Kasper P. Jensen

Performance of density functionals for first row transition metal systems

This article investigates the performance of five commonly used density functionals, B3LYP, BP86, PBE0, PBE, and BLYP, for studying diatomic molecules consisting of a first row transition metal bonded to H, F, Cl, Br, N, C, O, or S. Results have been compared with experiment wherever possible. Open-shell configurations are found more often in the order PBE0>B3LYP>PBE approximately BP86>BLYP. However, on average, 58 of 63 spins are correctly predicted by any functional, with only small differences. BP86 and PBE are slightly better for obtaining geometries, with errors of only 0.020 A. Hybrid functionals tend to overestimate bond lengths by a few picometers and underestimate bond strengths by favoring open shells. Nonhybrid functionals usually overestimate bond energies. All functionals exhibit similar errors in bond energies, between 42 and 53 kJmol. Late transition metals are found to be better modeled by hybrid functionals, whereas nonhybrid functionals tend to have less of a preference. There are systematic errors in predicting certain properties that could be remedied. BLYP performs the best for ionization potentials studied here, PBE0 the worst. In other cases, errors are similar. Finally, there is a clear tendency for hybrid functionals to give larger dipole moments than nonhybrid functionals. These observations may be helpful in choosing and improving existing functionals for tasks involving transition metals, and for designing new, improved functionals.

Accurate Computed Enthalpies of Spin Crossover in Iron and Cobalt Complexes

Despite their importance in many chemical processes, the relative energies of spin states of transition metal complexes have so far been haunted by large computational errors. By the use of six functionals, B3LYP, BP86, TPSS, TPSSh, M06, and M06L, this work studies nine complexes (seven with iron and two with cobalt) for which experimental enthalpies of spin crossover are available. It is shown that such enthalpies can be used as quantitative benchmarks of a functionals ability to balance electron correlation in both the involved states. TPSSh achieves an unprecedented mean absolute error of approximately 11 kJ/mol in spin transition energies, with the local functional M06L a distant second (25 kJ/mol). Other tested functionals give mean absolute errors of 40 kJ/mol or more. This work confirms earlier suggestions that 10% exact exchange is near-optimal for describing the electron correlation effects of first-row transition metal systems. Furthermore, it is shown that given an experimental structure of an iron complex, TPSSh can predict the electronic state corresponding to that experimental structure. We recommend this functional as current state-of-the-art for studying spin crossover and relative energies of close-lying electronic configurations in first-row transition metal systems.

Comparison of the chemical properties of iron and cobalt porphyrins and corrins.

Density functional calculations have been used to compare various geometric, electronic and functional properties of iron and cobalt porphyrin (Por) and corrin (Cor) species. The investigation is focussed on octahedral MII/III complexes (where M is the metal) with two axial imidazole ligands (as a model of b and c type cytochromes) or with one imidazole and one methyl ligand (as a model of methylcobalamin). However, we have also studied some five‐coordinate MII complexes with an imidazole ligand and four‐coordinate MI/II complexes without any axial ligands as models of other intermediates in the reaction cycle of coenzyme B12. The central cavity of the corrin ring is smaller than that of porphine. We show that the cavity of corrin is close to ideal for low‐spin CoIII, CoII, and CoI with the axial ligands encountered in biology, whereas the cavity in porphine is better suited for intermediate‐spin states. Therefore, the low‐spin state of Co is strongly favoured in complexes with corrins, whereas there is a small energy difference between the various spin states in iron porphyrin species. There are no clear differences for the reduction potentials of the octahedral complexes, but [CoICor] is more easily formed (by at least 40 kJ mole−1) than [FeIPor]. Cobalt and corrin form a strong CoC bond that is more stable against hydrolysis than iron and porphine. Finally, FeII/III gives a much lower reorganisation energy than CoII/III; this is owing to the occupied d  z 2 orbital in CoII. Altogether, these results give some clues about how nature has chosen the tetrapyrrole rings and their central metal ion.

