Weinhold's lower bound formulas are used on rather accurate wavefunctions for the 1's ground states of H-, He, and Li+, and the 2IS and Z3S excited states of He. The results are found to be of very high quality, as judged by comparison with the best available variational calculations, and can be used to rule out many of the values calculated by Scherr and Knight from high-order perturbation theory. 260 (1973) Introduction The concept of attaching rigorous error limits to theoretical estimates of quantummechanical properties is attractive to many chemists and physicists. Such upper and lower bounds not only provide internal and a pviori measures of reliability, but also enable one to make more meaningful comparisons with experimental results. One of the recent developments in this direction is the application of Gramian determinantal ineq~alities.~ For the lower bounds to expectation values of positive operators, Weinhold (2-5) derived a wide variety of relatively simple formulas and illustrated their use with the familiar Is2 and lsls' trial functions for the 1'S ground state of the helium atom, with promising results. The purpose of this work is to test some of these procedures on better wavefunctions. On the basis of certain preliminary results, we were encouraged to employ some rather accurate wavefunctions which could be expected to yield bounds of a definitive quality for the simple 2-electron atomic systems.
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