Smeared Coulomb potential orbitals: I—asymptotic expansion

We consider an 1-electron model Hamiltonian, whose potential energy corresponds to the Coulomb of infinite wire with charge Z distributed according a Gaussian function. The time independent Schrödinger equation for this Hamiltonian is solved perturbationally in asymptotic limit small amplitude vibration (Gaussian function width close zero). propose use naturally polarized functions so-obtained, as orbital basis sets quantum chemical calculations. In particular, they should be well suited perform electron-nucleus mean field configuration interaction Since free-parameters have remarkable property factorize perturbative corrections eigenfunctions, these corrective part factor can simply added additional standard sets, leaving it molecular calculation optimize free parameters within coefficients.