Chemical Bond Energies of 3d Transition Metals Studied by Density Functional Theory

Abstract

Despite their vast importance to inorganic chemistry, materials science, and catalysis, the accuracy of modeling the formation or cleavage of metal-ligand (M-L) bonds depends greatly on the chosen functional and the type of bond in a way that is not systematically understood. In order to approach a state of high-accuracy DFT for rational prediction of chemistry and catalysis, such system-dependencies need to be resolved. We studied 30 different density functionals applied to a "balanced data set" of 60 experimental diatomic M-L bond energies; this data set has no bias toward any d configuration, metal, bond type, or ligand as all of these occur to the same extent, and we can therefore identify accuracy bottlenecks. We show that the performance of a functional is very dependent on data set choice, and we dissect these effects into system type. In addition to the use of balanced data sets, we also argue that the precision (rather than just accuracy) of a functional is of interest, measured by standard deviations of the errors. There are distinct system dependencies both in the ligand and metal series: Hydrides are best described by a very large HF exchange percentage, possibly due to self-interaction error, whereas halides are best described by very small (0-10%) HF exchange fractions, and double-bond enforcing oxides and sulfides favor 10-25% HF exchange, as is also average for the full data set. Thus, average HF requirements hide major system-dependent requirements. For late transition metals Co-Zn, HF percentage of 0-10% is favored, whereas for the early transition metals Sc-Fe hybrid functionals with 20% HF exchange or higher are commonly favored. Accordingly, B3LYP is an excellent choice for early d-block but a poor choice for late transition metals. We conclude that DFT intrinsically underestimates the bond strengths of late vs early transition metals, correlating with increased effective nuclear charge. Thus, the revised RPBE, which reduces the overbinding tendency of PBE, is mainly an advantage for the early and mid transition metals and not very much for the late transition metals, i.e. there is a metal-dependent effect of the relative performance of RPBE vs PBE, which are widely used to study adsorption energetics on metal surfaces. Overall, the best performing functionals are PW6B95, the MN15 and MN15-L functionals, and the double hybrid B2PLYP.

Performance of Density Functional Theory for Transition Metal Oxygen Bonds

“…The local density functional SVWN was included for completeness as a reference point, which is mainly of theoretical interest as a limit of DFT, but which is still used. As expected SVWN over‐binds massively with an MAE and MSE of 178 kJ/mol.…”

“…However, most of the trends observed for the overall data set prevail for groups individually. Almost all groups are best described by hybrids with 10–20 % HF‐exchange (or the double hybrid B2PLYP), in contrast to what is seen for some other ligands . The most notable exception is group 12, for which the GGAs perform well.…”

“…Zero‐point energies (ZPE), relativistic corrections to electronic energies, and used spin states for the 60 diatomics were taken from previous work where these parameters were carefully evaluated against the best experimental data and CCSD(T) . Thus, for example, the previously observed uniform accuracy of CCSD(T) across the 3d, 4d, and 5d series shows that the applied spin orbit coupling and scalar relativistic corrections capture accurately (errors of ∼5 kJ/mol) the full d‐block as a whole as required for DFT applications across all three periods . For convenience these corrections are summarized in the supporting information Tables S6–S9.…”

“…The basis set used for single‐point energies was def2‐QZVPPD for the metals (Sc−Zn, Y−Cd and La−Hg) and aug‐cc‐pV5Z for the very electronegative oxygen. This basis set is saturated to within 2–3 kJ/mol in terms of errors in BDEs as shown from previous work …”

“…In particular, the use of the BDEs of metalligand bonds are receiving significant attention as best-practice benchmark properties for chemical reactivity across the dblock. [30,[33][34][35][36][37][38][39][40] The success largely relates to the fact that the diatomic MÀ O BDEs correlate better than any other known single descriptor to the chemisorption energies of pure metal surfaces, with R 2 approaching 0.89 when computed with the same methods, [30] across a range of more than 500 kJ/mol in both O 2 chemisorption energies and MÀ O BDEs within the dblock. Coordinative saturation, metalÀ metal modulations and solvent effects contribute smaller errors to the DFT-modelled process than the local MÀ O bond, because the relative MÀ O bond energies vary by an order of magnitude more than the metalÀ metal modulating influences, or correspondingly, the trend in cohesive energy changes upon ligand dissociation from different metal surfaces.…”