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Consistent GMTKN55 and molecular-crystal accuracy using minimally empirical DFT with XDM(Z) dispersion

Kyle R. Bryenton, Erin R. Johnson

TL;DR

This work tests a one-parameter Z-damping variant for the XDM dispersion correction across a broad GMTKN55 molecular benchmark and several molecular-crystal solids, comparing it with the traditional Becke–Johnson damping. The study demonstrates that XDM(Z) resolves overbinding seen with XDM(BJ) in metal clusters, while maintaining competitive accuracy for main-group chemistry, as evidenced by a best-in-class WTMAD-4 (5.43) for revPBE0-XDM(Z) and strong solid-state performance when paired with PBE0, revPBE0, or B86bPBE0. The analysis emphasizes outliers as a critical diagnostic tool, arguing that improved physics to reduce large errors can be more valuable than adding empirical parameters. Overall, XDM(Z) provides a simple, transferable, minimally empirical dispersion correction that performs reliably across both molecular and solid-state contexts, with revPBE0-XDM(Z) and B86bPBE0-XDM(Z) highlighted as especially robust choices.

Abstract

Density-functional theory (DFT) has become the workhorse of modern computational chemistry, with dispersion corrections such as the exchange-hole dipole moment (XDM) model playing a key role in high-accuracy modelling of large-scale systems. All previous production implementations of XDM have used the two-parameter Becke--Johnson damping function based on atomic radii. Here, we introduce and implement a new XDM variant that uses a one-parameter damping function based on atomic numbers, recently proposed by Becke. Both this new Z damping and the canonical BJ-damping variants of XDM are benchmarked on the comprehensive GMTKN55 database using minimally empirical generalised-gradient-approximation, global hybrid, and range-separated hybrid functionals. This marks the first time that the XDM (and many-body dispersion, MBD) corrections have been tested on the GMTKN55 set. Using the new WTMAD-4 metric, an outlier analysis is performed for all new data, as well as for top-ranking functionals from the literature at each rung, providing insight into both performance and consistency across the dataset. To test Z damping's transferability to the solid state, four benchmarks involving molecular crystals are also considered. Across these molecular and solid-state benchmarks, the revPBE0 and B86bPBE0 hybrid functionals, paired with the Z damped XDM variant, show excellent performance.

Consistent GMTKN55 and molecular-crystal accuracy using minimally empirical DFT with XDM(Z) dispersion

TL;DR

This work tests a one-parameter Z-damping variant for the XDM dispersion correction across a broad GMTKN55 molecular benchmark and several molecular-crystal solids, comparing it with the traditional Becke–Johnson damping. The study demonstrates that XDM(Z) resolves overbinding seen with XDM(BJ) in metal clusters, while maintaining competitive accuracy for main-group chemistry, as evidenced by a best-in-class WTMAD-4 (5.43) for revPBE0-XDM(Z) and strong solid-state performance when paired with PBE0, revPBE0, or B86bPBE0. The analysis emphasizes outliers as a critical diagnostic tool, arguing that improved physics to reduce large errors can be more valuable than adding empirical parameters. Overall, XDM(Z) provides a simple, transferable, minimally empirical dispersion correction that performs reliably across both molecular and solid-state contexts, with revPBE0-XDM(Z) and B86bPBE0-XDM(Z) highlighted as especially robust choices.

Abstract

Density-functional theory (DFT) has become the workhorse of modern computational chemistry, with dispersion corrections such as the exchange-hole dipole moment (XDM) model playing a key role in high-accuracy modelling of large-scale systems. All previous production implementations of XDM have used the two-parameter Becke--Johnson damping function based on atomic radii. Here, we introduce and implement a new XDM variant that uses a one-parameter damping function based on atomic numbers, recently proposed by Becke. Both this new Z damping and the canonical BJ-damping variants of XDM are benchmarked on the comprehensive GMTKN55 database using minimally empirical generalised-gradient-approximation, global hybrid, and range-separated hybrid functionals. This marks the first time that the XDM (and many-body dispersion, MBD) corrections have been tested on the GMTKN55 set. Using the new WTMAD-4 metric, an outlier analysis is performed for all new data, as well as for top-ranking functionals from the literature at each rung, providing insight into both performance and consistency across the dataset. To test Z damping's transferability to the solid state, four benchmarks involving molecular crystals are also considered. Across these molecular and solid-state benchmarks, the revPBE0 and B86bPBE0 hybrid functionals, paired with the Z damped XDM variant, show excellent performance.
Paper Structure (11 sections, 11 equations, 1 figure, 5 tables)

This paper contains 11 sections, 11 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Data Sets
  4. Damping-Parameter Fit Set
  5. Molecular Benchmarks
  6. Solid-State Benchmarks
  7. Computational Methods
  8. Results and Discussion
  9. Molecular Benchmarks
  10. Molecular-Crystal Benchmarks
  11. Summary

Figures (1)

  • Figure 1: Comparison of BJ- and Z-damping functions. The plots use XDM data for the free atoms only, computed with the B86bPBE functional and tight basis settings using FHI-aims.