0.21[0.1]
2.60 1.94 1.74
40.56[2.0] 41.30[1.8] 40.81[1.3]
0.66[0.3] 0.24[0.1]
2.96 2.51 2.12
41.58[2.2] 39.40[1.2] 40.46[0.7]
0.97[0.4] 0.66[0.2]
3.15 3.04 2.87
is antibonding with respect to the O—N bond but bonding for the N—N bond. The LUMO is a *-orbital with antibonding character for both the N—O and N—N bonds. The charge transfer from Mo to the *-orbital upon the formation of the adduct complex destabilizes both the N—O and N—N bonds leading to a lengthening of these bonds. Consequently, the N2O molecule loses its linear structure when the LUMO is populated. Recent theoretical works have reported the tilting of nitrous oxide after the attachment of an electron.42,43 The back-donation interaction between the HOMO and a symmetry allowed orbital of the metal stabilizes the Mo—N bonding. As has been previously underlined,44 the molybdenum atom can only react as an electron donor because of its electronic configuration (5s1 4d5). Consequently, the reactivity of Mo atoms strongly depends on the nature of the ligands. To provide a deeper understanding of the reaction mechanism along the reaction pathway, the bonding characterisation has been made by using topological approaches. We have gathered in Table 1 the electronic populations of the different basins involved in the reaction. The C(Mo) stands for the molybdenum core basin population and S z is its integrated spin density. V(Mo) and S z represent the monosynaptic Mo valence basin population and its integrated spin density, respectively. The disynaptic valence basins of the N—N and N—O bondings are denoted as V(N1,N2) and V(N,O), respectively. The monosynaptic basin of oxygen is labeled as V(O), whereas that of the ending N as V(N1) and the one corresponding to the second nitrogen atom as V(N2). The analysis of the sign of the laplacian of the electronic density at the N—N and N—O bond critical points showed that these bonds can be described as a shared-interaction (ⵜ2 ⬍ 0) in the adduct complexes. For the transition structures, a BCP has been found between Mo and N atoms in both the quintet and triplet states but not in the septet state. In the later state, the presence of a BCP indicates the binding between Mo and O atoms. In the case of the inserted complexes, the value of the electron density at the Mo—N bond critical point is quite small (less than 0.12 e), indicating the weakness of this interaction. In addition, the charge
V(O)[S z ]
transfered from the MoO moiety to the N2 one has been calculated to be 0.22, 0.27, and 0.36 e for the septet, quintet, and triplet inserted compounds, respectively. The ELF basin populations (see Table 1) allows us to explain the weakening of the N—N and N—O bonds upon the formation of the adduct complexes. In line with the N—N and N—O bond lengthenings in all the studied compounds, the population of the V(N,N) basin decreases more and more when the spin multiplicity decreases. In agreement with previous works on the electron attachment to nitrous oxide,42,43 the tilting of the N–N–O upon interaction with Mo is a consequence of the charge transfer from the metal center to the nitrous oxide. The appearance of a monosynaptic valence basin around of central N atom reflects this geometrical change (see Fig. 3). It should be noted that the monosynaptic valence basin of the nitrogen atom (located towards Mo) mostly belongs to the nitrogen atom; therefore, its interaction with Mo has a dative character. Inspecting the population of C(Mo) (less than 41 e) and that of V(Mo) (less than 1 e) in all the studied compounds clearly shows that both the core and valence basins of Mo participate in the interaction with N2O. This picture explains the importance of the 5s–4d hybrid orbital (d shell belongs to the outer shell of the core basin45) in the interaction between Mo and N2O. With respect to N2O, the anion is characterized by the presence of a monosynaptic basin on the central nitrogen atom, which explains the NNO bond angle and the weakening of all disynaptic basin populations, which is consistent with the increase of the bond lengths and with the spreading of the spin density among the monosynaptic basins. The minimisation of the Pauli repulsion between the central N monosynaptic basin and the metal center is the most important process upon the formation of the adduct complex. We should expect that the septet equilibrium geometry would be a cis-configuration to minimize the Pauli repulsion between the Mo core and the monosynaptic basin located on the central N. The variance of the Mo core basin is small (0.65) in the septet complex. In the case of the quintet and triplet states, the spin density is mostly localized in the C(Mo) basin with a
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Figure 3. Evolution of the ELF attractors (represented by ●) along the Mo(7S) ⫹ N2O reaction.
rather large variance (1.35). The charge transfer from metal center to the ligand implies a possible resonance structure between the [Kr]d 4 and [Kr]d 6 configurations. Therefore, we consider that the formation of the Mo⫹ NNO⫺ ionic pair is the driving force in the complex formation. The attractors of different localization domains of all the compounds involved in the reaction between Mo and N2O are represented by ● in Figure 3. As shown in Figure 3, the formation of the adduct complex corresponds to the appearance of a new monosynaptic basin around of the central N atom, whose population ranges from 2.04 to 3.05 e, depending on the spin state of the complex (see Table 1). As discussed in the previous section, three steps along the reaction have to be considered: 1. First, from the quintet complex to septet TS characterized by lowering the number of attractors by one corresponding to two bonding brokens: the Mo—N dative and N—O covalent bondings. These topological changes do not occur easily, because the transition structure is of cis-shape whereas the quintet complex is of trans-form. A path with the least topological changes implies that the quintet complex passes again by the septet one and then goes towards the septet TS. This process corresponds topologically to a fold catastrophe. 2. Second, going from the septet TS to the quintet inserted compound does not change the number of attractors. However, it should be noted that the MoO unit forms a dative bond with the N2 molecule in the triplet inserted compound. As a matter of fact, the topological instability of the septet inserted interme-
diate [with a torus-shape V(Mo) basin] and the topologically favorable situation for the interaction between N2 and MoO in the triplet and quintet surfaces are the topological mechanisms for the spin-conversion upon the inserted compound formation. 3. The last step, the N2 detachment, is topologically characterized by the nature of the bonding within MoO monoxide. As shown in the last column of Figure 3, the Mo—O bonding in the MoO monoxide is rather of a covalent character only in the quintet state (because of the presence of two attractors standing for two disynaptic basins), whereas, the Mo—O bonding in the triplet and septet states is essentially assumed to be due to the C(Mo) and V(O) delocalization. In other words, the 4s(Mo)—2s(O) bond in the quintet spin state oxide favors the quintet dissociation channel, and, as a consequence, a new spin conversion (triplet to quintet). In summary, as shown from our energetic and bonding analyses, the spin crossing effect and the sequence of topological catastrophes play an important role in the reaction mechanism and rate constants of the Mo ⫹ N2O reaction, indicating the occurrence of TSR (Two-State Reactivity) scenarios.46
Mo2 ⴙ N2O Interaction Structural and Energetic Analyses
We have performed geometrical optimizations for several electronic states: singlet, which correlates with the ground state of the
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Figure 5. Structural parameters of the Mo2–N2O complexes at singlet state. Distances are in Å, and angles in degrees.
