Ab Initio Molecular Dynamics Using Recursive, Spatially Separated, Overlapping Model Subsystems Mixed within an ONIOM-Based Fragmentation Energy Extrapolation Technique

Abstract

Here, we demonstrate the application of fragment-based electronic structure calculations in (a) ab initio 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: H₉O₄⁺, H₁₃O₆⁺ and H(H₂O)₂₁⁺. 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 H₉O₄⁺ system. For the larger H(H₂O)₂₁⁺ 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. Ab initio dynamics calculations were performed for H₉O₄⁺ and H₁₃O₆⁺, 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.

Embedded, graph‐theoretically defined many‐body approximations for wavefunction‐in‐DFT and DFT‐in‐DFT: Applications to gas‐ and condensed‐phase ab initio molecular dynamics, and potential surfaces for quantum nuclear effects

“…As we will see later, and as shown in refs. [39‐45], Equation ) does indeed provide a very good estimate of higher level electronic structure energies and gradients, and hence through this approach we achieve high‐quality calculations at reduced computational cost. In summary In refs.…”

“…The innovative idea in refs. [39‐45] is that the terms on the right side of Equation ) are obtained using graph‐theoretic and set‐theoretic paradigms. Specifically where the summation over α r is over all rank‐ r or order‐ r many‐body terms, and E level, 1 ( α r , r ) is an electronic energy for the α r th rank‐ r many‐body contribution.…”

“…In refs. [39‐45], we have shown this adaptive and general form of electronic energy to be a robust and powerful way to estimate higher order correlation effects at the cost of DFT. To further clarify Equations ), (), and () in Appendix A, we explicitly write out these expressions for a few increasing values of ℛ.…”

“…In summary In refs. [39‐42] we demonstrated DFT scaling while achieving MP2 and CCSD accuracy during AIMD simulations for protonated water clusters and polypeptide fragments. The associated computational scaling is depicted in Figure 2A. In ref.…”

“…[ 59 ] If link atoms are included, then is a Jacobian term needed to transform the r ‐rank many‐body gradients back to the full system gradients. [ 39,99 ] The formation of these gradients enable the direct use of Born–Oppenheimer MD using Equation ), as demonstrated in refs. [39‐43].…”