J. Phys. Chem. 1992, 96, 21 15-21 18
An ab Initio CASSCF Study of the HO
2115
+ NOCl Reaction
Antonio Mirquez, Julio Anguiano, and Javier Fernindez Sanz* Department of Physical Chemistry, Faculty of Chemistry, University of Sevilla, E-41 01 2, Sevilla, Spain (Received: August 9, 1991; In Final Form: October 22, 1991)
A theoretical open-shell study of the chlorine abstraction process occurring in the reaction between hydroxyl radical and nitrosyl chloride has been carried out. Fully optimized geometries were obtained from complete active space multiconfigurational self-consistent-field (CASSCF) calculations using the standard 6-3 1G(*) basis set. Three stationary points on the potential energy hypersurface were located. The reaction occurs via formation of a reactive complex previous to a transition state at a slightly lower energy than reactants. The third stationary point was found between the transition state and products. Energetics of reaction and barrier height have been computed from MR-CISD+Q calculations. The process appears to occur in a plane with an activation energy of 3.6 kcal mol-' and a reaction enthalpy of AfZo298 = -15.3 kcal mol-', in agreement with experiment (2.25 and -18.2 kcal mol-I). The kinetic analysis is coherent with a bimolecular homolytic substitution (SH2), and a reaction profile fairly similar to that proposed for the SN2 mechanism is suggested.
Introduction Nitrosyl chloride (NOCI) reactivity is a topic of major interest in atmospheric chemistry because it may be formed in polluted marine areas from the reaction of NOz with sea salt. Although photolysis of NOCl is rapid,' interaction with other highly reactive species, such as radicals, must be considered. However, only a few papers concerning this reaction have been publi~hed.~-~ The first study was reported by Poulet et al.,2 who investigated kinetically the reaction between the radical HO and NOCI. They concluded that the reaction occurs at room temperature and also showed that it takes place via two primary steps:
HO
+ NOCl +
-+
HNOz
HClO
+ NO
(la)
C1
Channel l a is a chlorine abstraction energetically favored (AH -18 kcal m01-I)~whereas channel l b is an exchange process (AH -1 1 kcal In two subsequent papers, Finlayson-Pitts et al. reported temperaturedependent experiments on this r e a c t i ~ n ,suggesting ~,~ that process l b is an unusual surface reaction. More recently, Abbatt et al. reported an experimental comparative study of the reactivity of NOCl faced with a series of radical^.^ Their relative reactivities were rationalized in terms of frontier orbital interactions. From a theoretical viewpoint, and with the exception of the topological study of Abbatt, no attempts of computational analysis of the reaction have been published. We report in this paper a quantum mechanical study of the energetically favored process occurring in the reaction HO NOCl (channel la). The geometrical structure and electronic properties of the transition state and other supermolecule species involved in the process have been optimized from ab initio multiconfigurational (CAS) SCF calculations using two different basis sets. For a more reliable description of the energetics of the process, effects due to dynamical electron correlation were introduced by means of second-order CI (SOCI) and multireference CI (MR-CISD+Q) calculations.
=
=
+
Computational Methods Three different levels of theory were used in these calculations: complete active space multiconfigurational SCF (CASSCF),6 (1) Finlayson-Pitts, B. J. Nature (London) 1983, 306, 676.
(2) Poulet, G.; Jourdain, J. L.; Laverdet, G.; Le Bras, G. Chem. Phys. Leu.
1981, 81, 573.
(3) Finlayson-Pitts, B. J.; Ezell, M. J.; Grant, C. E. J . Phys. Chem. 1986, 90. . - ,1-7..
(4) Finlayson-Pitts, B. J.; Ezell, M. J.; Wang, S. Z.; Grant, C. E. J . Phys. Chem. 1987, 91, 2377. (5) Abbatt, J. P. D.; Toohey, D. W.; Fenter, F. F.; Stevens, P. S.;Brune, Wm. H.; Anderson, J. G. J . Phys. Chem. 1989, 93, 1022.
