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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.

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.

We present a hybrid ab initio molecular dynamics scheme that includes both DFT and Hartree–Fock-based extended Lagrangian and converged post-Hartree–Fock Born–Oppenheimer components, combined within the framework of a molecular fragmentation-based electronic structure. 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 approximated by invoking the principle of inclusion–exclusion at the chosen higher level of theory and within a “real” calculation performed at the chosen lower level of theory. Furthermore, here, the lower level electronic structure of the full system is propagated through an extended Lagrangian formalism, whereas the fragments, treated using post-Hartree–Fock electronic structure theories, are computed using the normal converged Born–Oppenheimer treatment. This conservative dynamical approach largely reduces the computational cost to approximate on-the-fly...

Background: Measurement of the energy dependence of the fusion cross section at sub-barrier energies provides an important test for theoretical models of fusion.Purpose: The aim of the study is to extend the measurement of fusion cross sections in the sub-barrier domain for the $^{18}\mathrm{O}+^{12}\mathrm{C}$ system, and to use the new experimental data to confront microscopic calculations of fusion.Method: Evaporation residues produced in fusion of $^{18}\mathrm{O}$ ions with $^{12}\mathrm{C}$ target nuclei were detected with good geometric efficiency and identified by measuring their energy and time-of-flight. Theoretical calculations with a density-constrained time-dependent Hartree-Fock (DC-TDHF) theory include for the first time the effect of pairing on the fusion cross section.Results: Comparison of the measured fusion excitation function with the predictions of the DC-TDHF calculations reveal that the experimental data exhibit a smaller decrease in cross section with decreasing energy than is theoretically predicted.Conclusion: The larger cross sections observed at the lowest energies measured indicate a larger tunneling probability for the fusion process. This larger probability can be associated with a smaller, narrower fusion barrier than presently included in the theoretical calculations.