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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...