The artificial creaton of ionospheric holes by the release of highly reactive molecules (e.g., H2 or H2O) into the F region is investigated. Through ion-atom interchange or charge transfer reactions, H2 or H2O reacts with O+ to form OH+ or H2O+, respectively, which subsequently dissociatively recombines with electrons at a very rapid rate. The diffusion of H2 is also modified by chemical loss to the ambient atomic oxygen atmosphere. The limited spatial and temporal extent of the hole-making process allows several approximations to be made which permit three-dimensional analytic solutions of the continuity equations for the released particles, the O+ and e- densities, and the intermediary molecular ions. A versatile formalism is developed whereby the hole-making capability of virtually any spatial-temporal configuration of released particles can be determined by convolving a set of 'destruction operators' which can be viewed as Green's functions for the problem. Sample calculations are presented which demonstrate the competing effects of differences in the molecular weight of the released particles, the altitude of the release, the reactivity of the released molecules with the ambient atomic oxygen atmosphere, and the quantity and distribution of the released molecules. As a specific application of the techniques developed, the modification of a winter nighttime ionosphere over Millstone Hill is described by simulating the release (for example, from the space shuttle) of 1000 kg of water vapor (?3¿1028 molecules) near a height of 300 km.