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

DFT study of the mechanism for methane hydroxylation by soluble methane monooxygenase (sMMO): effects of oxidation state, spin state, and coordination number

The exact structure of the active site of intermediate Q, the methane-oxidizing species of soluble methane monooxygenase (sMMO), and the reaction mechanism of Q with methane molecule are still not fully clear. To gain further insights into the structure and reaction mechanism, five diiron models of Q that differ in shape, oxidation state, spin state, and coordination number of the two iron centers are studied. Different mechanisms in different spin states were explored. Density functional theory (DFT) calculations show that Fe(III)Fe(IV)(μ-O)(μ-OH) is more reactive than Fe(IV)(2)(μ-O)(2) in the oxygen-rich environment and that the reactivity of the active core of sMMO-Q is not enhanced by converting its oxo bridge into a terminal ligand. A four-coordinated diiron model is the most effective for methane hydroxylation. Both radical and non-radical intermediates are involved in the reactions for the four-coordinated diiron model.

Water 16-mers and hexamers: assessment of the three-body and electrostatically embedded many-body approximations of the correlation energy or the nonlocal energy as ways to include cooperative effects

This work presents a new fragment method, the electrostatically embedded many-body expansion of the nonlocal energy (EE-MB-NE), and shows that it, along with the previously proposed electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), produces accurate results for large systems at the level of CCSD(T) coupled cluster theory. We primarily study water 16-mers, but we also test the EE-MB-CE method on water hexamers. We analyze the distributions of two-body and three-body terms to show why the many-body expansion of the electrostatically embedded correlation energy converges faster than the many-body expansion of the entire electrostatically embedded interaction potential. The average magnitude of the dimer contributions to the pairwise additive (PA) term of the correlation energy (which neglects cooperative effects) is only one-half of that of the average dimer contribution to the PA term of the expansion of the total energy; this explains why the mean unsigned error (MUE) of the EE-PA-CE approximation is only one-half of that of the EE-PA approximation. Similarly, the average magnitude of the trimer contributions to the three-body (3B) term of the EE-3B-CE approximation is only one-fourth of that of the EE-3B approximation, and the MUE of the EE-3B-CE approximation is one-fourth that of the EE-3B approximation. Finally, we test the efficacy of two- and three-body density functional corrections. One such density functional correction method, the new EE-PA-NE method, with the OLYP or the OHLYP density functional (where the OHLYP functional is the OptX exchange functional combined with the LYP correlation functional multiplied by 0.5), has the best performance-to-price ratio of any method whose computational cost scales as the third power of the number of monomers and is competitive in accuracy in the tests presented here with even the electrostatically embedded three-body approximation.

Significant effect of spin flip on the oxygen atom transfer reaction from (oxo)manganese(V) corroles to thioanisole: insights from density functional calculations

The electronic and structural features of (oxo)manganese(V) corroles and their catalyzed oxygen atom transfers to thioanisole in different spin states have been investigated by the B3LYP functional calculations. Calculations show that these corrole-based oxidants and their complexes with thioanisole generally have the singlet ground state, and their triplet forms are also accessible in consideration of the spin-orbit coupling interaction. Due to strong d-π conjugation interactions between Mn and the corrole ring arising from the π electron donation of the corrole moiety, the five-coordinated Mn approximately has the stable 18-electron configuration. The predicted free energy barriers for the singlet oxygen atom transfer reactions are generally larger than 22 kcal mol(-1), while the spin flip in reaction may remarkably increase the reactivity. In particular, the bromination on β-pyrrole carbon atoms of the meso-substituted (oxo)manganese(V) corrole strikingly enhances the spin-orbit coupling interaction and results in the dramatic increase of reactivity. The multiple spin changes are predicted to be involved in the low-energy reaction pathway. The present results show good agreement with the experimental observation and provide a detailed picture for the oxygen atom transfer reaction induced by the (oxo)manganese(V) corroles.

Theoretical Investigation of the Electronic Structure of Fe(II) Complexes at Spin-State Transitions

