Validation of Exchange−Correlation Functionals for Spin States of Iron Complexes

Iron(II) and Iron(III) Spin Crossover: Toward an Optimal Density Functional

Spin crossover (SCO) plays a major role in biochemistry, catalysis, materials, and emerging technologies such as molecular electronics and sensors, and thus accurate prediction and design of SCO systems is of high priority. However, the main tool for this purpose, density functional theory (DFT), is very sensitive to applied methodology. The most abundant SCO systems are Fe(II) and Fe(III) systems. Even with average good agreement, a functional may be significantly more accurate for Fe(II) or Fe(III) systems, preventing balanced study of SCO candidates of both types. The present work investigates DFT's performance for well-known Fe(II) and Fe(III) SCO complexes, using various design types and customized versions of GGA, hybrid, meta-GGA, meta-hybrid, double-hybrid, and long-range-corrected hybrid functionals. We explore the limits of DFT performance and identify proficient Fe(II)-Fe(III)-balanced functionals. We identify and quantify remarkable differences in the DFT description of Fe(II) and Fe(III) systems. Most functionals become more accurate once Hartree-Fock exchange is adjusted to 10-17%, regardless of the type of functionals involved. However, this typically introduces a clear Fe(II)-Fe(III) bias. The most accurate functionals measured by mean absolute errors <10 kJ/mol are CAMB3LYP-17, B3LYP*, and B97-15 with 15-17% Hartree-Fock exchange, closely followed by CAMB3LYP and CAMB3LYP-15, OPBE, rPBE-10, and B3P86-15. While GGA functionals display a small Fe(II)-Fe(III) bias, they are generally inaccurate, except the O exchange functional. Hybrid functionals (including B2PLYP double hybrids and meta hybrids) tend to favor HS too much in Fe(II) vs Fe(III), which is important in many studies where the oxidation state of iron can vary, e.g. rational SCO design and studies of catalytic processes involving iron. The only functional with a combined bias <5 kJ/mol and a decent MAE (15 kJ/mol) is our customized PBE0-12 functional. Alternatively one has to sacrifice Fe(II)-Fe(III) balance to use the best functionals for each group separately. We also investigated the precision (measured as the standard deviation of errors) and show that the target accuracy for iron SCO is 10 kJ/mol for accuracy and 5 kJ/mol for precision, and DFT is probably not going to break this limit in the near future. Importantly, all four types of functional behavior (accurate/precise, accurate/imprecise, inaccurate/precise, inaccurate/imprecise) are observed. More generally, our work illustrates the importance not only of overall accuracy but also of balanced accuracy for systems likely to occur in context.

The role of spin states in the catalytic mechanism of the intra- and extradiol cleavage of catechols by O2

Iron-dependent enzymes and biomimetic iron complexes can catalyze the ring cleavage of very inert, aromatic compounds. The mechanisms of these transformations and the factors that lead either to extradiol cleavage or intradiol cleavage have not been fully understood. By using density functional theory we have elucidated the mechanism of the catalytic cycle for two biomimetic complexes, and explained the difference in the experimentally obtained products.

Assessment of the ground spin state of iron(i) complexes: insights from DFT predictive models

Factors governing the ground spin state of iron(i) complexes are analyzed by DFT methods. An efficient benchmarking procedure is reported.

Multiconfiguration Pair-Density Functional Theory Predicts Spin-State Ordering in Iron Complexes with the Same Accuracy as Complete Active Space Second-Order Perturbation Theory at a Significantly Reduced Computational Cost

The spin-state orderings in nine Fe(II) and Fe(III) complexes with ligands of diverse ligand-field strength were investigated with multiconfiguration pair-density functional theory (MC-PDFT). The performance of this method was compared to that of complete active space second-order perturbation theory (CASPT2) and Kohn-Sham density functional theory. We also investigated the dependence of CASPT2 and MC-PDFT results on the size of the active-space. MC-PDFT reproduces the CASPT2 spin-state ordering, the dependence on the ligand field strength, and the dependence on active space at a computational cost that is significantly reduced as compared to CASPT2.

