J. Phys. Chem. A 2010, 114, 11663–11669
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Ab Initio Study of Hydrazinyl Radical: Toward a DMBE Potential Energy Surface L. A. Poveda and A. J. C. Varandas* Departamento de Quı´mica, UniVersidade de Coimbra, 3004-535 Coimbra, Portugal ReceiVed: March 30, 2010; ReVised Manuscript ReceiVed: August 23, 2010
A series of stationary structures of the hydrazinyl radical have been characterized by optimization at the CCSD(T)/cc-pVTZ level of theory. CCSD(T)/aug-cc-pVXZ single-point calculations have also been carried out at the optimized geometries with basis sets of different cardinal numbers (X ) T, Q), which were used to obtain accurate energies via extrapolation to the complete basis set limit. A discussion on the analytical modeling of the potential energy surface of hydrazinyl is also presented. 1. Introduction The hydrazinyl radical has been suggested as an intermediary in the radical chain hydrogenation of nitrogen yielding ammonia,1 as well as in the combustion and pyrolysis of nitrogenate compounds,1,2 hydrazine oxidation reactions,3 and the chemistry of planetary atmospheres.4,5 Since its detection by Foner and Hudson6 in 1958, several studies have been devoted to characterize the ground electronic state of N2H3 and its first ionized species. Previous ab initio calculations1,7,8 suggest that in its neutral form, the title system assumes an unsymmetric nonplanar conformation with the NH2 terminal group slightly tilted by adopting a trigonal pyramidal hybridization. Stereomutations through rotational pathways along the N-N axis or in-plane inversion modes are then possible. In fact, Fantechi and Helcke´9 attributed the narrowing of the N2H3 electron spin resonance (ESR) spectrum with increasing temperature to a fast nonequivalent hydrogen-atom interchange through a rotational pathway. Using CNDO/2 calculations, the authors predicted a nonplanar structure for the hydrazinyl radical with a pyramidal NH2 group, allowing torsional interconversion. Moreover, Chandler and McLean7 reported the first accurate configuration interaction study of N2H3 using polarized basis sets of double-ζ quality (hereafter referred to as CI/DZ+P). They have computed an optimized geometry slightly deviated from planarity with the NH2 group depressed by 28° or so. Such a structure may undergo a planar inversion by overcoming a barrier of 0.5 kcal mol-1 above the minimum and in-plane shifting of the NH group by surmounting a barrier of 51 kcal mol-1. A rotational pathway with a barrier height of 24.9 kcal mol-1 has also been predicted, adopting for the corresponding saddle point a trans structure where the plane of symmetry that contains the HNN fragment bisects the HNH angle.7 As first noted by Kost and co-workers,10 the stereochemical behavior of the hydrazinyl radical can be derived from the three˙ H) and amido electron interaction model involving the imido (N (NH2) groups which compose the molecule. The authors10 distinguish torsional and inversion barriers for stereomutations of N2H3 and their parent ions by using simple frontier molecular orbital models and HF/4-31G ab initio calculations. They predict a similar torsional saddle point structure but located 29.6 kcal mol-1 above the minimum, even if the most stable geometry adopts a planar form.10 Such a result contradicts previous7,9 and subsequent1,8 findings that attribute a nearly pyramidal structure * To whom correspondence should be addressed.