The electronic structure relevant to low spin (LS)↔high spin (HS) transitions in Fe(II) coordination compounds with a FeN₆ core are studied. The selected [Fe(tz)₆]²⁺ (1) (tz = 1H-tetrazole), [Fe(bipy)₃]²⁺ (2) (bipy = 2,2′-bipyridine), and [Fe(terpy)₂]²⁺ (3) (terpy = 2,2′:6′,2″-terpyridine) complexes have been actively studied experimentally, and with their respective mono-, bi-, and tridentate ligands, they constitute a comprehensive set for theoretical case studies. The methods in this work include density functional theory (DFT), time-dependent DFT (TD-DFT), and multiconfigurational second order perturbation theory (CASPT2). We determine the structural parameters as well as the energy splitting of the LS–HS states (ΔE_HL) applying the above methods and comparing their performance. We also determine the potential energy curves representing the ground and low-energy excited singlet, triplet, and quintet d⁶ states along the mode(s) that connect the LS and HS states. The results indicate that while DFT is well suited for the prediction of structural parameters, an accurate multiconfigurational approach is essential for the quantitative determination of ΔE_HL. In addition, a good qualitative agreement is found between the TD-DFT and CASPT2 potential energy curves. Although the TD-DFT results might differ in some respect (in our case, we found a discrepancy at the triplet states), our results suggest that this approach, with due care, is very promising as an alternative for the very expensive CASPT2 method. Finally, the two-dimensional (2D) potential energy surfaces above the plane spanned by the two relevant configuration coordinates in [Fe(terpy)₂]²⁺ were computed at both the DFT and CASPT2 levels. These 2D surfaces indicate that the singlet–triplet and triplet–quintet states are separated along different coordinates, i.e., different vibration modes. Our results confirm that in contrast to the case of complexes with mono- and bidentate ligands, the singlet–quintet transitions in [Fe(terpy)₂]²⁺ cannot be described using a single configuration coordinate.

Experimental and time-dependent density functional theory characterization of the UV-visible spectra of monomeric and μ-oxo dimeric ferriprotoporphyrin IX

Speciation of ferriprotoporphyrin IX, Fe(III)PPIX, in aqueous solution is complex. Despite the use of its characteristic spectroscopic features for identification, the theoretical basis of the unique UV-visible absorbance spectrum of μ-[Fe(III)PPIX](2)O has not been explored. To investigate this and to establish a structural and spectroscopic model for Fe(III)PPIX species, density functional theory (DFT) calculations were undertaken for H(2)O-Fe(III)PPIX and μ-[Fe(III)PPIX](2)O. The models agreed with related Fe(III)porphyrin crystal structures and reproduced vibrational spectra well. The UV-visible absorbance spectra of H(2)O-Fe(III)PPIX and μ-[Fe(III)PPIX](2)O were calculated using time-dependent DFT and reproduced major features of the experimental spectra of both. Transitions contributing to calculated excitations have been identified. The features of the electronic spectrum calculated for μ-[Fe(III)PPIX](2)O were attributed to delocalization of electron density between the two porphyrin rings of the dimer, the weaker ligand field of the axial ligand, and antiferromagnetic coupling of the Fe(III) centers. Room temperature magnetic circular dichroism (MCD) spectra have been recorded and are shown to be useful in distinguishing between these two Fe(III)PPIX species. Bands underlying major spectroscopic features were identified through simultaneous deconvolution of UV-visible and MCD spectra. Computed UV-visible spectra were compared to deconvoluted spectra. Interpretation of the prominent bands of H(2)O-Fe(III)PPIX largely conforms to previous literature. Owing to the weak paramagnetism of μ-[Fe(III)PPIX](2)O at room temperature and the larger number of underlying excitations, interpretation of its experimental UV-visible spectrum was necessarily tentative. Nonetheless, comparison with the calculated spectra of antiferromagnetically coupled and paramagnetic forms of the μ-oxo dimer of Fe(III)porphine suggested that the composition of the Soret band involves a mixture of π→π* and π→d(π) charge transfer transitions. The Q-band and charge transfer bands appear to amalgamate into a mixed low energy envelope consisting of excitations with heavily admixed π→π* and charge transfer transitions.

Titanium as a Potential Addition for High-Capacity Hydrogen Storage Medium

We study the adsorption of hydrogen molecules on a titanium atom supported by a benzene molecule using generalized gradient corrected Density Functional Theory (DFT). This simple system is found to bear important analogies with titanium adsorption sites in (8, 0) titanium-coated single-walled carbon nanotubes (SWNTs) (T. Yildirim and S. Ciraci, 2005) In particular, we show that up to fourH2molecules can coordinate to the metal ion center, with adsorption patterns similar to those observed in Ti-SWNTs and no more than one molecule dissociating in the process. We analyze in detail the orbital interactions responsible for Ti-benzene binding and for the electron transfer responsible for theH2dissociation. We find the latter to involve a transition from a triplet to a singlet ground state as the hydrogen molecule approaches the adsorption site, similar to what has been observed in Ti-SWNTs. The total Ti-H2-binding energy for the first dissociative addition is somewhat inferior (~0.4 eV) to the value estimated for adsorption on Ti-SWNTs. We analyze in detail the orbital interactions responsible for theH2binding.

