What Levels of Coupled Cluster Theory Are Appropriate for Transition Metal Systems? A Study Using Near-Exact Quantum Chemical Values for 3d Transition Metal Binary Compounds

Abstract

Transition metal compounds are traditionally considered to be challenging for standard quantum chemistry approximations like coupled cluster (CC) theory, which are usually employed to validate lower level methods like density functional theory (DFT). To explore this issue, we present a database of bond dissociation energies (BDEs) for 74 spin states of 69 diatomic species containing a 3d transition metal atom and a main group element, in the moderately sized def2-SVP basis. The presented BDEs appear to have an (estimated) 3σ error less than 1 kJ/mol relative to the exact solutions to the nonrelativistic Born−Oppenheimer Hamiltonian. These benchmark values were used to assess the performance of a wide range of standard single reference CC models, as the results should be beneficial for understanding the limitations of these models for transition metal systems. We find that interactions between metals and monovalent ligands like hydride and fluoride are well described by CCSDT. Similarly, CCSDTQ appears to be adequate for bonds between metals and nominally divalent ligands like oxide and sulfide. However, interactions with polyvalent ligands like nitride and carbide are more challenging, with even CCSDTQ(P) Λ yielding errors on the scale of a few kJ/mol. We also find that many perturbative and iterative approximations to higher order terms either yield disappointing results or actually worsen the performance relative to the baseline low level CC method, indicating that complexity does not always guarantee accuracy.

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

“…This level of accuracy, but with respect to near-exact benchmark calculations, could only be attained via high orders of CC theory which are not scalable to larger systems. 26 Ref. 26 implies, as might be expected, that higher orders of CC theory are needed to describe increasing numbers of bonds; however, there were many exceptions to this trend.…”

“…26 Ref. 26 implies, as might be expected, that higher orders of CC theory are needed to describe increasing numbers of bonds; however, there were many exceptions to this trend. Considering even the simplest bonding motif (i.e.…”

“…Transition metal atoms with partially-filled valence d shells can exhibit substantial MR character due to the close energetic spacing of many low-lying electronic states, in contrast to the spectra of typical closed-shell organic compounds. 20 Transition metal diatomics have been studied extensively in recent years, 3,4,[20][21][22][23][24][25][26][27] and recent precise experiments from Morse et. al.…”

Predicting Ligand-Dissociation Energies of 3d Coordination Complexes with Auxiliary-Field Quantum Monte Carlo

“…A recent study by Head-Gordon and co-workers found that high levels of CC, up to CCSDTQ, are required for chemical accuracy against an exact method known as Adaptive Sampling Configuration Interaction (ASCI) results, albeit in a small basis set. 42 Wilson and co-workers collected a set of 225 heats of formation for compounds with first row transition metal atoms. 24 They found good performance for their composite CC scheme vs. a subset of experimental data with small uncertainties, but the mean absolute error (MAE) of around 3 kcal/mol may be insufficient for many chemical applications.…”

Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Towards Benchmark Quantum Chemistry for Transition Metals

“…While the data sets enumerated above contained many very challenging electronic structure problems for which the accuracy of coupled cluster methods is expected to be lower than for organic molecules, 28,30,57 one could argue that the molecular structures that were studied are not representative of those considered relevant by inorganic chemists to biology, catalysis, and materials science. Firstly, the diatomic systems are small and coordinatively unsaturated; one could argue that the failures of DFT for some of these cases are not relevant to practical applications.…”