to the NH2 fragment. In fact, as reported later in this work, the minimum of the hydrazinyl radical is nonplanar but only slightly tilted from the planar geometry associated with the intermediary connecting the two equivalent minima. Other studies dealing with experimental and theoretical characterization of the hydrazinyl radical are available in the literature. Pople and Curtiss8 estimated the ionization potential (IP) of N2H3 using the Gaussian-2 (G2) method and MP2/631G* optimized geometries for the neutral and cationic species. The calculated adiabatic IP is found to be in good agreement with the experimental data from mass spectrometry.11 In turn, Linder et al.12 have determined temperature-dependent rate constants for hydrogen abstraction in collisions of trans-N2H2 with H atoms using the potential energy attributes along the minimum-energy path as computed at the multiconfiguration self-consistent field and multireference configuration interaction (MRCI) levels of theory. The same reaction has been studied by Chuang and Truhlar13 using a dual-level direct dynamics method that combines the high-level calculations of Linder et al.12 with lower-level ones based on the AM1, MNDO, and NDDO-SRP semiempirical methods. More recently, Hwang and Mebel1 employed a modified version of G2 theory, G2M(MP2),14 to investigate the participation of the hydrazinyl species in radical chain mechanisms leading to ammonia formation. The present study builds on previous work by the authors15-20 toward the ab initio calculation and modeling of potential energy surfaces (PESs) for nitrogen/hydrogen-containing systems using double many-body expansion (DMBE) theory.21,22 Since full details of the method have been given elsewhere,22 suffice it to say that in DMBE, a PES is written as a cluster development in terms of the energies of the various n-body molecular fragments that compose the system, which are then modeled using well-defined analytic forms. Another key characteristic is that such n-body contributions are further split into shortrange and long-range components, thus warranting a proper formal representation of the PES up to dissociation. The major goal here will then be to map the reaction pathways for the title species by using high-level ab initio methods, hoping for a subsequent DMBE representation of the full PES. Thus, a new approach is discussed aimed at handling the multidimensinal character of the PES with a simplified, yet accurate, description of a stationary point in its neighborhood. The paper is organized as follows. Section 2 describes the ab initio methods and extrapolation schemes, while the major results are presented
10.1021/jp102841f 2010 American Chemical Society Published on Web 10/08/2010
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and discussed in section 3. Some concluding remarks are gathered in section 4. 2. Methods 2.1. Electronic Structure Calculations. The reported structures for the title system have been obtained as optimized geometries at the coupled cluster singles and doubles level of theory with perturbative triple corrections23 [CCSD(T)], using the cc-pVTZ (VTZ) basis sets of Dunning.24,25 In order to test the reliability of a method here suggested to allow an analytical representation of the PES, three transition states were optimized at the higher CCSD(T)/aug-cc-pVTZ level of theory. All of the optimizations have been followed by force field calculations to ascertain the nature of the stationary points. Well-established complete basis set (CBS) extrapolation schemes26-30 have then been utilized at the CCSD(T)/VTZ stationary structures via single-point CCSD(T) calculations. The two-point extrapolated energies using the basis set pair aug-cc-pVTZ (AVTZ) and augcc-pVQZ (AVQZ) will be denoted as AV(T,Q)Z and generally AV(X1,X2)Z when involving the X1- and X2-tuple basis sets. Single-point calculations using the multireference configuration interaction method (including the Davidson correction, MRCI+Q) have been performed along selected reaction paths computed at the CCSD(T)/VTZ level. All of the above calculations have been done with Molpro31 at the Coimbra Theoretical & Computational Chemistry Group. Although some of the numerical results are tabulated below, the complete set of calculated CCSD(T) (and MRCI) energies and geometries is reported as Supporting Information (SI). 2.2. CBS Extrapolations. All CBS extrapolations have been performed using well-established schemes26-30 relying on the asymptotic dependence of the calculated energy (EX) as a function of the cardinal number. As usual,30,32 the strategy involves the partitioning of the total energy into reference (EHF X ) and correlation (EXcor) contributions since they show different rates of convergence when X approaches infinity. The CBS/HF/AV(T,Q)Z extrapolations have been performed using the protocol E∞ + AX-5.34 suggested by Karton and Martin.33 In turn, the correlation energies have been extrapolated with the uniform singlet- and triplet-pair extrapolation (USTE30) scheme
EXcor ) E∞cor +
A3 (X + R)
3
+
A5 (X + R)5
(1)
where
A5 ) A5(0) + cAn3
(2)
and the offset factor is R ) -3/8. A5(0), c, and n are universal parameters for a specific level of theory; A5(0) ) 0.16606993, c ) -1.42225121, and n ) 1.0 for the CC family of methods (for details, see ref 30). 3. Results and Discussion 3.1. N2H3 Stationary Structures. The ab initio calculations reported here predict a nonplanar and unsymmetrical minimum for N2H3, with NH2 out of the plane that includes the N-N direction and the imido group (hereafter referred to as the HNN plane). The fully optimized structure at the CCSD(T)/VTZ level shows the NH2 group depressed by 38° with respect to the HNN plane. In fact, each hydrogen atom of NH2 deviates differently
Figure 1. Localized molecular orbital scheme for the N2H3 radical and its cationic species. The N-N distances correspond to optimized values at the CCSD(T)/VTZ level of theory.
