<i>Ab Initio</i> Molecular Dynamics Using
Recursive, Spatially Separated, Overlapping Model Subsystems Mixed
within an ONIOM-Based Fragmentation Energy Extrapolation Technique
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Abstract
Here,
we demonstrate the application of fragment-based electronic
structure calculations in (a) <i>ab initio</i> molecular
dynamics (AIMD) and (b) reduced dimensional potential calculations,
for medium- and large-sized protonated water clusters. The specific
fragmentation algorithm used here is derived from ONIOM, but includes
multiple, overlapping “model” systems. The interaction
between the various overlapping model systems is (a) approximated
by invoking the principle of inclusion-exclusion at the chosen higher
level of theory and (b) within a real calculation performed at the
chosen lower level of theory. The fragmentation algorithm itself is
written using bit-manipulation arithmetic, which will prove to be
advantageous, since the number of fragments in such methods has the
propensity to grow exponentially with system size. Benchmark calculations
are performed for three different protonated water clusters: H<sub>9</sub>O<sub>4</sub><sup>+</sup>,
H<sub>13</sub>O<sub>6</sub><sup>+</sup> and H(H<sub>2</sub>O)<sub>21</sub><sup>+</sup>. For potential energy surface benchmarks, we sample the normal
coordinates and compare our surface energies with full MP2 and CCSD(T)
calculations. The mean absolute error for the fragment-based algorithm
is <0.05 kcal/mol, when compared with MP2 calculations, and <0.07
kcal/mol, when compared with CCSD(T) calculations over 693 different
geometries for the H<sub>9</sub>O<sub>4</sub><sup>+</sup> system. For the larger H(H<sub>2</sub>O)<sub>21</sub><sup>+</sup> water cluster,
the mean absolute error is on the order of a 0.1 kcal/mol, when compared
with full MP2 calculations for 84 different geometries, at a fraction
of the computational cost. <i>Ab initio</i> dynamics calculations
were performed for H<sub>9</sub>O<sub>4</sub><sup>+</sup> and H<sub>13</sub>O<sub>6</sub><sup>+</sup>, and the energy conservation was found
to be of the order of 0.01 kcal/mol for short trajectories (on the
order of a picosecond). The trajectories were kept short because our
algorithm does not currently include dynamical fragmentation, which
will be considered in future publications. Nevertheless, the velocity
autocorrelation functions and their Fourier transforms computed from
the fragment-based AIMD approaches were found to be in excellent agreement
with those computed using the respective higher level of theory from
the chosen hybrid calculation