Figure 4. Relative energies of the quintet, triplet, and singlet (denoted as Q, T, and S, respectively) with respect to the fragments ground state. The geometrical shapes of the different structures (denoted as Complex1, Insert1, and Trans) are also displayed.
free fragments, triplet, and quintet states (the lowest lying excited states). For each spin state, three different approaches between Mo2 and N2O have been studied: the end-on approach (N- or O-bonded), the perpendicular arrangements (Mo2 axis perpendicular to the N—N or N—O bonds), and the parallel approach (Mo2 axis parallel to the N–N–O axis). The energetic results are partially displayed in Figure 4. The singlet, triplet, and quintet states are labeled as S, T, and Q, respectively. The relative energies of the three types of optimized geometries are reported in that figure, namely, the first complex (in which the Mo2 dimer forms an N-end-on structure with the N2O molecule), the first insertion intermediate (in which the N—O bond of N2O is already activated), and the final insertion structure (in which only one of the nitrogen of N2 is bonded to one of the Mo atoms). As indicated in Figure 4, the first complex (hereafter labeled as Complex1) has a cis-shape (with respect to the N—N bond) at the singlet state, a trans-shape at the quintet state, and a nonplanar tilted-trans at the triplet state. For all the three electronic states, the intermediate compound, Insert1, resembles now to a complex formed between Mo2O and N2 molecules with a skewed structure. In contrast, in the final insertion structure (labeled as Trans in Fig. 4) the N2 fragment forms a planar geometry with Mo2O in which only one N atom is bonded to one of the Mo atoms. The relative energies reported in that figure for the three optimized structures clearly show that the triplet and quintet states do not participate in the Mo2 ⫹ N2O reaction. In other words, this interaction fully evolves on a single potential energy surface: namely, the singlet state. However, it should be noted that the triplet and singlet states are
mostly iso-energetic for the Complex1 and Insert1 structures so that it lets us think that a higher level of calculation than the one used in this article could reverse the relative stability of these structures, but not for the last structure (Trans) for which the triplet state is less stable than the singlet one by 9 kcal/mol. Consequently, in the following discussion we analyze the reaction only for the singlet spin state surface. In Figures 5– 6 are displayed all the Mo2–N2O optimized geometries at the singlet state. The first complex (Complex1), the
Figure 6. Structural parameters of the N2–Mo2O inserted compounds at singlet state. Distances are in Å, and angles in degrees.
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mol). We note that the formation of the Trans compound is highly exothermic, and consequently, at this point of the reaction the system has enough internal energy to overcome an energy barrier of 27.3 kcal/mol. The N2 detachment process is therefore probable. Reaction Mechanism: ELF Analysis
Figure 7. Energetic pathway for the Mo2 ⫹ N2O reaction from the initial fragments to the N2 detachment.
second complex (Complex2), and the Cis and Trans insertion intermediates are planar, while the other structures are of C s symmetry. The first complex formed between Mo2 and N2O is an N-bonded structure in which the N2O molecule loses its linearity and the Mo—Mo, N—N and N—O bond distances are slightly longer than the correspondent ones in the free fragments. The lost of planarity leads to the first transition structure (labeled as TS1 in Fig. 5), which connects the first and second complexes. The out-of-plane bending of ONMo (Complex2) gives the second transition structure, which connects the second complex with the third one (Complex3). We note that the third complex is nonplanar and presents a large increase of the N—N and N—O bond distances; that is, ⫹0.308 and ⫹0.169 Å, with respect to free N2O. This complex is actually the last step for the N—O bond-breaking process. The third transition structure (TS3 in Fig. 6) connects the Complex3 with the first inserted compound (labeled as Insert1). The Insert1 compound is nonplanar, in which the two nitrogen atoms of N2 unit are unequally bonded to one of the Mo atoms of the Mo2O oxide. From Insert1, two paths have been studied: the first path connects this insertion intermediate (Insert1) to the Cis insertion structure (with respect to the Mo—Mo bond), whereas the second one leads to a Trans geometry. The transition states of these two paths are labeled respectively TS5 and TS4, in Figure 6. The geometrical analysis along the reaction path shows that the structural evolution of the Mo2 ⫹ N2O interaction substantially depends on the motion of the oxygen atom. The energetic evolution of this reaction at the singlet state is presented in Figure 7. One can distinguish two parts along the pathway: the first one going from fragments (F) to the third complex (C3), which requires an activation energy of around 15 kcal/mol, and a second part, which connects the C3 complex to the final insertion intermediate (Trans) by overcoming a barrier height of around 11 kcal/mol. At this point, the Trans structure could evolve to the N2 detachment at the triplet state via an intersystem crossing between the singlet and triplet surfaces (see Fig. 7) slightly higher in energy than the Trans singlet state (27.3 kcal/
The evolution of the ELF attractors (represented by ●) along the Mo2( 1 ⌺ ⫹ g ) ⫹ N2O reaction is displayed in Figure 8. For the ground state of free Mo2, the ELF value for the V(Mo) basins ( ⫽ 0.35) is twice smaller than that of the V(Mo,Mo) one ( ⫽ 0.61), indicating a large excess of kinetic energy density due to the Pauli repulsion.47 It is therefore normal to attribute to the V(Mo) basins a higher binding ability than the corresponding V(Mo,Mo) ones. Furthermore, in the free molybdenum dimer the attractor of V(Mo,Mo) is degenerated on a torus shape (represented by four attractors) and therefore the ELF gradient field is structurally unstable. Consequently, the interaction between Mo2 and N2O should lead to the formation of a chemical bonding between V(Mo) and the N2O molecule and to the splitting of the V(Mo,Mo) basin. The topological evolution along the Mo2 ⫹ N2O reaction could be considered as follows. 1. The first topological event corresponding to the formation of an adduct complex (labeled as C1) should be considered as the formation of a Mo—N dative bond, the appearance of a monosynaptic basin on the central N atom, and the splitting of the V(Mo,Mo) basin. It is a “cusp catastrophe.” The geometrical changes of the complex then proceeds from the Complex1 (C1) to Complex2 (C2), within the same topological domain (no new changes in the number of basins). 2. The second catastrophe takes place during the formation of Complex3 (C3) by increasing the number of attractors by 1. At this stage, the Mo—Mo bonding is assumed by a large C(Mo)—C(Mo) delocalization (variance ⫽ 2 e) and there are two disynaptic Mo—N basins. The population of each Mo—N basin is 1.65 e, in which the contribution of Mo is of 0.5 e. In addition, in Complex3 the V(O,N) population is very low (0.78 e) with respect to Complex2 (1.52 e). Accordingly, we can
Figure 8. Evolution of the ELF attractors (represented by ●) along the Mo2( 1 ⌺ ⫹ g ) ⫹ N2O reaction.
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consider the Complex3 as an important step in the preparation for the N2 detachment. 3. A new topological catastrophe (fold) occurs in going from Complex3 to the TS3 structure: the lowering in the number of the attractors leading to the oxygen detachment from N2O. The geometrical changes from TS3 to the Trans structure belongs to the same topological domain without any topological change. The charge transfer from Mo2O to N2 has been calculated to be 0.5 e and 0.4 e in the Trans and Cis structures, respectively. This difference explains the fact that the Trans structure is more stable than the Cis one. 4. Finally, the last topological change from the Trans structure to the N2 detachment transforms the Mo—N dative basin into a V(N) monosynaptic basin accomplished by a spin change from singlet to triplet state.
then the activation barrier could not explain the experimental nondetection of reactivity between Mo(a 7 S) and N2O in a depletion kinetics experiment. 2. Although the energetic barrier is mostly the same for both studied reactions, the energetic pathways are very different. The reaction between the ground state Mo(a 7 S) and nitrous oxide occurs through three spin states: starting from septet state goes to the quintet, triplet state, and finally the products correlates with the quintet state of the reactants. Consequently, the Mo(a 7 S) ⫹ N2O reaction should be very slow (because of the spin-forbidden transitions), giving then a very weak signal, which is probably out of the experimental detection limit. In contrast, the Mo2 ⫹ N2O reaction evolves on a single potential surface: the singlet spin state. Its experimental detection would then be feasible if enough energy is provided to overcome the activation barrier height.