The axial N-base has minor influence on Co-C bond cleavage in cobalamins

We have investigated the properties of cobalamin complexes with imidazolate using the density functional B3LYP method, In particular, we have compared imidazolate (Imm) with imidazole and 5,6-dimethylbenzimidazole (DMB), and studied how constraints in the axial Co-N bond length may affect the strength of the Co-C bond. The results show that the optimum Co-N-Imm bond is similar to0.2 Angstrom shorter than that of imidazole. There is no indication from crystal structures that the histidine ligand would be deprotonated in the enzymes. However, it is likely that it attains some imidazolate character through its hydrogen bond to a conserved aspartate residue. The Co-N bond with imidazolate is three times more rigid than that with imidazole or DMB, but twice as flexible as the Co-C bond. Constraints in the Co-N-Imm bond length give rise to a larger change in the corrin conformation than imidazole, but smaller than for DMB. The resulting effect for the Co-C bond dissociation energy is larger for imidazolate than for imidazole or DMB. However, even the largest reasonable distortion can only enhance catalysis by 15 kJ mol(-1). Therefore, we conclude that, irrespective of the nature of the N-base, constraints in the axial Co-N bond lengths cannot be the main reason for the catalytic power of cobalamin enzymes. (Less)

The reaction mechanism of iron and manganese superoxide dismutases studied by theoretical calculations

We have studied the detailed reaction mechanism of iron and manganese superoxide dismutase with density functional calculations on realistic active‐site models, with large basis sets and including solvation, zero‐point, and thermal effects. The results indicate that the conversion of O  2− to O2 follows an associative mechanism, with O  2− directly binding to the metal, followed by the protonation of the metal‐bound hydroxide ion, and the dissociation of 3O2. All these reaction steps are exergonic. Likewise, we suggest that the conversion of O  2− to H2O2 follows an at least a partly second‐sphere pathway. There are small differences in the preferred oxidation and spin states, as well as in the geometries, of Fe and Mn, but these differences have little influence on the energetics, and therefore on the reaction mechanism of the two types of superoxide dismutases. For example, the two metals have very similar reduction potentials in the active‐site models, although they differ by 0.7 V in water solution. The reaction mechanisms and spin states seem to have been designed to avoid spin conversions or to facilitate them by employing nearly degenerate spin states.

The role of axial ligands for the structure and function of chlorophylls

We have studied the effect of axial ligation of chlorophyll and bacteriochlorophyll using density functional calculations. Eleven different axial ligands have been considered, including models of histidine, aspartate/glutamate, asparagine/glutamine, serine, tyrosine, methionine, water, the protein backbone, and phosphate. The native chlorophylls, as well as their cation and anion radical states and models of the reaction centres P680 and P700, have been studied and we have compared the geometries, binding energies, reduction potentials, and absorption spectra. Our results clearly show that the chlorophylls strongly prefer to be five-coordinate, in accordance with available crystal structures. The axial ligands decrease the reduction potentials, so they cannot explain the high potential of P680. They also redshift the Q band, but not enough to explain the occurrence of red chlorophylls. However, there is some relation between the axial ligands and their location in the various photosynthetic proteins. In particular, the intrinsic reduction potential of the second molecule in the electron transfer path is always lower than that of the third one, a feature that may prevent back-transfer of the electron.

Importance of proximal hydrogen bonds in haem proteins

We have used the density functional B3LYP method to study the effect of hydrogen bonds from the histidine ligand in various haem proteins to carboxyl groups or to the carbonyl backbone. Hydrogen bonds to carbonyl groups (encountered in globins and cytochromes, for example) have a small influence on the geometry and properties of the haem site. However, hydrogen bonds to a carboxyl group (encountered in peroxidases and haem oxidase) may have a profound effect. The results indicate that in the Fe3+ state, this leads to a deprotonation of the histidine ligand, whereas in the Fe2+ state, the proton involved in the hydrogen bond may reside on either histidine or the carboxylate group, depending on the detailed structure of the surroundings. If the histidine is deprotonated, the axial Fe-N bond length decreases by 0.15 Å, whereas the equatorial bond lengths increase. Moreover, the charge on iron and histidine is reduced, as is the spin density on iron. Most importantly, the energy difference between the high and intermediate spin states changes so that whereas the two spin states are degenerate in the Fe2+ state for the protonated histidine, they are degenerate for the Fe3+ state when it is deprotonated. This may facilitate the spin-forbidden binding of dioxygen and peroxide substrates, which takes place for the Fe2+ state in globins but in the Fe3+ state in peroxidases. The reduction potential of the haem group decreases when it hydrogen-bonds to a negatively charged group. The inner-sphere reorganization energy of the Fe2+/Fe3+ transition in a five-coordinate haem complex is ∼30 kJ mol−1, except when the histidine ligand is deprotonated without any hydrogen-bond interaction.

