FINITE-ELEMENT-METHOD EXPECTATION VALUES FOR CORRELATED 2-ELECTRON WAVE-FUNCTIONS

The Schrodinger equation for the ground state of correlated two-electr on atoms is treated by an accurate finite-element method (FEM) yieldin g energy eigenvalues of - 2.903 724 377 021 a.u. for the helium atom a nd -0.527 751 016 532 a.u. for the hydrogen ion H-. By means of an ada ptive multilevel grid refinement the FEM energy eigenvalue is improved to a precision of 1 X 10(-11) a.u., which is comparable to results ob tained with sophisticated global basis sets. The local and overall pre cision of the FEM wave function approximation is studied and discussed . Benchmark values for the expectation values [r(2)],[r], [1/r], and [ 1/r(12)] are presented.