Necessary and sufficient conditions in the problem of optimal investment in incomplete markets

Adsorbate interactions and reactions on metal surfaces have been investigated using scanning tunneling microscopy. The manners in which adsorbates perturb the surface electronic structure in their vicinity are discussed. The effects these perturbations have on other molecules are shown to be important in overlayer growth. Interactions of molecules with surface steps are addressed, and each moleculeʹs electron affinity is shown to dictate its adsorption sites at step edges. Standing waves emanating from steps are demonstrated to effect transient molecular adsorption up to 40 A away from the step edge. Halobenzene derivatives are used to demonstrate how the surface is important in aligning reactive intermediates.