Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Projector-Based Quantum Embedding Study of Iron Complexes

Projection-based embedding theory (PBET) is used to calculate and assess the challenging spin-crossover energies for a selection of small Fe-containing systems by embedding the metal center into the frozen potential of the ligands. MP2, CCSD, and CCSD(T) are embedded in potentials from the SCAN and r2SCAN functionals and compared with the canonical values for the constituent methods and previously reported reference values. Considering the PBET calculations as a correction for the underlying DFT, the embedding calculations are able to provided improvement for most cases. In some cases, the PBET methods are able to compensate for limitations in the wave function methods and produce results similar to more rigorous calculations from the literature. For the systems with spin-crossover energies near zero, the current methodology fails to provide consistent improvement. The isolated recalculation of the electronic structure around the metal center when embedded into a DFT treatment of the ligand field shows promise as a pragmatic and lower cost treatment compared to the canonical treatment of the whole system of the difficult class of spin-crossover complexes.

Performance of quantum chemistry methods for a benchmark set of spin-state energetics derived from experimental data of 17 transition metal complexes (SSE17)

Accurate prediction of spin-state energetics for transition metal (TM) complexes is a compelling problem in applied quantum chemistry, with enormous implications for modeling catalytic reaction mechanisms and computational discovery of materials. Computed spin-state energetics are strongly method-dependent and credible reference data are scarce, making it difficult to conduct conclusive computational studies of open-shell TM systems. Here, we present a novel benchmark set of first-row TM spin-state energetics, which is derived from experimental data of 17 complexes containing FeII, FeIII, CoII, CoIII, MnII, and NiII with chemically diverse ligands. The estimates of adiabatic or vertical spin-state splittings, which are obtained from spin crossover enthalpies or energies of spin-forbidden absorption bands, suitably back-corrected for the vibrational and environmental effects, are employed as reference values for benchmarking density functional theory (DFT) and wave function methods. The results demonstrate a high accuracy of the coupled-cluster CCSD(T) method, which features the mean absolute error (MAE) of 1.5 kcal mol-1 and maximum error of -3.5 kcal mol-1, and outperforms all the tested multireference methods: CASPT2, MRCI+Q, CASPT2/CC and CASPT2+δMRCI. Switching from Hartree-Fock to Kohn-Sham orbitals is not found to consistently improve the CCSD(T) accuracy. The best performing DFT methods are double-hybrids (PWPB95-D3(BJ), B2PLYP-D3(BJ)) with the MAEs below 3 kcal mol-1 and maximum errors within 6 kcal mol-1, whereas the DFT methods so far recommended for spin states (e.g., B3LYP*-D3(BJ) and TPSSh-D3(BJ)) are found to perform much worse with the MAEs of 5-7 kcal mol-1 and maximum errors beyond 10 kcal mol-1. This work is the first such extensive benchmark study of quantum chemistry methods for TM spin-state energetics making use of experimental reference data. The results are relevant for the proper choice of methods to characterize TM systems in computational catalysis and (bio)inorganic chemistry, and may also stimulate new developments in quantum-chemical or machine learning approaches.

Structural and energetic properties of cluster models of anatase-supported single late transition metal atoms: a density functional theory benchmark study

CONTEXT

Single-atom catalytic systems constitute an intriguing research topic due to their inherently different chemical behavior as compared to classic heterogeneous catalysts. In this study, cluster systems representing single late transition metal atoms adsorbed on anatase were constructed starting from previously generated periodic models and subjected to a density functional theory (DFT) benchmark study. The ability of different density functional approximations representing all rungs of the Jacob's Ladder classification to accurately describe bond lengths and adsorption energies was assessed for these clusters with the aim of revealing the functional that allows to retain the structural characteristics of the initial periodic system, while also delivering reliable energetics. In this regard, our results indicate that optimisation of the clusters with the meta-GGA functionals TPSS or RevTPSS provides the lowest mean unsigned error and root-mean-square deviations with respect to the periodic models. Moreover, these functionals and, to a slightly lesser degree, PW91 were also found to provide adsorption energies that are statistically the least deviating from the CCSD(T) reference data. More complex hybrid functionals appear to be performing less well.