0022-365419212096-211 S$03.00/0
second-order configuration interaction (SOCI), and multireference single and double CI (MR-CISD+Q). CASSCF and SOCI calculations were carried out using a vectorized version of the HONDO-7 package' we implemented on a Convex C-210 computer. In CASSCF, the active MO's were the HO u orbital bearing the lone electron and the u and u* orbitals corresponding to the Cl-N bond. However, it is known that the a* bond of NOCl is rather low lying, and so in order to get the states and energies of NOCl correct, the a and a* orbitals were also included. At HO-NOCI intermolecular distances close to the transition state, this 5MO/S-electron active space was roughly the same as that arising from analysis of the UHF natural orbital (UHFNOs)occupations as suggested by Pulay.* The number of configurations arising from this active space was 39 in C, symmetry and 75 without symmetry. In these calculations, two basis sets were used. First, a rough examination of the potential hypersurface was performed using the standard 3-21G basis sets9 The absence of d orbitals on the chlorine atom was justified by a faster convergence in the SCF procedure. Then, the stationary points found were refined using the 6-31G(*) basis set.I0 Only results obtained with the extended basis set are reported in this work. Singlepoint SOCI calculations on the optimized structures were performed by diagonalizing all configurations obtained by allowing single and double excitations of the CASSCF space in the virtual MO's set (15 174 configurations). MR-CISD+Q calculations were carried out using the system of programs written by Buenker et al." and coupled to the HONDO package. A multiconfigurational zeroth-order wave function was built by taking all configurations with a coefficient in the CASSCF wave function larger than 0.001. Configurations arising from single and double excitations of this multireference function were then selected through the Raylegh-Schroedinger perturbation theory. Those configurations with a contribution larger than a threshold of 2 X 1 W were then diagonalized (15000 maximum). The convergence limit of the perturbational series was estimated by extrapolation (MR-CISD). The full CI correction, MRCISD+Q level, was obtained as proposed by Langhoff and Davidson.I2 In these calculations, the core electrons of heavy (6) Roos, B. 0.;Taylor, P. R.; Siegbahn, P. E. M. Chem. Phys. 1980, 48, 152. (7) Dupuis, M.; Wats, J. D.; Villar, H. 0.;Hurst, G.J. B. HONDO-7: IBM Technical Report KGN-169, Kingston, NY, 1988. (8) Pulay, P.; Hamilton, T. P. J . Chem. Phys. 1988, 88, 4926. (9) Binkley, J. S.;Pople, J. A.; Hehre, W. J. J . Am. Chem. Soc. 1980, 102, 939. Gordon, M. S.;Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. J . Am. Chem. SOC.1982, 104, 2797. (IO) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acfa 1973, 28, 213. Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. ( I 1) Buenker, R. J.; Peyerimhoff, S. Chem. Phys. 1975,8, 56. Buenker, R. J.; Peyerimhoff, S. Theor. Chim. Acta 1975, 39, 217.
0 1992 American Chemical Society
2116 The Journal of Physical Chemistry, Vol. 96, No. 5, 1992
Mirquez et al. TABLE I: Optimized Geometries (8, and deg), Bond Indices, and Total Bonds for Reactive Complex (RC), Transition State (TS), and Product Complex (PC) from CASSCF Calculations
RC
TS
PC
2.0090 1.1809 111.7 3.3454 179.4 0.9659 176.7
2.3492 1.1667 112.7 2.3806 170.9 0.9660 97.6
3.3770 1.1699 165.8 1.8016 179.3 0.9605 104.1
0.640 1.486 0.792 0.006
0.245 1.535 0.788 0.141
0.006 1.531 0.769 0.744
0.728 2.126 1.568 0.798 0.793
0.423 1.783 1.576 0.931 0.788
0.750 1.537 1.533 1.514 0.767
geometry rCI-N
TN-0
LC1-N-0
TG-CI
LO-CI-N TH-0
0 C l d
H
b NO,
H-0
0 0Q
6
CI
0
6N-06 00
LH-0-CI bond indices CI-N N-0 H-0 0-CI total bond“
c1 N
0 0 (hydroxyl)
H
“Sum of bond indices over all pairs. RC
f‘
TS
’n. A’ Prod.
