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New Benchmark Set of Transition-Metal Coordination Reactions for the Assessment of Density Functionals
Thomas Weymuth, Erik P. A. Couzijn, Peter Chen, Markus Reiher
TL;DR
Existing databases have poor coverage of large transition-metal complexes, which can matter for practical applications. The paper presents WCCR10 and benchmarks contemporary density functionals, finding that dispersion corrections can overshoot experimental reaction energies for some reactions.
Problem
Existing databases have rather poor coverage of large transition-metal complexes, a deficiency that can be significant for practical purposes.
Method
The paper presents WCCR10, a database of ten ligand dissociation energies, and assesses broad functional classes including GGA, meta-GGA, and hybrid functionals.
Results
Dispersion corrections yield reaction energies that overshoot experiment and uncorrected results for some reactions.
Takeaways & Limitations
WCCR10 provides a reference set for evaluating density-functional approximations on ligand dissociation energies in large transition-metal complexes.
Takeaways & Limitations
Contemporary density-functional accuracy often cannot be expected to suffice for a given application.
Abstract
from arXiv · showhide
We present the WCCR10 data set of ten ligand dissociation energies of large cationic transition metal complexes for the assessment of approximate exchange--correlation functionals. We analyze nine popular functionals, namely BP86, BP86-D3, B3LYP, B3LYP-D3, B97-D-D2, PBE, TPSS, PBE0, and TPSSh by mutual comparison and by comparison to experimental gas-phase data measured with well-known precision. The comparison of all calculated data reveals a large, system-dependent scattering of results with nonnegligible consequences for computational chemistry studies on transition metal compounds. Considering further the comparison with experiment, the non-empirical functionals PBE and TPSS turn out to be among the best functionals for our reference data set. The deviation can be lowered further by including Hartree--Fock exchange. Accordingly, PBE0 and TPSSh are the two most accurate functionals for our test set, but also these functionals exhibit deviations from experiment by up to 50 kJ/mol for individual reactions. As an important result we found no functional to be reliable for all reactions. Furthermore, for some of the ligand dissociation energies studied in this work, dispersion corrections yield results which increase the deviation from experiment. This deviation increases further if structure optimization including dispersion corrections is performed. Finally, we compare our results to other benchmark studies and highlight that the performance assessed for different density functionals depends significantly on the reference molecule set chosen.
1 Introduction
Existing density-functional benchmarks provide useful assessments, but they cover large transition-metal complexes poorly and often rely on small or uncertain reference systems. This motivates WCCR10, a database of ten accurately measured gas-phase ligand dissociation energies for evaluating nine widely used density functionals.
- Benchmarking gap: Large transition-metal complexes are poorly represented in existing benchmark databases, limiting their relevance to coordination chemistry.Coordination chemistry commonly involves complex, spatially extended ligand environments.
- Reference-data limitations: Existing transition-metal databases often contain small compounds, while many experimental reference data have substantial uncertainties that can mislead functional assessments.The Jiang database includes 225 molecules, but most are rather small; other databases likewise emphasize small compounds.
- Benchmarking gap: Small transition-metal molecules and reactions do not reliably predict density-functional performance for larger compounds.Large complexes also experience stronger dispersion effects, making size-dependent transfer especially problematic.
- Reference-data limitations: Reliable gas-phase reference energies are needed because high-level ab initio data are unavailable for large complexes and solvent effects should be excluded.The authors therefore resort to accurately measured gas-phase ligand dissociation energies obtained by tandem mass spectrometry.
- WCCR10 contribution: WCCR10 contains ten selected ligand dissociation energies and evaluates nine widely used density functionals.The experimental energies were determined from collision-induced dissociation measurements and Monte Carlo simulations of the dissociation process.
2 Computational Methodology
The WCCR10 benchmark comprises ten ligand-dissociation reactions in large, closed-shell, charged transition-metal complexes, with experimental energies obtained through collision-induced dissociation and RRKM-based analysis. Computational values were evaluated using nine density functionals, dispersion variants, unconstrained structure optimizations, large basis sets, relativistic effective core potentials, and zero-point-energy corrections.
- Benchmark database: WCCR10 contains ten ligand-dissociation reactions selected to balance transition metals and ligand types while avoiding similar reaction duplicates.All molecules have closed-shell electronic structures, and the complexes are charged because the experimental measurements use mass spectrometry.
- Experimental reference data: Experimental ligand-dissociation energies were derived from collision-induced dissociation measurements and Monte Carlo simulations using reaction rates interpreted with approximate RRKM theory.The resulting energies are treated as free energies at 0 K and compared with computed electronic energies corrected for zero-point vibrational energies.
- Electronic-structure calculations: Structures were generally optimized without symmetry constraints for each functional using def2-QZVPP basis sets, scalar-relativistic effective core potentials, and tight convergence thresholds.The protocol was intended to avoid errors from inconsistent molecular structures and reduce basis-set superposition error.
3 Results
The results show that functional choice can substantially alter optimized structures and ligand dissociation energies, with dispersion corrections often producing especially large structural and energetic deviations. Across the benchmark, PBE0 performs best by MAD, but no functional is reliable for every reaction and rankings depend on the reference set.
- Structures: 91% of optimized structures have RMSD below 30 pm relative to BP86 structures.These structures are visually almost identical to the BP86 reference, especially for PBE.
- Structures: Dispersion-corrected functionals produce most structures with RMSD values larger than 30 pm and can induce contracted, stacked, nearly coplanar conformations.Large intramolecular dispersion effects are identified as responsible for the structural differences.
- Ligand dissociation energies: BP86-D3 predicts reaction 2 at 296 kJ mol−1 versus 161 kJ mol−1 with BP86 and 204.4 kJ mol−1 experimentally.Dispersion corrections therefore worsen agreement with experiment in this case and do not necessarily improve coordination energies.
- Comparison with other benchmark studies: No functional is clearly preferred for all reactions, and absolute errors vary significantly with the data set used.The qualitative ordering of functionals appears more stable across benchmark studies than the numerical error values.
4 Conclusions
The WCCR10 benchmark evaluates nine density functionals against accurately measured gas-phase ligand dissociation energies for large transition-metal complexes. Results show substantial system dependence: Hartree–Fock exchange can improve errors, but dispersion corrections and test-set choice can worsen or alter conclusions.
- WCCR10 comprises ten ligand dissociation energies for large transition-metal complexes with accurately measured experimental reference values.
- Nine functionals spanning GGA, meta-GGA, hybrid, and dispersion-corrected classes were compared under calculations designed to isolate functional effects.
- Dispersion corrections can overshoot experimental energies, produce divergent structures, and increase deviations after structure optimization.
- 39 kJ mol−1 is B3LYP’s mean absolute deviation among uncorrected functionals, whereas PBE and TPSS have clearly smaller mean and maximum errors.
- Adding Hartree–Fock exchange further improves the performance of the non-empirical functionals.
- Functional error values depend heavily on the chosen test set, so benchmark results require careful interpretation.
- More than 20 kJ mol−1 is PBE0’s average deviation, and its maximum deviation reaches 55 kJ mol−1, despite being the best WCCR10 functional.
Supporting Information
The Supporting Information provides structural coordinates and additional analyses underlying the benchmark calculations. It also documents reaction mechanisms and redetermined energies for selected reactions.
- Cartesian coordinates for all optimized structures are provided in the Supporting Information.
- Additional materials discuss dispersion-induced structural changes, reaction mechanisms for reactions 2 and 3, and redetermined energies for reactions 4 and 5.