Entropy of binding two rigid bodies together in a closed system (e.g. forming a diatomic out of two monatomic gas particles)

Question

When I bind two molecular complexes together, or in the simplest case, form a diatomic out of two atoms in a monatomic gas, the entropy of my (closed) system will decrease. We can perhaps understand this as an increase in the "correlation" between the coordinates for the two molecules or atoms that are bonded together. However, how can I derive the entropic penalty of this process? Is there a clean approximation similar to the notion that we lose $\approx \frac{1}{2} k_b T$ worth of energy per degree of freedom (or dimension available to a diffusing gas particle)?