Quantum Monte Carlo study of the classical barrier height for the H + H 2 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 + H 2 exchange reaction. Using a spin‐restricted, single‐determinant trial function Ψ T , the authors find that the reaction barrier E b 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 〈Ψ T | H |Ψ T 〉 for an SCF Ψ T must be lower for the un restricted case, this is not true generally for QMC. In fact, we show that if the unrestricted SCF Ψ T has the lower QMC energy, then there exists another spin‐restricted, single‐determinant Ψ T whose QMC energy is lower than the QMC energy of the spin‐restricted SCF Ψ T .