Conclusions
Finally, we should emphasize that the detachment of the N2 molecule, as product of both reactions, is kinetically an effective process, owing to the high exothermicity, and consequently, to the high internal energy of the insertion complexes, although it should be a slow process (due to the spin-forbidden transitions) for the Mo ⫹ N2O reaction.
The interaction between Mo atom and its dimer with N2O has been studied within the framework of DFT. It has been shown that the N2 detachment and the formation of a molybdenum oxide are the reaction products in both cases. In the case of Mo–N2O, the oxidation of the Mo atom takes place via the participation of three low-lying electronic states: septet, quintet, and triplet, corresponding to a Triple Surface process. It has been established that the septet state plays an important role along the whole of pathway. From a topological viewpoint, the core and valence basins of Mo are effectively involved in the process, indicating the importance of the 5s–4d hybrid orbital (in traditional terminology) in the reaction. The evolution of the topological properties along the pathway provides keys to understand the geometrical changes that take place during the reaction. The energetic and topological evolution of the Mo ⫹ N2O interaction showed that the N2 detachment does not occur easily because the spin conversion. Therefore, this work confirms the experimental hypothesis that production of spin-forbidden states could be considered as a major constraint to the experimental detection of the N2 detachment. In contrast to the Mo ⫹ N2O reaction, it has been shown that the reaction between Mo2 and N2O can be characterized as a Single-Surface process, which fully evolves on the singlet state without participation of the low-lying excited states of the metal center (triplet and quintet spin states), except in the exit channel stage. The geometrical and topological changes proceed in parallel, partitioning the pathway into three regions: the first one corresponding to the formation a Mo2–N2O complex in which the N—N and N—O bonds are slightly weakened, the second region in which the N—O bond is actually lengthened, and finally the third region corresponding to the breaking of the N—O bond and the formation of the Mo2O oxide. Also in this case, our theoretical results agree with the experimental detection of an increase in reactivity in going from the atom to the dimer. In summary, our theoretical results allow us to explain the experimental trends by means of these statements: 1. Because the calculated activation barriers at the entrance channel, for both reactions (Mo(a 7 S) ⫹ N2O and Mo2(X 1 ⌺ ⫹ g ) ⫹ N2O), are found to be very similar (13.2 vs. 15.3 kcal/mol),
Acknowledgments One of us (M.E. Alikhani) is grateful of allocation of computer time. Universite´ Pierre et Marie Curie (Paris, France) is gratefully acknowledged by N. Russo for a 1-month invited professor position.
References 1. Stirling, A. J Phys Chem A 1998, 102, 6565. 2. Kiran, B.; Vinckier, C.; Nguyen, M. T. Chem Phys Lett 2001, 344, 213. 3. Delabie, A.; Vinckier, C.; Flock, M.; Pierloot, K. J Phys Chem A 2001, 105, 5479. 4. Tishchenko, O.; Kryachko, E. S.; Vinckier, C.; Nguyen, M. T. Chem Phys Lett 2002, 363, 550. 5. Delabie, A.; Pierloot, K. J Phys Chem A 2002, 106, 5679. 6. Stirling, A. J Am Chem Soc 2002, 124, 4058. 7. Kryachko, E. S.; Tishchenko, O.; Nguyen, M. T. Int J Quantum Chem 2002, 89, 329. 8. Lian, L.; Mitchell, S. A.; Rayner, D. M. J Phys Chem 1994, 98, 11637. 9. McClean, R. E.; Campbell, M. L.; Goldwin, R. H. J Phys Chem 1996, 100, 7502. 10. Campbell, M. L. J Chem Phys 1996, 104, 7515. 11. Fournier, R. J Chem Phys 1995, 102, 5396. 12. Lacaze–Dufaure, C.; Mineva, T.; Russo, N. J Comput Chem 2001, 22, 1557. 13. Michelini, M. C.; Russo, N.; Alikhani, M.; Silvi, B. J Comput Chem 2004, 25, 1647. 14. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hase-
Oxidation Reaction between Mon (n ⴝ 1, 2) and N2O
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gawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision B.02; Gaussian, Inc.; Pittsburgh, PA, 2003. Burke, K.; Perdew, J. P.; Wang, Y. In Electronic Density Functional Theory: Recent Progress and New Directions; Dobson, J. F.; Vignale, G.; Das, M. P., Eds.; Plenum: New York, 1998. Perdew, J. P. In Electronic Structure of Solid ’91; Ziesche, P.; Eschrig, H., Eds.; Akademie Verlag, Berlin, 1991, p. 11. Perdew, J. P.; Burke, K.; Wang, Y. Phys Rev B 1996, 54, 16533. Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys Rev B 1992, 46, 6671. Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys Rev B 1993, 48, 4978. Hay, P. J.; Wadt, W. R. J Chem Phys 1985, 82, 284. Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J Chem Phys 1980, 72, 650. Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. V. R. J Comput Chem 1983, 4, 294. Frisch, M. J.; Pople, J. A.; Binkley, J. S. J Chem Phys 1984, 80, 3265. Noury, S.; Krokidis, X.; Fuster, F.; Silvi, B. Topmod package; 1997. Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford Univ. Press: Oxford, 1994. Becke, A. D.; Edgecombe, K. E. J Chem Phys 1990, 92, 5397.
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27. Silvi, B.; Savin, A. Nature 1994, 371, 683. 28. Aslangul, C.; Constanciel, R.; Daudel, R.; Jottis, P. In Advances in Quantum Chemistry; Lo¨wdin, P.-O., Ed.; Academic Press: New York, 1972; p. 93, vol. 6. 29. Gillespie, R. J.; Popelier, P. L. A. From Lewis to Electron Densities; Oxford University Press: New York, 2001. 30. Silvi, B. J Phys Chem A 2003, 107, 3081. 31. Noury, S.; Colonna, F.; Savin, A.; Silvi, B. J Mol Struct 1998, 450, 59. 32. Thom, R. Stabilite´ Structurelle et Morphoge´ne`se; Interdictions: Paris, 1972. 33. Krokidis, X.; Noury, S.; Silvi, B. J Phys Chem A 1997, 101, 7277. 34. Godbout, N.; Salahub, D. R.; Andzelm, J.; Wimmer, E. Can J Chem 1992, 70, 560. 35. Sosa, C.; Andzelm, J.; Elkin, B. C.; Wimmer, E.; Dobbs, K. D.; Dixon, D. A. J Phys Chem 1992, 96, 6630. 36. Bauernschmitt, R.; Ahlrichs, R. J Chem Phys 1996, 104, 9047. 37. Li, J.; Balasubramanian, K. J Phys Chem 1990, 94, 545. 38. Martı´nez, A.; Simard, B.; Salahub, D. R. J Phys Chem A 2003, 107, 4136. 39. Moore, C. E. Atomic Energy Levels, Natl Bur Stand; U.S. GPO: Washington, DC; 1949, 1971, Circ. No. 467. 40. Dewar, M. J. S. Bull Soc Chim Fr 1951, 18, C71. 41. Chatt, J.; Duncanson, L. A. J Chem Soc 1953, 2939. 42. Kryachko, E. S.; Vinckier, C.; Nguyen, M. T. J Chem Phys 2001, 114, 7911. 43. Suter, H. U.; Greber, T. J Phys Chem B 2004, 108, 14511. 44. Martı´nez, A.; Ko¨ster, A. M.; Salahub, D. R. J Phys Chem A 1997, 101, 1532. 45. Calatayud, M.; Andre´s, J.; Beltra´n, A.; Silvi, B. Theor Chem Acc 2001, 105, 299. 46. Schro¨der, D.; Shaik, S.; Schwarz, H. Acc Chem Res 2000, 33, 139. 47. Savin, A.; Becke, A. D.; Flad, J.; Nesper, R.; Preuss, H.; von Schnering, H. G. Angew Chem Int Ed Engl 1991, 30, 409.
