8653
J . Phys. Chem. 1991, 95, 8653-8660
Theoretical Studies of the Hydrogen Peroxide Potential Surface. 2. An ab Initio, OH(2n) Potential Long-Range, OH(*n)
+
Lawrence B. Harding Chemistry Division, Argonne National Laboratory. Argonne, Illinois 60439 (Received: April 23, 1991)
Ab initio, multireference, CI calculations have been used to characterize the long-range interaction potentials between two OH radicals. The calculations predict that the four singlet surfaces correlating with ground-state OH radicals interact very strongly, resulting in a complex addition reaction path. At very long range (0-0 separations of more than 8 A) the character of the surfaces is dominated by the electrostatic, dipole-dipole interaction, and consequently, the four surfaces are nearly degenerate. At intermediate distances (0-0separations of 3-6 A) hydrogen bonding is found to be the dominant attractive force. In this region the four singlet surfaces split into two pairs, with one pair being significantly more attractive than the other. At shorter distances (0-0separations less than 2.5 A), covalent bonding becomes important. In this region there is only one attractive singlet surface. Sharp, avoided crossings occur at 0-0 separations between 2.5 and 3 A where the lowest energy wave function switches from hydrogen bonding in character to covalent bonding. In this region, the orientation of the minimum-energy path also changes rapidly from a hydrogen-bonding orientation (OOH angle of 0') to a covalent bonding orientation (OOH angle of 90').
I. Introduction Hydrogen peroxide has become an important testing ground for theoretical studies of unimolecular reactions. The combination of its small size and an increasingly large array of detailed experimental studies on the unimolecular dissociation of hydrogen peroxide make it an ideal candidate for theoretical studies. To date, however, theoretical studies of hydrogen peroxide dynamics have been hampered by the lack of an accurate potential surface. This is the second in a series of papers reporting the results of accurate ab initio calculations on the ground-state potential surface of hydrogen peroxide. In the first paper,' an accurate, anharmonic potential describing the vicinity of the hydrogen peroxide minimum was reported. The present paper focuses on the long-range interaction between two ground-state O H radicals. The ultimate goal of these studies is the development of an accurate ground-state global potential surface. Several years ago Benson2 speculated on the nature of the long-range interaction potential between two OH radicals. Benson2 noted that three distinct forces must play a role in this interaction: (i) electrostatic forces (dipole-dipole): at long range favor a linear, head-to-tail orientation, as shown in 1 H-0- - -H-0 1
(ii) hydrogen-bonding forces: favor an orientation with one hydrogen bent off-axis as shown in 2 H
I
0---H -0 I
(iii) covalent bonding forces: favor having both 0-H bonds roughly perpendicular to the 0-0bond, as shown in 3 H
I
0--0
I
H
3
Benson2 speculated that the longer range electrostatic and hydrogen-bonding forces may influence the course of the reaction. In the following discussion, planar structures such as 1-3 will be denoted by listing the two HOO bond angles. Using this notation then, we will refer to structure 1 as (Oo,18O0) and structure 2 as (9Oo,O0). In order to distinguish between cis and (1) Harding, L. B. J . Phys. Chem. 1989, 93, 8004. (2) Benson, S. W.Arc. Chem. Res. 1986, 19, 335.