from the HNN plane such that the hydrogen on the near cis arrangement with respect to the NH group undergoes a stronger steric repulsion than its geminal partner (see Figure 1a). The observed preferred conformation for the minimum of the hydrazinyl radical can be attributed to a conjugative interaction between the lone pair and the singly occupied 2p nitrogen orbitals located on the NH2 and NH groups, as displayed in Figure 1a. Figure 1b shows that by removing one electron from the system followed by geometry optimization, an unambiguous planar structure is observed with a typical double bond NN distance. In terms of a localized orbital picture, one can then state that an sp2 rehybridization of the NH2 group in N2H3+ has taken place, providing a pure 2p orbital and hence a stronger π-bonding interaction (Figure 1b). The first two entry columns of Table 1 show the geometric parameters and harmonic vibrational frequencies for the neutral and first ionized structures. From Table 1, the predicted value of 1597 cm-1 for the N-N vibrational stretching frequency in N2H3+ is as high as those observed in diazene,18 thus corresponding to an essentially double bond in the cationic species. Also large are the out-ofplane wagging and twisting frequencies when compared with the values for the neutral parental species, stressing the stiffness gained by the system upon ionization. The first entry of Table 2 shows the energy difference between the cationic optimized structures and the neutral ones, as computed at the CCSD(T) level of theory. For comparison, previous theoretical estimates8,10 and experimental values11 are also given. As shown in Table 2, our CBS/CCSD(T) value is in excellent agreement with the one obtained by Pople and Curtis8 using G2 theory while also being close to the earlier estimate from uncorrelated HF/4-31G calculations.10 Furthermore, the extrapolated IP reported in the present work closely matches the experimental value for the hydrazinyl radical,11 even if non-negligible Franck-Condon factors may be expected for a system bound to severe changes in geometry upon ionization (Figure 1). The neutral system exhibits four transition states associated with isomerization pathways and another four connecting the minimum to the various dissociation limits. Ball-and-stick drawings of such stationary structures are shown in Figure 2, while the complete set of geometric, spectroscopic, and energetic attributes are collected in Tables 1 and 2. The presence of a trigonal pyramidal geometry of the NH2 group at the N2H3 minimum implies that the molecule shows an inversion barrier at a planar conformation, as observed in ammonia. Such a saddle point, TS1, shows a fully planar structure and is predicted to be 0.5 kcal mol-1 at the CBS/CCSD(T) level, which matches the CI/DZ+P estimate reported by Chandler and McLean.7 When zero-point energy (ZPE) corrections are included, a
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TABLE 1: CCSD(T)/VTZ Stationary Geometries (in bohr and degrees) and Harmonic Frequencies (in cm-1)a propertyb r1 r2 r3 r4 φ1 φ2 φ3 φ4 τc ω1(NN) ω2(NH) ω3(NHsym) ω4(NHasym) ω5(NNH) ω6(sciss) ω7(rock) ω8(wagg) ω9(twist)
N 2H 3
N2H3+
TS1
2.565 1.934 1.911 1.904 104.9 118.8 112.4 113.5 97.1d
2.332 1.951 1.942 1.938 110.1 124.5 117.2 118.3
2.543 1.931 1.898 1.892 105.0 124.1 116.8 119.1
