Theoretical study of the reaction of OH with HNO

ChemicalPhysics 153 (1991) 415-426 North-Holland

Theoretical study of the reaction of OH with HNO

Maribel R. Soto ‘, Michael Page Laboratory for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Code 4410, Washington, DC 203 75-5000, USA

and

Michael L. McKee Department of Chemistry, Auburn University, Auburn, AL 36849, USA

Received 29 October 1990

A complete-active-space (US) multiconfguration self-consistent tield (MCSCF) wavefunction with a polarized correlation- consistent basis set was used to determine the stationary points on the OH+HNO potential energy surface. The single-point energies were determined with a multireference confguration interaction (MRCI ) wavefunction consisting of single and double excitations from selected configurations chosen from the reference wavefunction. Saddle points were confirmed at the Bveelec- tron, tive-active-orbital CASSCF level by calculating analytical second derivatives. Segments of the minimum-energy paths (MEPs) for the hydrogen abstraction reaction and for the radical addition to nitrogen were calculated. It was found that the zero-point energy contribution for the abstraction pathway increases as one moves away from the MCSCF saddle point toward the reactants. An evaluation of the MRCI energy and the MCSCF zero-point energy contribution on the MEP at a few points towards the reactants suggests that the true transition state is earlier than the computed MCSCF saddle point, and that abstraction occurs with little or no activation barrier. At the MRCI level, the maximunt in the vibrationally adiabatic potential along the MEP for the addition of OH to the nitrogen of HNO occurs at 5.6 kcal mol-’ above the reactants and, like the abstraction, this structure is earlier than the MCSCF saddle point. The resulting product of the OH addition, HN(O)OH, is not expected to decompose to H + HONO because the barrier to H elimination (3 1.4 kcal mol- ’ ) is significantly higher than the barrier for the reaction back to OH+HNO (20.3 kcal mol-’ ). Statistical rate calculations have been performed for the abstraction and addition reactions, and the results are fitted to standard three-parameter temperaturedependent rate expressions.

1. Introduction

Modeling combustion processes requires kinetic data for a large number of elementary reactions [ 1,2]. Normally, this rate information is obtained from a variety of experimental techniques; however, kinetic data from high-level ab initio calculations [ 31 on reactants and transition states are an important aid to, and in some cases replacement for, experimental information, particularly for reactions that may be difficult to study experimentally.

The very exothermic abstraction reaction, OH + HNO+H*O +NO, has been suggested to be important in the combustion of nitrogen-containing

’ ONT/NRL postdoctoral associate

fuels such as NH3 [ 4-6 ] and CHsNH2 [ 7 1. Proposed mechanisms for the reduction of NO, in coal-fired combustion also include the above reaction [ 81. However, little is known experimentally about the rate of this reaction and its temperature dependence. Bulewicz and Sugden [ 91 measured NO-catalyzed H +OH radical recombination in premixed flames and obtained a rate for the OH+HNO abstraction reaction of 1.5X 10-‘” cm3 mol-’ s-‘, with no sig- nificant temperature dependence between 1600 K and 2000 K. Subsequently, Halstead and Jenkins [ lo] used the same techniques and method of analysis, and obtained a rate constant at 2000 K of ( 6 + 2 ) x 10 - ’ ’ cm3 mol- ’ s- ‘, a factor of three smaller than that obtained by Bulewicz and Sugden at the same temperature. Halstead and Jenkins ascribed the difference

0301-0104/91/$03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)

416 M.R. Soto et al. / The reaction of OH with HNO

to the greater volume of data used in their work and the greater accuracy of their determination of the hydrogen-atom concentrations. The abstraction reaction has since been modeled by several authors by & temperature-independent rate constant of 6.0 X 10-l ’ cm3mol-‘s-’ [5-111.