0022-365419 1 12095-8653$02.50/0
trans structures, a sign will be associated with each of the angles. A positive sign implies the 0-H bond is displaced in a counterclockwise direction from the 0-0bond, while a negative sign will signify a clockwise displacement. Structure 3 then is referred to as (9Oo,9O0), while the corresponding cis structure, 4, will be H
H
I
I
0--0 4
denoted (+9Oo,-9O0). Note that the order of the angles is not important because interchanging the two angles leads to an equivalent structure. Also, changing the sign of both angles leads to an equivalent structure, so only the relative sign is significant. Consider now the interaction of two OH radicals in somewhat more detail. Two OH(211) radicals combine to give four singlet states and four triplet states. The orbital occupations of these states are depicted schematically in Figure 1. If the radicals are brought together on a triplet surface, the lowest energy reactive pathway is disproportionation which leads to H,O and O(3P) with a barrier of 1 kcal/mol. As noted by Benson? the hydrogenbonding forces will tend to align the approaching OH radicals in a configuration suitable for disproportionation. A theoretical study of this reaction has been reported by Harding and Wagner.3 If the radicals are brought together on a singlet surface, disproportionation is much less favorable because it leads to the products H,O and O('D), which are 26 kcal/mol endothermic relative to the reactants. Instead, addition forming hydrogen peroxide becomes the most favorable reactive channel. We now look in more detail a t the electronic wave functions associated with configurations 1-3 and the effects the above forces will have on the course of the addition reaction. Consider the wave functions associated with the hydrogenbonded configuration, 2. In order to form a hydrogen bond the donated hydrogen must line up with a doubly occupied, lone-pair orbital on the accepting oxygen. There are clearly two such states, a 7r3 state and a r 2state, shown in Figure 2. If we now consider the orbital occupancy required for planar addition (Figure l), it is immediately apparent that, to form ground-state hydrogen peroxide, a r4 state is required. So, neither of the two hydrogen-bonded states will correlate directly with the ground electronic state of hydrogen peroxide. Taking these electronic structure considerations into account, a minimum-energy path for the planar approach of two OH(211) radicals can be described as follows. At long range, the path is
-
(3) Harding, L. B.; Wagner, A. F. In Proceedings ojrhe 22ndSymposium (Internotional)on Combustion;The Combustion Institute: Pittsburgh, PA, 1988; p 983.
0 1991 American Chemical Society
8654 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
Harding
A’ Wavefunctions
.g.$ -B”: A” Wavefunctions
2.5
Figure 1. Schematic diagrams of the orbital occupations of the four
singlet (and four triplet) states correlating with two OH(211) radicals. Only the three 2p orbitals of the oxygens are shown. The two oxygen p~ orbitals are each depicted with a circle centered on the oxygen. A Wavefunctions
A” Wavefunctions
Figure 2. Schematic diagrams of the orbital occupations of the two hydrogen-bonded configurations.
expected to be linear, (Oo,18O0). In this region the four singlet surfaces should all be nearly degenerate. At intermediate distances, on the two lowest surfaces, l(’A’) and l(IA”), one hydrogen should bend significantly off-axis, as in 2. In this region, these two lower surfaces should be nearly degenerate while the 2(’A’) and 2(IA”) surfaces will lie at significantly higher energies. In this region the 1 (!A’) wave function will be dominantly n2 in character (as shown in Figure 2). Finally at shorter distances, the character of the 1 (IA’) wave function will change to 7r4, and the preferred orientation will change to (90°,900) as shown in 3. In this region only the 1 (IA’) will be attractively; the other three surfaces will quickly become repulsive. The above discussion is a qualitative description of the longrange interaction of two OH radicals. In this paper we use large-scale, ab initio calculations to quantify this interaction potential. We focus only on the four singlet potential surfaces. In section I1 the details of the calculational methods used are presented, and in section 111 the results are discussed. 11. Calculational Results
Ab initio calculations on the addition of two ground-state OH radicals are complicated by the presence of four nearly degenerate singlet states in the long-range region of the potential. For reasons to be described below, these four states are strongly interacting. This necessitates the use of a technique capable of treating all four states on an equal footing. In this section the method used
2.75
3
3.25
5
Roo (4 Figure 3. Addition potential curves for the lowest singlet state and comparison of methods and basis sets. The orientation is planar, trans, (9Oo,9O0), with both 0-H bond lengths fixed at 0.98 A. The curves are as follows: solid, multireference CI using averaged orbitals with [3s2pld/2slp] basis set; dash, GVB(I/PP) with [3s2pld/2slp] basis set; dot, multireference CI using GVB( 1/PP) orbitals with [3s2pld/2slp] basis set; dash-dot, multireference C1 using averaged orbitals with [4s3p2d/3s2p] basis set.