1.167
0.966
Correlation diagram for the chlorine abstraction by HO radical following a path in which the XY plane remains a plane of symmetry.
Figure 1.
atoms were frozen (chlorine Is, 2s, and 2p, oxygen Is, and nitrogen 1s).
Results and Discussion A simple model of the chlorine abstraction step is depicted in Figure 1. In this model the H O radical approaches NOCl interacting with its u electronic system, Le., on the opposite side of the CI-N bond. The nature of the reaction in terms of its symmetry properties will be considered first. When both reactants and products are infinitely separated, the overall reaction can be written HO(*II)
+ NOCl(’A’)
-
HCIO(’A’)
+ N0(211)
It seems reasonable to assume this allowed process occurs along a path in which a plane of symmetry remains during the entire reaction. Considering the molecular plane of NOCl as the symmetry plane, at interacting distances, the 211states of the HO radical arising from the open-shell electronic configuration x3split into 2A’ and 2A” states. Since the 211 system of the NO radical ( T I configuration) splits in the same way, two potential energy hypersurfaces could be expected, each one interconnecting the 2A’ or 2A” components of the two 211systems. In Figure 1, the most significant electronic contributions to the main configuration for both 2A’ and 2A“ cases are depicted. As can be seen in Figure la, the A’ component of reactants correlates smoothly with the A’ of products. Interchanging one electron between the a’ and a” orbitals of HO radical leads to the A” component, H0(211,2A’’) + NOCI(’A’) (Figure lb). Seen from the viewpoint of products, (12) Langhoff, S.R.; Davidson. E. R. In?.J . Quantum Chem. 1974, 8,61.
1.804
-
__
3.377
PC 0.960
1.170
Q
Structures of the reactive complex (RC), transition state (TS), and product complex (PC) on the 5-in-5 CASSCF/6-31G(*) potential energy surface for the chlorine abstraction by HO radical in the HO + NOCl reaction. Figure 2.
this electronic arrangement corresponds to a configuration in which one electron has been promoted from an oxygen lone pair toward the u*cIo orbital: HCIO(no NO(211,2A’). The 2A” ground configuration of products could be built by passing electron NO(211,2A”) (Figure IC). a’ to the a” orbital: HClO(’A’) However, when this configuration is seen from the point of view of reactants, it corresponds to an excited state of NOCl: no A*CINO. The correlation diagram of Figure Id summarizes this analysis. The A’ component of the A system correlates directly, going from reactants to products. In turn, those of A” correlate with an excited configuration of their respective partner. From these considerations, it appears clear that the A’’ hypersurface will be more energetic than that of A’, and only the latter will be examined in this work. Three stationary points were found at the CASSCF level. Their fully optimized geometrical parameters are reported in Table I and their structures in Figure 2. The first stationary point is a
-
+
+
-
CASSCF Study of the HO
+ NOCl Reaction
TABLE II: Vibrational Frequencies (cm-') and Main Components of Normal Coordinates for the Transition-StateStructure freq normal coordinate 3811 str rsH 1770 str r,, 624 356 179
150 85
68 4821
bend LH-O-CI bend LCI-N-0 tor LO-CI-N-O tor LH-0-C1-N str k 1 - N str r,, bend LO-CI-N tor LH-O-CI-N str r,, - str fC1-N
+
+
