Theoretical Characterization of the Electronic and Spin Structures for Iron–Sulfur Cubane in Reduced High-Potential Iron–Sulfur Proteins Using Density Functional Theory

Abstract

In this work, density functional theory and natural bond orbital analysis are used to investigate the electronic structures of the [4Fe-4S] cluster in reduced high-potential iron–sulfur proteins. Calculated 3d-orbital occupancies of Fe atoms in the [4Fe-4S] cluster revealed a spin structure with two ferromagnetically coupled [2Fe-2S]⁺ subclusters that are antiferromagnetically coupled to each other. In addition, the chemical bonds between S–Fe were found to form primarily through the donation of electrons from S to Fe atoms.

1 Introduction

Iron–sulfur proteins function as active centers in essential life-sustaining processes, such as photosynthesis, respiration, and nitrogen fixation. The electronic structures of the Fe-S cluster are key to their functions. Therefore, developing an understanding of the intrinsic electronic structure of the Fe-S cluster in iron–sulfur proteins is of great importance.

The primary focus of this work is to further study the reduced high-potential iron–sulfur protein (HiPIP). HiPIP is an electron-transporting protein, with a cubane-type [4Fe-4S] cluster at its active center, that functions as a part of a photosynthetic electron-transfer system. The formal charge of the Fe atoms in reduced HiPIP is 2Fe(III) 2(II); and recently, its structure was revealed by high-resolution X-ray structural analysis at the 0.48 Å scale [1].

Various theoretical calculations have been applied to determine the electronic structures of the [4Fe-4S] cluster. The results indicated that the [Fe₄S₄]²⁺ clusters contain two ferromagnetically coupled [Fe₂S₂]⁺ subclusters in high-spin states, which are antiferromagnetically coupled to each other [2]. Recently, we discussed the influence of amino acids around the [4Fe-4S] cluster on the electronic structure in reduced HiPIP [3]. However, currently available information on the chemical bonding within the [4Fe-4S] cluster in reduced HiPIP is insufficient. This work, therefore, investigates the electronic structure and chemical bonding schemes of the [4Fe-4S] cluster. For this purpose, natural bond orbital (NBO) analysis is employed using density functional theory (DFT) with various functionals.

2 Method

All DFT calculations were performed using the Gaussian 16 package [4]. To investigate the dependency of DFT functionals on the electronic structures, we used B3LYP, CAM-B3LYP, BP86, and ωB97XD functionals and the 6-311G* basis set. NBO analysis was carried out using the NBO 7.0 package [5]. We focused on the reduced HiPIP in the singlet state, and constructed initial structures based on the X-ray crystal structure [1]; the calculational model for this is shown in Figure 1. The computational model considered the structural environment surrounding the [4Fe-4S] cluster, up to its first coordination sphere. To describe the spin antiferromagnetic coupling in the [4Fe-4S] cluster, we utilized the spin-unrestricted broken-symmetry (BS) approach, which was applied for Fe-S cluster in the previous work [2, 3, 6]. During structural optimization, all C and N atoms in the main chain of Cys were fixed. Among the 12 possible spin configurations, this study focused on the energetically stable spin configuration, which was confirmed by B3LYP/6-31G* [3], in the open-shell singlet state.

Figure 1.

 Computational [4Fe-4S] cluster model with four Cys coordinated to each iron.

3 Results and Discussion

Table 1 lists the 3d orbital electron occupancy for each Fe atom, as obtained by the NBO analysis using the B3LYP/6-311G* level of theory. A single α electron occupied all five orbitals on Fe1 and Fe2, while a single β electron occupied all five orbitals on Fe3 and Fe4. This trend was also observed when using other DFT functionals, except for when the BP86 functional was used. This difference in trend is thought to be because of either the presence or absence of Hartree-Fock exchange functionals in the DFT framework. From this information, it can be concluded that the [4Fe-4S] cluster has a spin structure with two ferromagnetically coupled [2Fe-2S]⁺ subclusters that are antiferromagnetically coupled to each another.

Table 1. 3d Orbital occupancy of Fe atoms in the [4Fe-4S] cluster, as obtained by the B3LYP/6-311G* level of theory

α	dxy	dxz	dyz	dx2y2	dz2
Fe1	0.993	0.991	0.988	0.991	0.987
Fe2	0.993	0.993	0.987	0.993	0.994
Fe3	0.257	0.259	0.081	0.269	0.494
Fe4	0.200	0.231	0.164	0.302	0.390
β	dxy	dxz	dyz	dx2y2	dz2
Fe1	0.150	0.306	0.155	0.279	0.483
Fe2	0.210	0.336	0.287	0.262	0.120
Fe3	0.998	0.989	0.992	0.992	0.990
Fe4	0.993	0.991	0.993	0.989	0.993

Table 2 shows the percentages of the natural atomic hybrids (NAH) that make up the NBOs of the S–Fe bonding orbitals in the [4Fe-4S] cluster, as calculated using the B3LYP/6-311G* level of theory. NBOs of S–Fe bonds formed by β-electrons were obtained for Fe1 or Fe2 atoms, while those formed by α-electrons were obtained for Fe3 or Fe4 atoms. It was found that the NBOs are formed with an approximate >75% contribution from the S atom. This trend was also observed when using other DFT functionals. Therefore, it can be concluded that the chemical bonds between S–Fe involving Fe1 and Fe2 mainly form by the donation of β electrons from S to Fe atoms, while those involving Fe3 and Fe4 mainly form by the donation of α electrons from S to Fe atoms.

