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Simulating water accurately has been a challenge due to the complexity of describing polarization and intermolecular charge transfers. Quantum mechanical (QM) electronic structures provide an accurate description of polarization in response to local environments, which is nevertheless too expensive for large water systems. In this study, we have developed a polarizable water model integrating Charge Model 5 atomic charges at the level of second-order M{\o}ller-Plesset perturbation theory, predicted by an accurate and transferable Charge Neural Network (ChargeNN) model. The spontaneous intermolecular charge transfer has been explicitly accounted for, enabling a precise treatment of hydrogen bonds and out-of-plane polarization. Our ChargeNN water model successfully reproduces various properties of water in gas, liquid and solid phases. For example, ChargeNN correctly captures the hydrogen-bond stretching peak and bending-libration combination band, which are absent in the spectra using fixed charges, highlighting the significance of accurate polarization and charge transfers. Finally, the molecular dynamical simulations using ChargeNN for liquid water and a large water droplet with a $\sim$4.5 nm radius reveal that the strong interfacial electric fields are concurrently induced by the partial collapse of the hydrogen-bond network and surface-to-interior charge transfers. Our study paves the way for QM-informed force fields, aiming for large-scale molecular simulations with high accuracy.

Accurate ab-initio prediction of electronic energies is very expensive for macromolecules by explicitly solving post-Hartree-Fock equations. We here exploit the physically justified local correlation feature in compact basis of small molecules, and construct an expressive low-data deep neural network (dNN) model to obtain machine-learned electron correlation energies on par with MP2 and CCSD levels of theory for more complex molecules and different datasets that are not represented in the training set. We show that our dNN-powered model is data efficient and makes highly transferable prediction across alkanes of various lengths, organic molecules with non-covalent and biomolecular interactions, as well as water clusters of different sizes and morphologies. In particular, by training 800 (H$_2$O)$_8$ clusters with the local correlation descriptors, accurate MP2/cc-pVTZ correlation energies up to (H$_2$O)$_{128}$ can be predicted with a small random error within chemical accuracy from exact values, while a majority of prediction deviations are attributed to an intrinsically systematic error. Our results reveal that an extremely compact local correlation feature set, which is poor for any direct post-Hartree-Fock calculations, has however a prominent advantage in reserving important electron correlation patterns for making accurate transferable predictions across distinct molecular compositions, bond types and geometries.

We present a many-body expansion (MBE) formulation and implementation for efficient computation of analytical energy gradients from OSV-MP2 theory based on our earlier work (Zhou et al. J. Chem. Theory Comput. 2020, 16, 196-210). The third-order MBE(3) expansion of OSV-MP2 wavefunction was developed to adopt the orbital-specific clustering and long-range termination schemes, which avoids term-by-term differentiations of the MBE energy bodies. We achieve better efficiency by exploiting the algorithmic sparsity that allows to prune out insignificant fitting integrals and OSV relaxations. With these approximations, the present implementation is benchmarked on a range of molecules that show an economic scaling in the linear and quadratic regimes for computing MBE(3)-OSV-MP2 amplitude and gradient equations, respectively, and yields normal accuracy comparable to the original OSV-MP2 results. The MPI-3-based parallelism through shared memory one-sided communication is further developed for improving parallel scalability and memory accessibility by sorting the MBE(3) orbital clusters into independent tasks that are distributed on multiple processes across many nodes, supporting both global and local data locations in which selected MBE(3)-OSV-MP2 intermediates of different sizes are distinguished and accordingly placed. The accuracy and efficiency level of our MBE(3)-OSV-MP2 analytical gradient implementation is finally illustrated in two applications: we show that the subtle coordination structure differences of mechanically interlocked Cu-catenane complexes can be distinguished when tuning ligand lengths; and the porphycene molecular dynamics reveals the emergence of the vibrational signature arising from softened N-H stretching associated with hydrogen transfer, using an MP2 level of electron correlation and classical nuclei for the first time.

We propose an exact algorithm for computing the analytical gradient within the framework of the orbital-specific-virtual (OSV) second-order M{\o}ller-Plesset (MP2) theory in resolution-of-identity (RI) approximation. We implement the exact relaxation of perturbed OSVs through the explicit constraints of the perturbed orthonormality, the perturbed diagonality and the perturbed singular value condition. We explicitly show that the rotation of OSVs within the retained OSV subspace makes no contribution to gradients, as long as the iterative solution of the unperturbed Hylleraas residual equation is well converged. The OSV relaxation is solved as the perturbed non-degenerate singular value problem between the retained and discarded OSV subspaces. The detailed derivation and preliminary implementations for gradient working equations are discussed. The coupled-perturbed localization method is implemented for meta-L\"owdin localization function. The numerical accuracy of computed OSV-MP2 gradients is demonstrated for the geometries of selected molecules that are often discussed in other theories. Moreover, the OSV-MP2 analytical gradients can generate atomic forces that are utilized to drive the Born-Oppenheimer molecular dynamics (BOMD) simulation for studying structural and vibrational properties with respect to OSV selections. By performing the OSV-MP2 NVE BOMD calculation using the normal OSV selection, the structural and vibrational details of protonated water cations are well reproduced. The 200 picoseconds NVT well-tempered metadynamics at 300 K has been simulated to compute the OSV-MP2 rotational free energy surface of coupled hydroxyl and methyl rotors for ethanol molecule.