Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

“…This method allows access to higher-quality (post-Hartree–Fock) electronic structure methodologies at a lower computational cost. The approach has been used to (a) efficiently compute post-Hartree–Fock Born–Oppenheimer ,− and extended Lagrangian − AIMD trajectories, (b) obtain multidimensional potential energy surfaces for the treatment of nuclear quantum effects where the surfaces are obtained at post-Hartree–Fock accuracy, , (c) provide efficient ML protocols, , (d) derive efficient methods for tensor network-based quantum nuclear dynamics strategies, and (e) obtain efficient, reduced quantum circuit depth algorithms for quantum computing. ,, The cost reduction, robustness, and accuracy demonstrations render great promise to the methods discussed here.…”

“…As a result of such an exciting development, a variety of ML techniques such as neural networks (NN) and Gaussian process regression have been used for computing accurate potential energy surfaces. − The key idea here is that as long as a reasonable training set can be assembled, a potentially nonlinear extrapolation scheme can be constructed, presumably using NN, that can provide reasonable accuracy. One of the key issues that affect the training process in potential energy surface calculations is the fact that the size of a suitable training data set may increase drastically with system size. ,− In refs and , we create a family of neural networks that each yield an estimate for eq given by normalΔ E α , r → normalM normalL normalΔ E α , r normalM normalL and thus .25ex2ex E scriptR , M L e x t r a p ‐ C C S D ( x̅ ) = E normalD normalF normalT ( x̅ ) + ∑ r = 0 R false( − 1 false) r ∑ α ∈ V …”

“…That is, ML estimates, Δ E α, r ML , replace Δ E α, r in eq . As shown in Figure and in refs and , training models can be constructed to reproduce AIMD data with roughly 10% of the effort needed as compared to that for the full fragmentation calculations. The idea is depicted in Figure .…”

“…It is expected that for large systems N normalA normalt normalo normalm normals R ≪ N normalA normalt normalo normalm normals , the total number of atoms in the full system. The algorithm has been demonstrated for surface–adsorbate interactions in ref , for protonated water clusters in ref , and in Figure , where the horizontal axis refers to results from eq , whereas the vertical axes refer to the energy value at CCSD. Clearly, the agreement is very high between the fragment-based ΔML model and the more expensive higher-level electronic structure treatment.…”

“…Here, we present an alternate reformulation of all ONIOM-type molecular fragmentation methods and many-body theories from a newly introduced graph-theoretic perspective, ,− which allows us to derive new approaches for post-Hartree–Fock ab initio molecular dynamics ,− for gas- and condensed-phase , systems, computing high-quality molecular potential surfaces for quantum nuclear dynamics, ,, efficient machine learning (ML) transfer learning protocols, , new algorithms for quantum computing, ,, and new algorithms for performing quantum nuclear dynamics with tensor networks . We briefly highlight some of these aspects in this publication.…”