Weighted-Graph-Theoretic Methods for Many-Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms.

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.

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.

Efficient, "On-the-Fly", Born-Oppenheimer and Car-Parrinello-type Dynamics with Coupled Cluster Accuracy through Fragment Based Electronic Structure.

We recently developed two fragment based ab initio molecular dynamics methods, and in this publication we have demonstrated both approaches by constructing efficient classical trajectories in agreement with trajectories obtained from "on-the-fly" CCSD. The dynamics trajectories are obtained using both Born-Oppenheimer and extended Lagrangian (Car-Parrinello-style) options, and hence, here, for the first time, we present Car-Parrinello-like AIMD trajectories that are accurate to the CCSD level of post-Hartree-Fock theory. The specific extended Lagrangian implementation used here is a generalization to atom-centered density matrix propagation (ADMP) that provides post-Hartree-Fock accuracy, and hence the new method is abbreviated as ADMP-pHF; whereas the Born-Oppenheimer version is called frag-BOMD. The fragmentation methodology is based on a set-theoretic, inclusion-exclusion principle based generalization of the well-known ONIOM method. Thus, the fragmentation scheme contains multiple overlapping "model" systems, and overcounting is compensated through the inclusion-exclusion principle. The energy functional thus obtained is used to construct Born-Oppenheimer forces (frag-BOMD) and is also embedded within an extended Lagrangian (ADMP-pHF). The dynamics is tested by computing structural and vibrational properties for protonated water clusters. The frag-BOMD trajectories yield structural and vibrational properties in excellent agreement with full CCSD-based "on-the-fly" BOMD trajectories, at a small fraction of the cost. The asymptotic (large system) computational scaling of both frag-BOMD and ADMP-pHF is inferred as [Formula: see text], for on-the-fly CCSD accuracy. The extended Lagrangian implementation, ADMP-pHF, also provides structural features in excellent agreement with full "on-the-fly" CCSD calculations, but the dynamical frequencies are slightly red-shifted. Furthermore, we study the behavior of ADMP-pHF as a function of the electronic inertia tensor and find a monotonic improvement in the red-shift as we reduce the electronic inertia. In all cases a uniform spectral scaling factor, that in our preliminary studies appears to be independent of system and independent of level of theory (same scaling factor for both MP2 and CCSD implementations ADMP-pHF and for ADMP DFT), improves on agreement between ADMP-pHF and full CCSD calculations. Hence, we believe both frag-BOMD and ADMP-pHF will find significant utility in modeling complex systems. The computational power of frag-BOMD and ADMP-pHF is demonstrated through preliminary studies on a much larger protonated 21-water cluster, for which AIMD trajectories with "on-the-fly" CCSD are not feasible.