Solution of the Hartree–Fock problem by expansion onto nested bases

A method for solving the Hartree–Fock problem in a finite basis set is derived, which permits each orbital to be expanded in a different basis. If the basis set for each orbital ϕ i contains the basis functions for the preceding orbitals, ϕ i −1 , ϕ i −2 ,… ϕ 1 , then the ϕ i form an orthonormal set. One advantage over the standard Hartree–Fock method is that a different long range behavior for each orbital, as for example is required in the Hartree–Fock‐Slater method, can be forced. A calculation on the ground state of beryllium is performed using the nested procedure. Very little energy is lost because of nesting, and the node in the 1 s orbital disappears.