van der Waals complex (RC) formed by the radical HO and NOCl with a large Dc1 bond length, 3.34 A. Both bond lengths and bond angles are close to those of separated reactants. The hydrogen atom is almost collinear with the C1-N bond, indicating a Q attack of the radical on the C1-N bond. Further evolution of this complex toward structures with a shorter oxygen (HO)-chlorine interatomic distance allowed us to find a second stationary point in which both the C1-N and N-O bonds were considerably perturbed. Thus, the Cl-N bond increases from 2.009 to 2.349 A while the N-O distance decreases from 1.181 to 1.166 A. The oxygen (HO)-chlorine interatomic distance appears to be considerably shortened (2.380 instead of 3.345 A). The vibrational analysis showed this structure to have one imaginary frequency (Table 11). The associated normal coordinate to this frequency is a mix of r w l and rCl-, internal coordinates with opposing signs (Table 11). Thus,this result allows us to characterize properly this structure as a transition state (TS). A third stationary point is reported in Figure 2. Analysis of geometrical parameters shows this structure to be essentially a van der Waals complex (PC) built up from the two products HClO and N O and separated by a distance of 3.337 A. Examination of the bond indices issued from CASSCF wave functions13 of the three stationary points clearly shows what is occurring along the reaction pathway (Table I). On RC, there is a bond order of almost 0.7 between the chlorine and nitrogen atoms. Going toward TS and PC, this bond index decreases dramatically, and the low value found in TS (0.24) suggests that the bond is nearly broken. In turn, going from R C to TS, the N - O bond index increases moderately with no sensitive changes between that of TS and PC. These considerations suggest an early transition state for the reaction. On the other hand, the values found for the 0-C1 bond order a t the various stationary points are surprising. Its value in R C is low, according to a small interaction between the radical H O and NOCl. Passage from R C to TS involves a significant enhancement, but its TS value seems to be somewhat low with respect to the C1-N bond index. Effectively, since the value for the latter result is 0.24, one could expect the former to be about 0.5-0.6, according to a total bond of 1 for chlorine. However, examination of Table I shows a chlorine total bond of 0.42, revealing that in the transition state structure the bonding capabilities of the chlorine atom are considerably lowered. In electronic rearrangement terms, the homolytic break of the Cl-N bond is almost achieved, but a significant C1-O bond has not yet been established. Concerning the energies of stationary points, reactants, and products, we have reported in Table I11 values of the total energy obtained at several calculation levels. At the CASSCF level, the reactive complex RC appears at an energy close to that of reactants and slightly lower (-0.4 kcal mo-I). Similarly, the product complex PC energy is lower than that of products by 1.4 kcal mol-'. The transition state TS lies about 6.9 kcal mol-' higher than reactants while the energetic gap between reactants and products is -12.2 kcal mol-'. In order to incorporate dynamical electron correlation effects, SOCI and MR-CISD+Q single-point calculations a t CASSCF equilibrium geometries were performed. SOCI energies are close to those of CASSCF, revealing that little dynamical (13) Villar, H. 0.; Dupuis, M. Chem. Phys. Lett. 1987, 142, 59 and references therein.
The Journal of Physical Chemistry, Vol. 96, No. 5, 1992 2117
-
TABLE III: Total Energies"and Relative Energiesbwith Respect to Reactants (in Parentheses) for the Reaction HO + NOCl HClO NO (Activation Energy, E,, and Reaction Enthalpy, AHo%, Also CASSCF HO + ClNO RC TS PC HClO NO
-0.042 91 -0.043 59 -0.031 84 -0.06459 -0.06238
Ea
7.6 -11.1
SOCI
+
MR-CISD+Q
~~
+
M0298
(-0.4) (6.9) (-13.6) (-12.2)
-0.055 28 -0.055 90 -0.04449 -0.07639 -0.07423
(-0.4) (6.7) (-13.2) (-11.9)
7.4 -10.8
-0.456 95 -0.457 21 (-0.2) -0.45209 (3.0) -0,48963 (-20.5) -0.483 14 (-16.4) 3.6 -15.3
'In hartrees. Shifted by 664 hartrees. kcal mol-'. 'In the ZPE corrections, the TS frequencies are those of Table I1 scaled by 0.9. For HO, NOCI, HCIO, and NO, experimental frequencies are taken from refs 15-18.
