Conservation of Bond Order during Radical Substitution Reactions: Implications for the BEBO Model Paul Blowers and Richard I. Masel* Department of Chemical Engineering, UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3792 ReceiVed: July 8, 1998; In Final Form: September 2, 1998 The bond energy-bond order model has been used extensively to predict behaviors and energetics of species where ab initio calculations are still too expensive. However, the accuracy of bond order conservation, even for small polyatomic systems, is still unknown. In this paper, we use ab initio calculations at the PMP2 ) (full)/6-31 g* and G-2 level to examine bond order conservation for the following gas-phase radical substitution reactions: H* + CH 3 OH f CH 3 H* + OH, H* + CH 3 OH f HOH* + CH 3 , H* + CH 3 OH f HH* + CH 2 OH, H* + CH 3 OH f HH* + CH 3 O, H* + CH 3 OH f H + CH 2 H*OH, H* + CH 3 OH f H + CH 3 - OH*. We find that total bond order is approximately conserved during atom transfer reactions, but is not conserved during the more complicated hydrogenolysis reactions or during hydrogen exchange on oxygen. An early transition state is predicted for hydrogen exchange on oxygen, and late ones for the hydrogenolysis reactions. Even though the transition state structures may differ greatly from the ab initio predictions, the barrier heights predicted with bond order conservation are only incorrect by 1-2 kcal/mol. This behavior arises because the potential energy surfaces are relatively flat in the region where the transition states are found. Consequently, the energies of the transition state predicted with either method are in close agreement, even though the structures are poorly represented by bond order conservation methods. Introduction The bond energy-bond order (BEBO) method introduced by Johnston and Parr 1-3 has been used extensively to predict chemical phenomena since it was first introduced in 1967. The BEBO model is essentially an empirical method that yields energies of species as a function of bond strengths and bond lengths via the bond order as defined by Pauling. 4 Initially, the BEBO model was used to describe the reactive behavior of small sized systems and to predict the energies of species. 5-9 This type of use also led to the development of qualitatively correct potential energy surfaces for simple reac- tions. 10,11 As ab initio calculations were developed, it became possible to model these simple systems more exactly with quantum mechanics. However, larger systems are still too calculationally expensive for ab initio calculations to handle, and the BEBO model is used instead. 12-15 One key assumption of the BEBO model is that the total bond order of the system remains constant throughout a reaction. This same assumption is also a key underpinning of the UBI-QEP and BOC-MP methods proposed by Shustorovich and Sellers 16-20 to describe surface phenomena. These surface problems are still mostly too expensive to examine fully with quantum mechanics, and assumptions, like bond order conservation, are often made to evaluate energetic behavior. As ab initio calculations have become cheaper through code and computer architecture improvements, the validity of bond order conservation has been investigated. So far, gas-phase three-center linear reactions, 21-23 gas-phase isomerizations, 24-27 small group transfer reactions in the gas phase, 28-30 and pericyclic reactions 31 have been studied. Also, its validity has been verified for diatomic dissociation on some metal surfaces. 20 Most of the reactions examined so far involve highly symmetric behavior during the reaction, where the forming and breaking bonds are essentially equivalent, which may lead to better bond order conservation. The forming and breaking bond order curves have been used to predict the location of the transition state. The transition state has previously been located at the inflection point of the forming and breaking bond order curves 25-27 for three-center isomerization reactions. On the other hand, the transition state has also been found to lie at the minimum of the total bond order curve for polyatomic atom reactions. 28 If it is possible to use bond order curves to predict the structures of transition states, computational effort could be reduced. In this paper, the gas-phase reaction of radical hydrogen with methanol was used to examine the validity of bond order conservation during symmetric and asymmetric reactions. The six reactions studied were: * Author to whom correspondence should be addressed. H* + CH 3 OH f CH 3 H* + OH (1) H* + CH 3 OH f HOH* + CH 3 (2) H* + CH 3 OH f HH* + CH 2 OH (3) H* + CH 3 OH f HH* + CH 3 O (4) H* + CH 3 OH f H + CH 2 H*OH (5) 9957 J. Phys. Chem. A 1998, 102, 9957-9964 10.1021/jp9829243 CCC: $15.00 © 1998 American Chemical Society Published on Web 10/29/1998