A theoretical study of the different reaction pathways of OH+HNO was undertaken in order to determine the temperature dependence of the reaction rate and also to assess the competition between the hydrogen abstraction and radical addition reactions. There are three pathways involving the OH radical and HNO that we consider: hydrogen abstraction (reaction 1)) addition to the nitrogen of HNO (reaction 2), and addition to the oxygen of HNO (reaction 3 ) ,

OH+HNO-+H,O+NO, (RI)

OH+HNO-tHN(O)OH*, WI

OH+HNO-+HNOOH* . (R3)

The complex formed in (R2) can then either decompose back to the reactants, decompose to H + HONO, or be collisionally stabilized,

HN(O)OH*+OH+HNO, (R-2)

HN(O)OH*-+H+HONO, (R4)

HN(O)OH* (+M)+HN(O)OH. WI

We report here on multiconfigurational self-consistent-field (MCSCF) and multireference configuration-interaction (MRCI) calculations of features of the potential-energy surface (PES) for reactions (Rl ) to (R4). In particular, the stationary points on the PES corresponding to the reactants, products, and transition states as well as harmonic vibrational frequencies and portions of the minimum-energy paths (MEPs) are determined at the MCSCF level of theory. Large-scale MRCI calculations are then em- ployed at the MCSCF stationary points and at selected points along the MEPs to improve the energetics. Calculated features of the PES are then used as input to transition state theory calculations of the temperature-dependent reaction rate coefficients.

2. Theoretical method

The MCSCF wavefunctions that were used, complete-active-space (CAS)SCF wavefunctions, were constructed by including all the possible configurations generated by excitations within the active space consistent with doublet spin symmetry [ 111. With one exception, the same active space was used for all geometry optimizations and frequency calculations. At the OH + HNO asymptote, this space consists of the A~_~, R&,, (T~_~, o$&H orbitals and the orbital containing the unpaired electron. These orbitals smoothly transform into other orbitals at the products’ asymptote. For example, at the products’

asymptote of (R 1) the oN_“. c&H orbitals and the radical orbital on oxygen become oo_“, ti&, and a radical orbital on nitrogen, respectively. The resulting five-electron, five-active-orbital (five-in-five) CAS contains 75 doublet configurations. The exception referred to above involved the search for the transition state for OH addition to the nitrogen of HNO, where the inclusion of an oxygen lone-pair orbital in the active space was required (seven-in-six CAS, 2 10 configurations). The five-in-five (or seven- in-six) CAS wavefunction was used to determine the optimized geometries, the MEP from the transition state, and the vibrational frequencies. An MRCI calculation, including all the single and double excitations from all the reference configurations in the five- in-five or seven-in-six CAS, is prohibitively large. To limit the number of configurations, the reference space for the MRCI calculations was reduced to include only those references generated by a three-in- three CI using the natural orbitals of the larger five- in-five or seven-in-six CASSCF wavefunction. The smaller three-in-three reference space generated 506850 configurations in the MRCI. The active space for the MRCI calculations was determined by including only the active orbitals necessary to describe a particular reaction. For example, ( R 1) and ( R4 ) required the ON_“, &N-H orbitals and the orbital containing the unpaired electron, while (R2 ) and (R3 ) required the KN_O, A&, orbitals and the orbital containing the unpaired electron. The reduction of the active space for the MRCI calculations meant that two MRCI calculations, one in each space, were required for OH + HNO and HN (0 )OH because the former occurs in (Rl )-(R3) and the latter in (R2) and

MR. Soto et al. / The reaction of OH with HNO 417

(R4). Supermolecule calculations were performed for OH + HNO and Hz0 + NO with the molecules sepa- rated by 100 A because the MRCI calculations are not size consistent. All calculations were carried out using the MESA [ 12 ] system of programs.

The basis set used was Dunning’s recently devel- oped correlation-consistent polarized valencedou- ble-zeta (cc-pVDZ) basis set [ 13 1. This basis consists of a (9s5pld) primitive set contracted to [ 3s2pld] for first-row atoms and a (4s) primitive set contracted to [ 2s] and augmented with a ( 1 p ) polarization function for hydrogen. Comparisons have also been made with structures optimized with standard single-configurational methods [ 14 ] using the 6-31G’basis [ 15,161.

Table 1 contains geometric parameters of critical points along the MEP of ( R 1) , while table 2 contains relative energies for species for which the NH o bond was included in the three-in-three active space of the MRCI calculation ( (R 1) and (R4) ), at various levels of theory. Tables 3 and 4 contain geometric parameters of species for which the NO II bond was in-

eluded in the three-in-three active space of the MRCI calculation ( ( R2 ) and ( R3 ) ) , while table 5 contains relative energies at various levels of theory. Struc- tures of the CASSCF transition states (saddle points) are given for reactions R( 1)-R(3) in figs. l-3, respectively.

