General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case Study

Abstract

We present a general framework for the development of datadriven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantummechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from density functionals belonging to different rungs across Jacob's ladder of approximations within density functional theory (MB-DFT) and from Møller−Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using density-corrected functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.

Elevating density functional theory to chemical accuracy for water simulations through a density-corrected many-body formalism

“…Building upon the demonstrated accuracy of the MB-pol PEF for water 78 – 81 and following the same theoretical/computational approach employed in the development of DFT-based many-body PEFs 51 , 90 , 107 , we used Eq. ( 4 ) to develop a data-driven many-body PEF, MB-SCAN(DC), that consistently reproduces each term of the MBE for water calculated using the DC-SCAN functional.…”

“…( 4 ) is represented by the Partridge−Schwenke PEF 108 , while ϵ 2B and ϵ 3B are represented by terms describing permanent electrostatics, dispersion energy, and induction, which are combined with short-range permutationally invariant polynomials (PIPs) 109 fitted to reproduce 2B and 3B energies calculated with DC-SCAN for the same training sets of water dimers and trimers used in the development of MB-pol 79 , 80 . A detailed description of the theoretical and computational framework adopted in the development of data-driven many-body PEFs for water can be found in the original references 51 , 79 , 80 , 90 , 107 . It should be noted that, since our many-body PEFs directly target the underlying molecular interactions, differences in the representation of the 1-body (1B) term of Eq.…”

“…It should be noted that, since our many-body PEFs directly target the underlying molecular interactions, differences in the representation of the 1-body (1B) term of Eq. ( 5 ) have been found to be negligible for modeling the properties of liquid water 107 and the air/water interface 110 .…”

The MD17 Datasets from the Perspective of Datasets for Gas-Phase "Small" Molecule Potentials

“…Our group has been active for some time developing MLPs using Permutationally Invariant Polynomials (PIPs) 13,[22][23][24][25][26][27][28][29] for "small molecules"; some early examples include CH + 5 and H 5 O + 2 , malonaldehyde and the 10-atom formic acid dimer. 30 More recently, we have reported PIP PESs for 10-15 atom molecules, listed in Table I using enhancements to the PIP basis.…”

Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods

“…This ML method, introduced for CH + 5 in 2003, 10 is actively used [11][12][13][14] and further developed. 15-17 a) Electronic mail: plh2@cornell.edu b) Electronic mail: apurba.nandi@emory.edu c) Electronic mail: riccardo.conte1@unimi.it d) Electronic mail: q.yu@yale.edu e) Electronic mail: jmbowma@emory.edu PIPs have also been incorporated in Neural Network methods, 6,[18][19][20] , Gaussian Process Regression 21 , and recently to atom-centered Gaussian Process Regression.…”