The Kato electron-nuc~eue (Coulomb) and eleeiron-electroo (correktion} cusp conditions are shown to be satisfied by the natural p-particle functions for atomic states. In particular, a necessary anti s&f& cient condition that a wave function satisfy the Coulomb cusp constraint is that ita occupied oaturai spin orbitals do. Similarly a wave function will satisfy the correlation cusp constraiot E and on& if its occupied natural spin geminale are 60 constrained.
These may be exploited in the construction OF variational wave fuoctions.
Knowledge of properties obeyed by the exact wave functions are of interest for they give insight into the construction of vax3ationa.l approximations and may possibly be included as constraints in the variation process. As is well-known, some important physical properties are sensitive to the accuracy of the wave function in the neighborhood of the nuclexxs while the variation principle attempts to give the 'best' wave function over all space in an average way. For these reasons, the knowledge that the exact wave function satisfies the K&to [I] electron-nuclear (Coulomb) cusp conditions has fed to an extensive interest in them [Z-13] and their possible use as constraints in variational calcu?.ations fll-131. Similarly, some correlation dependent properties (see e.g. CM]} would be expected to be sensitive to the behavior of the wave function at the electron-electron coalescence points where the Kate ff] electron-electron (correlation) cusp constraint would govern.
Our interest is in these cusp conditions for the natural functions of an atomic system. The most familiar of "these natural functions are the natural spin orbit&s gfl)(l) and natnra? spin gem-s