1231 3419 3511 3654 1497 1662 1148 636 729
1597 3366 3349 3484 1497 1739 1196 1069 1247
TS2
1271 3433 3601 3751 1487 1661 1103 519i 701
TS3t
2.441 1.862 1.915 1.915 180.0 118.2 118.2 114.6
Geometries 2.748 1.940 1.932 1.932 102.4 103.0 103.0 101.2 180.0d Frequenciese 963 3358 3404 3464 1390 1629 1188 1095 891i
1444 3974 3421 3517 1531i 1699 1321 562 1243i
TS3c
TS4t
TS4c
2.731 1.953 1.933 1.933 106.6 106.5 106.5 102.9 0.0d
2.376 1.947 3.481 1.945 106.0 120.7 107.0 100.0 178.7
2.374 1.954 1.954 3.347 111.1 112.9 118.7 98.4 1.0
963 3256 3373 3455 1381 1599 1174 1082 902i
369 404 824i 1293 1338 1510 1597 3292 3324
377 436 880i 1219 1354 1520 1544 3185 3262
TS5t 2.340 1.952 2.107 2.242 106.4 106.3 171.4 0.0 180.0 355 526 1289 1292 1484 1539i 1553 1655 3261
TS5c 2.344 1.961 2.029 2.639 112.1 111.7 160.5 0.0 0.0 255 415 709i 1248 1354 1514 1582 2271 3178
a The notation t and c are abbreviations for trans and cis, respectively. b For minimum isomerization TSs, TS4t and TS4c are as indicated in the top panel (left-hand side) of Figure 2 for TS1. For TS5t and TS5c are as indicated in the bottom panel (rhs) of Figure 2 for TS5c. c For TS4t (TS4c) and TS5t (TS5c), τ represents the dihedral angle of the H-N-N-H diazenic fragment. d Dihedral angle of H-N-N-X, with X lying on the bisector of the H-N-H angle. e For TS4t (TS4c) and TS5t (TS5c), frequencies are written by increasing order.
TABLE 2: Ionization Potential (in eV) and Energetics (in kcal mol-1) of N2H3 CCSD(T)a feature AVTZ AVQZ CBS CBS+ ZPEb N2H3+
7.5
7.5
TS1 TS2 TS3t TS3c
0.8 46.9 17.2 20.9
0.6 46.5 17.7 21.4
TS4ti TS4cj
2.5 2.6
2.4 2.6
TS4t TS4c
-51.2 -56.6
TS5ti TS5cj
3.3 0.6
TS5t TS5c
-37.6 -42.5
other c
Ionization Potential 7.5 7.6 7.5e, 7.4f
d e7.61 ( 0.01g
Isomerization Barrier 0.5 -0.2 0.5h 46.2 44.0 51.0h 18.0 16.6 24.9h 21.7 19.9 Hydrogen Addition Barrier 2.4 3.4 2.5 3.6 4.2
Hydrogen Addition Exothermicity -51.6 -51.8 -44.6 -56.9 -57.2 -49.5 -55.3 Hydrogen Abstraction Barrier 3.4 3.5 2.1 4.1, 6.0k 0.7 0.7 0.2
6.4
-47.2 4.2, 4.3k
Hydrogen Abstraction Exothermicity -37.2 -37.1 -40.3 -36.0, -33.6k -37.5, -38.2k -42.5 -42.5 -45.3
a This work; single-point calculations over CCSD(T)/VTZ optimized geometries. b Zero-point energy corrected values based on CCSD(T)/VTZ frequency calculations. c Except if indicated otherwise, energies have been calculated with the G2M(MP2) method.1 d Except if indicated otherwise, scaled zero-point corrected energies using MP2/6-31G** harmonic frequencies.1 e Reference 8. f Reference 10. g Experimental value.11 h Reference 7. i Energies relative to cis-N2H2(1A′) + H. j Energies relative to trans-N2H2(1A′) + H. k Reference 12.
barrier-free inversion mode is predicted (Table 2), suggesting a possible vibrationally delocalized minimum structure which is planar on average. Clearly, further studies44 including anharmonic corrections must be done to decide the true structure of hydrazinyl. One should add that a preliminary calculation using the reported45 vibrational frequency scaling factor of 0.9748 leads to the same barrierless inversion mode. Another inversion mode refers to flipping of the H atom in the NH group. The corresponding transition state, TS2, is located
Figure 2. Ball-and-stick drawings of the reported transition states for N2H3. The parameters used to characterize the stationary geometries are indicated in the TS1 and TS5c drawings.
