  The density matrix renormalization group (DMRG) of White 1992 remains to this
day an integral component of many state-of-the-art methods for efficiently
simulating strongly correlated quantum systems. In quantum chemistry, QC-DMRG
became a powerful tool for ab initio calculations with the non-relativistic
Schr\"odinger equation. An important issue in QC-DMRG is the so-called ordering
problem -- the optimal ordering of DMRG sites corresponding to electronic
orbitals that produces the most accurate results. To this end, a commonly used
heuristic is the grouping of strongly correlated orbitals as measured via
quantum mutual information. In this work, we show how such heuristics can be
directly related to minimizing the entanglement entropy of matrix product
states and, consequently, to the truncation error of a fixed bond dimension
approximation. Key to establishing this link is the strong subadditivity of
entropy. This provides rigorous theoretical justification for the orbital
ordering methods and suggests alternate ordering criteria.