electron correlation is obtained at this level. Relative energies are also quite similar. The multireference scheme introduces substantial modifications. Also, much more electron correlation is gained through lowering of about 0.4 hartree. From MRCISD+Q calculations, the relative energy of TS with respect to reactants decreases to 3.0 kcal mol-', whereas going from reactants to products, the energetic gap is -16.4 kcal mol-'. Taking into account zero-point energy (ZPE) and thermal corrections, the enthalpy of activation at 298.15 K, computed from the MRCISD+Q barrier height, the scaled CASSCF transition-state frequencies, and the experimental frequencies for reactants, is 2.43 kcal mol-'. Similarly, the enthalpy of reaction at 298.15 K is -15.3 kcal mol-'. Using the well-known relation between the activation energy E, and the activation enthalpy for an ideal bimolecular gas-phase reaction'* E, = A f l + 2RT
(2)
the activation energy for the process at 298.15 K is 3.62 kcal mol-'. Both the energy of activation and the enthalpy of reaction are in good agreement with the experimental5values E, = 2.25 and AH0298 = -18.2 kcal mol-'. Finally, kinetics of the reaction will be considered. Since the molecular structure and frequencies of reactants and transition state are known, the conventional transition-state theory ('ET)'"' allows for calculation of the rate constant. Assuming a negligible tunneling at rmm temperature, the constant k( Z+) can be evaluated using the standard TST expression (3) where kB is Boltzmann's constant, T i s the temperature, AHo*is the activation enthalpy at 0 K, and Q*and QR are the total partition functions per unit volume for transition state and reactants. Quantum mechanical vibrational partition functions were evaluated using experimental frequencies for H O and NOCl and those of Table I1 scaled by 0.9 for the transition state. The electronic partition function for the HO radical was evaluated using the experimental split between the 2111,2and 2113 levels (139.7 cm-1).22 Using AHo*obtained from the MR-CfSD+Q (14) See for instance: Atkins, P. W. Physical Chemistry; Oxford Universitv Press: Oxford. 1987: D 750. (is) Cazzoli, G.; 'Degli 'Esponti, C.; Palmieri, P.; Simeone, S. J. Mol. Spectrosc. 1983, 97, 165. (16) Anderson, W. D.; Geny, M. C. L.; Davis, R. W. J. Mol. Specrrosc.
----. ---. (17) Gillette, R. H.; Eyster, E. H. Phys. Reo. 1939, 56, 1113. 1986. 1 1 1 . 117.
(18) Oldenberg, 0. J . Chem. Phys. 1935, 3, 266. (19) McClelland, B. J. Statistical Thermodynamics; Wiley: New York, 1973. (20) Laidler, K. J. Chemical Kinetics, 3rd ed.; Harper and Row: New York, 1987. (21) Kreevoy, M. M.; Truhlar, D. G. In Inuestigarion of Rates and Mechanisms of Reactions; Bernasconi, C. F., Ed.; Wiley: New York, 1986; Part I. (22) Richards, W. G.; Trivedi, H. P.; Cooper, D. L. Spin Orbit Coupling in Molecules; Clarendon: Oxford, 1981.
J . Phys. Chem. 1992, 96, 2118-2122
2118
I' J.
T
I/
-16.4
-20.5
Figure 3. MR-CISD+Q energy profile in kcal mol'l.
barrier height and the frequencies as indicated above, the rate constant at 298.15 K is 2.5 X cm-3 molecule-I s-', thus one-sixth the experimental constant5 2.0 X cm-3 molecule-l s-I. In order to compare the preexponential factor with the experiment, a set of 11 rate constants k( T ) calculated in the 220-420 K temperature range using eq 3 has been fitted to the Arrhenius equation: k(T) = A exp(-E,/RT). From the slope of the plot, the value of the activation energy is 3.64 kcal mol-', in agreement with that deduced using eq 2. In turn, the theoretical preexponential factor A is 1.63 X lo-" cm-3 molecule-' s-I, in quite good agreement with the experiment: 9.0 X cm-3 molecule-' s-l. This result suggests that although the calculated activation energy is somewhat overestimated, the theoretical analysis reported in this work seems to be essentially correct. In other words, the chlorine abstraction by the HO radical in this process appears to be a bimolecular homolytic substitution (SH2) of the type classified by Ingoldz3as synchronous.
