Benchmark Calculations of Energetic Properties of Groups 4 and 6 Transition Metal Oxide Nanoclusters Including Comparison to Density Functional Theory

Abstract

The heats of formation and the normalized clustering energies (NCEs) for the group 4 and group 6 transition metal oxide (TMO) trimers and tetramers have been calculated by the Feller-Peterson-Dixon (FPD) method. The heats of formation predicted by the FPD method do not differ much from those previously derived from the NCEs at the CCSD(T)/aT level except for the CrO3 nanoclusters. New and improved heats of formation for Cr3O9 and Cr4O12 were obtained using PW91 orbitals instead of Hartree-Fock (HF) orbitals. Diffuse functions are necessary to predict accurate heats of formation. The fluoride affinities (FAs) are calculated with the CCSD(T) method. The relative energies (REs) of different isomers, NCEs, electron affinities (EAs), and FAs of (MO2)n (M = Ti, Zr, Hf, n = 1-4) and (MO3)n (M = Cr, Mo, W, n = 1-3) clusters have been benchmarked with 55 exchange-correlation density functional theory (DFT) functionals including both pure and hybrid types. The absolute errors of the DFT results are mostly less than ±10 kcal/mol for the NCEs and the EAs and less than ±15 kcal/mol for the FAs. Hybrid functionals usually perform better than the pure functionals for the REs and NCEs. The performance of the two types of functionals in predicting EAs and FAs is comparable. The B1B95 and PBE1PBE functionals provide reliable energetic properties for most isomers. Long range corrected pure functionals usually give poor FAs. The standard deviation of the absolute error is always close to the mean errors, and the probability distributions of the DFT errors are often not Gaussian (normal). The breadth of the distribution of errors and the maximum probability are dependent on the energy property and the isomer.

Gas Phase Hydrolysis and Oxo‐Exchange of Actinide Dioxide Cations: Elucidating Intrinsic Chemistry from Protactinium to Einsteinium

“…We also performed calculations by changing the starting orbitals for the CCSD(T) calculations from the Hartree–Fock orbitals to Kohn–Sham orbitals from DFT, generated using the PW91 generalized gradient exchange‐correlation functional . The reference energy in CCSD arises from diagonalizing the normal HF Hamiltonian with these Kohn–Sham orbitals.…”

Benchmarking Density Functionals on First Row Transition Metal Fluorides (ScF−MnF)

“…If there are no experimental results available, then we compare our DFT results with CCSD(T) result. Because earlier studies suggests that, the CCSD(T) values are highly accurate [7]. From the Fig.…”

“…Theoretical studies on structure and energetic calculations of transition metal compounds are difficult, because of its partially filled and near degenerate d orbitals [4], [6]. The above problem can be overcome with the use of coupled-cluster method (CCSD(T)) and multi-reference approaches (MRCI) [7].…”

“…Because of these problems, many research groups are carried out DFT benchmark studies. Especially Truhlar et al [8]− [12] and Dixon et al [7], [13], [14] have studied most DFT benchmark calculations on metal containing complexes. Earlier, we have performed DFT benchmark studies on 3d-transition metal oxides (MOs) [15] and 3d-transition metal nitrides (MNs) [16].…”

Hydrogenation of 3d‐metal oxide clusters: Effects on the structure and magnetic properties

“…Close agreement between the results of BPW91/6–311 + G* computations and experimental data has been found for Fe n O − ( n = 2–6), M O 3 and M O 4 ( M ScZn), MnO n − ( n = 1–4), (FeO) n ( n = 1–4), and Cr 3 O 8 , The BPW91 functional was found to reliably reproduce the results of calculations obtained using the couple‐cluster method with singles, doubles, and non‐iterative inclusion of triples [CCSD(T)] for (TiO 2 ) n , (CrO 3 ) n , and FeO 2 clusters. Computations of the atomization energies of ( M O 3 ) n ( M Cr, Mo, W; n = 1–4), as well as the energetic properties of groups 4 and 6 transition metal oxide nanoclusters, and finally the binding energies using standard reference sets by a variety of different DFT and hybrid DFT methods have shown the BPW91 accuracy to be comparable to that of more recently developed exchange‐correlation functionals.…”