Anisotropic Valence Density Overlap Model Achieves Sub-kcal/mol Accuracy for Molecular Exchange-Repulsion with One Parameter

Accurate prediction of how molecules interact relies heavily on modelling Pauli repulsion, the fundamental force preventing atoms from occupying the same space. Dahvyd Wing and Alexandre Tkatchenko, both from the University of Luxembourg, have developed a new approach to this problem, called the anisotropic valence density overlap (AVDO) model, which significantly simplifies calculations without sacrificing accuracy. Current methods require numerous parameters to achieve reliable results, hindering the creation of broadly applicable molecular force fields, but the AVDO model achieves sub-kcal/mol accuracy using only a single universal parameter. This breakthrough offers a promising route towards developing next-generation force fields capable of accurately simulating complex chemical systems and accelerating advances in fields like drug discovery and materials science.

Researchers currently rely on over 20 atom types to achieve chemical accuracy in molecular simulations, but the large number of parameters in these approaches hinders the development of force fields with quantum-chemical accuracy that are transferable across many chemical systems. This work presents the anisotropic valence density overlap (AVDO) model for exchange-repulsion, which achieves sub-kcal/mol accuracy for dimers of organic molecules from the S101x7 dataset, a representative set of the most common biologically relevant intermolecular interactions. The model also demonstrates accuracy for acene dimers of increasing size, and importantly, it utilises a single universal parameter related to an atomic cross-sectional area, thereby offering improved transferability across diverse chemical systems. This represents a significant step forward, building on recent progress in machine learning techniques for molecular modelling.

Valence Density Overlap Model for Pauli Repulsion

Investigations into the accuracy of reference energies used to calibrate the model revealed that improving these energies only modestly improved performance. This suggests the primary challenge lies in accurately modelling the repulsive forces between molecules with a simple density overlap model. Further analysis demonstrated that the model remains remarkably robust and transferable even when used with different quantum chemical methods, such as PBE0 and Hartree-Fock, for calculating reference energies and densities. The key scaling factor within the model, known as the K parameter, changed by only a small amount, approximately 5%, when switching between these methods.

This highlights the model’s ability to maintain accuracy regardless of the underlying calculation method. Researchers also explored the impact of basis set convergence on model accuracy. Comparing models fitted using a converged basis set with those using a smaller basis set revealed a small but noticeable increase in error with the smaller set, particularly at longer distances. However, the K parameter remained relatively stable, reinforcing the importance of a reasonably converged basis set without being overly sensitive to its specific details. Testing the model on acene dimers, larger and more complex systems, validated its applicability to a wider range of molecular structures.

These results demonstrate the model’s scalability and consistent performance. Key findings emphasize the crucial role of valence density in the model, simplifying calculations and improving transferability. The model’s robustness and transferability were consistently demonstrated across different methods, basis sets, and systems. While the model still encounters challenges accurately representing repulsive forces at very short distances, the K parameter remains a key factor in achieving accurate results. These investigations confirm the importance of basis set convergence for optimal accuracy, and demonstrate the model’s potential for broader applications.

Universal Parameter Accurately Models Pauli Repulsion

Scientists developed a new model, the anisotropic valence density overlap (AVDO) model, to accurately calculate Pauli exchange-repulsion, a crucial intermolecular interaction. The work demonstrates a significant reduction in the number of parameters needed to achieve high accuracy in molecular force fields, moving from 78 parameters in existing models to a single universal parameter within the AVDO model. Testing on the S101x7 dataset, a collection of 101 organic molecule dimers sampled at seven distances, revealed the AVDO model achieves a relative root mean square error (RMSE) of 7% for equilibrium geometries, compared to standard SAPT(DFT) reference calculations. Further analysis using a test set of fluorinated hydrocarbons and other molecules not included in the initial training data confirmed the model’s transferability, maintaining an accuracy with a relative RMSE of 9%.

Researchers observed that removing core electrons and specific orbitals from oxygen and nitrogen atoms further improved the model’s performance, achieving the lowest RMSE values. Specifically, the model with oxygen and nitrogen 2s orbitals removed delivered the best results, demonstrating nearly twice the accuracy of the all-electron model. Measurements of acene homodimers, systems of increasing size, validated the model’s scalability and consistent performance across different molecular systems. While acknowledging a slight decrease in accuracy at very short intermolecular distances, the team demonstrated the AVDO model achieves comparable results to existing models with significantly fewer parameters. For example, the AMOEBA force field requires 26 atom types and 78 fitted parameters to achieve an RMSE of 0. 4 kcal/mol, while the AVDO model achieves comparable accuracy with a single universal parameter.

Universal Parameter Accurately Models Exchange Repulsion

This work presents a new model for calculating Pauli exchange-repulsion, a crucial intermolecular interaction, with significantly improved transferability and accuracy. Current methods often require a large number of parameters dependent on specific atom types, hindering the development of broadly applicable force fields. Researchers have developed the anisotropic valence density overlap (AVDO) model, which achieves sub-kcal/mol accuracy for common biologically relevant molecular interactions and larger acene molecules using a single, universal parameter. This parameter relates to atomic cross-sectional area and demonstrates consistent performance across diverse chemical systems.

The AVDO model represents a substantial advancement by simplifying the representation of exchange-repulsion while maintaining high accuracy. By focusing on valence density rather than all-electron density, the model achieves improved transferability, performing well even with molecules containing atom types not present in its training data. While the AVDO model is computationally more demanding than simpler approaches, the researchers suggest its integration into machine-learned force field frameworks could offset this cost. Future work aims to combine the AVDO model with machine learning techniques to predict density, further reducing the size of datasets needed for accurate simulations.

This research brings the field closer to developing transferable, high-accuracy force fields for applications such as drug discovery and the generation of synthetic data for machine learning. The authors acknowledge that the accuracy of the model relies on the quality of the underlying density calculations. Future research will focus on improving computational efficiency and exploring the use of higher-accuracy methods for calculating density.