Summary and Conclusions We report in this paper a theoretical study of the chlorine abstraction process occurring in the reaction of HO radical with nitrosyl chloride. The reaction is assumed to occur in a plane, and we have argued from symmetry considerations that the A' potential energy hypersurface should be favored. Three stationary points have been located from CASSCF calculations. The first one is a van der Waals complex in which a small interaction between the radical H O and NOCl is observed. The second stationary point has been properly characterized as a transition state, which appears early according to an exothermic reaction. A third stationary point on the potential energy hypersurface has been found in which the products HClO and N O are separated by 3.37 A. A summary of the calculated potential energy profile for the reaction is shown in Figure 3. The reaction enthalpy and activation energy, calculated at the MR-CISD+Q level, including the ZPE and thermal corrections, are -15.3 and 3.6 kcal mol-', in agreement with the experimental values of -18.2 and 2.25 kcal mol-', respectively. The kinetic analysis of the process agrees with a bimolecular homolytic substitution (SH2) type reaction, and its mechanism appears to be fairly similar to that generally accepted for the SN2 nucleophilic ~ u b s t i t u t i o n . ~ Our ~ ~ ~reactive ' and product van der Waals complexes would play the same role as that of ion-dipole adducts. Acknowledgment. This work was supported by the Direccidn General de InvestigaciQ Cientifica y Tknica (PB89-0561). We are grateful to M. Dupuis for a copy of the HONDO-7 code and to F. Diez for his help in implementing HONDO-7 on a C-210 Convex computer. We also thank a referee for useful suggestions on symmetry aspects. Registry No. OH, 3352-57-6; NOCI, 2696-92-6. (23) Ingold, K. U. In Free Radicals; Kochi, J. K., Ed.; Wiley: New York, 1976; Vol. I, p 67. Ingold, K. U.; Roberts, B. P. Free-Radical Substirution Reactions; Wiley: New York, 1971. (24) Larson, J. W.; McMahon, T. B. J . Am. Chem. SOC.1984,106, 517. (25) Tucker, S.C.; Truhlar, D. G. J . Phys. Chem. 1989, 93, 8138 and references therein.
Theoretical Study of the Bonding of the First-Row Transition-Metal Positive Ions to Ethylene M. Sodupe, Charles W. Bauschlicher Jr.,* Stephen R. Langhoff, and Harry Partridge NASA Ames Research Center, Moffett Field, California 94035 (Received: August 19, 1991)
Ab initio calculations have been performed to study the bonding of the first-row transition-metal ions with ethylene. While Sc+ and Ti+ insert into the T bond of ethylene to form a three-membered ring, the ions V+ through Cu+form an electrostatic complex with ethylene. The binding energies are compared with those from experiment and with those of comparable calculations performed previously for the metal-acetylene ion systems.
I. Introduction Activation of hydrocarbons by transition-metal ions is currently an area of active experimental research.'-'* The determination
of bond energies of isolated metal-ligand bonds is important for predicting stable structures and reaction mechanisms. Experi(6) Schultz, R. H.; Elkind, J. L.; Armentrout, P. B. J . Am. Chem. Soc.
(1) Sunderlin, L. S.; Armentrout, P. B. J . Am. Chem. SOC.1989, 1 1 1 , 3845. (2) Sunderlin, L. S.; Aristov, N.; Armentrout, P. B. J . Am. Chem. Soc. 1981, 109, 78. ( 3 ) Sunderlin, L. S.; Armentrout, P. 9. Inr. J . Mass Spectrom. Ion Processes 1989, 94, 149. (4) Aristov, N.; Armentrout, P. B. J . Am. Chem. SOC.1986, 108, 1806. (5) Georgiadis, R.; Armentrout, P. B. Int. J . Mass Spectrom. Ion Processes 1989, 89, 227.
0022-365419212096-2118$03.00/0
1988, 110, 411.
(7) Fisher, E. R.; Armentrout, P. B. J . Phys. Chem. 1990, 94, 1674. (8) Tolbert, M. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1984,106,8117. (9) Armentrout, P. 9.; Beauchamp, J. L. J . Am. Chem. SOC.1981, 103, 6628. (10) Hanratty, M. A.; Beauchamp, J. L.; Illies, A. J.; van Koppen, P.; Bowers, M. T. J . Am. Chem. SOC.1988, 110, 1 . (1 1 ) Jacobson, D. B.; Freiser, B. S . J . Am. Chem. SOC.1983, 105,7492. (12) Burnier, R. C.; Byard, G . D.; Freiser, B. S . Anal. Chem. 1980, 52, 1641.
0 1992 American Chemical Society