Dipartimento di Chimica and Centro di Calcolo ad Alte Prestazioni per Elaborazioni Parallele e Distribuite-Centro d’Eccellenza MURST, Universita` della Calabria, I-87030 Arcavacata di Rende, Italy 2 Laboratoire de Dynamique, Interactions et Re´activite´ (UMR 7075), Universite´ P. et M. Curie, Boıˆte 49, baˆtiment F74, 4 Place Jussieu 75252 Paris Cedex 05, France 3 Laboratoire de Chimie The´orique (UMR 7616), Universite´ P. et M. Curie, Boıˆte 137, Tour 2223, 4 Place Jussieu 75252 Paris Cedex 05, France Received 19 November 2004; Accepted 9 March 2005 DOI 10.1002/jcc.20269 Published online in Wiley InterScience (www.interscience.wiley.com).
Abstract: The interaction between molybdenum, atom, and dimer, with nitrous oxide has been investigated using density functional theory. The analysis of the potential energy surfaces for both reactions has revealed that a single molybdenum atom can activate the N—O bond of N2O requiring a small activation energy. However, the presence of several intersystem crossings between three different spin states, namely, septet, quintet and triplet states, seems to be the major constraint to the Mo ⫹ N2O reaction. Contrarily, the low-lying excited states (triplet and quintet) do not participate in the reaction between the molybdenum dimer and N2O. The latter reaction fully evolves on the singlet spin surface. Three different regions have been distinguished along the pathway: formation of an adduct complex, formation of an inserted compound, and the N2 detachment. The connection between the two first regions has been characterized by the formation of a special complex in which the N—O bond is so weakened that it could be considered as a first step in the insertion process. It has been shown that the topological changes along the pathways provide a clear explanation for the geometrical changes that occur along the reaction pathway. In summary, the detachment of the N2 molecule is found to be kinetically an effective process for both reactions, owing to the high exothermicity and consequently to the high internal energy of the insertion intermediates. However, in the case of Mo atom, the reaction should be a slow process due to the presence of spin-forbidden transitions. These results fully agree with previous experimental works. © 2005 Wiley Periodicals, Inc.
J Comput Chem 26: 1284 –1293, 2005
Key words: electronic structure; reaction pathways; mono- and di-molybdenum oxidation; nitrous oxide reduction;
bonding description; AIM and ELF topological analyses
Introduction The reaction of gas-phase metal atoms with N2O have been previously studied both theoretically1–7 and experimentally,8 –10 due to its importance in many fields, such as oxidation of transition metals, catalytic activation of the N—O bond, and earth’s atmosphere. Nitrous oxide, other than a well-known catalytic oxidant, is one of the greenhouse gases, and is also involved in the depletion of stratospheric ozone. Although there are many known natural and anthropogenic sources, emissions of nitrous oxide have been difficult to quantify on a global scale, primarily because it has been one of the least studied greenhouse gases to date. In contrast to carbon dioxide and methane, nitrous oxide is released in small
quantities from anthropogenic sources. The largest source of emissions is energy use, which includes mobile source combustion (i.e., emissions from motor vehicles) and stationary source combustion from residential, industrial, and electric utility energy use. The second-largest source of nitrous oxide emissions is agriculture, primarily fertilizer application and a small amount released from the burning of crop residues. Nitrous oxide emission arise during
Correspondence to: N. Russo; e-mail: [email protected] Contract/grant sponsor: CNRS; contract/grant number: 041730 Contract/grant sponsor: Universita` degli Studi della Calabria Contract/grant sponsor: MUIR
© 2005 Wiley Periodicals, Inc.
Oxidation Reaction between Mon (n ⴝ 1, 2) and N2O
the oxidation of NH3 in the nitric acid production, which is a key ingredient in nitrogen-based fertilizer industry. Therefore, it becomes fundamental for the development of theoretical studies to obtain a detailed description of catalytic processes involving N2O. On the other hand, due to its importance as one of the essential elements in biology as well as because of its applications in heterogeneous catalysis, it is of great interest to the study the gas-phase chemistry of molybdenum. Previous experimental8 and theoretical works11,12 indicate that transition metal atoms and dimers show remarkable differences in reactivity with respect to adduct formation reactions depending on the electron acceptor/donor capabilities of the ligand. In the case of Lewis base ligands, an increase of reactivity in going from the atom to the dimer has been observed, whereas for -acceptor ligands the opposite behavior has been manifested. Experimental studies have shown that molybdenum atoms and dimers show differences in reactivity with respect to N2O. In particular, Lian et al.8 have reported flow tube kinetic measurements that indicate that nitrous oxide reacts with Mo2, leading to the N—O bond activation, but the Mo ⫹ N2O assembly is a nonreactive process at room temperature. On the other hand, McLean et al.9 have presented experimental data of depletion kinetics of Mo(a7S3, a5S2, a5DJ ) by several small molecules, including N2O. In that work it has been determined that ground state Mo is unreactive toward N2O at room temperatures; however, observable reaction rates were measured for Mo(a7S3) ⫹ N2O as the temperature was increased. The authors have suggested that the inefficiency of the reaction could be attributed to the production of spin-forbidden states. On the theoretical side, DFT calculations for the oxygen abstraction from N2O by the ground state of the first row transition metal (TM) atoms have been recently reported.1,3,6 The main finding of these works is that the reactions with Sc, Ti, and V proceed almost without energy barriers, and that the 3d n⫹1 4s 1 configuration gives rise to a higher reactivity than the 3d n 4s 2 configuration. The N—O cleavage has been mostly explained as an electron transfer model (electron transfer from the metal to the N2O molecule via initially 3d, then 4s ⫺ 3d hybrid orbitals) against a direct oxygen abstraction one. In a recent work,13 we have presented an energetic and topological study of the adduct formation process for the interaction of Mo and Mo2 with different small ligands, namely NH3, C2H2, and C2H4. We have shown that Mo and Mo2 essentially interact with C2H2 and C2H4 via an electron pair transfer from the metalliccenter to the ligand, forming a chemical bond with the carbon atoms, while the interaction between Mo (or Mo2) and NH3 has mostly an electrostatic character. In the present work, our main interest is the investigation of the whole oxygen-transfer process and the complete analysis of the potential energy profiles corresponding to the interaction of N2O with Mo atom and dimer. To gain insight into the reaction mechanisms of the N—O bond activation we report a complete analysis of the reaction pathways for the ground and low-lying excited states of Mo and Mo2. The chemical bonding evolution along the effective reaction pathways has been also investigated from a topological point of view.
