Quantum chemistry by random walk: Linear H3

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Abstract
The random walk method for calculating wave functions and energies of molecular systems is investigated in its application to the H3 system in a symmetric linear configuration (R=1.757 a.u.) matching the expected saddle point for the reaction H+H2→H2+H. Four different types of trial wave functions were examined for the importance sampling method used. A product type of wave function explicitly incorporating interelectron distances and having a simple node structure was found optimum. The calculated total energy is −1.6582±0.0003 a.u. which corresponds to a reaction barrier height of 10.2±0.2 kcal/mol. This energy is slightly lower than the upper bound of 10.28 kcal/mol previously established in variational calculations by Liu and 0.5 kcal/mol above Liu’s estimate of 9.68 kcal/mol as the exact value. The value 10.2 kcal/mol lies at the upper extreme of the range of barrier heights compatible with reaction rates measured experimentally. For the linear asymmetric configuration with R=1.41, 4.33 a.u. the calculated energy is 0.6±0.4 kcal/mol below Liu’s value. Further optimization of node structure for the random walk calculations may (or may not) result in lower values.