Aspects of the present invention are directed to novel methods for making discrete polyethylene compounds selectively and specifically to a predetermined number of ethylene oxide units. Methods which can be used to build up larger dPEG compounds (a) containing a wider range of utility to make useful homo- and heterofunctional and branched species, and (b) under reaction configurations and conditions that are milder, more efficient, more diverse in terms of incorporating useful functionality, more controllable, and more versatile then any conventional method reported in the art to date. In addition, the embodiments of the invention allow for processes that allow for significantly improving the ability to purify the intermediates or final product mixtures, making these methods useful for commerial manufacturing dPEGs. Protecting groups and functional groups can be designed to make purification at large scale a practical reality. The novel dPEG products form the compositional and material basis for making other novel compounds of valuable application in the fields of diagnostics and therapeutics, amongst others.