3.OH+HNO+OH,+NO

A common practice in computational studies is to evaluate stationary points at one level of theory and to calculate energies at fixed geometries with a more sophisticated method, typically one including more basis functions or including more electron correlation. The assumption that the geometry of the stationary point is the same at the higher level may be dictated by necessity because optimizing the geometry at the higher level can be computationally prohib- itive. However, the location of a saddle point on the PES might be affected by the level of theory, particularly when the exothermicity of the reaction is af-

Table 1 Structural parameters and harmonic vibrational frequencies at critical points along the MEP of H-atom abstraction calculated at the five-in-five CASSCF level

HO+HNO RP ‘) TS H,O+NO

RN,6 (A) 1.200 1.199 1.182 1.139 RNrHa (A) 1.066 1.043 1.168 RHG (A) 1.590 1.412 0.967 RO,Hs (A) 0.957 0.959 0.956 0.947

L02NIH3 (de&r) 107.6 109.8 108.4 LNtH304 (de& 160.5 163.9 LH,Od% (deg) 97.4 96.4 103.5

CASSCF harmonic vibrational frequencies (cm-‘)

4019 2944 1716 1621

4008 4035 4154 3058 1795 3806 1730 1620 2048 1592 832 1760 502 579 209 565 592i 172 146i 142

b) 3361i

ZPE Cl (kcal mol-‘) 14.73 15.86 13.92 16.83

‘) At the position s=O.4 arnur” bohr on the MEP in the direction of HO+HNO. ‘) Only 3n - 7 modes are present because the reaction path mode has been projected out. ‘) Zero-point vibrational energy.

Table 2 Relative energies of the reactants, transition states and products for the abstraction reaction (kcal mol-’ )

Wavefunction ‘) HO+HNO RP TS b, HaO+NO HN(O)OH TS”

C,

HF/6-3lG* 0.0 PMP2/6-3lG’ 0.0 PMP4/6-3 1 G’ 0.0 PMP4/6-3lG*+ZPE ‘) 0.0 3-in-3 CASSCF 0.0 5-in-5 CASSCF 0.0 MRCI *’ 0.0 MRCI + ZPE =) 0.0 Exp r) 0.0

10.6

6.5 9.2 6.9 10.9 0.8 2.5 2.0 1.7

- 56.6 -71.7 -68.1 -66.5 -57.7 -50.1 -66.0 -63.9 - 69.4

- 17.8 - 33.4 -30.1 -24.5 - 12.8 26.0

-2.8 36.1 -24.7 12.6 -18.7 12.7

a) The level of optimization for the first four entries is UHF/6-3 1G” and for the next four entries the level of optimization is five-in-five CASSCF.

b, The transition state is for the syn arrangement of the two hydrogens. The anti arrangement is also a transition state and is 0.6 kcal mol- ’ higher in energy at the UHF/63 1 G*//UHF/6-3 1 G* level.

‘) The transition state is for the elimination of H from HN(O)OH. d, Multireference CI with a three-in-three active space including the oi.,_u and a& orbitals and the orbital containing the unpaired

electron. ‘i Including zero-point corrections. ‘) Heats of formation are from ref. [ 27 1.

Table 3 Structural parameters and harmonic vibrational frequencies at critical points along the MEP of OH addition to nitrogen and NH bond cleavage of HN(O)OH at the five-in-five CASSCF level

RN02 (A) RN&s (A) RG,Hd (A) RN~Hs (A)

LO~NJ% (deg) LN,GaH, (deg) LHSNIGz (deg) L H&ND2 (deg) LHNOH s I 3 4 (deg)

OH+HNO RP 0.b) TS a+) HN(O)OH HN(O)OH TSd’

C, C.

1.200 1.192 1.194 1.260 1.219 1.188 1.983 1.875 1.429 1.403 1.438

0.957 0.955 0.954 0.948 0.952 0.950 I .066 1.062 1.054 1.029 1.020 1.567

115.3 117.2 113.7 121.3 109.0 95.2 96.4 103.3 102.1 103.0

109.8 110.8 112.6 113.0 126.3 103.5 165.2 266.1 263.2 0.0 168.4 147.7 145.5 138.9 180.0 76.8


4019 4064 4076 4115 2944 2965 3078 3437 1716 1712 1654 1562 1621 1546 1474 1452

823 1018 1336 589 756 1008 226 354 767 183 204 576

e) 5491 283

ZPE f, (kcal mol-i) 14.73 17.31 18.03 20.78

n) The optimization was performed at the seven-in-six CASSCF level. b, At position s=O.6 am~‘/~ bohr on the MEP in the direction of HO+HNO. ‘) The transition state is for addition of OH to the nitrogen of HNO. d, The transition state is for elimination of H from HN(O)OH. ‘i Only 3n- 7 modes are present because the reaction path mode has been projected out. ‘) Zero-point vibrational energy.

