Exact results on the curvature of the electron density at the cusp in certain highly excited states of atoms

Exact results on the general higher-order cusp relations involving the seco nd derivative of electron density are derived for atoms and molecules inclu ding highly excited states wherein the spherical average of the derivative of the wave function is zero at a nucleus. The curvature of the electron de nsity at the nucleus is found to be a direct measure of the extent of excit ation. An expression relating the one-electron eigenvalues to quantities at the cusp and the atomic number is also obtained. Numerical. tests on sever al excited-state atoms are presented. (C) 2000 Elsevier Science B.V. All ri ghts reserved.