  Many algorithms for finding reaction pathways require an initial estimate of
the minimum energy path (MEP). Most estimation methods use a variational
approach and thus must be seeded from an even simpler path, such as one
generated by Cartesian interpolation. Often, care must be taken to avoid atomic
intersections in this seed path, and the estimator itself may potentially
converge to multiple undesirable local minima. As an alternative we form an
initial estimate by numerically integrating a velocity vector field that is
projected from redundant internal coordinates into the Cartesian manifold. We
compare this method to the image dependent pair potential, the geodesic method,
and linear Cartesian interpolation using three test cases: the rotation of a
methyl group in ethane, HCN$\to$HNC tautomerization, and HONO elimination from
dimethylnitramine. In the first test case, a zero-temperature string
calculation seeded with our method converges to the MEP in significantly fewer
geometry and SCF cycles than any of the others, while in the second, only the
geodesic method slightly outperformed ours. In the third test case, we used the
midpoint of each path as an initial guess for a transition state calculation.
Our midpoint was geometrically the closest to the true transition state and
converged in the fewest geometry and SCF cycles.
