Ab initio potential energy surface for the reactions between H2O and H

ion saddle 6-311G(d ,p) 6-3111G(3d f ,2p) 97.2 90.1 6-3111G(2d f ,2pd) 94.7 88.8 6-31111G(2d f ,2pd) 94.5 88.6 6-31111G(3d f ,2pd) 95.3 89.0 6-31111G(3d f ,3pd) 95.3 88.8 aug-cc-pVTZ 92.7 85.8 aug-cc-pV5Z ̄ 89.5 OH1H2 6-311G(d ,p) 6-3111G(3d f ,2p) 67.5 63.0 6-3111G(2d f ,2pd) 68.4 65.0 6-31111G(2d f ,2pd) 68.3 64.9 6-31111G(3d f ,2pd) 68.9 65.2 6-31111G(3d f ,3pd) 69.0 65.5 aug-cc-pVTZ 66.6 63.0 aug-cc-pV5Z ̄ 66.7 Structures were obtained by constraining the structure planer and performing a full optimization at the CCSD~T!/6-31111G(d ,p) level. Energies relative to H2O1H, using Eq. ~2.3!. Energies relative to H2O1H, using single-point energies at the QCISD~T!/ large basis level. Energies relative to H2O1H, using UCCSD~T!/@aug-cc-pV5Z on oxygen, pV5Z on hydrogen#. These energies were evaluated using the MOLPRO suite of programs ~Ref. 28!. FIG. 1. A schematic representation of the structure of the saddle point for the abstraction reaction ~1.1!, evaluated using the additivity approximation of Eq. ~2.3! with the 62311G(d ,p) and 623111G(2d f ,2pd) basis sets. The bond lengths are given in Angstrom and the bond angles are given in degrees. 10164 J. Chem. Phys., Vol. 112, No. 23, 15 June 2000 Bettens et al. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 130.56.106.27 On: Fri, 16 Oct 2015 03:14:26 calculations. The barrier obtained at this level of theory was 89.5 kJ mol, and the energy difference from equilibrium reactants to products was 66.8 kJ mol. It is worth noting that the additive approach saves more than an order of magnitude in CPU time compared to a direct calculation of the PES data points at the QCISD~T!/6-3111G(2d f ,2pd) level. The vibrational energy levels of OH, H2, and H2O have been calculated on this surface, which enabled us to calculate the enthalpy of reaction ~1.1! at 0 K:DH~0K!561.8 kJ mol. This value compares very well with the experimental value of 61.361.2 kJ mol21. Table II compares some of the properties of stationary points on the OH3 surface obtained with this additivity approach to those reported by Alagia et al. and Schatz and Elgersma. It is clear from Table II that our results agree well with the high level calculations of Alagia et al. The PES construction method used herein requires the first and second derivatives of the energy at each data point. From Eq. ~2.1!, it is apparent that we therefore require the first and second derivatives of the MP2/6-311G(d ,p), MP2/6-3111G(2d f ,2pd), and QCISD~T!/6-311G(d ,p) energies at each data point. Analytic first and second derivatives of the MP2 energies were evaluated using the GAUSSIAN94 suite of programs. The corresponding derivatives of the QCISD~T!/6-311G(d ,p) surface were obtained from central differences of 43 single-point energy calculations. It is important to note that accurate derivatives could only be obtained when both the self-consistent field ~SCF! wave function and QCISD iteration were very tightly converged; the electron density in the SCF procedure was converged to 10, and the QCISD energy was converged to 10. D. Domain of the PES We have evaluated the PES throughout much of the configuration space in which the potential energy is no more than about 260 kJ mol above the energy of separated H2O1H. However, we have not evaluated the PES in much of the OH1H2 region of the surface for the following reasons. The electronic ground state of OH is P . Thus, when (Sg )H2 is infinitely separated from OH there exists a spatial double degeneracy. Except for collinear geometries, this degeneracy is lifted as H2 approaches OH. Geometries on the minimum energy path ~MEP! for reaction ~1.1!, for example, possess only Cs symmetry. In this case, the two states which correlate with the asymptotic P state are labeled A8 and A9, depending on whether the unpaired electron lies in a molecular orbital in the plane of OH3 or not, respectively. The A8 state correlates with the ground state of the H2O1H products. Figure 2 shows the energy @as given by Eq. ~2.3!# of the two electronic states originating from the P state of OH, as H2 approaches OH along this MEP until the saddle point has been reached. Figure 3 is an enlargement of this energy profile which clearly indicates that the splitting of these two states does not reach 1.5 kJ mol until the H2 is quite close to the OH ~when the forming O–H bond is about 2.6 Å TABLE II. Properties of the OH3 potential energy surfaces of Schatz and Elgersma ~Ref. 10!, Alagia et al. ~Ref. 11!, and this work. Property SE fit CMRCI1Q This work Experimental