Bond order quantifies the number of electrons dressed-exchanged between two atoms in a material and is important for understanding many chemical properties. Diatomic molecules are the smallest molecules possessing chemical bonds and play key roles in atmospheric chemistry, biochemistry, lab chemistry, and chemical manufacturing. Here we quantum-mechanically calculate bond orders for 288 diatomic molecules and ions. For homodiatomics, we show bond orders correlate to bond energies for elements within the same chemical group. We quantify and discuss how semicore electrons weaken bond orders for elements having diffuse semicore electrons. Lots of chemistry is effected by this. We introduce a first-principles method to represent orbital-independent bond order as a sum of orbital-dependent bond order components. This bond order component analysis (BOCA) applies to any spin-orbitals that are unitary transformations of the natural spin-orbitals, with or without periodic boundary conditions, and to non-magnetic and (collinear or non-collinear) magnetic materials. We use this BOCA to study all period 2 homodiatomics plus Mo 2 , Cr 2 , ClO, ClO - , and Mo 2 (acetate) 4 . Using Manz's bond order equation with DDEC6 partitioning, the Mo-Mo bond order was 4.12 in Mo 2 and 1.46 in Mo 2 (acetate) 4 with a sum of bond orders for each Mo atom of ∼4. Our study informs both chemistry research and education. As a learning aid, we introduce an analogy between bond orders in materials and message transmission in computer networks. We also introduce the first working quantitative heuristic model for all period 2 homodiatomic bond orders. This heuristic model incorporates s-p mixing to give heuristic bond orders of ¾ (Be 2 ), 1¾ (B 2 ), 2¾ (C 2 ), and whole number bond orders for the remaining period 2 homodiatomics.