How good is good agreement: Evaluating the reliability of quantum-mechanically calculated observables

The practical value of a wave function derives from its ability to estimate or predict the chemical and physical properties of the electronic structure which it describes. Reliability is defined as a property to be evaluated on the basis of (i) the magnitude of the difference between the measured and calculated values of the observable together with (ii) the sign of the difference, (ii) the number and nature of observables correctly estimated, and (iv) the number and type of electronic structures that are correctly estimated. Systematic statistical comparison implies the existence of both internally consistent sets of wave functions for homologous series of molecules and their corresponding experimental values together with reliable error estimates. The most complete data base currently available for comparison is the spectroscopic constants for the first and second row diatomic hydrides. Utilizing appropriate statistical comparison techniques, four approximations (CEPA , PNO -CI , GTO -SCF , and STO -SCF ) are compared among themselves and against experimentally measured values. The CEPA approximation yields differences from experiment that approximate a normal error distribution, while the other approximations show systematic departures from experiment. Two values, ω_e and ω_eχ_e, for SH exhibit differences large enough to cast doubt upon the calculated value, the experimental value, or both.