The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The
effective fragment molecular orbital (EFMO) method has been
developed to predict the total energy of a very large molecular system
accurately (with respect to the underlying quantum mechanical method)
and efficiently by taking advantage of the locality of strong chemical
interactions and employing a two-level hierarchical parallelism. The
accuracy of the EFMO method is partly attributed to the accurate and
robust intermolecular interaction prediction between distant fragments,
in particular, the many-body polarization and dispersion effects,
which require the generation of static and dynamic polarizability
tensors by solving the coupled perturbed Hartree–Fock (CPHF)
and time-dependent HF (TDHF) equations, respectively. Solving the
CPHF and TDHF equations is the main EFMO computational bottleneck
due to the inefficient (serial) and I/O-intensive implementation of
the CPHF and TDHF solvers. In this work, the efficiency and scalability
of the EFMO method are significantly improved with a new CPU memory-based
implementation for solving the CPHF and TDHF equations that are parallelized
by either message passing interface (MPI) or hybrid MPI/OpenMP. The
accuracy of the EFMO method is demonstrated for both covalently bonded
systems and noncovalently bound molecular clusters by systematically
examining the effects of basis sets and a key distance-related cutoff
parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by
the chosen ab initio method or calculated using the
effective fragment potential (EFP) method (separated dimers). Decreasing
the value of Rcut increases the number
of separated (EFP) dimers, thereby decreasing the computational effort.
It is demonstrated that excellent accuracy (<1 kcal/mol error per
fragment) can be achieved when using a sufficiently large basis set
with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total
EFMO wall time is substantially reduced, especially with a high number
of MPI ranks. Given a sufficient workload, nearly ideal strong scaling
is achieved for the CPHF and TDHF parts of the calculation. For the
first time, EFMO calculations with the inclusion of long-range polarization
and dispersion interactions on a hydrated mesoporous silica nanoparticle
with explicit water solvent molecules (more than 15k atoms) are achieved
on a massively parallel supercomputer using nearly 1000 physical nodes.
In addition, EFMO calculations on the carbinolamine formation step
of an amine-catalyzed aldol reaction at the nanoscale with explicit
solvent effects are presented.