4074 4098 3576 1630 1742 1430 1516 836 1431 690 985 650 579 615 101 400

715i 2223i

20.02 14.79

M.R. Soto et al. / The reaction of OH with HNO 419

Table 4 CASSCF structural parameters and harmonic vibrational frequencies for the hydrogen bonded HO + HNO complex and the peroxide isomer HNOOH calculated at the five-in-five CASSCF level

HO...HNO ‘) HNOOH

1.198 RN& 1.331 0.960 R0203 1.481 2.254 RO3K 0.951 1.062 RN& 1.043 137.5 LN,0203 106.7 108.4 L 0203H.9 99.6

11.4 L KN,Oz 99.8 163.8 LHOON 4321 98.5 180.0 LWJ,‘&03 177.2


3989

3004 1728 1618 439 434 145 127 61

3282 1501 1438 1205 716 548 520 168

ZPE ‘) (kcal mol-‘) 16.50 19.25

‘) Hydrogen-bonded complex. b, Zero-point vibrational energy.

Table 5 Relative energies of the reactants, transition states and products for the addition reaction (kcal mol- ’ )

Wavefunction *) HO+HNO H-bonded RP b).C) TS b).d) HN(O)OH HN(O)OH HNOOH complex C, C,

HF/6-3lH* 0.0 -4.7 - 17.8 - 13.4 20.4 PMP2/6-3lG” 0.0 0.5 -33.4 -35.3 4.2 PMP4/6-3lG* 0.0 -2.4 -30.1 -29.7 5.6 PMP4/6-3lG*+ZPE ‘) 0.0 -1.8 -24.5 -25.3 10.0 3-in-3 CASSCF 0.0 -4.0 10.7 17.6 -3.6 -1.1 23.3 5-in-5 CASSCF 0.0 -3.8 8) I) -2.8 2.8 25.6 7-in-6 CASSCF -1.2 0.0 MRCI =) 0.0 -4.4 3.0 -2.9 -20.7 -19.4 10.5 MRCI+ZPE ‘) 0.0 -2.6 5.6 0.4 - 14.7 -‘14.1 6.0

a) The level of optimization for the first four entries is UHF/6-3 lG* and for the next four entries the level of optimization is five-in-five CASSCF.

b, The optimization was performed at the seven-in-six CASSCF level. =) At maximum along MEP (position s=O.6 amu iI2 bohr ) in the nitrogen direction of HO + HNO. d, The transition state is for the addition of OH to the nitrogen of HNO. ‘) Multireference CI with a three-in-three active space including the n wd and a& orbitals of HNO or the au,, and oL orbitals of

HN( 0)OH and HNOOH, and the orbital containing the unpaired electron. r) Including zero-point corrections. *) The seven-in-six CASSCF energy was calculated rather than the five-in-five CASSCF.


=o c 5 4-c -a-_ /- ---_ H

Fig. 1. Structure of the saddle point on the five-in-five CASSCF potential energy surface for H-atom abstraction from HNO by OH.

fected. For example in (R 1) , the exothermicity is 15.9 kcal mol- ’ greater at the MRCI level compared to the five-in-live CAS level. By Hammond’s postulate, a very exothermic reaction should have an early saddle point, and increasing the exothermicity should move the transition state towards the reactants. One

Fig. 2. Structure of the saddle point on the seven-in-six CASSCF potential energy surface for OH addition to the nitrogen atom of HNO.

Fig. 3. Structure of the saddle point on the five-in-five CASSCF potential energy surface for H elimination from HN(O)OH.

means of compensating for this effect is to calculate the MEP at the MCSCF level and to evaluate the MRCI energy at several points along this path. In this manner, the effect of the zero-point vibrational energy (ZPE) on the location of the transition state [ 171 can also be included, provided these correo tions are available from the MEP at the MCSCF level.

