  A benchmark-quality potential energy curve is reported for the H$_3$ system
in collinear nuclear configurations. The electronic Schr\"odinger equation is
solved using explicitly correlated Gaussian (ECG) basis functions using an
optimized fragment initialization technique that significantly reduces the
computational cost. As a result, the computed energies improve upon recent
orbital-based and ECG computations. Starting from a well-converged basis set, a
potential energy curve with an estimated sub-parts-per-billion precision is
generated for a series of nuclear configurations using an efficient ECG
rescaling approach.