Toward accurate theoretical thermochemistry of first row transition metal complexes

The recently developed correlation consistent Composite Approach for transition metals (ccCA-TM) was utilized to compute the thermochemical properties for a collection of 225 inorganic molecules containing first row (3d) transition metals, ranging from the monohydrides to larger organometallics such as Sc(C(5)H(5))(3) and clusters such as (CrO(3))(3). Ostentatiously large deviations of ccCA-TM predictions stem mainly from aging and unreliable experimental data. For a subset of 70 molecules with reported experimental uncertainties less than or equal to 2.0 kcal mol(-1), regardless of the presence of moderate multireference character in some molecules, ccCA-TM achieves transition metal chemical accuracy of ±3.0 kcal mol(-1) as defined in our earlier work [J. Phys. Chem. A2007, 111, 11269-11277] by giving a mean absolute deviation of 2.90 kcal mol(-1) and a root-mean-square deviation of 3.91 kcal mol(-1). As subsets are constructed with decreasing upper limits of reported experimental uncertainties (5.0, 4.0, 3.0, 2.0, and 1.0 kcal mol(-1)), the ccCA-TM mean absolute deviations were observed to monotonically drop off from 4.35 to 2.37 kcal mol(-1). In contrast, such a trend is missing for DFT methods as exemplified by B3LYP and M06 with mean absolute deviations in the range 12.9-14.1 and 10.5-11.0 kcal mol(-1), respectively. Salient multireference character, as demonstrated by the T(1)/D(1) diagnostics and the weights (C(0)(2)) of leading electron configuration in the complete active self-consistent field wave function, was found in a significant amount of molecules, which can still be accurately described by the single reference ccCA-TM. The ccCA-TM algorithm has been demonstrated as an accurate, robust, and widely applicable model chemistry for 3d transition metal-containing species with versatile bonding features.

VALIDITY AND INTERPRETATION OF HUND'S MULTIPLICITY RULE FOR MOLECULES: A DENSITY FUNCTIONAL STUDY

Validity and interpretation of Hund's multiplicity rule for one molecular system, boron hydride, is investigated from the density functional framework in the present work. Performance of a number of approximate exchange-correlaton energy denstiy functionals from LDA, GGA and hybrid models have been examined. It has been shown that all approximate functionals are able to predict the correct energy order, both adiabatically and vertically, for different spin states of the molecule, reproducing that a higher spin state from the same electronic configuration possesses a lower total energy. It is only the hybrid functionals, however, that render the picture derived for the exact density functionl theory of excited states and multiplets, that is, the validity of Hund's rule can be interpreted by the sole contribution from the outmost orbital (i.e. HOMO) of the spin states. Systematic discrepancy between the total and HOMO energy differences have been observed for both LDA and GGA forms, indicating that they are not as good in simulating the same-spin electron correlation effect as the Hartree–Fock method. We also show that it is the same as what we have found from the Hartree–Fock theory, and justification via either the nuclear-electron attraction or the exchange energy alone is not adequate to interpret the validity of the rule.

Cu(bipy)2+/TEMPO-catalyzed oxidation of alcohols: radical or nonradical mechanism?

In the oxidation of alcohols with TEMPO as catalyst, the substrate has alternatively been postulated to be oxidized but uncoordinated TEMPO(+) (Semmelhack) or Cu-coordinated TEMPO(•) radical (Sheldon). The reaction with the Cu(bipy)(2+)/TEMPO cocatalyst system has recently been claimed, on the basis of DFT calculations, to not be a radical reaction but to be best viewed as electrophilic attack on the alcohol C-H(α) bond by coordinated TEMPO(+). This mechanism combines elements of the Semmelhack mechanism (oxidation of TEMPO to TEMPO(+)) and the Sheldon proposal ("in the coordination sphere of Cu"). The recent proposal has been challenged on the basis of DFT calculations with a different functional, which were reported to lead to a radical mechanism. We carefully examine the results for the two functionals and conclude from both the calculated energetics and from an electronic structure analysis that the results of the two DFT functionals are consistent and that both lead to the proposed mechanism with TEMPO not acting as radical but as (coordinated) positive ion.

