Multicenter integrals over long-range operators using Cartesian Gaussian functions

Analytic expressions are derived for the multicenter (one-particle) integrals over {}r^-k-type operators (mᵢ,k{∈}openN₀, k2) employing Cartesian Gaussian basis sets of any angular momentum number. A Laplace transform of r^-k is used for solving the different kinds of integrals. In order to remove the pole at the origin and ensure the existence of the integrals a Gaussian cutoff function of the form [1-exp (-{α}r²{)]}q[q∈openN, q≥κ(k)-{J}ᵢ₌₁³κ({m}ᵢ$)-1], {κ}(n)=n/2 if n is even and {κ}(n)=(n+1)/2 if n is odd, is used. The integral has applications in atomic, molecular, and nuclear structure or scattering calculations.