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Computational Details All calculations have been performed with the Gaussian 2003 quantum chemical package14 using the density functional (DFT) method. The DFT calculations have been carried out with the Perdew and Wang (1991) density gradient correction to the exchange and correlation functionals (denoted hereafter as PW91PW91).15–19 The singlet state optimization has been done within the restricted Kohn–Sham formalism, while the open-shell structures have been investigated using the unrestricted Kohn– Sham formalism. In the latter case, the spin-contamination has been found as always negligible (⬍5%). The LANL2DZ effective core potential20 has been employed for the molybdenum atom. In LANL2DZ, the 14 electrons of the valence shell are represented explicitly using a double zeta basis. The 6-311G⫹⫹(2d,2p) extended basis set21–23 has been employed for the other atoms. The TopMod package24 has been used to analyze the chemical bonding of the studied species from a topological point of view. Topological analysis of the one-electron density function (known as the Atoms in Molecules Theory25: AIM), and of the electron localization function (ELF)26,27 represent for the chemical bonding description an alternative to the standard molecular orbital approaches. They rely upon the gradient field analysis of the corresponding local functions. Their common aim is “to provide a mathematical bridge between chemical intuition and Quantum Mechanics.”28 Because both Lewis and Gillespie’s phenomenological29 models describe the bonding within a molecule in the usual three-dimensional space, the mathematical model makes a partition of this space into regions related to chemical properties. According to the AIM topology, positive values of the electron density Laplacian (ⵜ2 ⬎ 0) at bond critical points (BCP: points for which ⵜ ⫽ 0) are associated with closed-shell interactions (ionic bonds, hydrogen bonds, and van der Waals interactions), while ⵜ2 ⬍ 0 indicates shared interactions (covalent bonds). Also, the partitioning of the molecular space allows the definition of atomic volumes in the molecules and by integrating any property density function over an atomic basin, it is possible to estimate the corresponding atomic property.30 For instance, the integration of the electron density function over an atomic basin gives the atomic electron population, and consequently, the net atomic charge. The topological description of the chemical bond proposed by Silvi and Savin27 is based on the gradient field analysis of the electron localization function (ELF) of Becke and Edgecombe.26 In a region of space dominated by an antiparallel spin pair, the Pauli repulsion is weak, and therefore, the value of the ELF function (labeled as ) is close to 1. Near the boundary between two such regions, where same spin electrons necessarily come close together, they exert a significant Pauli repulsion that decreases the value of ELF function to low values. In particular, ⫽ 0.5 corresponds to the homogeneous electron gas case. Therefore, the topological analysis of the ELF function provides a partition scheme of the molecular space into basins of attractors that have a clear chemical meaning. These basins are either core basins [labeled as C(A)] surrounding nuclei or valence basins, V(A, . . . ), belonging to the outermost shell and characterized by their coordination number with core basins, which is called the synaptic order. The basin population are evaluated by integration of the one-electron density over the volume of the basin. In addition, a
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measure of the delocalization is provided by considering the fluctuations of the basin populations.31 Within the framework provided by the ELF analysis, a chemical reaction is viewed as a series of topological changes occurring along the reaction path. The parameters defining the reaction pathway, such as the nuclear coordinates and the electronic states, constitute the control space. Therefore, the topological behavior of the gradient field can be studied by using Thom’s catastrophe theory.32 This type of analysis is the so-called bonding evolution theory (BET).33 There are two important indicators in using this technique: the morphic number, that is, the number of basins, and the before-mentioned synaptic order of valence basins. Each structure is only possible for values of the control parameters belonging to definite ranges called structural stability domains. For any two points of the control space belonging to a given structural stability domain, there is the same number of critical points of each type in the ELF gradient field. This technique shows how the bonds are formed and broken, and also emphasizes the importance of the geometrical constraints in a chemical reaction. Moreover, the identification of the elementary catastrophe and, therefore, the knowledge of its universal unfolding yield the dimension of the active control space governing the reaction. In addition, from a quantitative viewpoint, the evolution of the total and spin basin populations along the path provides keys to understand the role played by the different chemical interactions. Chemical processes are then classified into three groups: the plyomorphic one, in which an increase of the morphic number is observed (e.g., a covalent bond breaking); the tautomorphic diffeosynaptic process, in which the number of basins is conserved, but there is a variation of the synaptic order of at least one basin (e.g., a breaking of a dative bond); and the miomorphic process in which there is a decrease in the number of basins (e.g., covalent bond formation). Along the reactions there exist several domains of structural stability. Within a domain of structural stability, the topology of the ELF gradient field is not altered by the variation of the control space parameters, which belong to a definite range. Between two successive domains of structural stability the evolution is ruled by a bifurcation catastrophe. At this point, at least the type of catastrophe gives access to its unfolding and, therefore, to the minimal dimension of the control space enabling the modification of the topology. To account for the core electron effect in the topological study, the ELF calculations have been carried out on the global minima using an all-electron double- quality basis set (DGDZVP34,35) for the Mo atom. The other atoms are treated again using the 6-311⫹⫹G(2d,2p) basis set. For the reaction pathway analysis we have ensured that every transition structure has only one imaginary frequency, and that connects the reactants to the appropriate product species running IRC (Intrinsic Reaction Coordinate) calculations. In addition, we have paid much attention to two other points for the completion of the present calculations. 1. The size-consistency property has been checked when calculating the binding energies. In particular, we have checked the size-consistency for the Mo–ligand interaction by comparing the total calculated energy for a large distance with the sum of
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the two entities at the same spin state. It is an interesting feature, which clearly shows the reliability of the PW91PW91 functional at large interfragment distances. 2. Furthermore, because it is important to test the stability of restricted closed-shell structure calculated within Kohn–Sham formalism,36 the stability of the singlet states has been checked and no instability has been found. In a previous article,13 we have already checked the reliability of the level of theory employed in the present work by studying the bare molybdenum atom and dimer. For the energetic gap between the first excited state ( 5 S(d 5 s 1 )) and the ground state ( 7 S(d 5 s 1 )) of Mo, the PW91PW91/LANL2DZ level of theory is the one that better reproduce the measured value (1.38, 1.45, 1.42, and 1.33 eV, the PW91PW91,13 CI,37 BPW91,38 and experimental39 values, respectively). We have found a good agreement between the 3 ⫹ spectroscopic parameters of the two states of Mo2 ( 1 ⌺ ⫹ g and ⌺ u ) calculated at PW91PW91 level, with those obtained by means of highly correlated methods and with experimental data. See ref. 13 for details.
Mo ⴙ N2O Interaction Several approaches have been studied for the metal atom interaction with the nitrous oxide molecule: the “side-on” approach with respect to the N—O and N—N bonds, and “end-on” one, in which Mo interacts with the ending atoms (O or N) of N2O with a nearly linear arrangement. In the initial geometries for the geometrical optimization, we slightly displaced the atoms of N2O from the perfect collinear arrangement. Each geometrical approach has been studied for three low-lying electronic states of Mo: the septet ground state, and the quintet and triplet excited states. Structural and Energetic Analyses
The optimized geometrical parameters of all the Mo–N2O structures are displayed in Figure 1. All the structures have a C s symmetry, in which four atoms form a planar structure. The electronic states of the calculated Mo–N2O structures are A⬘ for all the three spin multiplicities, except in the case of the inserted compound in the septet spin state, which has a linear structure (II symmetry). In that figure the first column shows the adduct complexes formed between Mo and N2O, in which the metal atom interacts with the ending N atom of nitrous oxide. The second column shows the transition structures between the adduct complexes and the inserted compounds, which are shown in the third column. The adduct complex has a cis-structure (with respect to the N—N bond) in the septet state and a trans-structure in the quintet and triplet ones. The N—N and N—O bond lengths increase upon the complex formation between Mo and N2O. They also increase with the decrease of the spin multiplicity, whereas, the Mo–N distance shows the opposite trend. The transition state (TS) structures are of cis-shape geometry for all the three electronic states. Mo is found to be bound to the oxygen atom of N2O in the TS septet state, while it is N-bounded in the quintet and triplet TSs. In the septet and quintet TSs, the N–O distance is so large that we can assume that there is no bonding between O and
Oxidation Reaction between Mon (n ⴝ 1, 2) and N2O
Figure 1. Structural parameters of different electronic states of the adduct complexes (column 1), transition states (column 2), and insertion intermediates (column 3) of the Mo–N2O reaction. Distances are in Å, and angles in degrees.