The MEP, the path of steepest descent in a mass- scaled coordinate system, was determined by solving the differential equations that define the path by the local-quadratic-approximation (LQA) method [ 18,19 1. The MEP for the abstraction reaction (Rl ) was determined beginning at the saddle point and ex- tending for an arc-length of 0.4 arnui” bohr towards the reactants in eight steps of 0.05 amu”’ bohr. At each point along the MEP, the vibrational frequencies were calculated after the reaction path direction and overall rotations were projected out of the force constant matrix. The variation of the 3n - 7 vibrational frequencies with respect to the path position,


-0.40 -0.30 -0.20 -0.10 0.00

Arc Length (&iii bohr)

Fig. 4. Plot of the variation of vibrational frequencies with respect to the reaction path position (s) for the abstraction of H from HNO by OH. The position s=O.O is the MCSCF saddle point. Negative values of s correspond to points closer to the reactants OH + HNO.

s, is shown in fig. 4 for the abstraction pathway. Typ- ical of hydrogen abstraction reactions, there is a dramatic increase of the in-phase O-H-N stretching frequency that correlates with the N-H stretch of HNO in the reactants. The out-of-phase O-H-N stretch corresponds to motion along the reaction coordinate. The in-phase O-H-N stretching frequency is 576 cm- ’ at the saddle point (MEP position S= 0) and increases more than fivefold to 2944 cm-’ by position S= -0.4 amull bohr. While the frequencies of the other modes decrease in the same interval, with a corresponding decrease in the ZPE, the frequency increase of this one mode contributes 3.4 kcal mol- ’ to the vibrationally adiabatic potential along the path. Thus, while the electronic energy may decrease along the MEP away from the saddle point, the sum of the electronic and the zero-point energies may increase. We calculated the MRCI energy at live points along the MEP for the abstraction reaction. The MRCI energy at a position of S= -0.4 amu1’2 bohr along the MEP is 0.8 kcal mol- ’ above OH + HNO, a decrease of 1.7 kcal mol- ’ from the MRCI energy at the saddle point (s= 0). However, when the effects of the zero-point energy are included, the s= - 0.4 position

is 0.2 kcal mol-’ higher in energy than the MRCI +ZPE energy at s=O. At points just beyond s= -0.4 amu*lZ bohr, the MRCI energy decreases slowly toward the reactant asymptote, while the ZPE has finished its dramatic change in the interaction region and is relatively constant. The maximum in the vibrationally adiabatic potential at this level of theory is therefore close to s= -0.4 amu1’2 bohr, and is about 2.0 kcal mol-’ above the reactants.

A second feature to note in fig. 4 is the path dependence of the two modes that are the lowest frequency bound modes at the saddle point. The frequencies of these modes become imaginary shortly beyond the saddle point in the reactant direction. This does not mean that the MEP has become unstable with respect to motion in these transverse directions; rather, this is a consequence of the particular choice of coordinates for solving the vibrational problem in directions transverse to the MEP. Unlike stationary points, where the harmonic vibrational frequencies are independent of the choice of coordinates, harmonic vibrational frequencies calculated at points on the MEP for which the gradient is non-zero do depend on the coordinates. The usual reaction path Hamiltonian procedure [ 201 used here, although well-defined, ap- pears to provide an unreasonable model for low-frequency modes that correlate with free rotations of either products of reactants. One of these modes corresponds to a nearly free internal rotation, while the other mode corresponds to a low-frequency in-plane bend that correlates with the in-plane free rotations in the reactants. For the purposes of computing the zero-point vibrational energy and for evaluating the partition functions, we treat the out-of-plane internal rotation mode as a free rotor, and we treat the in-plane bend as a harmonic oscillator for which the frequency is assumed to decay from its saddle point value towards zero at the same rate as the in-plane bending mode that is 83 1.6 cm-’ at the saddle point.

4. HN(O)OH

The product of OH addition to the nitrogen of HNO, HN(O)OH, was optimized in two different point groups, C, and C,. The resonance form that best describes each is given below.

422 M.A. Soto et al. / The reaction of OH with HNO

ldl 1.219 1.260 II

1.029

H/

l.o;o/‘~O/H

nonplanar C, planar C,

In the planar structure the N-O bond is 0.041 A shorter (table 3) and the N-O stretching frequency is 180 cm- ’ higher ( 1742- 1562 cm- ’ ) than the nonplanar C, structure. In addition, the unpaired electron is much more localized on nitrogen in the planar structure. These observations are all consistent with partial x-bond formation in the planar structure. At the PMP2/6-31G*//6-31G* level the C, structure is less stable than the C, structure by 1.9 kcal mol-‘, whereas at the PMP4/6-3 lG*//6-3 lG* level, the order is reversed by 0.4 kcal mol-‘. Inclusion of the zero-point energy reverses the order yet again yields C, more stable than C, by 0.8 kcal mol-‘.

