We present a many-body expansion (MBE) formulation and implementation for efficient computation of analytical energy gradients from the orbital-specific-virtual second-order Møllet-Plesset perturbation theory (OSV-MP2) 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 amplitudes and density matrices 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 us 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 Møller-Plesset (MP2) theory in resolution-of-identity (RI) approximation. We implement the exact relaxation of perturbed OSVs through sufficient and necessary 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-Löwdin 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. From OSV-MP2 with the normal OSV selection, the † Equal contributions 1 arXiv:1908.03674v1 [physics.chem-ph] 10 Aug 2019 canonical RI-MP2/def2-TZVP gradients can be reproduced within 10 −4 a.u. The OSV-MP2/def2-TZVPP covalent bond lengths, angles and dihedral angles are in good agreement with canonical RI-MP2 structures by 0.017 pm, 0.03 • and 0.2 • , respectively. No particular accuracy gains have been observed for molecular geometries compared to the recent local pair-natural-orbital MP2 by using the predefined orbital domains. 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 N V E BOMD calculation using the normal OSV selection, the structural and vibrational details of protonated water cations are well reproduced. The 200 picoseconds N V T 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.

Criegee intermediates (CIs) are important carbonyl oxides that may react with atmospheric trace chemicals and impact the global climate. The CI reaction with water has been widely studied and is a main channel for trapping CIs in the troposphere. Previous experimental and computational reports have largely focused on reaction kinetic processes in various CI−water reactions. The molecular-level origin of CI's interfacial reactivity at the water microdroplet surface (e.g., as found in aerosols and clouds) is unclear. In this study, by employing the quantum mechanical/molecular mechanical (QM/MM) Born−Oppenheimer molecular dynamics with the local second-order Møller− Plesset perturbation theory, our computational results reveal a substantial water charge transfer up to ∼20% per water, which creates the surface H 2 O + /H 2 O − radical pairs to enhance the CH 2 OO and anti-CH 3 CHOO reactivity with water: the resulting strong CI−H 2 O − electrostatic attraction at the microdroplet surface facilitates the nucleophilic attack to the CI carbonyl by water, which may counteract the apolar hindrance of the substituent to accelerate the CI−water reaction. Our statistical analysis of the molecular dynamics trajectories further resolves a relatively long-lived bound CI(H 2 O − ) intermediate state at the air/water interface, which has not been observed in gaseous CI reactions. This work provides insights into what may alter the oxidizing power of the troposphere by the next larger CIs than simple CH 2 OO and implicates a new perspective on the role of interfacial water charge transfer in accelerating molecular reactions at aqueous interfaces.

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 a 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 predictions 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 (H2O)8 clusters with the local correlation descriptors, accurate MP2/cc-pVTZ correlation energies up to (H2O)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.