N. The Mo–N distance in all three inserted compounds is of around 2 Å. In these compounds, the N–N distance is larger than free N2 by at least 0.025 Å. In Figure 2 are shown the relative energies (in kcal/mol) of the nine studied structures as well as those of products (corresponding to the N2 detachment), with respect to the Mo( 7 S) ⫹ N2O(1⌺⫹) fragments. We note that the most stable adduct complex is of the quintet spin state, which correlates with the first excited state of the Mo atom. The quintet adduct complex is found to be slightly more stable than the septet one (ca. 4.1 kcal/mol). Indeed, the formation of the quintet adduct complex is assumed to occur through a crossing point between the two potential energy profiles (septet and quintet ones) at the entrance channel. For the inserted compounds, the septet structure is much less stable than the quintet and triplet ones. In fact, the triplet inserted structure is the ground state for the insertion intermediate, being slightly more stable than the quintet one (ca. 4.3 kcal/mol). As shown in Figure 2, the formation of the ground state of the inserted structure takes place through two intersystem crossings between three surfaces when going from the adduct complex to the inserted compound. First, the quintet adduct complex crosses the septet pathway allowing the evolution of the reaction via the septet TS, which requires a small activation energy (⬇13 kcal/mol). Second, the crossing between triplet and septet pathway leads to the formation of the triplet insertion intermediate. The energetic gain during the above-mentioned pathway is therefore around of 91.5 kcal/mol. Consequently, the formation of the ground-state insertion complex is energetic enough so that the exit channel leading to the formation of the N2 and MoO products could be kinetically reached. We note that the exit channel proceeds on the quintet surface via a new intersystem crossing between the triplet and quintet surfaces. The barrier height for the last part of the pathway, that is, the N2 detachment, is of about 22 kcal/mol.
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These considerations show that the N—O bond activation of the nitrous oxide by a single molybdenum atom is energetically favorable owing to the small barrier height in the septet surface, which starts from the ground state of the fragments. It is worthy to emphasize on the substantial role played by the ground state of the molybdenum atom leading to the formation of the molybdenum monoxide and N2. At this point we would like to compare our theoretical results on the reactivity of Mo with N2O with previous experimental results.8,9 As previously mentioned, flow tube kinetics studies on the reactivity of Mo and Mo2 with N2O have shown no reaction (second-order rate coefficient, k (2) , less than 5 10⫺15 cm3s⫺1) in the case of the Mo atom, whereas for the dimer it has been measured as a second-order rate coefficient of 4.4 10⫺12 cm3s⫺1 at 296 ⫾ 1 K.8 On the other side, on the basis of depletion kinetics data,9 experimental researchers concluded that the ground-state Mo is unreactive toward N2O at room temperature, whereas observable reaction rates were measured as the temperature was increased, attributing the inefficiency of the reaction to the production of spin-forbidden states. The calculated activation barrier for Mo(a 7 S) ⫹ N2O 3 MoO ⫹ N2 (13.2 kcal/mol) is in quite good agreement with the experimental data (9.8 kcal/mol),9 indicating the reliability of our theoretical work. Reaction Mechanism: ELF Analysis
From a qualitative point of view (the Chatt–Dewar–Duncanson scheme40,41), the reaction between Mo and N2O could be mainly understood as an interaction between the Mo 4d- and 5s-orbitals with the N2O HOMO and LUMO. The N2O HOMO is a -orbital, which
Figure 2. Energetic pathway for the Mo ⫹ N2O reaction from the initial fragments to the N2 detachment.
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Table 1. ELF Basin Populations (e) of the Mo ⴙ N2O Compounds.
Compounds N2( 1 ⌺ ⫹ g ) N2O(1⌺⫹) N2O⫺( 2 A⬘) Adduct Complex: Septet Quintet Triplet Transition state: Septet Quintet Triplet Insertion complex: Septet Quintet Triplet
C(Mo)[S z ]
V(Mo)[S z ]
V(N1,N2)
V(N,O)
V(N1)
V(N2)
3.34 3.78 2.45
3.26 4.31 4.41
3.26
1.98 1.13
2.58
5.60 6.18
1.42 1.45 1.38
4.45 4.71 4.93
2.04 2.72 3.05
5.70 5.75 5.71
1.15
3.65 4.28 4.68
3.21 3.47 3.12
6.70 5.88 5.91
3.43 3.50 3.70
3.57 3.68 3.85
5.60[0.5] 7.14[0.2] 6.22[0.1]
40.80[2.3] 40.70[1.8] 40.68[1.2]
0.69[0.3] 0.50[0.2] 0.21[0.1]
2.60 1.94 1.74
40.56[2.0] 41.30[1.8] 40.81[1.3]
0.66[0.3] 0.24[0.1]
2.96 2.51 2.12
41.58[2.2] 39.40[1.2] 40.46[0.7]
0.97[0.4] 0.66[0.2]
3.15 3.04 2.87
is antibonding with respect to the O—N bond but bonding for the N—N bond. The LUMO is a *-orbital with antibonding character for both the N—O and N—N bonds. The charge transfer from Mo to the *-orbital upon the formation of the adduct complex destabilizes both the N—O and N—N bonds leading to a lengthening of these bonds. Consequently, the N2O molecule loses its linear structure when the LUMO is populated. Recent theoretical works have reported the tilting of nitrous oxide after the attachment of an electron.42,43 The back-donation interaction between the HOMO and a symmetry allowed orbital of the metal stabilizes the Mo—N bonding. As has been previously underlined,44 the molybdenum atom can only react as an electron donor because of its electronic configuration (5s1 4d5). Consequently, the reactivity of Mo atoms strongly depends on the nature of the ligands. To provide a deeper understanding of the reaction mechanism along the reaction pathway, the bonding characterisation has been made by using topological approaches. We have gathered in Table 1 the electronic populations of the different basins involved in the reaction. The C(Mo) stands for the molybdenum core basin population and S z is its integrated spin density. V(Mo) and S z represent the monosynaptic Mo valence basin population and its integrated spin density, respectively. The disynaptic valence basins of the N—N and N—O bondings are denoted as V(N1,N2) and V(N,O), respectively. The monosynaptic basin of oxygen is labeled as V(O), whereas that of the ending N as V(N1) and the one corresponding to the second nitrogen atom as V(N2). The analysis of the sign of the laplacian of the electronic density at the N—N and N—O bond critical points showed that these bonds can be described as a shared-interaction (ⵜ2 ⬍ 0) in the adduct complexes. For the transition structures, a BCP has been found between Mo and N atoms in both the quintet and triplet states but not in the septet state. In the later state, the presence of a BCP indicates the binding between Mo and O atoms. In the case of the inserted complexes, the value of the electron density at the Mo—N bond critical point is quite small (less than 0.12 e), indicating the weakness of this interaction. In addition, the charge
V(O)[S z ]
transfered from the MoO moiety to the N2 one has been calculated to be 0.22, 0.27, and 0.36 e for the septet, quintet, and triplet inserted compounds, respectively. The ELF basin populations (see Table 1) allows us to explain the weakening of the N—N and N—O bonds upon the formation of the adduct complexes. In line with the N—N and N—O bond lengthenings in all the studied compounds, the population of the V(N,N) basin decreases more and more when the spin multiplicity decreases. In agreement with previous works on the electron attachment to nitrous oxide,42,43 the tilting of the N–N–O upon interaction with Mo is a consequence of the charge transfer from the metal center to the nitrous oxide. The appearance of a monosynaptic valence basin around of central N atom reflects this geometrical change (see Fig. 3). It should be noted that the monosynaptic valence basin of the nitrogen atom (located towards Mo) mostly belongs to the nitrogen atom; therefore, its interaction with Mo has a dative character. Inspecting the population of C(Mo) (less than 41 e) and that of V(Mo) (less than 1 e) in all the studied compounds clearly shows that both the core and valence basins of Mo participate in the interaction with N2O. This picture explains the importance of the 5s–4d hybrid orbital (d shell belongs to the outer shell of the core basin45) in the interaction between Mo and N2O. With respect to N2O, the anion is characterized by the presence of a monosynaptic basin on the central nitrogen atom, which explains the NNO bond angle and the weakening of all disynaptic basin populations, which is consistent with the increase of the bond lengths and with the spreading of the spin density among the monosynaptic basins. The minimisation of the Pauli repulsion between the central N monosynaptic basin and the metal center is the most important process upon the formation of the adduct complex. We should expect that the septet equilibrium geometry would be a cis-configuration to minimize the Pauli repulsion between the Mo core and the monosynaptic basin located on the central N. The variance of the Mo core basin is small (0.65) in the septet complex. In the case of the quintet and triplet states, the spin density is mostly localized in the C(Mo) basin with a
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Figure 3. Evolution of the ELF attractors (represented by ●) along the Mo(7S) ⫹ N2O reaction.