METHODS

Cluster geometries were determined at the Kohn-Sham DFT level using the LANL2DZ basis set for the transition metals and the Pople 6-31G(d) basis set for O and H. The density functional approximations considered were SVWN, PBE, BP86, BLYP, PW91, TPSS, RevTPSS, M06L, M11L, B3LYP, PBE0, M06, M06-2X, MN15, ωB97X-D, CAM-B3LYP, M11, and MN12-SX. Reference adsorption energies of the metals on the support cluster were obtained at the CCSD(T)/LANL2TZ (transition metals)/6-311 +  + G(d,p)//RevTPSS/LANLD2DZ (transition metals)/6-31G*. Besides the above-mentioned functionals, energy calculations using the double-hybrid functionals, DSDPBEP86, PBE0-DH, and B2PLYP, were also performed. All adsorption energy calculations were carried out on the RevTPSS geometries.

Catalytic engineering of transition metal (TM: Ni, Pd, Pt)-coordinated Ge-doped graphitic carbon nitride (Ge@g-c3n4) nanostructures for petroleum hydrocarbon separation: An outlook from theoretical calculations

The extraction, processing, and utilization of petroleum often results in the release of diverse hydrocarbon pollutants into the environment, leading to severe ecological and health implications. Herein, the adsorption and separation of ethane (EAN), ethene (EEN), ethyne (EYN), and benzene (BZN) fractions of paraffin, olefin, acetylene, and aromatic petroleum hydrocarbons were investigated via the catalytically engineered nickel group transition metals; nickel (Ni), palladium (Pd), and platinum (Pt). These transition metals were coordinated on Germanium-doped graphitic carbon nitride (Ge@g-C3N4) nanostructures, and the behavior of the systems was studied through Kohn-Sham density functional theory (KS-DFT) with the B3LYP-D3(BJ)/Def2-SVP computational method. The adsorption of petroleum hydrocarbons decreased in the order Ge_Ni@C3N4 > Ge_Pd@C3N4 > Ge_Pt@C3N4>Ge_Pt@C3N4. These results showed that the coordination of Ni, Pd, and Pt within Ge@C3N4 improved the separation of petroleum hydrocarbons.

Improving the Accuracy in the Prediction of Transition-Metal Spin-State Energetics Using a Robust Variation-Based Approach: Density Functional Theory, CASPT2 and MC-PDFT Applied to the Case Study of Tris-Diimine Fe(II) Complexes

Designing ligands for transition metal complexes with a specified low-spin, high-spin or spin-crossover behavior is challenging. A major advance was recently made by Phan et al. [J. Am. Chem. Soc. 2017, 139, 6437-6447] who showed that the spin state of a homoleptic tris-diimine Fe(II) complex can be predicted from the N-N distance in the free diimine. They could thus predict the change in magnetic behavior on passing from the complexes of 2,2'-bipyridine (bpy), 2,2'-biimidazole (bim) and 2,2'-bis-2-imidazoline (bimz) ligands to those obtained with the modified analogs 4,5-diazafluoren-9-one (dafo), 1,1'-(α,α'-o-xylyl)-2,2'-bisimidazole (xbim) and 2,3,5,6,8,9-hexahydrodiimidazo[1,2-a:2', 1'-c]pyrazine (etbimz), respectively. Theoretically, the challenge lies in the accurate determination of the HS-LS zero-point energy difference ΔEHL°. The issue can be circumvented by using a variation-based approach, wherein ΔEHL° is not directly evaluated but obtained from the estimate of its variation Δ(ΔEHL°) in series of related systems, which include one whose ΔEHL° is accurately known [Phys. Chem. Chem. Phys. 2013, 15, 3752-3763; J. Phys. Chem. A 2022, 126, 6221-6235]. In this study, density functional theory (DFT), second-order multireference perturbation theory in its CASPT2 formulation, multiconfigurational pair DFT (MC-PDFT) and its hybrid formulation (HMC-PDFT) have been applied to the determination of Δ(ΔEHL°) in the pairs of complexes ( [ F e ( b p y ) 3 ] 2 + , [ F e ( d a f o ) 3 ] 2 + ) , ( [ F e ( b i m ) 3 ] 2 + , [ F e ( x b i m ) 3 ] 2 + ) and ( [ F e ( b i m z ) 3 ] 2 + , [ F e ( e t b i m z ) 3 ] 2 + ) . In DFT, we used several semilocal functionals and their global hybrids, as well as their D2, D3, D3BJ and D4 dispersion-corrected forms; and in MC-PDFT, different translated and fully translated functionals. The results are consistent with one another and in very good agreement with experiments. They show small to vanishing dependence on key details of the methods used: namely, the exact-exchange contribution to global hybrids; the ionization potential-electron affinity shift and basis sets used in the CASPT2 calculations; and the active spaces employed for the CASSCF wave functions used in the MC-PDFT and HMC-PDFT calculations. Insights into the change in the spin-state energetics accompanying the ligand exchanges were gained through a complexation energy analysis. Using the accurate CCSD(T) estimate of the HS-LS adiabatic energy difference in [ F e ( N C H ) 6 ] 2 + [J. Chem. Theory Comput. 2012, 8, 4216-4231], the Δ(ΔEHL°)-approach has been applied to the determination of ΔEHL° in the diimine complexes. The CASPT2 and DFT-D2 methods only give results in agreement with experiments. This suggests for the other methods a limitation in their treatment of dispersion which prevents them from accurately describing the spin-state energetics change accompanying the passing from [ F e ( N C H ) 6 ] 2 + with the tetragonal arrangement of its nitrile ligands to the tris-diimine complexes with the trigonal packing of their bulkier ligands.