is first described, and then the results of the ab initio calculations are presented. The electronic structure calculations employ Dunning’s4valence double-[ basis set of contracted Gaussian functions with d polarization functions (a= 0.85) on each oxygen and p polarization functions (a = 1.O) on each hydrogen. With this basis set, orbitals are optimized a t each geometry by using a state-averaged Hamiltonian. The coefficients of this Hamiltonian are determined by averaging the open-shell, triplet, restricted Hartree-Fock Hamiltonians for each of the four states depicted in Figure 1. These orbitals are then used in a multireference, single and doubles, configuration interaction (CI) calculation to determine the energies of the individual singlet states. The reference space of the CI calculations consists of 10 configurations, corresponding to all possible occupations of six electrons, among the four oxygen p orbitals (see Figure 1). For planar geometries, single and double excitations from these reference configurations lead to 100 374 configuration state functions of A‘ symmetry and 100 548 of A“ symmetry. All calculations were carried out using the Argonne QUEST programs’ on an FPS/164 attached processor. The key assumption in these calculations is that the state-averaged orbitals are sufficiently close to optimum for all four states that the multireference CI based on these orbitals will yield accurate energies for each of the individual states. In order to test this assumption, averaged state calculations were carried out on the long-range portion of the H + OH potential surface. These calculations were then compared to calculations on the 1A’ and 1A” surfaces obtained from separate CI calculations using MCSCF orbitals optimized for each of these states. It was found that the use of averaged orbitals introduces errors of less than 1% in the interaction energy, for interaction energies of up to 2 kcal/mol and errors of less than 2% for interaction energies up to 50 kcal/mol. It is expected that errors in the OH + O H potential surface should be comparable. As a further test of the averaged orbital, C I method, conventional GVB+1+2 calculations were carried out for the ‘Ag state as a function of Roo for a fixed, planar orientation (trans, with both HOO bond angles equal to goo). A comparison of the addition potential curves obtained in the GVB and GVB+I+2 (4) Dunning, T. H., Jr.; Hay, P. J. In Methods in Electronic Structure Theory; Schaefer, H. F., 111.. Ed.; Plenum: New York, 1971. ( 5 ) Shepard, R.; Bair, R. A.; Eades, R. A.; Wagner, A. F.; Davis, M.J.; Harding, L. B.;Dunning, T. H., Jr. Int. J. Quontum Chem. 1983, 17, 613. ( 6 ) Meerts, W.L.;Dymanus, A. Chem. Phys. Lett. 1973, 23, 45.
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8655
Hydrogen Peroxide Potential Surface calculations with those from the averaged orbital CI calculations is given in Figure 3. The calculations show a maximum error of 0.1 3 kcal/mol introduced by the use of averaged orbitals in the region of interest here (Roo > 2.5 A). Note that the GVB potential curve is significantly higher than either the GVB+1+2 or the averaged orbital CI curves due to the neglect of interpair correlations. Another important source of error in the present calculations is in the choice of a relative small, polarized, double-{ basis set. This choice was necessitated by the need to explore a large portion of the potential surface. As a test of the magnitude of the errors introduced by this basis set, the calculations were repeated, again as a function of Roo for a fixed orientation, with a larger (4s,3p,2d/3s,2p) basis set. The resulting potential curve is also shown in Figure 3, along with the smaller basis set results. The maximum difference in interaction energies occurs at the smallest R? distance (2.5 A) where the calculated small and large basis set interaction energies are -4.9 and -4.5 kcal/mol, respectively, a difference of 0.4 kcal/mol. The longest range interaction between two OH radicals is the electrostatic dipole-dipole force. As a test of the accuracy of the present calculations in reproducing this interaction, the angular dependence of the interaction energy was calculated at 0-0 separations of 40 and 50 A, and the result compared to that expected for the dipoldipole interaction alone. For both distances the effective dipole moment determined, from the a b initio interaction energy, was found to be approximately 10% larger than the experimental dipole moment of OH, 1.67 D, indicating the polarity of the 0-H bonds in the present calculations are slightly overestimated. At large 0-0distances, the use of averaged orbitals and a small basis set is necessary for the reasons outlined above. At shorter 0-0 distances (