rather large variance (1.35). The charge transfer from metal center to the ligand implies a possible resonance structure between the [Kr]d 4 and [Kr]d 6 configurations. Therefore, we consider that the formation of the Mo⫹ NNO⫺ ionic pair is the driving force in the complex formation. The attractors of different localization domains of all the compounds involved in the reaction between Mo and N2O are represented by ● in Figure 3. As shown in Figure 3, the formation of the adduct complex corresponds to the appearance of a new monosynaptic basin around of the central N atom, whose population ranges from 2.04 to 3.05 e, depending on the spin state of the complex (see Table 1). As discussed in the previous section, three steps along the reaction have to be considered: 1. First, from the quintet complex to septet TS characterized by lowering the number of attractors by one corresponding to two bonding brokens: the Mo—N dative and N—O covalent bondings. These topological changes do not occur easily, because the transition structure is of cis-shape whereas the quintet complex is of trans-form. A path with the least topological changes implies that the quintet complex passes again by the septet one and then goes towards the septet TS. This process corresponds topologically to a fold catastrophe. 2. Second, going from the septet TS to the quintet inserted compound does not change the number of attractors. However, it should be noted that the MoO unit forms a dative bond with the N2 molecule in the triplet inserted compound. As a matter of fact, the topological instability of the septet inserted interme-
diate [with a torus-shape V(Mo) basin] and the topologically favorable situation for the interaction between N2 and MoO in the triplet and quintet surfaces are the topological mechanisms for the spin-conversion upon the inserted compound formation. 3. The last step, the N2 detachment, is topologically characterized by the nature of the bonding within MoO monoxide. As shown in the last column of Figure 3, the Mo—O bonding in the MoO monoxide is rather of a covalent character only in the quintet state (because of the presence of two attractors standing for two disynaptic basins), whereas, the Mo—O bonding in the triplet and septet states is essentially assumed to be due to the C(Mo) and V(O) delocalization. In other words, the 4s(Mo)—2s(O) bond in the quintet spin state oxide favors the quintet dissociation channel, and, as a consequence, a new spin conversion (triplet to quintet). In summary, as shown from our energetic and bonding analyses, the spin crossing effect and the sequence of topological catastrophes play an important role in the reaction mechanism and rate constants of the Mo ⫹ N2O reaction, indicating the occurrence of TSR (Two-State Reactivity) scenarios.46
Mo2 ⴙ N2O Interaction Structural and Energetic Analyses
We have performed geometrical optimizations for several electronic states: singlet, which correlates with the ground state of the
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Figure 5. Structural parameters of the Mo2–N2O complexes at singlet state. Distances are in Å, and angles in degrees.
Figure 4. Relative energies of the quintet, triplet, and singlet (denoted as Q, T, and S, respectively) with respect to the fragments ground state. The geometrical shapes of the different structures (denoted as Complex1, Insert1, and Trans) are also displayed.
free fragments, triplet, and quintet states (the lowest lying excited states). For each spin state, three different approaches between Mo2 and N2O have been studied: the end-on approach (N- or O-bonded), the perpendicular arrangements (Mo2 axis perpendicular to the N—N or N—O bonds), and the parallel approach (Mo2 axis parallel to the N–N–O axis). The energetic results are partially displayed in Figure 4. The singlet, triplet, and quintet states are labeled as S, T, and Q, respectively. The relative energies of the three types of optimized geometries are reported in that figure, namely, the first complex (in which the Mo2 dimer forms an N-end-on structure with the N2O molecule), the first insertion intermediate (in which the N—O bond of N2O is already activated), and the final insertion structure (in which only one of the nitrogen of N2 is bonded to one of the Mo atoms). As indicated in Figure 4, the first complex (hereafter labeled as Complex1) has a cis-shape (with respect to the N—N bond) at the singlet state, a trans-shape at the quintet state, and a nonplanar tilted-trans at the triplet state. For all the three electronic states, the intermediate compound, Insert1, resembles now to a complex formed between Mo2O and N2 molecules with a skewed structure. In contrast, in the final insertion structure (labeled as Trans in Fig. 4) the N2 fragment forms a planar geometry with Mo2O in which only one N atom is bonded to one of the Mo atoms. The relative energies reported in that figure for the three optimized structures clearly show that the triplet and quintet states do not participate in the Mo2 ⫹ N2O reaction. In other words, this interaction fully evolves on a single potential energy surface: namely, the singlet state. However, it should be noted that the triplet and singlet states are
mostly iso-energetic for the Complex1 and Insert1 structures so that it lets us think that a higher level of calculation than the one used in this article could reverse the relative stability of these structures, but not for the last structure (Trans) for which the triplet state is less stable than the singlet one by 9 kcal/mol. Consequently, in the following discussion we analyze the reaction only for the singlet spin state surface. In Figures 5– 6 are displayed all the Mo2–N2O optimized geometries at the singlet state. The first complex (Complex1), the
Figure 6. Structural parameters of the N2–Mo2O inserted compounds at singlet state. Distances are in Å, and angles in degrees.
