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

Modeling the MoFe nitrogenase system with broken symmetry density functional theory

Density functional theory (DFT) represents a unified framework for gaining molecular level insight into molybdenum-iron (MoFe) nitrogenase. However, accurately describing the electronic structure of the spin-polarized and spin-coupled iron-molybdenum cofactor (FeMo-co) where N(2) reduction occurs within MoFe nitrogenase is challenging. Therefore, the enhancement of DFT to include broken symmetry (BS-DFT) plus approximate spin projection has proven valuable because it provides a procedure to compute reliable geometries, energies, redox potentials, and quantities relevant to Mössbauer and ENDOR spectroscopies. After describing the theoretical tools necessary to obtain this information, we show by way of examples how BS-DFT is a very powerful partner to experiment. We expect that quantitative quantum chemical theory of this type will play an ever-increasing role in helping to decipher complex bioinorganic systems like those found in MoFe nitrogenase.

Density functional theory analysis of structure, energetics, and spectroscopy for the Mn-Fe active site of Chlamydia trachomatis ribonucleotide reductase in four oxidation states

Models for the Mn-Fe active site structure of ribonucleotide reductase (RNR) from pathogenic bacteria Chlamydia trachomatis (Ct) in different oxidation states have been studied in this paper, using broken-symmetry density functional theory (DFT) incorporated with the conductor like screening (COSMO) solvation model and also with finite-difference Poisson-Boltzmann self-consistent reaction field (PB-SCRF) calculations. The detailed structures for the reduced Mn(II)-Fe(II), the met Mn(III)-Fe(III), the oxidized Mn(IV)-Fe(III) and the superoxidized Mn(IV)-Fe(IV) states are predicted. The calculated properties, including geometries, (57)Fe Mossbauer isomer shifts and quadrupole splittings, and (57)Fe and (55)Mn electron nuclear double resonance (ENDOR) hyperfine coupling constants, are compared with the available experimental data. The Mössbauer and energetic calculations show that the (mu-oxo, mu-hydroxo) models better represent the structure of the Mn(IV)-Fe(III) state than the di-mu-oxo models. The predicted Mn(IV)-Fe(III) distances (2.95 and 2.98 A) in the (mu-oxo, mu-hydroxo) models are in agreement with the extended X-ray absorption fine structure (EXAFS) experimental value of 2.92 A (Younker et al. J. Am. Chem. Soc. 2008, 130, 15022-15027). The effect of the protein and solvent environment on the assignment of the Mn metal position is examined by comparing the relative energies of alternative mono-Mn(II) active site structures. It is proposed that if the Mn(II)-Fe(II) protein is prepared with prior addition of Mn(II) or with Mn(II) richer than Fe(II), Mn is likely positioned at metal site 2, which is further from Phe127.

Comparison of electronic structures and light-induced excited spin state trapping between [Fe(2-picolylamine)(3)](2+) and its iron(III) analogue

We investigated mer- and fac-[Fe(II)(2-pic)(3)](2+) (pic = picolylamine) and Fe(iii) analogue, mer-[Fe(III)(2-pic)(3)](3+), by the DFT method to clarify the mechanism of light-induced excited spin state trapping (LIESST). In mer-[Fe(II)(2-pic)(3)](2+), the potential energy surface (PES) of the triplet state is the least stable but it is close to the PESs of the singlet and quintet states at the equilibrium geometry of the triplet state within 5 kcal mol(-1). This indicates that intersystem crossing occurs from the triplet state to either the singlet state or the quintet state around the equilibrium geometry of the triplet state. The quintet state is as stable as the singlet state in their equilibrium geometries. All Fe-N bonds of the quintet state are longer than those of the singlet state by about 0.19 A. These are consistent with the general understanding that the Fe-ligand distances are considerably different but the relative stability is little different between the low spin and high spin states in LIESST complexes. Actually, a large activation barrier is calculated for the conversion between the singlet and quintet states, which is enough to suppress thermal spin transition and tunneling between them. The d-d transition energies are calculated with the TD-DFT method to be 2.05, 2.07, and 2.09 eV in the singlet state and 1.46 and 1.64 eV in the quintet state. Because of the significantly large difference in excitation energy between the singlet and quintet states, irradiation of visible light with different wavelengths selectively induces the excitation to the singlet excited state or the quintet one. All these results are consistent with the fact that both LIESST and reverse-LIESST are observed in mer-[Fe(II)(2-pic)(3)](2+). The fac-isomer is also useful for the LIESST/reverse-LIESST, though the mer-isomer is better. In the Fe(iii) analogue, mer-[Fe(III)(2-pic)(3)](3+), the DFT-computational results indicate small activation barriers and a large overlap of absorption spectra between the doublet and sextet states. Also, the Fe(III)-N bond distances are less different between the low spin and high spin states than the Fe(II)-N ones, leading to the narrow potential wall between the doublet and sextet states. As a result, the LIESST and reverse-LIESST cannot be observed in this Fe(iii) complex.

