Quantum Monte Carlo study of the classical barrier height for the H + H2 exchange reaction: Restricted versus unrestricted trial functions

The fixed-node quantum Monte Carlo (QMC) method is used to obtain the classical barrier height for the H + H2 exchange reaction. Using a spin-restricted, single-determinant trial function ΨT, the authors find that the reaction barrier Eb is less than 9.69 ± 0.25 kcal/mol. This mean value is below the calculated energy barrier obtained by Liu in the most extensive CI calculations on this system. Furthermore, the QMC saddle-point energy of – 1.65903 ± 0.00040 hartrees at the CI-determined geometry lies 0.00027 a.u. (0.17 kcal/mol) below Liu's best CI value. Finally, spinrestricted and spin-unrestricted single-determinant trial functions are contrasted. Although the variational energy 〈ΨT|H|ΨT〉 for an SCF ΨT must be lower for the unrestricted case, this is not true generally for QMC. In fact, we show that if the unrestricted SCF ΨT has the lower QMC energy, then there exists another spin-restricted, single-determinant ΨT whose QMC energy is lower than the QMC energy of the spin-restricted SCF ΨT.