Coupled cluster and configuration interaction diagnostics have been examined in order to assess the reliability of single reference quantum methods for a series of 3d transition metal species including hydrides, nitrides, chalcogenides, halides, small clusters, coordination complexes, and metal dimers. Several means of diagnostics have been considered including T₁ and D₁ diagnostics (the Frobenius norm and matrix 2-norm of coupled cluster amplitudes for single excitations, respectively), C₀² (the weight of leading configuration of a complete active space wave function), and %TAE (percent total atomization energy). T₁ and D₁ diagnostics are strongly correlated for certain metal–ligand bonding types. The use of T₁ and D₁ together with %TAE can provide more reliable assessment of the severity of nondynamical correlation than a single indicator can provide. New criteria, namely T₁ > 0.05, D₁ > 0.15, and |%TAE| > 10, are suggested to identify inorganic species with substantial nondynamical correlation. For these systems, energies and spectroscopic properties computed using single reference electronic correlation methods may suffer from large errors and unpredictable behavior. Conversely, a computation where a molecule is below one or more of these thresholds does not always imply domination by a single reference. Some historically pathological molecules such as Mn₂ and Cr₂ show T₁ < 0.05 and D₁ < 0.15. Current implementations of coupled cluster diagnostics may still be insufficient for categorization of molecules that have pronounced nondynamical correlation.

An alternative to the Gaussian-n (G1, G2, and G3) composite methods of computing molecular energies is proposed and is named the “correlation consistent composite approach” (ccCA, ccCA-CBS-1, ccCA-CBS-2). This approach uses the correlation consistent polarized valence (cc-pVXZ) basis sets. The G2-1 test set of 48 enthalpies of formation (ΔHf), 38 adiabatic ionization potentials (IPs), 25 adiabatic electron affinities (EAs), and 8 adiabatic proton affinities (PAs) are computed using this approach, as well as the ΔHf values of 30 more systems. Equilibrium molecular geometries and vibrational frequencies are obtained using B3LYP density functional theory. When applying the ccCA-CBS method with the cc-pVXZ series of basis sets augmented with diffuse functions, mean absolute deviations within the G2-1 test set compared to experiment are 1.33kcalmol−1 for ΔHf,0.81kcalmol−1 for IPs, 1.02kcalmol−1 for EAs, and 1.51kcalmol−1 for PAs, without including the “high-level correction” (HLC) contained in the original Gn methods. Whereas the HLC originated in the Gaussian-1 method as an isogyric correction, it evolved into a fitted parameter that minimized the error of the composite methods, eliminating its physical meaning. Recomputing the G1 and G3 enthalpies of formation without the HLC reveals a systematic trend where most ΔHf values are significantly higher than experimental values. By extrapolating electronic energies to the complete basis set (CBS) limit and adding G3-like corrections for the core-valence and infinite-order electron correlation effects, ccCA-CBS-2 often underestimates the experimental ΔHf, especially for larger systems. This is desired as inclusion of relativistic and atomic spin-orbit effects subsequently improves theoretical ΔHf values to give a 0.81kcalmol−1 mean absolute deviation with ccCA-CBS-2. The ccCA-CBS method is a viable “black box” method that can be used on systems with at least 10–15 heavy atoms.

The recently developed correlation consistent Composite Approach for transition metals (ccCA-TM) was utilized to compute the thermochemical properties for a collection of 225 inorganic molecules containing first row (3d) transition metals, ranging from the monohydrides to larger organometallics such as Sc(C₅H₅)₃ and clusters such as (CrO₃)₃. Ostentatiously large deviations of ccCA-TM predictions stem mainly from aging and unreliable experimental data. For a subset of 70 molecules with reported experimental uncertainties less than or equal to 2.0 kcal mol^–1, regardless of the presence of moderate multireference character in some molecules, ccCA-TM achieves transition metal chemical accuracy of ±3.0 kcal mol^–1 as defined in our earlier work [J. Phys. Chem. A 2007, 111, 11269–11277] by giving a mean absolute deviation of 2.90 kcal mol^–1 and a root-mean-square deviation of 3.91 kcal mol^–1. As subsets are constructed with decreasing upper limits of reported experimental uncertainties (5.0, 4.0, 3.0, 2.0, and 1.0 kcal mol^–1), the ccCA-TM mean absolute deviations were observed to monotonically drop off from 4.35 to 2.37 kcal mol^–1. In contrast, such a trend is missing for DFT methods as exemplified by B3LYP and M06 with mean absolute deviations in the range 12.9–14.1 and 10.5–11.0 kcal mol^–1, respectively. Salient multireference character, as demonstrated by the T₁/D₁ diagnostics and the weights (C₀²) of leading electron configuration in the complete active self-consistent field wave function, was found in a significant amount of molecules, which can still be accurately described by the single reference ccCA-TM. The ccCA-TM algorithm has been demonstrated as an accurate, robust, and widely applicable model chemistry for 3d transition metal-containing species with versatile bonding features.