Femtosecond Core-Level Spectroscopy Reveals Involvement of Triplet States in the Gas-Phase Photodissociation of Fe(CO)5

Excitation of iron pentacarbonyl [Fe(CO)5], a prototypical photocatalyst, at 266 nm causes the sequential loss of two CO ligands in the gas phase, creating catalytically active, unsaturated iron carbonyls. Despite numerous studies, major aspects of its ultrafast photochemistry remain unresolved because the early excited-state dynamics have so far eluded spectroscopic observation. This has led to the long-held assumption that ultrafast dissociation of gas-phase Fe(CO)5 proceeds exclusively on the singlet manifold. Herein, we present a combined experimental-theoretical study employing ultrafast extreme ultraviolet transient absorption spectroscopy near the Fe M2,3-edge, which features spectral evolution on 100 fs and 3 ps time scales, alongside high-level electronic structure theory, which enables characterization of the molecular geometries and electronic states involved in the ultrafast photodissociation of Fe(CO)5. We assign the 100 fs evolution to spectroscopic signatures associated with intertwined structural and electronic dynamics on the singlet metal-centered states during the first CO loss and the 3 ps evolution to the competing dissociation of Fe(CO)4 along the lowest singlet and triplet surfaces to form Fe(CO)3. Calculations of transient spectra in both singlet and triplet states as well as spin-orbit coupling constants along key structural pathways provide evidence for intersystem crossing to the triplet ground state of Fe(CO)4. Thus, our work presents the first spectroscopic detection of transient excited states during ultrafast photodissociation of gas-phase Fe(CO)5 and challenges the long-standing assumption that triplet states do not play a role in the ultrafast dynamics.

Predicting spin states of iron porphyrins with DFT methods including crystal packing effects and thermodynamic corrections

Accurate computational treatment of spin states for transition metal complexes, exemplified by iron porphyrins, lies at the heart of quantum bioinorganic chemistry, but at the same time represents a great challenge for approximate density functional theory (DFT) methods, which are predominantly used. Here, the accuracy of DFT methods for spin-state splittings in iron porphyrin is assessed by probing the ability to correctly predict the ground states for six FeIII or FeII complexes experimentally characterized in solid state. For each case, molecular and periodic DFT calculations are employed to quantify the effect of porphyrin side substituents and the crystal packing effect (CPE) on the spin-state splitting. It is proposed to partition the total CPE into additive components, the direct and structural one, the importance of which is shown to significantly vary from case to case. By knowing the substituent effect, the CPE, and the Gibbs free energy thermodynamic correction from calculations, one can employ the experimental ground-state information in order to derive a quantitative constraint on the electronic energy difference for a simplified (porphin) model of the experimentally characterized metalloporphyrin. The constraints derived in such a way-in the form of single or double inequalities-are used to assess the accuracy of dispersion-corrected DFT methods for 6 spin-state splittings of [FeIII(P)(2-MeIm)2]+, [FeIII(P)(2-MeIm)]+, [FeII(P)(THF)2] and [FeII(P)] models (where P is porphin, 2-MeIm is 2-methylimidazole, THF is tetrahydrofuran). These data constitute the new benchmark set of spin states for crystalline iron porphyrins (SSCIP6). The highest accuracy is obtained in the case of double-hybrid functionals (B2PLYP-D3, DSD-PBEB95-D3), whereas hybrid functionals, especially those with reduced admixture of the exact exchange (B3LYP*-D3, TPSSh-D3), are found to considerably overstabilize the intermediate spin state, leading to incorrect ground-state prediction in FeIII porphyrins. The present approach, which can be generalized to other transition metal complexes, is not only useful in method benchmarking, but also sheds light on the interpretations of experimental data for metalloporphyrins, which are important models to understand the electronic properties of heme proteins.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.