Chemistry’s Core Calculations Become More Accurate with Simplified Modelling Technique

Researchers are continually striving to improve the accuracy and efficiency of density-functional theory (DFT) calculations, a cornerstone of modern chemistry. Kyle R. Bryenton and Erin R. Johnson, both from the Department of Physics and Atmospheric Science at Dalhousie University, alongside et al., present a novel implementation of the exchange-hole dipole moment (XDM) dispersion correction. Their work addresses a long-standing need for minimally empirical methods capable of consistently modelling both molecular and solid-state systems with high accuracy. By introducing a new, one-parameter damping function and benchmarking it against the comprehensive GMTKN55 database, a first for XDM and many-body dispersion corrections, this research demonstrates a pathway towards more reliable and transferable DFT calculations, ultimately advancing our ability to predict the behaviour of complex chemical systems.

Dispersion corrections, such as the exchange-hole dipole moment (XDM) model, play a crucial role in these calculations. All existing implementations of XDM have relied on the two-parameter Becke, Johnson damping function, which is based on atomic radii.

This work introduces and implements a novel XDM variant employing a one-parameter damping function grounded in atomic numbers, a concept recently proposed by Becke. Both this new Z damping and the established BJ-damping versions of XDM have been rigorously benchmarked against the comprehensive GMTKN55 database.
This benchmarking utilised a range of minimally empirical generalised-gradient-approximation, global hybrid, and range-separated hybrid functionals, marking the first time XDM, and many-body dispersion (MBD) corrections, have been systematically tested on the GMTKN55 set. An outlier analysis, utilising the new WTMAD-4 metric, was performed on all generated data, alongside top-performing functionals from existing literature at each level of theory.

This analysis provides valuable insight into both the performance and consistency of these methods across the dataset. To assess the Z damping’s applicability to solid-state systems, four benchmarks involving molecular crystals were also investigated. Across these molecular and solid-state benchmarks, the revPBE0 and B86bPBE0 hybrid functionals, when combined with the Z-damped XDM variant, consistently demonstrate excellent performance.

The research addresses a known deficiency in the original XDM formulation, specifically its inaccurate prediction of binding energies for certain alkali-metal clusters. The error stemmed from the Becke, Johnson damping function, prompting the development of the Z-dependent alternative, which simplifies the model by using only one empirical parameter.

This new approach not only improves accuracy but also enhances the computational efficiency of dispersion corrections within density-functional theory. The implementation of Z damping within the FHI-aims software and the open-source PostG code broadens its accessibility and potential impact on diverse quantum-chemical calculations.

Implementation and benchmarking of Z-damping within exchange-hole dipole moment dispersion corrections

A central focus of this work involved implementing a new variant of the exchange-hole dipole moment (XDM) dispersion correction within the FHI-aims code and the open-source PostG program. The research introduced Z damping, a one-parameter damping function based on atomic numbers, as an alternative to the conventional Becke, Johnson (BJ) damping function which relies on two parameters derived from atomic radii.

Both Z damping and BJ damping were integrated into XDM to assess their performance across a range of chemical systems and density functionals. To rigorously benchmark these damping functions, calculations were performed on the comprehensive GMTKN55 database, comprising 55 chemical systems with associated thermochemical data.

Minimally empirical generalised-gradient-approximation, global hybrid, and range-separated hybrid functionals were employed in conjunction with both XDM variants. This represents the first application of XDM, and many-body dispersion (MBD) corrections, to the GMTKN55 benchmark set, enabling a detailed comparison of performance.

An outlier analysis utilising the WTMAD-4 metric was conducted on the newly generated data, alongside top-ranking functionals from existing literature, to evaluate both accuracy and consistency across the entire dataset. Beyond molecular benchmarks, the transferability of Z damping to solid-state systems was investigated through calculations on four molecular crystal benchmarks.

These calculations assessed the ability of Z damping to accurately model intermolecular interactions within crystalline structures. The revPBE0 and B86bPBE0 hybrid functionals, when paired with the Z-damped XDM variant, consistently demonstrated excellent performance across both molecular and solid-state benchmarks, highlighting the potential of this combination for high-accuracy modelling of diverse chemical systems.

Z damping improves dispersion corrections for alkali metals and noble gases

Across molecular and solid-state benchmarks, revPBE0 and B86bPBE0 hybrid functionals, paired with the Z damped XDM variant, demonstrate excellent performance. The Z-damping function consistently reduces the magnitude of the dispersion energy compared to Becke, Johnson damping, particularly for lighter atoms like lithium and sodium.

Calculations involving lithium and sodium reveal a substantial increase in damping strength with Z damping, correcting overbinding observed with Becke, Johnson damping in Li8 and Na8 clusters. In the united-atom limit, the trend of dispersion energies shifts from Na>Li>Ar>Ne with Becke, Johnson damping to Ar>Na≈Ne>Li with Z damping, aligning with expectations for correlation energies proportional to atomic number.

The study benchmarked both Z damping and the canonical Becke, Johnson damping variants of XDM on the comprehensive GMTKN55 database, marking the first time these corrections were tested on this set. An outlier analysis utilising the new WTMAD-4 metric was performed on all new data, alongside top-ranking functionals from the literature at each rung of Jacob’s ladder.

The WTMAD-4 metric assigns weights to each subset of benchmarks based on the mean error obtained from ten representative minimally empirical hybrid functionals, allowing for a nuanced evaluation of performance. Specifically, weights are calculated as wi = 100 Nbench * (3.5 / MAD10-DFA i), where Nbench is the total number of benchmarks and MAD10-DFA i represents the mean error for each subset.

To assess performance, the number of benchmarks exceeding a specified error threshold was also quantified, with the goal of minimising Nr>2 and Nd>2, indicating cases where errors more than double the 10-DFA mean or exceed 2 kcal/mol. Four benchmarks involving molecular crystals were also considered to test Z damping’s transferability to the solid state, including the X23 set with 23 molecular crystals, HalCrys4 with four halogen crystals, and ICE13 evaluating ice polymorphs. This new approach was benchmarked against a comprehensive database of chemical systems, GMTKN55, and also assessed for its performance with molecular crystals, representing a significant first for XDM and many-body dispersion (MBD) corrections.

The study systematically evaluated various combinations of exchange-correlation functionals with both the new Z damping and the established Becke, Johnson (BJ) damping, providing detailed insight into their performance and consistency across diverse chemical scenarios. Evaluations utilising the WTMAD-4 metric revealed that the revPBE0 hybrid functional, when paired with Z-damped XDM, exhibited particularly strong performance, achieving the lowest overall error and minimising the occurrence of significant outliers.

The B86bPBE0 functional with Z-damped XDM also demonstrated excellent results, offering a comparable level of accuracy. While the performance of different dispersion corrections, D3(BJ), XDM(BJ), and XDM(Z), was generally similar, notable distinctions emerged when applied to systems containing metals, influencing the distribution of outliers.

The authors acknowledge that the W4-11 set of atomisation energies consistently represented a significant outlier for several functionals, indicating a potential limitation in accurately modelling these specific systems. Future research could focus on further refining the treatment of metal-containing systems within DFT, potentially through the development of more specialised functionals or dispersion corrections.

The demonstrated transferability of the Z-damped XDM to solid-state systems suggests a promising avenue for extending its application to materials science and condensed-phase chemistry. The consistent strong performance of XDM-corrected functionals with GGAs and global hybrid functionals establishes a reliable foundation for high-accuracy modelling of large-scale systems, offering a valuable tool for a wide range of chemical investigations.