Reactivity and regioselectivity of noble gas endohedral fullerenes Ng@C(60) and Ng(2)@C(60) (Ng=He-Xe)

Recently, it was shown that genuine Ng-Ng chemical bonds are present in the endohedral fullerenes Ng(2)@C(60) in the case of Ng=Xe, while it is more debatable whether a chemical bond exist for Ng=Ar and Kr. The lighter homologues with helium and neon are weakly bonded van der Waals complexes. The presence of a noble gas dimer inside the cage is expected to modify the exohedral reactivity of the C(60) cage with respect to that of free C(60). To investigate the impact of encapsulated diatomic noble gas molecules on the chemical reactivity of C(60), we analyzed the thermodynamics and the kinetics of [4+2] Diels-Alder cycloaddition of 1,3-cis-butadiene at all nonequivalent bonds in free C(60), Ng@C(60), and Ng(2)@C(60) (Ng=He, Ne, Ar, Kr, and Xe). Our BP86/TZP calculations reveal that introduction of single noble gas atoms in Ng@C(60) and noble gas dimers He(2) and Ne(2) in Ng(2)@C(60) has almost no effect on the exohedral reactivity compared to free C(60), in agreement with experimental results. In all these cases cycloaddition is clearly favored at the [6,6] bonds in the fullerene cage. For the endohedral compounds He(2)@C(60) and Ne(2)@C(60) a slight preference (by less than 2 kcal mol(-1)) for bonds closer to the C(5) symmetry axis is found. This picture changes dramatically for the endohedral compounds with heavier noble gas dimers. Encapsulation of these noble gas dimers clearly enhances the reaction, both under thermodynamic and kinetic control. Moreover, in the case of Xe(2)@C(60), addition to [6,6] and [5,6] bonds becomes equally viable. These reactivity changes in endohedral fullerenes are attributed to stabilization of the LUMO, increased fullerene strain energy, and greater compression of the encapsulated Ng(2) unit along the He to Xe series.

DFT calculations of comparative energetics and ENDOR/Mössbauer properties for two protonation states of the iron dimer cluster of ribonucleotide reductase intermediate X

Two models (I and II) for the active site structure of class-I ribonucleotide reductase (RNR) intermediate X in subunit R2 have been studied in this paper, using broken-symmetry density functional theory (DFT) incorporated with the conductor like screening (COSMO) solvation model and with the finite-difference Poisson-Boltzmann self-consistent reaction field (PB-SCRF) calculations. Only one of the bridging groups between the two iron centers is different between model-I and model-II. Model-I contains two mu-oxo bridges, while model-II has one bridging oxo and one bridging hydroxo. These are large active site models including up to the fourth coordination shell H-bonding residues. Mössbauer and ENDOR hyperfine property calculations show that model-I is more likely to represent the active site structure of RNR-X. However, energetically our pK(a) calculations at first highly favored the bridging oxo and hydroxo (in model-II) structure of the diiron center rather than having the di-oxo bridge (in model-I). Since the Arg236 and the nearby Lys42, which are very close to the diiron center, are on the protein surface of RNR-R2, it is highly feasible that one or two anion groups in solution would interact with the positively charged side chains of Arg236 and Lys42. The anion group(s) can be a reductant, phosphate, sulfate, nitrate, and other negatively charged groups existing in biological environments or in the buffer of the experiment. Since sulfate ions certainly exist in the buffer of the ENDOR experiment, we have examined the effect of the sulfate (SO(4)(2-), surrounded by explicit water molecules) H-bonding to the side chain of Arg236. We find that when sulfate interacts with Arg236, the carboxylate group of Asp237 tends to be protonated, and once Asp237 is protonated, the Fe(iii)Fe(iv) center in X favors the di-oxo bridge (model-I). This would explain that the ENDOR observed RNR-X active site structure is likely to be represented by model-I rather than model-II.

