Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. We illustrate with catastrophic failures of a toy functional applied to H2+ at varying bond lengths, where the standard fitting procedure misses the exact functional; Grimme’s D3 fit to noncovalent interactions, which can be contaminated by large density errors such as in the WATER27 and B30 data sets; and double-hybrids trained on self-consistent densities, which can perform poorly on systems with density-driven errors. In these cases, more accurate results are found at no additional cost by using Hartree–Fock (HF) densities instead of self-consistent densities. For binding energies of small water clusters, errors are greatly reduced. Range-separated hybrids with 100% HF at large distances suffer much less from this effect.
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Extending density functional theory with near chemical accuracy beyond pure water
Abstract Density functional simulations of condensed phase water are typically inaccurate, due to the inaccuracies of approximate functionals. A recent breakthrough showed that the SCAN approximation can yield chemical accuracy for pure water in all its phases, but only when its density is corrected. This is a crucial step toward first-principles biosimulations. However, weak dispersion forces are ubiquitous and play a key role in noncovalent interactions among biomolecules, but are not included in the new approach. Moreover, naïve inclusion of dispersion in HF-SCAN ruins its high accuracy for pure water. Here we show that systematic application of the principles of density-corrected DFT yields a functional (HF-r 2 SCAN-DC4) which recovers and not only improves over HF-SCAN for pure water, but also captures vital noncovalent interactions in biomolecules, making it suitable for simulations of solutions.
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- Award ID(s):
- 2154371
- PAR ID:
- 10396687
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 14
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of “gold standard” coupled-cluster theory. Building upon the accuracy of DC-SCAN within a many-body formalism, we introduce a data-driven many-body potential energy function, MB-SCAN(DC), that quantitatively reproduces coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, molecular dynamics simulations carried out with MB-SCAN(DC) also reproduce the properties of liquid water, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the liquid phase.
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We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/
from about 42 meV/ for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes. -
Density functional theory (DFT) has been applied to modeling molecular interactions in water for over three decades. The ubiquity of water in chemical and biological processes demands a unified understanding of its physics, from the single molecule to the thermodynamic limit and everything in between. Recent advances in the development of data-driven and machine-learning potentials have accelerated simulation of water and aqueous systems with DFT accuracy. However, anomalous properties of water in the condensed phase, where a rigorous treatment of both local and non-local many-body (MB) interactions is in order, are often unsatisfactory or partially missing in DFT models of water. In this review, we discuss the modeling of water and aqueous systems based on DFT and provide a comprehensive description of a general theoretical/computational framework for the development of data-driven many-body potentials from DFT reference data. This framework, coined MB-DFT, readily enables efficient many-body molecular dynamics (MD) simulations of small molecules, in both gas and condensed phases, while preserving the accuracy of the underlying DFT model. Theoretical considerations are emphasized, including the role that the delocalization error plays in MB-DFT potentials of water and the possibility to elevate DFT and MB-DFT to near-chemical-accuracy through a density-corrected formalism. The development of the MB-DFT framework is described in detail, along with its application in MB-MD simulations and recent extension to the modeling of reactive processes in solution within a quantum mechanics/MB molecular mechanics (QM/MB-MM) scheme, using water as a prototypical solvent. Finally, we identify open challenges and discuss future directions for MB-DFT and QM/MB-MM simulations in condensed phases.more » « less
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Second-order Møller–Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeling problems in organic and biological chemistry. However, MP2 suffers from known limitations in the description of van der Waals (London) dispersion interactions and reaction thermochemistry. Here, a spin-component-scaled, dispersion-corrected MP2 model (SCS-MP2D) is proposed that addresses these weaknesses. The dispersion correction, which is based on Grimme's D3 formalism, replaces the uncoupled Hartree–Fock dispersion inherent in MP2 with a more robust coupled Kohn–Sham treatment. The spin-component scaling of the residual MP2 correlation energy then reduces the remaining errors in the model. This two-part correction strategy solves the problem found in earlier spin-component-scaled MP2 models where completely different spin-scaling parameters were needed for describing reaction energies versus intermolecular interactions. Results on 18 benchmark data sets and two challenging potential energy curves demonstrate that SCS-MP2D considerably improves upon the accuracy of MP2 for intermolecular interactions, conformational energies, and reaction energies. Its accuracy and computational cost are competitive with state-of-the-art density functionals such as DSD-BLYP-D3(BJ), revDSD-PBEP86-D3(BJ), ωB97X-V, and ωB97M-V for systems with ∼100 atoms.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41467-023-36094-y