44 kcal mol-1 above the minimum. In turn, this is comparable to the saddle point for trans-cis inversion in diazene (N2H2), which has been predicted18 to be ∼50 kcal mol-1 above the absolute trans minimum. At TS2, the NH2 group of hydrazinyl appears less pyramidal, with a tilting angle of 29° when optimized at the CCSD(T)/VTZ level of theory, showing also a shortening of the N-N bond distance (Table 1). Indeed, when the H atom of NH is at an apical position (aligned with the N-N axis), the steric constraints between the NH and NH2 groups diminish, and the conjugative interaction dominates,
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Figure 3. Pseudo-minimum-energy path for the isomerization processes of the N2H3 as computed at the CCSD(T)/AVTZ level of theory.
leading to a less pyramidal amido fragment. As shown in Table 1, the CCSD(T)/VTZ frequency calculations predict such a structure (TS2) to be a transition state of index 2 (with two imaginary frequencies). The highest vibrational mode connects the two equivalent minima, whereas the other mode evolves in the HNN plane perpendicular to the previous one and connects the rotational transition states TS3t and TS3c. Figure 3 shows a pseudo-minimum-energy path (PMEP) linking the isomerization saddle points and the N2H3 minimum. Each profile was obtained as a single-point calculation at the CCSD(T)/AVTZ level, over geometries whose parameters were linearly interpolated between two CCSD(T)/VTZ stationary structures. As reaction coordinate, we chose an appropriate internal coordinate, φ1 for the TS3c-TS2-TS3t path and the angle between the HNN plane and the plane bisecting the NH2 group for the TS3c-N2H3-TS3t route. From Figure 3, the TS2 saddle point lies on the 2A′ PES, which appears lower in energy than the 2A′′ state for that region of configuration space. The crossing between the 2A′ and 2A′′ energy sheets of hydrazinyl was first noted by Chandler and McLean,7 suggesting possible excitation isomerization pathways. However, it is unlikely that TS2 has a major role in the dynamics of the title system. As shown in Figures 2 and 3, TS3t and TS3c correspond to trans and cis rotamers, respectively. Their structural parameters, given in Table 1, indicate a lengthening of the bond distances during rotation and large deviation of the NH2 group. For TS3t, the tilt of the amido group rises to 69° and can be attributed to the strong repulsion between the NH2 lone pair and the bonding electron pair of the NH σ-bond. In turn, TS3c shows a NH2 depressed by about 63° due to the repulsion of the electron lone pairs on the nitrogen atoms. The CBS/CCSD(T) results from Table 2 show that the rotational barrier leading to the trans rotamer is of 16.6 kcal mol-1. Moreover, the torsional motion involving the cis intermediary appears to be less favorable than the trans pathway by about 3 kcal mol-1. Transition states for dissociation are labeled in Figure 2 and Tables 1 and 2 as TS4t(TS5t) and TS4c(TS5c). The TS4t and TS5t structures have in common the trans-N2H2 + H asymptote when a hydrogen dissociates from the N2H2 fragment, whereas the cis-N2H2 + H limit is reached through the pathways involving the TS4c and TS5c saddle points. Indeed, for all such stationary geometries, the N2H2 fragments are nearly planar, closely resembling the trans and cis isomers of diazene (see Table 1). Thus, when a hydrogen atom approaches N2H2, one of four possibilities may occur depending on whether diazene
Poveda and Varandas
Figure 4. Reaction parthways for hydrogen addition and abstraction processes of the N2H3 as computed at the CCSD(T)/AVTZ level of theory.
