A MOMENTUM-SPACE PICTURE OF THE CHEMICAL-BOND

The derivation of the reciprocal-space Schrodinger equation is reviewe d, as well as Fock's method for solving it for hydrogenlike atoms. It is shown that Fock's solutions (which represent Fourier transformed hy drogenlike orbitals in terms of 4-dimensional hyperspherical harmonics ) can be used as basis sets for solving other problems in quantum chem istry. Such basis sets are of the Sturmian type (i.e., all the members of the set correspond to the same energy), and they obey weighted ort honormality relations in both direct and reciprocal space. The kernel of the reciprocal-space Schrodinger equation is expanded in terms of S turmian basis sets, and this expansion is used to solve the problem of a particle moving in a many-center potential. Both Coulomb and non-Co ulomb potentials are treated, and a new method for evaluating the nece ssary integrals is discussed. (C) 1996 John Wiley & Sons, Inc.