Success of quantum mechanical approximations for molecular geometries and electronndash;nuclear attraction expectation values: Gift of the Coulomb potentialquest;

摘要

A perturbation theory is derived for the study of molecular structure. For a large class of approximate formulations (including Hartreendash;Fock and higherhyphen;level schemes and exact exchangehyphen;only densityhyphen;functional theory), it is proved that thechangein theerrorof the energy, upon geometry change, iszerothrough thesecondhyphen;orderperturbation term, thus helping to explain why approximate energy curves oftencloselyparallelexact curves and give accurate geometries. In contrast, for each nonhyphen;Coulomb potential considered, the error change isnotzero through second order, suggesting that accurate geometries are due, in part, to a special quality of the Coulomb potential. Comparable results are obtained for atomic electronndash;nuclear attraction expectation values (isoelectronic energy changes), which are exact through second order in the Coulomb cases. The conclusions are supported by a nonperturbative argument and by a numerical example.