is in the trans or cis conformation and the relative orientation of the reactants. The addition reaction of the incoming hydrogen atom through a direct interaction with one of both the transand cis-diazene nitrogen atoms shows an early character with the N-H bond at the critical point as long as ∼3.4 Å. A slightly shorter N-H distance of 3.16 Å at TS4c was reported by Hwang and Mebel1 at the MP2/6-31G** level. As shown in Table 2, the CBS/CCSD(T)+ZPE transition states here predicted for both pathways show an almost equal barrier height with values of 3.4 and 3.6 kcal mol-1 for TS4t and TS4c, respectively. In turn, the barrier for addition of a hydrogen atom to the cis-diazene appears appreciably lower than the 6.4 kcal mol-1 value obtained at the G2M(MP2) level of theory.1 The curves on the left-hand side (lhs) of Figure 4 show the PMEP conecting the N2H3 minimum with the trans- and cis-N2H2 dissociation limits through the TS4t and TS4c transition states. The solid dots correspond to the CCSD(T)/AVTZ//CCSD(T)/VTZ energies along the N-H reaction coordinate, whereas the open circles represent MRCI+Q/AVTZ energies along the same path. From Figure 4, good agreement is observed between the CC and MRCI curves, suggesting the reliability of a single reference description at the CCSD(T) level to account for the correlation effects involved in the N2H2 nitrogen hydrogenation event. In turn, the MRCI+Q/AVTZ method predict even lower barrier heights of 1.8 kcal mol-1 for both pathways. Hence, the present results suggests that hydrogenation of diazene may occur easier and faster than predicted before.1 If the incoming hydrogen atom approaches N2H2 along a line close to a N-H bond direction, a hydrogen abstraction reaction may occur, leading to the HN2 + H2 dissociation channel. In Tables 1 and 2, TS5t and TS5c characterize the geometries of the transition states for such reactions. From Table 1, the abstraction of a hydrogen atom from cis-diazene shows a marked early character with the H-H distance ∼0.6 Å larger than the N-H bond at the saddle point (TS5c). In turn, the transHNNH · · · H transition state for abstraction (TS5t) takes place with the forming hydrogen bond having a length similar to, although larger than, the broken NH one. Conversely, Hwang and Mebel1 obtained at the MP2/6-31G** level, a TS5t optmized structure with a shorter H-H bond, indicating a former transHNNH · · · H abstraction pathway. The authors predict a barrier height for this reaction of 4.2 kcal mol-1, twice larger than the one here reported at the CBS/CCSD(T) level. Moreover, our extrapolated value involving cis-diazene was found to be only
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0.2 kcal mol-1 above the cis-N2H2 + H dissociation limit. Such a result challenges previous work12,13 on reaction rate calculations for abstraction of a hydrogen atom from N2H2 by H. In these papers, the diazene reactant is constrained to the trans configuration, discarding any influence of N2H2 isomerization on the thermal rate constant.12,13 However, as predicted here, a H atom can be easily removed from cis-diazene, suggesting that cis-N2H2 + H reactions may play a significant role in the bimolecular hydrogen-abstraction mechanism. The rhs curves in Figure 4 show CCSD(T)/AVTZ (solid dots) and MRCI+Q/AVTZ (open circles) single-point energies for abstraction reactions, computed over the geometries along the MEP (calculated at the CCSD(T)/VTZ level). The last was obtained via an intrinsic reaction coordinates calculation using Molpro. The good agreement between the CC and MRCI profiles shows that a single reference approach may be reliable to explore the PES of hydrazinyl. 3.2. Potential Energy Surface Representation. Following previous work,19,34,35 an analytical representation of the potential energy surface for N2H3 can be obtained by using distributed polynomials fitted to ab initio data clustered around the stationary geometries. However, for an accurate description of the PES topography in the neighborhood of a critical point, at least 33N-6 single-point energy evaluations are required, with the base of the exponentiation indicating that three ab initio values need to be computed for each degree of freedom. Clearly, for a five-atom system (N ) 5), the task leads to an unbearable number (39) of computations, not to mention that more than one stationary structure may exist, including intermediate states along the MEP. However, the computational effort can be drastically reduced by approximating the potential energy via a simple Taylor series expansion, truncated at first-, second-, or any higher-order energy derivatives as one so wishes. In the following, we suggest a hybrid method that combines a Taylor series development of the PES with an ab-initio-based representation in the neighborhood of a stationary point. As particular cases, we examine below the TS4c, TS5t, and TS5c transition states. The approach relies on the observation that in the vicinity of such saddle points involving bond breaking/ formation, the largest geometry variations are often restricted to a small subset of coordinates [{Vk}, k ) 1, ..., n (
