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The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present "Molecular Geometry (MG)" as a theoretical framework accompanied by "MG Operating System (MGOS)" which consists of callable functions implementing the MG theory. MG allows researchers to model complicated molecular structure problems in terms of elementary yet standard notions of volume, area, etc. and MGOS frees them from the hard and tedious task of developing/implementing geometric algorithms so that they can focus more on their primary research issues. MG facilitates simpler modeling of molecular structure problems; MGOS functions can be conveniently embedded in application programs for the efficient and accurate solution of geometric queries involving atomic arrangements. The use of MGOS in problems involving spherical entities is akin to the use of math libraries in general purpose programming languages in science and engineering.