Lagrange-like spectrum of perfect additive complements

Two infinite sets $A$ and $B$ of non-negative integers are called perfect additive complements of non-negative integers if every non-negative integer can be uniquely expressed as the sum of elements from $A$ and $B$. We define a Lagrange-like spectrum of the perfect additive complements ($\mathfrak L$ for short). As a main result, we obtain the smallest accumulation point of the set $\mathfrak L$ and prove that $\mathfrak L $ is closed.