Chemical bonding and aromaticity in metalloporphyrins,

We report here the chemical bonding and aromaticity patterns in metalloporphyrins, which were obtained with density functional theory (DFT) calculations at the OPBE/TZP level. This level of theory was previously shown to be very accurate for determining spin-state splittings [J. Chem. Theory Comput. 2008, 4, 2057] of transition-metal complexes. We considered metalloporphyrins along the first-row transition metals (Sc–Zn) extended with alkaline-earth metals (Mg, Ca) and several second-row transition metals (Ru, Pd, Ag, Cd). An energy decomposition analysis was performed to study the metal–ligand interactions, which showed that almost all complexes are significantly stabilized through (covalent) orbital interactions. The only exception is with calcium as the central metal, which interacts with the porphyrin mainly through electrostatic interactions. Furthermore, we studied aromaticity patterns for these complexes by looking at a number of (structural and electronic) aromaticity descriptors, for both the inner-ring and outer-ring of the porphyrin and of the pyrroles. The inner-ring (N16) aromaticity is shown to be unaffected by metal complexation, while the outer-ring (N20) and the pyrrole (N5) aromaticities are found to increase significantly in the metal coordinated porphyrins.

Quantum cluster size and solvent polarity effects on the geometries and Mössbauer properties of the active site model for ribonucleotide reductase intermediate X: a density functional theory study

In studying the properties of metalloproteins using ab initio quantum mechanical methods, one has to focus on the calculations on the active site. The bulk protein and solvent environment is often neglected, or is treated as a continuum dielectric medium with a certain dielectric constant. The size of the quantum cluster of the active site chosen for calculations can vary by including only the first-shell ligands which are directly bound to the metal centers, or including also the second-shell residues which are adjacent to and normally have H-bonding interactions with the first-shell ligands, or by including also further hydrogen bonding residues. It is not well understood how the size of the quantum cluster and the value of the dielectric constant chosen for the calculations will influence the calculated properties. In this paper, we have studied three models (A, B, and C) of different sizes for the active site of the ribonucleotide reductase intermediate X, using density functional theory (DFT) OPBE functional with broken-symmetry methodology. Each model is studied in gas-phase and in the conductor-like screening (COSMO) solvation model with different dielectric constants ε = 4, 10, 20, and 80, respectively. All the calculated Fe-ligand geometries, Heisenberg J coupling constants, and the Mössbauer isomer shifts, quadrupole splittings, and the (57)Fe, (1)H, and (17)O hyperfine tensors are compared. We find that the calculated isomer shifts are very stable. They are virtually unchanged with respect to the size of the cluster and the dielectric constant of the environment. On the other hand, certain Fe-ligand distances are sensitive to both the size of the cluster and the value of ε. ε = 4, which is normally used for the protein environment, appears too small when studying the diiron active site geometry with only the first-shell ligands as seen by comparisons with larger models.

Toward a chemical mechanism of proton pumping by the B-type cytochrome c oxidases: application of density functional theory to cytochrome ba3 of Thermus thermophilus

A mechanism for proton pumping by the B-type cytochrome c oxidases is presented in which one proton is pumped in conjunction with the weakly exergonic, two-electron reduction of Fe-bound O 2 to the Fe-Cu bridging peroxodianion and three protons are pumped in conjunction with the highly exergonic, two-electron reduction of Fe(III)- (-)O-O (-)-Cu(II) to form water and the active oxidized enzyme, Fe(III)- (-)OH,Cu(II). The scheme is based on the active-site structure of cytochrome ba 3 from Thermus thermophilus, which is considered to be both necessary and sufficient for coupled O 2 reduction and proton pumping when appropriate gates are in place (not included in the model). Fourteen detailed structures obtained from density functional theory (DFT) geometry optimization are presented that are reasonably thought to occur during the four-electron reduction of O 2. Each proton-pumping step takes place when a proton resides on the imidazole ring of I-His376 and the large active-site cluster has a net charge of +1 due to an uncompensated, positive charge formally associated with Cu B. Four types of DFT were applied to determine the energy of each intermediate, and standard thermochemical approaches were used to obtain the reaction free energies for each step in the catalytic cycle. This application of DFT generally conforms with previously suggested criteria for a valid model (Siegbahn, P. E. M.; Blomberg, M. A. R. Chem. Rev. 2000, 100, 421-437) and shows how the chemistry of O 2 reduction in the heme a 3 -Cu B dinuclear center can be harnessed to generate an electrochemical proton gradient across the lipid bilayer.