Quantum mechanically derived AMBER-compatible heme parameters for various states of the cytochrome P450 catalytic cycle

Molecular mechanics (MM) methods are computationally affordable tools for screening chemical libraries of novel compounds for sites of P450 metabolism. One challenge for MM methods has been the absence of a consistent and transferable set of parameters for the heme within the P450 active site. Experimental data indicate that mammalian P450 enzymes vary greatly in the size, architecture, and plasticity of their active sites. Thus, obtaining X-ray-based geometries for the development of accurate MM parameters for the major classes of hepatic P450 remains a daunting task. Our previous work with preliminary gas-phase quantum mechanics (QM)-derived atomic partial charges greatly improved the accuracy of docking studies of raloxifene to CYP3A4. We have therefore developed and tested a consistent set of transferable MM parameters based on gas-phase QM calculations of two model systems of the heme-a truncated (T-HM) and a full (F-HM) for four states of the P450 catalytic cycle. Our results indicate that the use of the atomic partial charges from the F-HM further improves the accuracy of docked predictions for raloxifene to CYP3A4. Different patterns for substrate docking are also observed depending on the choice of heme model and state. Newly parameterized heme models are tested in implicit and explicitly solvated MD simulations in the absence and presence of enzyme structures, for CYP3A4, and appear to be stable on the nanosecond simulation timescale. The new force field for the various heme states may aid the community for simulations of P450 enzymes and other heme-containing enzymes.

Combined DFT and BS study on the exchange coupling of dinuclear sandwich-type POM: comparison of different functionals and reliability of structure modeling

The exchange coupling of a group of three dinuclear sandwich-type polyoxomolybdates [MM'(AsMo7O27)2](12-) with MM' = CrCr, FeFe, FeCr are theoretically predicted from combined DFT and broken-symmetry (BS) approach. Eight different XC functionals are utilized to calculate the exchange-coupling constant J from both the full crystalline structures and model structures of smaller size. The comparison between theoretical values and accurate experimental results supports the applicability of DFT-BS method in this new type of sandwich-type dinuclear polyoxomolybdates. However, a careful choice of functionals is necessary to achieve the desired accuracy. The encouraging results obtained from calculations on model structures highlight the great potential of application of structure modeling in theoretical study of POM. Structural modeling may not only reduce the computational cost of large POM species but also be able to take into account the external field effect arising from solvent molecules in solution or counterions in crystal.

DFT calculations for intermediate and active states of the diiron center with a tryptophan or tyrosine radical in Escherichia coli ribonucleotide reductase

Class Ia ribonucleotide reductase subunit R2 contains a diiron active site. In this paper, active-site models for the intermediate X-Trp48(•+) and X-Tyr122(•), the active Fe(III)Fe(III)-Tyr122(•), and the met Fe(III)Fe(III) states of Escherichia coli R2 are studied, using broken-symmetry density functional theory incorporated with the conductor-like screening solvation model. Different structural isomers and different protonation states have been explored. Calculated geometric, energetic, Mössbauer, hyperfine, and redox properties are compared with available experimental data. Feasible detailed structures of these intermediate and active states are proposed. Asp84 and Trp48 are most likely the main contributing residues to the result that the transient Fe(IV)Fe(IV) state is not observed in wild-type class Ia E. coli R2. Asp84 is proposed to serve as a proton-transfer conduit between the diiron cluster and Tyr122 in both the tyrosine radical activation pathway and the first steps of the catalytic proton-coupled electron-transfer pathway. Proton-coupled and simple redox potential calculations show that the kinetic control of proton transfer to Tyr122(•) plays a critical role in preventing reduction from the active Fe(III)Fe(III)-Tyr122(•) state to the met state, which is potentially the reason why Tyr122(•) in the active state can be stable over a very long period.

Spin-state crossover and hyperfine interactions of ferric iron in MgSiO(3) perovskite

Using density functional theory plus Hubbard U calculations, we show that the ground state of (Mg,Fe)(Si,Fe)O(3) perovskite, the major mineral phase in Earth's lower mantle, has high-spin ferric iron (S=5/2) at both dodecahedral (A) and octahedral (B) sites. With increasing pressure, the B-site iron undergoes a spin-state crossover to the low-spin state (S=1/2) between 40 and 70 GPa, while the A-site iron remains in the high-spin state. This B-site spin-state crossover is accompanied by a noticeable volume reduction and an increase in quadrupole splitting, consistent with recent x-ray diffraction and Mössbauer spectroscopy measurements. The anomalous volume reduction leads to a significant softening in bulk modulus during the crossover, suggesting a possible source of seismic-velocity anomalies in the lower mantle.

Cobalt-porphyrin catalyzed electrochemical reduction of carbon dioxide in water. 1. A density functional study of intermediates

The reduction of carbon dioxide by cobalt porphyrins is thought to be a multistep reaction with several possible intermediates and reaction pathways. We here investigate a number of possible intermediates in this reaction using density functional theory, including both hybrid (B3LYP) and pure (PBE and BP86) functionals. Optimum structures are located, and harmonic vibrational frequencies and thermal corrections are computed for the low-lying electronic states for all intermediates. Free energies of solvation are predicted for all species, providing a reaction profile in the aqueous phase, which enables identification of likely pathways. Finally, the reaction energy for the binding of carbon dioxide to the cobalt porphine cation is determined in the gas phase and in solution.