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Electronic Properties of Iron Sites and Their Active Forms in Porphyrin-Type Architectures

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Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes

Part of the book series: Springer Series on Bio- and Neurosystems ((SSBN,volume 8))

Abstract

This chapter is focused on recent advances in quantum chemical modeling of active sites in heme proteins and iron porphyrin complexes. After introducing the computational methods (density functional theory and correlated ab initio ones) several case studies are reviewed to show how these methods unravel the electronic structure of heme and heme-related systems; in particular, how they deal with description of: (a) spin state energetics in ferrous and ferric complexes; (b) binding properties of CO, NO, and \({\text {O}}_{2}\) ligands to heme; (c) electronic structure of P450 Cpd I and alike systems. Making conclusive calculations for the heme species requires a balanced treatment of electron correlation, which is a great challenge for the present computational methods. Further challenge is situated in a correct translation of the computational results into chemical terms. Achievements of modern ab initio methods on the two fronts are highlighted and discussed in relation to DFT calculations.

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Notes

  1. 1.

    One should be aware that these formally excited configurations merely serve to describe electron correlation and have here no direct connotation to electronically excited states.

  2. 2.

    The reader should also notice that the LS state is not shown for FeP in Fig. 2. The LS state discussed below for this complex is a closed-shell singlet, (d\(_{x^2-y^2}\))\(^2\)(d\(_{xz}\),d\(_{yz}\))\(^4\), which has analogous electronic structure to the singlet state in five- [FeP(Im)] and six-coordinated heme species. However, this is not the lowest singlet state of FeP, the latter being instead an open-shell singlet, (d\(_{x^2-y^2}\))\(^2\)(d\(_{z^2}\))\(^2\)(d\(_{xz}\),d\(_{yz}\))\(^2\)  [12, 136].

  3. 3.

    Just so, the active space for FeP was obtained by distributing six d electrons of Fe(II) in its 3d orbitals with added double-shell (4d), and a doubly occupied \(\sigma \) Fe–N\(_{{\text {porphyrin}}}\) orbital to account for covalency of the iron–N(porphyrin) bonding. This selection led to the active space of 8 electrons in 11 orbitals (8in11) for FeP. In case of FeP(Im), this active space was augmented with a doubly occupied \(\sigma \) Fe-N\(_{{\text {Im}}}\) orbital to account for covalency of the Fe–N(imidazole) bond, thus yielding the total active space of 10 electrons in 12 orbitals (10in12) [136]. For the ferric model, the active space was obtained by distributing five electrons of Fe(III) in its 3d orbitals with added double-shell (4d) and three doubly occupied orbitals: \(\sigma \) Fe–N\(_{{\text {porphyrin}}}\) (which play the same role as in the ferrous complexes), together with \(\sigma \) Fe–S and \(\pi \) Fe–S (describing covalency of the Fe–SH bond), yielding the total active space of 11 electrons in 13 active orbitals (11in13) [189].

  4. 4.

    A  minor exception from this rule, quoted for structures obtained from some hybrid functionals for the Fe–O\(_{2}\) complexes, is discussed in Ref. [136].

  5. 5.

    In CASPT2, due to its large computational cost, higher polarization functions were removed for H and C atoms of P and Im ligands, keeping the fully polarized triple-\(\zeta \) quality only in the first-coordination sphere of Fe and on the XO ligand.

  6. 6.

    First, since the occupation of the Fe 3d\(_{xy}\) is always small the corresponding double-shell Fe 4d\(_{xy}\) was removed from the active space. For XO=CO the Fe 3d\(_{z^2}\) was also practically unoccupied, thus the corresponding Fe 4d\(_{z^2}\) was not active either. In contrast, all the five CO orbitals (\(\sigma \), \(\pi \), and \(\pi ^*\)) appeared necessary, which led to active space of 14 electrons in 14 orbitals (14in14) for FeP(CO) and 16 electrons in 15 orbitals for FeP(Im)(CO). For XO=NO or \({\text {O}}_{2}\), the explicit \(\sigma \) orbital to describe \(\sigma \)-donation became less important thus only the \(\pi \) and \(\pi ^*\) orbitals of NO and \({\text {O}}_{2}\) were made active. On the other hand, both in oxyheme and nitrosylheme complexes the Fe 3d\(_{z^2}\) was at least partially occupied, thus the corresponding Fe 4d\(_{z^2}\) double-shell orbital was found important and added straight for the FeP(NO) and \({\text {FeP}}({\text {O}}_{2})\) complexes, which led to active spaces of (13in14) and (14in14), respectively. On the contrary, for FeP(Im)(NO) and \({\text {FeP}}({\text {Im}})({\text {O}}_{2})\), adding it on top of Im \(\sigma \) turned out to be unfeasible. Thus, here the effect of Fe 4d\(_{z^2}\) on the binding energy \(\varDelta E_{\text {BDE}}^{(0)}\) had to be estimated from separate calculation with Fe 4d\(_{z^2}\) either active or not, but without Im \(\sigma \) active, and used as a mere correction to the results obtained with Im \(\sigma \) active and Fe 4d\(_{z^2}\) virtual [i.e, employing (15in14) for FeP(Im)(NO) or (16in14) for \({\text {FeP}}({\text {Im}})({\text {O}}_{2})\)].