At the five-in-five CASSCF level the C1 structure is 5.6 kcal mol-’ more stable than the C, structure, but this difference is reduced to only 0.6 kcal mol-’ at the MRCI+ZPE level. From these results we are unable to ascertain whether the planar or pyramidal form is lower in energy, but the results indicate that the potential energy surface is very flat with respect to inversion about the nitrogen centre. A similar sit- uation applies to the HzNO molecule, which has been predicted to be planar [ 2 1 ] and pyramidal [ 22 1. At the UMP3/6-31G* level, H2N0 is predicted to be pyramidal with a barrier to inversion of 0.2 kcal mol- ’ [ 22 1. More recent calculations based on geometries optimized at the CI/cc-pVDZ level and energies at the CI + Q/cc-pVTZ + sp level plus a zero- point correction give an energy difference of 0.1 kcal mol- ’ in favor of the pyramidal structure [ 23 1.

Comment is warranted on the difference in the calculated N-OH bond dissociation energy in HN(O)OH as calculated by PMP4/6-31G*//6-31G* and the MRCI calculations. At the PMP4/6-31G’// 6-3 1 G* + ZPE level, the N-OH bond dissociation energy is 24.5 kcal mol- ‘, #’ which is 9.8 kcal mol- ’

larger than the MRCI + ZPE level ( 14.7 kcal mol- I, table 5). Part of the reason for this rather large energy difference may be seen from a consideration of the difference in the multiconfigurational nature of HNO and HN( 0)OH. The occupation numbers of the natural orbitals in the MCSCF calculations indicate that there is more multiconfigurational charac- ter in HNO than there is in HN(O)OH. In HNO the r&o and R&_~ orbitals have natural orbital populations of 1.88e- and O.l2e-, respectively, while the oN_o and of_o orbitals in the C, structure of HN( 0)OH have natural orbital populations of 1.96e- and O.O4e-, respectively. Therefore, HN( 0)OH is better described by a single-reference configuration than HNO, and methods based on a single-configuration reference (i.e. PMP4/6-3 1 G*) may thus underestimate the stability of HNO with respect to HN(O)OH. Inclusion of limited pertur- bative electron correlation (i.e. MP4) might not compensate fully for the poor zeroth-order description of HNO.

Since OH + HNO and HN (0 )OH were calculated with two different three-in-three CAS reference spaces in the MRCI, two different bond dissociation energies can be calculated. The correct space for calculating the bond dissociation energy includes the KN-0 and rr:,, orbitals of HNO and the oN_O and c$-~ orbitals of HN( 0)OH. In this space the MRCI+ZPE bond dissociation energy is 14.7 kcal mol-‘. Energies in the second three-in-three reference space, which included the oN_u and o&, orbitals, were required for the abstraction reaction (R 1) and the hydrogen elimination reaction (R4) _ Since the N-H bond is inactive for the bond dissociation energy, this three- in-three active-space MRCI is, for this case, similar to a single and double excitation CI from a single reference, and, therefore, might reveal the effect of ex- cluding important configurations from the reference. With only the N-H bond included in the three-in- three MRCI + ZPE, the N-OH bond dissociation energy increases by 4.0 kcal mol- ’ to 18.7 kcal mol- ’ (table 2). This difference suggests that HNO requires a multiconfigurational description that includes the AN-0 and ~cG_~ orbitals.

#’ The bond dissociation energy at the BAC-MP4 level is about 32 kcal mol-’ [24].


5. HN(O)OH+H+HONO

If (R2) is important, a further reaction to H + HONO ( R4 ) might be expected to occur. For that reason the transition state for the hydrogen atom elimination from I-IN (0 )OH was located. The length of the breaking N-H bond is calculated to be 1.567 A (table 3) and the conformation of HONO in the transition state ( HONO ‘dihedral angle = 168.4 O, fa- ble 3 ) indicates that the product will be truns-HONO. The barrier for H atom elimination is 3 1.4 kcal mol- ’ ( 18.7+ 12.7 kcal mol-‘, table 2) at the MRCI+ZPE level. Since the barrier for OH elimination is 20.3 kcal mol-’ ( 14.7 kcal mol-’ N-OH bond energy plus 5.6 kcal mol- ’ barrier, table 5 ) , the lowest unimolecular energy pathway for HN(O)OH destruction is OH elimination to form OH + HNO. Therefore, even if ( R2 ) were important, the product HONO would not be expected.

