Adaptive, Geometric Networks for Efficient Coarse-Grained Ab Initio Molecular Dynamics with Post-Hartree-Fock Accuracy.

We introduce a new coarse-graining technique for ab initio molecular dynamics that is based on the adaptive generation of connected geometric networks or graphs specific to a given molecular geometry. The coarse-grained nodes depict a local chemical environment and are networked to create edges, triangles, tetrahedrons, and higher order simplexes based on (a) a Delaunay triangulation procedure and (b) a method that is based on molecular, bonded and nonbonded, local interactions. The geometric subentities thus created, that is nodes, edges, triangles, and tetrahedrons, each represent an energetic measure for a specific portion of the molecular system, capturing a specific set of interactions. The energetic measure is constructed in a manner consistent with ONIOM and allows assembling an overall molecular energy that is purely based on the geometric network derived from the molecular conformation. We use this approach to obtain accurate MP2 energies for polypeptide chains containing up to 12 amino-acid monomers (123 atoms) and DFT energies up to 26 amino-acid monomers (263 atoms). The energetic measures are obtained at much reduced computational costs; the approach currently yields MP2 energies at DFT cost and DFT energies at PM6 cost. Thus, in essence the method performs an efficient "coarse-graining" of the molecular system to accurately reproduce the electronic structure properties. The method is comparable in principle to several fragmentation procedures recently introduced in the literature, including previous procedures introduced by two of the authors here, but critically differs by overcoming the computational bottleneck associated with adaptive fragment creation without spatial cutoffs. The method is used to derive a new, efficient, ab initio molecular dynamics formalism (both Born-Oppenheimer and Car-Parrinello-style extended Lagrangian schemes are presented) a critical hallmark of which is that, at each dynamics time-step, multiple electronic structure packages can be simultaneously invoked to assemble the energy and forces for the full system. Indeed, in this paper, as an illustration, we use both Psi4 and Gaussian09 simultaneously at every time-step to perform AIMD simulations and also the energetic benchmarks. The approach works in parallel (currently over 100 processors), and the computational implementation is object oriented in C++. MP2 and DFT based on-the-fly dynamics results are recovered to good accuracy from the coarse-grained AIMD methods introduced here at reduced costs as highlighted above.