Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion

The
balance between cost-effective and sufficiently accurate methods
represents the proverbial “promised land” for quantum
chemistry calculations. The burden thus falls upon theoretical and
computational chemists to provide such alternatives to mitigate the
issues that arise from the employ of finite computing resources. In
this paper, we attempt to demonstrate the importance of the quality
of the initial guess for the self-consistent field (SCF) calculation
when considering cost reduction techniques. We broach this challenge
by using the many body expansion (MBE) to yield high quality density
matrices (DMs) which, in turn, are applied as an SCF initial guess.
The MBE-DM approaches combined with purification schemes and distance-based
cutoff schemes can serve as initial guesses to reduce the SCF cycles
necessary for convergence or derive energy directly through one Fock
build. To this end, four unique types of clusters including water
clusters, fluoride anion water clusters, sodium cation water clusters,
and ammonium-bisulfate salt clusters have been used to test the performance
of MBE-DM where its truncation at three-body expansion, MBE(3)-DM,
shows vast improvement for those four clusters with reductions in
the number of SCF cycles up to 40% as compared with the traditional
superposition of atomic densities (SAD) guess. Other types of typical
initial guesses, superposition of atomic potentials (SAP) and basis
set projection (BSP), perform much worse than MBE-DM and SAD. In addition,
the MBE-DM shows consistency across an array of fragment types irrespective
of charges, size, level of theory, and basis set selection. Through
MBE­(3)-DM with the distance cutoff and the average purification scheme,
the energy can be obtained directly with a mere 3.2 mH of the mean
absolute deviation (MAD) for (H2O)N=6–55 which is at least 73 times better than the energy
prediction using the typical initial guesses (SAD, SAP, and BSP).
The corresponding MAD per monomer is only 0.14 mH which reaches the
threshold of the “dynamical accuracy”. The promising
results of the methods outlined in this paper not only indicate two
direct routes for computational cost reduction but also lay the possible
foundation for composite techniques (i.e., ab initio sampling) that make best use of near converged values as their starting
point.