- The random walk method of solving the Schrodinger equation with importance sampling has been used to obtain highly accurate total energies for the ground electronic states of the methane molecule, fluorine atom, hydrogen fluoride molecule and several FHH geometries which are close to the saddle point for the F + H$\sb2\to$ FH + H reaction.
Single- and double-zeta SCF trial functions were used to calculate fixed-node energies lower than all previous variational energies for methane in its equilibrium geometry. The DZ function was more efficient in the calculations and had a lesser fixed-node error. The calculated energy was only 5 kcal/mol above the experimental estimate for the nonrelativistic total energy with a statistical precision of $\pm1.4$ kcal/mol.
Slow improvement in expectation values with increasing complexity of positive definite correlation functions was found in Monte Carlo variational calculations on the hydrogen fluoride molecule. The most efficient random walk trial function found consisted of an extended s,p-basis SCF determinant multiplied by simple radial nuclear and electronic functions of the Pade-Jastrow type. In random walk calculations the molecular orbitals were evaluated rapidly by means of a small number of radial spline functions. Such a function halved the fixed-node error from that of a DZ trial function in calculations on the fluorine atom.
Results of random walk calculations on the linear FHH system predicted exothermicity of 29.1 $\pm$ 1.5 kcal/mol, roughly in agreement with experiment, and a classical barrier height of 3.4 $\pm$ 0.9 kcal/mol for the F + H$\sb2\to$ FH + H reaction. This result and the saddle-point geometry are qualitatively similar to the latest variational results but differ from the trend in convergence suggested by recent extrapolated analytical results. An estimate of the bending potential at 75$\sp\circ$ near the saddle point of 1.1 $\pm$ 1.3 kcal/mol was made from a single calculation at this geometry. This result agrees with other recent ab initio calculations which suggest a flat bending potential out to very large angles.
Computation costs were competitive with large-scale variational calculations and much smaller, completely vectorized codes were used. The results require less interpretation and extrapolation.
- Dissertation Note:
- Ph.D. The Pennsylvania State University 1987.
- Source: Dissertation Abstracts International, Volume: 48-10, Section: B, page: 2985.
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