Influence of the dipolar interactions on the relative stability in spin crossover systems

Molecules exhibiting a spin-crossover transition have been proposed for a number of applications such as molecular switches, spintronic tunable interfaces, and single molecule gates. Both the rational design of new spin-crossover systems and the improvement of the properties of the already existing ones require a theoretical understanding of the relative energy of the high (HS) and low spin state (LS) molecules in the solid-state. This has proved to be very challenging so far. Here, we shed some light on the importance of considering the symmetry and the geometry of the crystallographic cell to correctly evaluate the influence of the dipolar interactions on the relative energies of the molecular complex in both different spin states. Moreover, in the case of Fe(SCN)₂ (phen)₂ dipolar interactions are found to play an important role for the stabilization of the LS complex. © 2016 Wiley Periodicals, Inc.

Significance of the electron-density of molecular fragments on the properties of manganese(iii) β-diketonato complexes: an XPS and DFT study

The group electronegativity of the R-groups of the ligand influences the XPS binding energies and the amount of charge transferred in the Mn 2p_3/2 photoelectron lines. DFT studies illustrated different Jahn–Teller elongation bond stretch isomers.

Assessment of electronic structure methods for the determination of the ground spin states of Fe(ii), Fe(iii) and Fe(iv) complexes

We studied spin states of Fe²⁺ ion, gaseous FeO, and 14 Fe(ii), Fe(iii) and Fe(iv) complexes using density functional theory.

Spinning around in Transition-Metal Chemistry

The great diversity and richness of transition metal chemistry, such as the features of an open d-shell, opened a way to numerous areas of scientific research and technological applications. Depending on the nature of the metal and its environment, there are often several energetically accessible spin states, and the progress in accurate theoretical treatment of this complicated phenomenon is presented in this Account. The spin state energetics of a transition metal complex can be predicted theoretically on the basis of density functional theory (DFT) or wave function based methodology, where DFT has advantages since it can be applied routinely to medium-to-large-sized molecules and spin-state consistent density functionals are now available. Additional factors such as the effect of the basis set, thermochemical contributions, solvation, relativity, and dispersion, have been investigated by many researchers, but challenges in unambiguous assignment of spin states still remain. The first DFT studies showed intrinsic spin-state preferences of hybrid functionals for high spin and early generalized gradient approximation functionals for low spin. Progress in the development of density functional approximations (DFAs) then led to a class of specially designed DFAs, such as OPBE, SSB-D, and S12g, and brought a very intriguing and fascinating observation that the spin states of transition metals and the S_N2 barriers of organic molecules are somehow intimately linked. Among the many noteworthy results that emerged from the search for the appropriate description of the complicated spin state preferences in transition metals, we mainly focused on the examination of the connection between the spin state and the structures or coordination modes of the transition metal complexes. Changes in spin states normally lead only to changes in the metal-ligand bond lengths, but to the best of our knowledge, the dapsox ligand showed the first example of a transition-metal complex where a change in spin state leads also to changes in the coordination, switching between pentagonal-bipyramidal and capped-octahedron. Moreover, we have summarized the results of the thorough study that corrected the experimental assignment of the nature of the recently synthesized Sc³⁺ adduct of [Fe^IV(O)(TMC)]²⁺ (TMC = 1,4,8,11-tetramethylcyclam) and firmly established that the Sc³⁺-capped iron-oxygen complex corresponds to high-spin Fe^III. Last, but not least, we have provided deeper insight and rationalization of the observation that unlike in metalloenzymes, where the Fe^IV-oxo is usually observed with high spin, biomimetic Fe^IV-oxo complexes typically have a intermediate spin state. Energy decomposition analyses on the trigonal-bypiramidal (TBP) and octahedral model systems with ammonia ligands have revealed that the interaction energy of the prepared metal ion in the intermediate spin state is much smaller for the TBP structure. This sheds light on the origin of the intermediate spin state of the biomimetic TBP Fe^IV-oxo complexes.

Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH)6](2.)

