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.

Weak interactions have a critical role in accurately portraying conformational change. However, the computational study of these often requires large basis electronic structure calculations that are generally cost-prohibitive within ab initio molecular dynamics. Here, we present a new approach to efficiently obtain AIMD trajectories in agreement with large, triple-ζ, polarized valence basis functions, at much reduced computational cost. For example, it follows from our studies that AIMD trajectories can indeed be constructed in agreement with basis sets such as 6-311++G(2df,2pd) with computational effort commensurate with those from much smaller basis sets such as 6-31+G(d), for polypeptide systems with 100+ atoms. The method is based on molecular fragmentation and allows a range-specified repartitioning of intramolecular (and potentially intermolecular) interactions where noncovalent interactions are selectively assembled using a piece-wise reconstruction based on a set-theoretic inclusion−exclusion principle generalization of ONIOM. Through a simplex decomposition of molecular systems the approach efficiently provides the necessary many-body interactions to faithfully represent noncovalent interactions at the large basis limit. Conformational stabilization energies are provided at close to the complete-basis limit at much reduced cost, and similarly AIMD trajectories (both Born−Oppenheimer and Car−Parrinello-type) are obtained in agreement with very large basis set sizes, in an extremely efficient and accurate manner. The method is demonstrated through simulations on polypeptide fragments of a variety of sizes.

We present a weighted-graph-theoretic approach to adaptively compute contributions from many-body approximations for smooth and accurate post-Hartree−Fock (pHF) ab initio molecular dynamics (AIMD) of highly fluxional chemical systems. This approach is ONIOM-like, where the full system is treated at a computationally feasible quality of treatment (density functional theory (DFT) for the size of systems considered in this publication), which is then improved through a perturbative correction that captures local many-body interactions up to a certain order within a higher level of theory (post-Hartree−Fock in this publication) described through graph-theoretic techniques. Due to the fluxional and dynamical nature of the systems studied here, these graphical representations evolve during dynamics. As a result, energetic "hops" appear as the graphical representation deforms with the evolution of the chemical and physical properties of the system. In this paper, we introduce dynamically weighted, linear combinations of graphs, where the transition between graphical representations is smoothly achieved by considering a range of neighboring graphical representations at a given instant during dynamics. We compare these trajectories with those obtained from a set of trajectories where the range of local many-body interactions considered is increased, sometimes to the maximum available limit, which yields conservative trajectories as the order of interactions is increased. The weighted-graph approach presents improved dynamics trajectories while only using lower-order many-body interaction terms. The methods are compared by computing dynamical properties through time-correlation functions and structural distribution functions. In all cases, the weighted-graph approach provides accurate results at a lower cost.

a)), especially for the larger unit cells. The vertical axis in Figure (a) is in log-scale. Figure (b): Convergence of the lattice energy with increasing k-mesh density for the BLYP functional (log-scale). The error decreases with increase in unit cell size. The (H 2 O) n , n = 6,12,24 systems converge at 3 3 and demonstrate acceptable accuracy at 2 3 , while the 48 and 72 water unit cell systems converge at 2 3 and appear to be well represented at Γ-point. Note that the 72 water unit cell results are compared against the 3 3 mesh since the 4 3 mesh was computationally too expensive to perform for this system. Figure (c): Convergence of lattice energy with the increase in kinetic energy cutoff of the plane-wave basis for the bulk 6 water unit cell. BLYP, with a k-mesh of 4 3 , converges at 75 Ry. Structures used in this study are described in Section IIIB of the paper, and discussed in more detail in Section SI-1 below.

We present a graph-theoretic approach to adaptively compute many-body approximations in an efficient manner to perform (a) accurate post-Hartree-Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium-to large-sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed-phase simulations at the cost of pure density functionals, (c) reduced-cost on-the-fly basis extrapolation for gas-phase AIMD and condensed phase studies, and (d) accurate post-HF-level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM-like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many-body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph-theoretic methods. Specifically, a region of chemical interest is coarse-grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph, which forms the basis for developing the many-body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one-dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two-dimensional periodic boundary conditions.