  7. 7.

    It should be noted that this number does not include a BSSE correction, in view of Ref. [136], expected to reduce the BDE considerably.

  8. 8.

    The difference is most pronounced for the \([{\text {Fe}}({\text {H}}_{2}{\text {O}})_{5}{\text {NO}}]^{2+}\) complex, in which due to the linear Fe–N–O coordination the character of the nonbonding orbital is changed to pure Fe 3d\(_{z^2}\).

  9. 9.

    The assignment of oxidation states for a given VB-type structure comes down by calculating the number of electrons in the Fe 3d and NO \(\pi ^*\) fragment orbitals.

  10. 10.

    However, the active orbitals in this study were not obtained self-consistently at CASSCF level but were taken from restricted open-shell DFT (BP86) calculations.

  11. 11.

    The medium effect ranges from 2–4 kcal/mol for the five-coordinated \({\text {Fe}}({\text {=O}}){\text {P}}^{+}\) to 4–8 kcal/mol for the six-coordinated \({\text {Fe}}({\text {=O}}){\text {P}}({\text {Cl}})\) complex, with only slight dependence on the dielectric constant (\(\varepsilon =5.7\) and 78 were tested), but nearly not depending on the exchange-correlation functional used, nor on a specific solvent model (PCM, COSMO) used in the calculations. This suggests that the effect is rooted simply in larger electrostatic stabilization of the iron(IV)-oxo porphyrin cation radical states as compared to the iron(V)-oxo states with a closed-shell porphyrin.

  12. 12.

    In these calculations only 6 ferryl-based orbitals (\(\pi _{xz,yz},\pi ^*_{xz,yz},\sigma _{z^2},\sigma ^*_{z^2}\)) and all (remaining) singly occupied orbitals (e.g., a\(_{2u}\) in the tri-/pentaradicaloids) were placed in the RAS2 subspace (see Sect. 2.2), whereas the other active orbitals were placed in RAS1 (if nearly doubly occupied) or in RAS3 (if nearly empty).

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Acknowledgements

This research project was supported by grant no UMO-2011/01/B/ST4/02620 from the National Science Centre (Poland) and by grant no IP2011 044471 from the Ministry of Science and Higher Education (Poland). This scholarly work was made thanks to POWIEW project, which is co-funded by the European Regional Development Fund (ERDF) as a part of the Innovative Economy program. This publication was made possible through the financial support from the Foundation for Polish Science (START scholarship provided for M.R.). We also acknowledge computational grants from Academic Computer Center CYFRONET AGH in Kraków, WCSS in Wroclaw (grant no. 181), and CI TASK in Gdańsk.

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  1. Mariusz Radoń

    Present address: Faculty of Chemistry, Jagiellonian University in Krakow, Gronostajowa 2, 30-387, Kraków, Poland

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  1. Academic Computer Center CYFRONET AGH, Nawojki 11, 30-950, Kraków, Poland

    Mariusz Radoń

  2. Jerzy Haber Institute of Catalysis, Polish Academy of Sciences, Niezapominajek 8, 30-239, Kraków, Poland

    Ewa Broclawik

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    Adam Liwo

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Radoń, M., Broclawik, E. (2019). Electronic Properties of Iron Sites and Their Active Forms in Porphyrin-Type Architectures. In: Liwo, A. (eds) Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes. Springer Series on Bio- and Neurosystems, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-95843-9_23

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