  There has been recent interest in the deployment of ab initio density matrix
renormalization group computations on high performance computing platforms.
Here, we introduce a reformulation of the conventional distributed memory ab
initio DMRG algorithm that connects it to the conceptually simpler and
advantageous sum of sub-Hamiltonians approach. Starting from this framework, we
further explore a hierarchy of parallelism strategies, that includes (i)
parallelism over the sum of sub-Hamiltonians, (ii) parallelism over sites,
(iii) parallelism over normal and complementary operators, (iv) parallelism
over symmetry sectors, and (v) parallelism over dense matrix multiplications.
We describe how to reduce processor load imbalance and the communication cost
of the algorithm to achieve higher efficiencies. We illustrate the performance
of our new open-source implementation on a recent benchmark ground-state
calculation of benzene in an orbital space of 108 orbitals and 30 electrons,
with a bond dimension of up to 6000, and a model of the FeMo cofactor with 76
orbitals and 113 electrons. The observed parallel scaling from 448 to 2800 CPU
cores is nearly ideal.