The energy difference between the high spin and the low spin state of the model compound [Fe(NCH)6](2+) is investigated by means of Diffusion Monte Carlo (DMC), where special attention is dedicated to analyzing the effect of the fix node approximation on the accuracy of the results. For this purpose, we compare several Slater-Jastrow and multireference Slater-Jastrow trial wave functions. We found that a Slater-Jastrow trial wave function constructed with the generalized Kohn-Sham orbitals from hybrid DFT represents the optimal choice. This is understood by observing that hybrid functionals account for the subtle balance between exchange and correlation effects and the respective orbitals accurately describe the ligand-metal hybridization as well as the charge reorganization accompanying the spin transition. Finally the DMC results are compared with those obtained by Hartree-Fock, DFT, CASSCF, and CASPT2. While there is no clear reference value for the high spin-low spin energy difference, DMC and high level CCSD(T) calculations agree within around 0.3 eV.

Water Dissociation upon Adsorption onto Free Iron Clusters Is Size Dependent

Cationic iron clusters, produced through laser ablation and subsequently complexed with a water molecule Fen(+)-H2O (n = 6-15) are mass-selectively investigated via infrared multiple photon dissociation (IR-MPD) spectroscopy in the 300-1700 cm(-1) spectral range. The experimental data are complemented by density functional theory calculations at the OPBE/TZP level for the Fe13(+)-H2O system. The observed spectra can be explained by a mixture of clusters where for a majority water is adsorbed molecularly but for a small but significant fraction also dissociation of water molecules occurs. The bands observed at frequencies 300-700 cm(-1) exhibit regular, size-dependent frequency shifts, showing that (a) dissociation takes places on all cluster sizes and (b) the interaction of water with the cluster surface is not influenced much by the particular cluster structure. The intensity evolution of the absorption bands suggests that dissociation is increasingly probable for larger cluster sizes.

Synthesis and Characterization of a Stable High-Valent Cobalt Carbene Complex

The formally Co(IV) carbene Co(OR)2(═CPh2) is formed upon the reaction of diphenyldiazomethane with the cobalt bis(alkoxide) precursor Co(OR)2(THF)2. Structural, spectroscopic, and theoretical studies demonstrate that Co(OR)2(═CPh2) has significant high-valent Co(IV)═CPh2 character with non-negligible spin density on the carbene moiety.

Intrinsic Carbon-Carbon Bond Reactivity at the Manganese Center of Oxalate Decarboxylase from Density Functional Theory

The detailed manganese-dependent chemistry employed by oxalate decarboxylase (OxDC) to catalyze the nonoxidative decarboxylation of oxalic acid remains poorly understood. For example, enzyme activity requires the presence of dioxygen even though this compound is not a formal substrate in the reaction. We now report density functional theory (DFT) calculations upon a series of hypothetical OxDC active site model structures. Our results suggest that the function of the metal ion may be to position dioxygen and oxalate such that electrons can be shuttled directly between these species, thereby removing the need for the existence of Mn(III) as an intermediate in the mechanism. These calculations also indicate that the intrinsic, gas-phase reactivity of the Bacillus subtilis oxalate decarboxylase active center is to oxidize oxalate. Since this reactivity is not observed for OxDC, our DFT results suggest that protein environment modulates the intrinsic metallocenter reactivity, presumably by affecting the electronic distribution at the manganese center during catalysis.

Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions

The hybrid meta density functionals M05-2X and M06-2X have been shown to provide broad accuracy for main group chemistry. In the present article we make the functional form more flexible and improve the self-interaction term in the correlation functional to improve its self-consistent-field convergence. We also explore the constraint of enforcing the exact forms of the exchange and correlation functionals through second order (SO) in the reduced density gradient. This yields two new functionals called M08-HX and M08-SO, with different exact constraints. The new functionals are optimized against 267 diverse main-group energetic data consisting of atomization energies, ionization potentials, electron affinities, proton affinities, dissociation energies, isomerization energies, barrier heights, noncovalent complexation energies, and atomic energies. Then the M08-HX, M08-SO, M05-2X, and M06-2X functionals and the popular B3LYP functional are tested against 250 data that were not part of the original training data for any of the functionals, in particular 164 main-group energetic data in 7 databases, 39 bond lengths, 38 vibrational frequencies, and 9 multiplicity-changing electronic transition energies. These tests include a variety of new challenges for complex systems, including large-molecule atomization energies, organic isomerization energies, interaction energies in uracil trimers, and bond distances in crowded molecules (in particular, cyclophanes). The M08-HX functional performs slightly better than M08-SO and M06-2X on average, significantly better than M05-2X, and much better than B3LYP for a combination of main-group thermochemistry, kinetics, noncovalent interactions, and electronic spectroscopy. More important than the slight improvement in accuracy afforded by M08-HX is the conformation that the optimization procedure works well for data outside the training set. Problems for which the accuracy is especially improved by the new M08-HX functional include large-molecule atomization energies, noncovalent interaction energies, conformational energies in aromatic peptides, barrier heights, multiplicity-changing excitation energies, and bond lengths in crowded molecules.

