Authors: M. Devereux | Eric D. Boittier | Markus Meuwly
Source: Journal of Computational Chemistry (article, 2024-05-02)
Field: Chemistry — Physical and Theoretical Chemistry

Systematic improvement of empirical energy functions in the era of machine learning The impact of targeted replacement of individual terms in empirical force fields is quantitatively assessed for pure water, dichloromethane (CH <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> ), and solvated K <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msup><mml:mo> </mml:mo> <mml:mrow><mml:mo>+</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> and Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msup><mml:mo> </mml:mo> <mml:mrow><mml:mo>-</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> ions. For the electrostatic interactions, point charges (PCs) and machine learning (ML)-based minimally distributed charges (MDCM) fitted to the molecular electrostatic potential are evaluated together with electrostatics based on the Coulomb integral. The impact of explicitly including second-order terms is investigated by adding a fragment molecular orbital (FMO)-derived polarization energy to an existing force field, in this case CHARMM. It is demonstrated that anisotropic electrostatics reduce the RMSE for water (by 1.4 kcal/mol), CH <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> (by 0.8 kcal/mol) and for solvated Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msup><mml:mo> </mml:mo> <mml:mrow><mml:mo>-</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> clusters (by 0.4 kcal/mol). An additional polarization term can be neglected for CH <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> but further improves the models for pure water (by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>∼</mml:mo></mml:mrow> </mml:math> 1.0 kcal/mol) and hydrated Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msup><mml:mo> </mml:mo> <mml:mrow><mml:mo>-</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> (by 0.4 kcal/mol), and is key for solvated K <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msup><mml:mo> </mml:mo> <mml:mrow><mml:mo>+</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> , reducing the RMSE by 2.3 kcal/mol. A 12-6 Lennard-Jones functional form performs satisfactorily with PC and MDCM electrostatics, but is not appropriate for descriptions that account for the electrostatic penetration energy. The importance of many-body contributions is assessed by comparing a strictly 2-body approach with self-consistent reference data. Two-body interactions suffice for CH <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mo> </mml:mo> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> </mml:math> whereas water and solvated K <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msup><mml:mo> </mml:mo> <mml:mrow><mml:mo>+</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> and Cl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msup><mml:mo> </mml:mo> <mml:mrow><mml:mo>-</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> ions require explicit many-body corrections. Finally, a many-body-corrected dimer potential energy surface exceeds the accuracy attained using a conventional empirical force field, potentially reaching that of an FMO calculation. The present work systematically quantifies which terms improve the performance of an existing force field and what reference data to use for parametrizing these terms in a tractable fashion for ML fitting of pure and heterogeneous systems. Electrostatics ; Chemistry ; Water dimer ; Electric potential energy ; Force field (fiction) ; Ion ; Coulomb ; Computational chemistry ; Chemical physics ; Atomic physics ; Molecule ; Energy (signal processing) ; Physical chemistry ; Physics ; Quantum mechanics ; Hydrogen bond ; Organic chemistry Crystallography and molecular interactions ; Machine Learning in Materials Science ; Spectroscopy and Quantum Chemical Studies