Extensions of the Marcus equation for the prediction of approximate transition state geometries in hydrogen transfer and methyl transfer reactions

The objective of this work is to propose a way to calculate approximate transition state geometries that can then be used as initial guesses in ab initio calculations. Transition state geometries are calculated for 26 hydrogen transfer reactions and 6 methyl transfer reactions at the MP2/6-31G* and MP2/6-311 + + G(d,p) levels. Selected cases are also done at other levels including CCSD(T)/6-311 + + G(d,p). The transition state geometry obeys an equation which arises from an extension of the Marcus equation proposed by Blowers and Masel [8]. r(B)(t) +r(F)(t)/r(B,equ) + r(F,equ) = 1.25 +/- 0.04 In this equation, r(B,equ) is the equilibrium bond length for the bond that breaks during the reaction, r(F,equ) is the equilibrium bond length for the new bond which forms. r(B)(t) and r(F)(t) are the bond lengths at the saddle point in the potential energy surface, r(B)(t) and r(F)(t) are found to obey (r(B)(t) - r(B,equ)/r(B)(t) + r(F)(t) - r(B,equ) - r(F,equ)) = (r(B,equ)/r(B,equ) + r(F,equ) + (C-A)(0.5)DeltaU(r)/8E(A)(0)) r(F)(t) -r(F,equ)/r(B)(t) + r(F)(t) - r(B,equ) - r(F,equ)) = (r(F,equ)/r(B,equ) + r(F,equ) - (C-A)(0.5)DeltaU(r)/8E(A)(0)) with an average error of 0.04 Angstrom. In the last two equations above, DeltaU is the heat of reaction, E-A(0) is the intrinsic barrier, and C-A is a constant that comes from the model of Blowers and Masel [8]. It is proposed that the above three equations are useful in generating initial guesses for transition state geometries in ab initio calculations. In the cases that were tried, rapid convergence was found when these guesses were used.