He and Eugene G. Rochow independently discovered the direct process of organosilicon compounds in 1941.
That synthesis, also known as the Müller-Rochow process is the copper-catalysed reaction of chloromethane with silicon.
Müller was awarded the National Prize of East Germany in 1952 for his work.
From 1933 onwards he worked as a laboratory manager at Chemische Fabrik von Heyden, a large chemical plant located in Radebeul and famous as the world's first factory to produce salicylic acid on an industrial scale.
From 1954 to 1972 Müller taught as head of the Institute of Silicone and Fluorocarbon Chemistry at the Dresden University of Technology, where the Faculty of Mathematics and Science, awarded him an honorary doctorate in 1992 “in recognition of outstanding achievements in the field of organosilicon chemistry.” The citation particularly acknowledged his “seminal work on industrially applicable synthesis of methylchlorosilanes, research contributions to the development of silicon organic chemistry and the long years of teaching” at the university.