Table 2. Percentage (%) of NAHs that make up the NBOs in the bonding orbitals between S and Fe atoms, as calculated using the B3LYP/6-311G* level of theory

α	S	Fe	β	S	Fe
S1–Fe3	84.13	15.87	S1–Fe2	79.3	20.69
S1–Fe4	78.73	21.27	S2–Fe1	86.5	13.49
S2–Fe3	81.47	18.53	S3–Fe1	90.4	9.57
S2–Fe4	76.77	23.23	S3–Fe2	74.7	25.30
S3–Fe4	76.79	23.21	S4–Fe1	91.3	8.71
S4–Fe3	82.84	17.16	S4–Fe2	73.5	26.55

Table 3 shows the percentage contributions of S and Fe atomic orbitals to each NAH of table 2, as calculated using the B3LYP/6-311G* level of theory. All NBOs of S–Fe were formed by S-p orbitals and Fe-s and d orbitals, a trend which is consistent with calculations conducted using other DFT functionals. A previous theoretical study using a high-accuracy ab initio quantum chemical approach showed that S-3p orbitals interact with both the Fe-3d orbitals and the low-lying empty Fe-4s orbitals [7]. Therefore, it is expected that the cubane-type [4Fe-4S] cluster in reduced HiPIP is formed by the contributions from the S-3p and Fe-3d and −4s orbitals.

Table 3. Percentage (%) of S and Fe atomic orbitals that form each NAH, as calculated using the B3LYP/6-311G* level of theory

	S			Fe
α	s	p	d	s	p	d
S1–Fe3	6.36	93.44	0.20	21.49	0.86	77.63
S1–Fe4	6.34	93.37	0.29	23.80	0.86	75.33
S2–Fe3	5.50	94.27	0.23	21.29	0.88	77.82
S2–Fe4	5.95	93.76	0.29	24.96	0.73	74.30
S3–Fe4	7.11	92.60	0.30	27.36	0.48	72.15
S4–Fe3	9.81	89.95	0.24	25.82	0.73	73.43
	S			Fe
β	s	p	d	s	p	d
S1–Fe2	3.76	95.88	0.35	29.06	2.27	68.66
S2–Fe1	6.60	93.15	0.25	23.80	0.97	75.21
S3–Fe1	6.60	93.24	0.16	26.42	0.93	72.64
S3–Fe2	3.79	95.94	0.28	22.33	0.46	77.20
S4–Fe1	5.39	94.48	0.14	27.70	0.75	71.53
S4–Fe2	3.52	96.17	0.31	25.76	0.50	73.72

Acknowledgment

This work was partly supported by MEXT KAKENHI (JP21H00014, JP21H05419, and JP22H04800). Some of the computations were performed using computer facilities at the Research Institute for Information Technology, Kyushu University, and the Research Center for Computational Science, Okazaki, Japan (Project:22-IMS-C122).

Reference

• [1]   Y. Hirano, K. Takeda, K. Miki, Nature, 534, 281 (2016). doi:10.1038/nature18001 PMID:27279229
• [2]   A. Dey, C. L. Roche, M. A. Walters, K. O. Hodgson, B. Hedman, E. I. Solomon, Inorg. Chem., 44, 8349 (2005). doi:10.1021/ic050981m PMID:16270973
• [3]   A. Sato, Y. Hori, Y. Shigeta, Inorg. Chem., 62, 2040 (2023). doi:10.1021/acs.inorgchem.2c03617 PMID:36695190
• [4]Gaussian 16, Revision C.01, M. J. Frisch et al., Gaussian, Inc., Wallingford CT, 2016.
• [5]   NBO 7.0. E. D. Glendening et al., Theoretical Chemistry Institute, University of Wisconsin, Madison, WI (2018).
• [6]   I. Era, Y. Kitagawa, N. Yasuda, T. Kamimura, N. Amamizu, H. Sato, et al., Molecules, 26, 6129 (2021). doi:10.3390/molecules26206129 PMID:34684710
• [7]   C. Mejuto-Zaera, D. Tzeli, D. Williams-Young, N. M. Tubman, M. Matoušek, J. Brabec, et al., J. Chem. Theory Comput., 18, 687 (2022). doi:10.1021/acs.jctc.1c00830 PMID:35034448