Integral-Transform-Generated Basis Sets

Two alternative versions of a procedure for generating new basis sets via the integral‐transform (IT) method are outlined. The first version (fixed shape function, set of primitive functions) is tested on 3‐electron $\text{(Z=2, 3, 4, 5)}$ and 4‐electron $\text{(Z=3, 4, 5, 6)}$ atomic systems (ground state) and the 2¹P excited state of He. The set of primitive functions are either hydrogenic or Slater orbitals and the shape function is the square pulse that generates the Hulthèn transforms. In these calculations, a conjecture about the dependence of the parameters of higher principal quantum number (n) IT orbitals on the parameters of lower n IT orbitals is also tested and substantiated. The second version (single primitive function, set of shape functions) is tested on the 2¹P state of He. The primitive function is a 1s Gaussian function, the set of shape functions is related to the set of generalized Laguerre polynomials $L_n^{\text{v‐1}}\mathrm{(x)}$ . The first member of this set gives k_v(qr), the reduced modified Bessel function of the second kind, already used in ground state atomic and molecular calculations. The results are analyzed critically.