E2 and SN2 Reactions of X(-) + CH3CH2X (X = F, Cl); an ab Initio and DFT Benchmark Study

We have computed consistent benchmark potential energy surfaces (PESs) for the anti-E2, syn-E2, and SN2 pathways of X(-) + CH3CH2X with X = F and Cl. This benchmark has been used to evaluate the performance of 31 popular density functionals, covering local-density approximation, generalized gradient approximation (GGA), meta-GGA, and hybrid density-functional theory (DFT). The ab initio benchmark has been obtained by exploring the PESs using a hierarchical series of ab initio methods [up to CCSD(T)] in combination with a hierarchical series of Gaussian-type basis sets (up to aug-cc-pVQZ). Our best CCSD(T) estimates show that the overall barriers for the various pathways increase in the order anti-E2 (X = F) < SN2 (X = F) < SN2 (X = Cl) ∼ syn-E2 (X = F) < anti-E2 (X = Cl) < syn-E2 (X = Cl). Thus, anti-E2 dominates for F(-) + CH3CH2F, and SN2 dominates for Cl(-) + CH3CH2Cl, while syn-E2 is in all cases the least favorable pathway. Best overall agreement with our ab initio benchmark is obtained by representatives from each of the three categories of functionals, GGA, meta-GGA, and hybrid DFT, with mean absolute errors in, for example, central barriers of 4.3 (OPBE), 2.2 (M06-L), and 2.0 kcal/mol (M06), respectively. Importantly, the hybrid functional BHandH and the meta-GGA M06-L yield incorrect trends and qualitative features of the PESs (in particular, an erroneous preference for SN2 over the anti-E2 in the case of F(-) + CH3CH2F) even though they are among the best functionals as measured by their small mean absolute errors of 3.3 and 2.2 kcal/mol in reaction barriers. OLYP and B3LYP have somewhat higher mean absolute errors in central barriers (5.6 and 4.8 kcal/mol, respectively), but the error distribution is somewhat more uniform, and as a consequence, the correct trends are reproduced.

Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of Co(III)(diiminato)(NPh)

The electronic structure and low-lying electronic states of a Co(III)(diiminato)(NPh) complex have been studied using multiconfigurational wave function theory (CASSCF/CASPT2). The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

Density Functional Calculations of E2 and SN2 Reactions: Effects of the Choice of Method, Algorithm, and Numerical Accuracy

Herein we provide a detailed account on how the potential energy surfaces of the E2 and SN2 reactions of X(-) + CH3CH2X (X = F, Cl) depend on various methodological and technical choices in density functional calculations. We cover a choice of density functionals (OLYP, various M06-types, and the new SSB-D), basis sets (up to quintuple- and quadruple-ζ for Gaussian- and Slater-type orbitals, respectively, plus polarization and diffuse functions), and other aspects of the computations (among others: nonrelativistic versus zeroth-order regular approximation relativistic; numerical integration accuracy; all-electron versus frozen core; self-consistent field (SCF) versus post-SCF). The program codes ADF and NWChem are used for calculations with Slater- and Gaussian-type basis sets, respectively. The fluoride systems (X = F) appear to not only depend extremely sensitively on the basis set size (especially the presence of diffuse functions) but also on other technical settings, especially in the case of hybrid meta-generalized gradient approximation functionals. This work complements a recent contribution (Y. Zhao, D. G. Truhlar, J. Chem. Theory Comput. 2010, 6, 1104) and provides recommendations for density functionals, basis sets, and technical settings.