(469a) Bebop, a New Reactive Potential Using Bond-Energy/ Bond-Order Relationships

BEBOP is a reactive potential that has been developed for evaluating bond energies based on computed bond orders without explicit consideration of the geometry of the molecule. The use of molecular dynamics to describe chemical reactivity has been limited to relatively small, well-defined chemical systems due to the geometric basis of the current reactive force fields. In BEBOP, bond orders are quickly evaluated using an approximate electronic structure method. Then, using a relationship between bond energy and bond order, the bond energies can be evaluated taking the electronic structure of the molecule into account. More specifically, bond energies were assumed proportional to bond orders obtained using Mulliken population analysis from generalized valence bond (GVB) wave functions. The addition of an exponential repulsive term reproduced the potential energy curves of several diatomic molecules to within 1 kcal/mol. However, a semiempirical scheme based on GVB ab initio calculations would be impractical. As one alternative, the GVB bond orders have been accurately reproduced by convolution of Hartree-Fock bond orders with a Fermi-Dirac-like distribution mapped onto the interval from R_AB = 0 to R_AB = ∞ as shown in Fig. 1. The resulting bond-order to bond-energy "density functional" relationship is: E_AB ≈ BO(A,B)*B_AB / {1 + exp[b(R_AB / R_F - R_F / R_AB)]}, where B_AB, b, and R_F are empirical parameters adjusted to fit ab initio energies. In BEBOP, this functional is currently applied to bond orders obtained from LSDA (Local Spin Density Approximation) wave functions. Application of this relationship to LSDA bond orders provides a bond-energy/bond-order potential (BEBOP) that is sufficiently accurate to meet our goals. We plan to develop a semiempirical version of LSDA that can be generated rapidly enough to be used for reactive molecular dynamics of large systems. The initial testing of the potential used H atoms. Using an exponential term to allow for nuclear repulsion, BEBOP was successfully used to predict the potential energy surfaces of H₂ in the singlet ground state and the triplet excited state. Testing a simple transition state, the potential energy barrier height for the reaction of H+H₂ was predicted successfully using the LSDA bond orders (Fig. 3). The numerically accurate calculated value for this barrier height is 9.61 kcal/mol[1], and the BEBOP(LSDA) calculated value is 9.63 kcal/mol. By comparison to B3LYP/6-31G** calculations gives a barrier height of 4.24 kcal/mol. Bond bending in the H₃ transition state was also well-described without the use of any explicit geometric information or additional parameters (Fig. 4). 1. Diedrich, DL and Anderson, JB. Science, 258, 786 (1992).