Free complement method with Gaussian expanded complements: hierarchical decontraction to mitigate the exponential wall before selection

The previous work (arXiv:2508.04635 [physics.chem-ph]) of the free complement (FC) method with Gaussian expanded complement functions adopts the Slater initial wavefunction. This may introduce an exponential complexity of the variational coefficients associated to the Gaussian complement functions with respect to the number of electrons at a given order before the overlap matrix based selection, for more than one Gaussian function used in the expansion. The present work uses decontractions via the distinct exponents introduced by the $g$ functions to avoid this scenario at low order of the FC method. The exponential number of the variational parameters is postponed to higher orders of the FC expansion.