Hauptman-Karle 1953-1985 (Nobel 1985) direct methods: Sayre's equation + tangent formula + Karle-Hauptman determinants exploit positivity + atomicity to determine structure factor phases ab initio.
Hauptman-Karle 1953-1985 (Nobel 1985) direct methods: Sayre's equation + tangent formula + Karle-Hauptman determinants exploit positivity + atomicity to determine structure factor phases ab initio.