Multireference Character for 3d Transition-Metal-Containing Molecules

Abstract

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), C0(2) (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.

Ethylene Trimerisation with Cr-PNP Catalysts: A Theoretical Benchmarking Study and Assessment of Catalyst Oxidation State

“…[23] This being the case, some uncertainty in the relative energy of the doublet state can be tolerated, although the overall lack of convergence between G4(MP2,rel) and CCSD(T) is disappointing and again highlights the difficulties in obtaining highly accurate energies for multireference Cr systems. [26,27] Agreement between the two reference methods for quartet and sextet spin conversions (blue bars on Fig. 1a, b), and the 2 -3 reaction energy on the quartet and sextet surfaces (Fig.…”

“…Complications arise, however, from the possibility of spin-state changes during the reaction, [22][23][24] and the difficulty in accurately calculating the energies of transition metal systems. [25] Chromium in particular has been shown to be a very difficult metal in some instances, owing to the possibility of substantial multireference character, [26,27] such that the accuracy of commonly employed density functional theory (DFT) methods cannot be assumed. The only theoretical study of this system thus far focussed on the role of MAO in the reaction, and did include some validation of DFT methods.…”

PREDICTION OF THE SPECTROSCOPIC PARAMETERS OF NEW IRON COMPOUNDS: HYDRIDE OF IRON CYANIDE/ISOCYANIDE, HFeCN/HFeNC

“…A value of for the T1 diagnostic of less than 0.05 is proposed by Jiang et al (2012) for obtaining reliable energetics and spectroscopic properties in 3d transition metal compounds using single-reference based methods. From the results shown in Table 2, with the isomer HNCFe as the only exception (located more than 40 kcal/mol above the most stable isomer), it can be inferred that single-reference methods are suitable for describing these isomers (spin contamination values are negligible and T1 diagnostics are less than 0.05).…”

Structures of d4 MH3X: a Computational Study of the Influence of the Metal and the Ligands

“…However, a recent study of Jiang et al pointed out that the criteria established for organic molecules (T 1 < 0.02 and D 1 < 0.05) are no longer valid for molecular systems with transition metals element. 34 On the basis of a statistical analysis of a set of 225 species, these authors proposed T 1 < 0.05 and 9 give the same three minima but show that td is the most stable isomer. DFT calculations using a different ECP and a different functional for the metal 7a,9 from the one used in this work give td and pst as the only minima, with pst being 8.6 kcal mol −1 lower in energy relative to td.…”