6. HNOOH

The product of OH addition to the oxygen atom of HNO is the peroxide HNOOH (R3). Five different conformations of HNOOH were optimized at the UHF/6-3 1 G* level (not shown). The lowest energy conformation at this level consists of a truns-HNOO arrangement and a gauche-NOOH arrangement. This conformation also proved to be a minimum on the five-in-five CASSCF surface. The HNOOH molecule is predicted to have a negative O-OH bond energy, which means that OH+HNO is more stable than HNOOH. This observation has been made previ- ously by Melius and Binkley [ 241. HNOOH is predicted to be 6.0 kcal mol-’ above OH+HNO at the MRCI+ZPE level and 10.0 kcal mol- ’ above OH+HNO at the PMP4/6-31G*//6-31G*+ZPE level. The transition state for OH addition was not located because even with no additional activation, the reaction via (R3) would not be competitive with abstraction (R 1).

7. Hydrogen-bonded complex

A hydrogen-bonded complex between the hydrogen of OH and the nitrogen of HNO was investi-

gated. Structural parameters and vibrational frequencies are given in table 4, and the energetics at several levels of theory are given in table 5. At the MRCI+ZPE level, the complex is predicted to be bound by 2.6 kcal mol- I, which is similar to the 1.8 kcal mol- ’ binding energy predicted at the PMP4/6- 31G*//6-31G*+ZPE level. The N...H distance is predicted to be 2.254 A and the N...H-0 angle is 163.8’ at the five-in-five CASSCF level.

8. HNO+OH+HN(O)OH

The transition state for OH addition (R2 ) was located at the seven-in-six CASSCF level rather than at the five-in-five level. Because of convergence prob- lems, it was necessary to add an oxygen lone-pair orbital to the active space. As the addition of OH to HNO proceeds, the unpaired electron moves from the oxygen of OH to the oxygen of HNO. An orbital analysis indicates that the added lone pair allows the smooth transformation of the unpaired electron pri- marily in the ON0 plane to an unpaired electron pri- marily out of the ON0 plane.

A seven-in-six MCSCF MEP was constructed from the saddle point for the OH addition reaction back towards the reactants OH+HNO. Fourteen points were computed for a total reaction segment of 0.7 amu”* bohr. At the segment terminus closest to the reactants, the N-OH distance increased by 0.126 A, from 1.875 A to 2.001 A. The energy of the segment end is 1.6 kcal mol-’ lower than the energy of the saddle point. However, the MRCI energy of the segment end is 5.7 kcal mol-’ higher than the MRCI energy at the MCSCF saddle point. The highest MRCI energy along the MEP occurs at the position s= - 0.6, which is 5.9 kcal mol-’ above the MRCI energy at the MCSCF saddle point and occurs with a N-OH separation of 1.983 A. The zero-point energy at this point is 0.7 kcal mol- ’ smaller than the MCSCF zero- point energy at the saddle point (in contrast to the large increase in zero-point energy for the abstraction pathway). The maximum MRCI + ZPE energy along the MEP also occurs at s= -0.6, and it is 5.6 kcal mol-’ above OH+HNO, an increase of 5.2 kcal mol-’ from the MRCI+ZPE energy at the MCSCF saddle point ( s = 0 ) .

424 M.A. Soto ei al. /The reaction of OH with HNO

9. Rate calculations

We performed statistical rate calculations for the hydrogen abstraction and for the OH addition to the nitrogen of HNO. For reactions such as these that occur with little or no activation, variational effects on the location of the transition state and on the rates are expected to be important [ 17 1. However, the information available about the potential energy surface from our MCSCF and MRCI calculations is in- adequate for a complete, meaningful canonical variational treatment of the reaction rate. Instead, as in conventional transition state theory, we assume that the location of the transition state is independent of temperature. However, unlike conventional transition state theory, for which the transition state is assumed to be located at the saddle point on the PES, we assume that it is located at the position of the vibrationally adiabatic maximum along the reaction path at the MRCI level.