QUILD: QUantum-regions interconnected by local descriptions

A new program for multilevel (QM/QM and/or QM/MM) approaches is presented that is able to combine different computational descriptions for different regions in a transparent and flexible manner. This program, designated QUILD (for QUantum-regions Interconnected by Local Descriptions), uses adapted delocalized coordinates (Int J Quantum Chem 2006, 106, 2536) for efficient geometry optimizations of equilibrium and transition-state structures, where both weak and strong coordinates may be present. The Amsterdam Density Functional (ADF) program is used for providing density functional theory and MM energies and gradients, while an interface to the ORCA program is available for including RHF, MP2, or semiempirical descriptions. The QUILD optimization setup reduces the number of geometry steps needed for the Baker test-set of 30 organic molecules by approximately 30% and for a weakly-bound test-set of 18 molecules by approximately 75% compared with the old-style optimizer in ADF, i.e., a speedup of roughly a factor four. We report two examples of using geometry optimizations with numerical gradients, for spin-orbit relativistic ZORA and for excited-state geometries. Finally, we show examples of its multilevel capabilities for a number of systems, including the multilevel boundary region of amino acid residues, an S(N)2 reaction in the gas-phase and in solvent, and a DNA duplex.

Why does cyanide pretend to be a weak field ligand in [Cr(CN)5]3-?

Chemical reasoning based on ligand-field theory suggests that homoleptic cyano complexes should exhibit low-spin configurations, particularly when the coordination sphere is nearly saturated. Recently, the well-known chromium hexacyano complex anion [Cr(CN)6](4-) was shown to lose cyanide to afford [Cr(CN)5](3-) in the absence of coordinating cations. Furthermore, (NEt 4)3[Cr(CN)5] was found to be in a high-spin (S=2) ground state, which challenges the common notion that cyanide is a strong field ligand and should always enforce low-spin configurations. Using density functional theory coupled to a continuum solvation model, we examined both the instability of the hexacyanochromate(II) anion and the relative energies of the different spin states of the pentacyanochromate(II) anion. By making direct comparisons to the analogous Fe (II) complex, we found that cyanide electronically behaves as a strong-field ligand for both metals because the orbital interaction is energetically more favorable in the low-spin configuration than in the corresponding high-spin configuration. The Coulombic repulsion between the anionic cyanide ligands, however, dominates the overall energetics and ultimately gives preference to the high-spin complex, where the ligand-ligand separation is larger. Our calculations highlight that for a quantitative understanding of spin-state energetic ordering in a transition metal complex, ligand-ligand electrostatic interactions must be taken into account in addition to classical ligand-field arguments based on M-L orbital interaction energies.

Structural Model Studies for the High-Valent Intermediate Q of Methane Monooxygenase from Broken-Symmetry Density Functional Calculations

Mössbauer isomer shift parameters have been obtained for both density functional theory (DFT) OPBE and OLYP functionals by linear regressions between the measured isomer shifts and calculated electron densities at Fe nuclei for a number of Fe(2+,2.5+) and Fe(2.5+,3+,3.5+,4+) complexes grouped separately. The calculated isomer shifts and quadrupole splittings on the sample Fe complexes from OPBE and OLYP functionals are similar to those of PW91 calculations (J. Comput. Chem. 27 (2006) 1292), however the fit parameters from the linear regressions differ between PW91 and OPBE, OLYP. Four models for the active site structure of the hydroxylase component of soluble methane monooxygenase (MMOH) have been studied, using three DFT functionals OPBE, OLYP, and PW91, incorporated with broken-symmetry methodology and the conductor-like screening (COSMO) solvation model. The calculated properties, including optimized geometries, electronic energies, pK(a)'s, Fe net spin populations, and Mössbauer isomer shifts and quadrupole splittings, have been reported and compared with available experimental values. The high-spin antiferromagnetically (AF) coupled Fe(4+) sites are correctly predicted by OPBE and OLYP methods for all active site models. PW91 potential overestimates the Fe-ligand covalencies for some of the models because of spin crossover. Our calculations and data analysis support the structure (our current model II shown in Figure 8) proposed by Friesner and Lippard's group (J. Am. Chem. Soc. 123 (2001) 3836-3837), which contains an Fe(4+)(μ-O)(2)Fe(4+) center, one axial water which also H-bonds to both side chains of Glu243 and Glu114, and one bidentate carboxylate group from the side chain of Glu144, which is likely to represent the active site of MMOH-Q. A new model structure (model IV shown in Figure 9), which has a terminal hydroxo and a protonated His147 which is dissociated from a nearby Fe, is more asymmetric in its Fe(μ-O)(2)Fe diamond core, and is another very good candidate for intermediate Q.