Oxidation Reaction between Mon (n ⴝ 1, 2) and N2O
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mol). We note that the formation of the Trans compound is highly exothermic, and consequently, at this point of the reaction the system has enough internal energy to overcome an energy barrier of 27.3 kcal/mol. The N2 detachment process is therefore probable. Reaction Mechanism: ELF Analysis
Figure 7. Energetic pathway for the Mo2 ⫹ N2O reaction from the initial fragments to the N2 detachment.
second complex (Complex2), and the Cis and Trans insertion intermediates are planar, while the other structures are of C s symmetry. The first complex formed between Mo2 and N2O is an N-bonded structure in which the N2O molecule loses its linearity and the Mo—Mo, N—N and N—O bond distances are slightly longer than the correspondent ones in the free fragments. The lost of planarity leads to the first transition structure (labeled as TS1 in Fig. 5), which connects the first and second complexes. The out-of-plane bending of ONMo (Complex2) gives the second transition structure, which connects the second complex with the third one (Complex3). We note that the third complex is nonplanar and presents a large increase of the N—N and N—O bond distances; that is, ⫹0.308 and ⫹0.169 Å, with respect to free N2O. This complex is actually the last step for the N—O bond-breaking process. The third transition structure (TS3 in Fig. 6) connects the Complex3 with the first inserted compound (labeled as Insert1). The Insert1 compound is nonplanar, in which the two nitrogen atoms of N2 unit are unequally bonded to one of the Mo atoms of the Mo2O oxide. From Insert1, two paths have been studied: the first path connects this insertion intermediate (Insert1) to the Cis insertion structure (with respect to the Mo—Mo bond), whereas the second one leads to a Trans geometry. The transition states of these two paths are labeled respectively TS5 and TS4, in Figure 6. The geometrical analysis along the reaction path shows that the structural evolution of the Mo2 ⫹ N2O interaction substantially depends on the motion of the oxygen atom. The energetic evolution of this reaction at the singlet state is presented in Figure 7. One can distinguish two parts along the pathway: the first one going from fragments (F) to the third complex (C3), which requires an activation energy of around 15 kcal/mol, and a second part, which connects the C3 complex to the final insertion intermediate (Trans) by overcoming a barrier height of around 11 kcal/mol. At this point, the Trans structure could evolve to the N2 detachment at the triplet state via an intersystem crossing between the singlet and triplet surfaces (see Fig. 7) slightly higher in energy than the Trans singlet state (27.3 kcal/
The evolution of the ELF attractors (represented by ●) along the Mo2( 1 ⌺ ⫹ g ) ⫹ N2O reaction is displayed in Figure 8. For the ground state of free Mo2, the ELF value for the V(Mo) basins ( ⫽ 0.35) is twice smaller than that of the V(Mo,Mo) one ( ⫽ 0.61), indicating a large excess of kinetic energy density due to the Pauli repulsion.47 It is therefore normal to attribute to the V(Mo) basins a higher binding ability than the corresponding V(Mo,Mo) ones. Furthermore, in the free molybdenum dimer the attractor of V(Mo,Mo) is degenerated on a torus shape (represented by four attractors) and therefore the ELF gradient field is structurally unstable. Consequently, the interaction between Mo2 and N2O should lead to the formation of a chemical bonding between V(Mo) and the N2O molecule and to the splitting of the V(Mo,Mo) basin. The topological evolution along the Mo2 ⫹ N2O reaction could be considered as follows. 1. The first topological event corresponding to the formation of an adduct complex (labeled as C1) should be considered as the formation of a Mo—N dative bond, the appearance of a monosynaptic basin on the central N atom, and the splitting of the V(Mo,Mo) basin. It is a “cusp catastrophe.” The geometrical changes of the complex then proceeds from the Complex1 (C1) to Complex2 (C2), within the same topological domain (no new changes in the number of basins). 2. The second catastrophe takes place during the formation of Complex3 (C3) by increasing the number of attractors by 1. At this stage, the Mo—Mo bonding is assumed by a large C(Mo)—C(Mo) delocalization (variance ⫽ 2 e) and there are two disynaptic Mo—N basins. The population of each Mo—N basin is 1.65 e, in which the contribution of Mo is of 0.5 e. In addition, in Complex3 the V(O,N) population is very low (0.78 e) with respect to Complex2 (1.52 e). Accordingly, we can
Figure 8. Evolution of the ELF attractors (represented by ●) along the Mo2( 1 ⌺ ⫹ g ) ⫹ N2O reaction.
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consider the Complex3 as an important step in the preparation for the N2 detachment. 3. A new topological catastrophe (fold) occurs in going from Complex3 to the TS3 structure: the lowering in the number of the attractors leading to the oxygen detachment from N2O. The geometrical changes from TS3 to the Trans structure belongs to the same topological domain without any topological change. The charge transfer from Mo2O to N2 has been calculated to be 0.5 e and 0.4 e in the Trans and Cis structures, respectively. This difference explains the fact that the Trans structure is more stable than the Cis one. 4. Finally, the last topological change from the Trans structure to the N2 detachment transforms the Mo—N dative basin into a V(N) monosynaptic basin accomplished by a spin change from singlet to triplet state.
then the activation barrier could not explain the experimental nondetection of reactivity between Mo(a 7 S) and N2O in a depletion kinetics experiment. 2. Although the energetic barrier is mostly the same for both studied reactions, the energetic pathways are very different. The reaction between the ground state Mo(a 7 S) and nitrous oxide occurs through three spin states: starting from septet state goes to the quintet, triplet state, and finally the products correlates with the quintet state of the reactants. Consequently, the Mo(a 7 S) ⫹ N2O reaction should be very slow (because of the spin-forbidden transitions), giving then a very weak signal, which is probably out of the experimental detection limit. In contrast, the Mo2 ⫹ N2O reaction evolves on a single potential surface: the singlet spin state. Its experimental detection would then be feasible if enough energy is provided to overcome the activation barrier height.
Conclusions
Finally, we should emphasize that the detachment of the N2 molecule, as product of both reactions, is kinetically an effective process, owing to the high exothermicity, and consequently, to the high internal energy of the insertion complexes, although it should be a slow process (due to the spin-forbidden transitions) for the Mo ⫹ N2O reaction.
The interaction between Mo atom and its dimer with N2O has been studied within the framework of DFT. It has been shown that the N2 detachment and the formation of a molybdenum oxide are the reaction products in both cases. In the case of Mo–N2O, the oxidation of the Mo atom takes place via the participation of three low-lying electronic states: septet, quintet, and triplet, corresponding to a Triple Surface process. It has been established that the septet state plays an important role along the whole of pathway. From a topological viewpoint, the core and valence basins of Mo are effectively involved in the process, indicating the importance of the 5s–4d hybrid orbital (in traditional terminology) in the reaction. The evolution of the topological properties along the pathway provides keys to understand the geometrical changes that take place during the reaction. The energetic and topological evolution of the Mo ⫹ N2O interaction showed that the N2 detachment does not occur easily because the spin conversion. Therefore, this work confirms the experimental hypothesis that production of spin-forbidden states could be considered as a major constraint to the experimental detection of the N2 detachment. In contrast to the Mo ⫹ N2O reaction, it has been shown that the reaction between Mo2 and N2O can be characterized as a Single-Surface process, which fully evolves on the singlet state without participation of the low-lying excited states of the metal center (triplet and quintet spin states), except in the exit channel stage. The geometrical and topological changes proceed in parallel, partitioning the pathway into three regions: the first one corresponding to the formation a Mo2–N2O complex in which the N—N and N—O bonds are slightly weakened, the second region in which the N—O bond is actually lengthened, and finally the third region corresponding to the breaking of the N—O bond and the formation of the Mo2O oxide. Also in this case, our theoretical results agree with the experimental detection of an increase in reactivity in going from the atom to the dimer. In summary, our theoretical results allow us to explain the experimental trends by means of these statements: 1. Because the calculated activation barriers at the entrance channel, for both reactions (Mo(a 7 S) ⫹ N2O and Mo2(X 1 ⌺ ⫹ g ) ⫹ N2O), are found to be very similar (13.2 vs. 15.3 kcal/mol),
Acknowledgments One of us (M.E. Alikhani) is grateful of allocation of computer time. Universite´ Pierre et Marie Curie (Paris, France) is gratefully acknowledged by N. Russo for a 1-month invited professor position.
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