For the abstraction reaction, the MRCI energy slowly decreases going towards the reactants through the region of the PES for which the transverse vibrational modes are changing most dramatically (see fig. 4). The vibrationally adiabatic potential, the path energy plus the zero-point vibrational energy for modes transverse to the path, is strongly influenced by the zero-point contributions in this region; the maximum occurs at about s= -0.4 amu” bohr, just after the vibrational modes have finished their rapid change. As discussed in section 3, we treat the out-of- plane internal rotational mode as a free rotor, and we treat the in-plane bend as a harmonic oscillator for which the frequency is assumed to decay from its saddle point value towards zero at the same rate as does the in-plane bending mode that is 83 1.6 cm-’ at the saddle point. The transition state structural parameters and the frequencies for the remaining (harmonic oscillator) modes are those in the column labeled RP in table 1. For the rate calculations, we reduce the calculated MRCI energy at the vibrationally adiabatic maximum by 2.0 kcal mol-‘. This reduction is similar to the amount the barrier needed to be changed for other exothermic hydrogen abstraction reactions calculated at similar levels of theory (e.g., H+HCN [ 251) in order to show agree- ment with experiment. This reduction gives an activation barrier of 0.0 kcal mol-’ in this case. Fur-

thermore, the electronic partition function for the transition state was assumed to be 2.0, while that for the reactants was determined by summing over the spin-orbit components of OH [ 261.

Similar transition state theory calculations were performed for the high-pressure limit of the rate of the addition reaction. Here, the OH-hindered rotation was again modeled by a free internal rotor with a reduced moment of inertia corresponding to OH rotating against NO. The structural parameters and the frequencies of all the other (harmonic oscillator) modes are those in the column labeled RP in table 3. Like the abstraction reaction, the calculated barrier for addition was also lowered by 2.0 kcal mol- * to give a barrier of 3.6 kcal mol-I.

Arrhenius curves for the abstraction and addition reactions are shown in fig. 5. The abstraction reaction is at least an order of magnitude faster than the addition reaction over the entire temperature range of the figure. The calculated abstraction rate constant agrees well with the determination of Halstead and Jenkins [ IO] at 2000 K and it is considerably lower than the determination of Bulewicz and Sugden [ 9 1. In contrast to the early results of Bulewicz and Sug- den [ 91, the calculated rate constant shows a sub-

OH + HNO - HN(O)OH

Fig. 5. Arrhenius plots of the calculated rate constants for the reaction 0H+HNO-+H20+N0 and for the high-pressure limit of the reaction OH+HNO+HN(O)OH.


stantial temperature dependence between 1600 K and 2000 K. The abstraction reaction has a substantially curved Arrhenius plot, consistent with the low-frequency vibrational modes at the transition state be- coming active at relatively low temperatures. The calculated abstraction rate is well fitted over the entire temperature range by the following three-parameter expression: *

QT)=~.J~ox 1()-‘7y-~.884e0.9580/(0.001997-) ,

while the calculated high-pressure limit of the addition rate constant is well fitted over the entire temperature range by the following three-parameter expression:

10. Summary and conclusions

The calculated MRCI vibrationally adiabatic barriers for the hydrogen abstraction reaction, OH + HNO+ H20 + NO, and for the radical addition reaction, OH+HNO+HN(O)OH, are 2.0 and 5.6 kcal mol- ‘, respectively. Our best estimates of these quantities based on the calculated values and on ex- perience with other barriers calculated at similar levels of theory are 0.0 and 3.6 kcal mol- ‘, respectively. An increase in zero-point energy arising from an increase in the 0. ..H-N symmetric stretch frequency along the MEP moves the vibrationally adiabatic maximum for abstraction closer to the reactants. The addition product, HN(O)OH, is not expected to decompose appreciably to HONO because the barrier to H elimination is greater than the barrier back to the reactants OH + HNO. Transition state theory calculations of the rate of the abstraction reaction and of the high-pressure limiting rate of the addition reaction suggest that the radical addition does not com- pete well with the hydrogen abstraction reaction at any temperature. The calculated abstraction rate agrees well with the more recent of the two experimental determinations at 2000 K.

Acknowledgements

This work was supported by the US Office of Na-

val Research both through the Mechanics Division and through the Naval Research Laboratory. MLM thanks the donors of the Petroleum Research Fund, administered by the American Chemical Society, for financial support and also acknowledges the award of a Navy-ASEE Summer Faculty Research Grant. Cal- culations were performed on the Cray XMP/24 at the NRL facilities and on the Cray XMP/24 at Hunts- ville, AL operated by the Alabama Supercomputer Network.

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Theoretical study of the reaction of OH with HNO

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