Variational free complement method with Gaussian-expanded complement functions: convergence with fixed Gaussian expansion length

For the free complement theory with Gaussian-expanded complement functions, the energy convergence of $n_{\mathrm{G}}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}<\mathrm{\infty },n\to \mathrm{\infty }$ is discussed, where $n_{\mathrm{G}}$ is the number of the Gaussian functions in the STO-$n$G expansion.