Metal-Ligand Bonds of Second- and Third-Row d-Block Metals Characterized by Density Functional Theory

This paper presents systematic data for 200 neutral diatomic molecules ML (M is a second- or third-row d-block metal and L = H, F, Cl, Br, I, C, N, O, S, or Se) computed with the density functionals TPSSh and BP86. With experimental structures and bond enthalpies available for many of these molecules, the computations first document the high accuracy of TPSSh, giving metal-ligand bond lengths with a mean absolute error of approximately 0.01 A for the second row and 0.03 A for the third row. TPSSh provides metal-ligand bond enthalpies with mean absolute errors of 37 and 44 kJ/mol for the second- and third-row molecules, respectively. Pathological cases (e.g., HgC and HgN) have errors of up to 155 kJ/mol, more than thrice the mean (observed with both functionals). Importantly, the systematic error component is negligible as measured by a coefficient of the linear regression line of 0.99. Equally important, TPSSh provides uniform accuracy across all three rows of the d-block, which is unprecedented and due to the 10% exact exchange, which is close to optimal for the d-block as a whole. This work provides an accurate and systematic prediction of electronic ground-state spins, characteristic metal-ligand bond lengths, and bond enthalpies for many as yet uncharacterized diatomics, of interest to researchers in the field of second- and third-row d-block chemistry. We stress that the success of TPSSh cannot be naively extrapolated to other special situations such as, e.g., metal-metal bonds. The high accuracy of the procedure further implies that the effective core functions used to model relativistic effects are necessary and sufficient for obtaining accurate geometries and bond enthalpies of second- and third-row molecular systems.

Comparison of chemical properties of iron, cobalt, and nickel porphyrins, corrins, and hydrocorphins

Density functional calculations have been used to compare the geometric, electronic, and functional properties of the three important tetrapyrrole systems in biology, heme, coenzyme B12, and coenzyme F430, formed from iron porphyrin (Por), cobalt corrin (Cor), and nickel hydrocorphin (Hcor). The results show that the flexibility of the ring systems follows the trend Hcor > Cor > Por and that the size of the central cavity follows the trend Cor < Por < Hcor. Therefore, low-spin CoI, CoII, and CoIII fit well into the Cor ring, whereas Por seems to be more ideal for the higher spin states of iron, and the cavity in Hcor is tailored for the larger Ni ion, especially in the high-spin NiII state. This is confirmed by the thermodynamic stabilities of the various combinations of metals and ring systems. Reduction potentials indicate that the +I and +III states are less stable for Ni than for the other metal ions. Moreover, Ni–C bonds are appreciably less stable than Co-C bonds. However, it is still possible that a Ni–CH3 bond is formed in F430 by a heterolytic methyl transfer reaction, provided that the donor is appropriate, e.g. if coenzyme M is protonated. This can be facilitated by the adjacent SO3− group in this coenzyme and by the axial glutamine ligand, which stabilizes the NiIII state. Our results also show that a NiIII–CH3 complex is readily hydrolysed to form a methane molecule and that the NiIII hydrolysis product can oxidize coenzyme B and M to a heterodisulphide in the reaction mechanism of methyl coenzyme M reductase.

Computational Chemistry of Modified [MFe3S4] and [M2Fe2S4] Clusters: Assessment of Trends in Electronic Structure and Properties†

The aim of this work is to understand the molecular evolution of iron-sulfur clusters in terms of electronic structure and function. Metal-substituted models of biological [Fe(4)S(4)] clusters in oxidation states [M(x)Fe(4-x)S(4)](3+/2+/1+) have been studied by density functional theory (M = Cr, Mn, Fe, Co, Ni, Cu, Zn, and Pd, with x = 1 or 2). Most of these clusters have not been characterized before. For those that have been characterized experimentally, very good agreement is obtained, implying that also the predicted structures and properties of new clusters are accurate. Mean absolute errors are 0.024 A for bond lengths ([Fe(4)S(4)], [NiFe(3)S(4)], [CoFe(3)S(4)]) and 0.09 V for shifts in reduction potentials relative to the [Fe(4)S(4)] cluster. All structures form cuboidal geometries similar to the all-iron clusters, except the Pd-substituted clusters, which instead form highly distorted trigonal and tetragonal local sites in compromised, pseudocuboidal geometries. In contrast to other electron-transfer sites, cytochromes, blue copper proteins, and smaller iron-sulfur clusters, we find that the [Fe(4)S(4)] clusters are very insensitive to metal substitution, displaying quite small changes in reorganization energies and reduction potentials upon substitution. Thus, the [Fe(4)S(4)] clusters have an evolutionary advantage in being robust to pollution from other metals, still retaining function. We analyze in detail the electronic structure of individual clusters and rationalize spin couplings and redox activity. Often, several configurations are very close in energy, implying possible use as spin-crossover systems, and spin states are predicted accurately in all but one case ([CuFe(3)S(4)]). The results are anticipated to be helpful in defining new molecular systems with catalytic and magnetic properties.