# Synergistic Charge Transfer Effect in Ferrous Heme–CO Bonding within Cytochrome P450

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Wave Function Analysis: Relative Significance of Different VB Structures

_{K}) of the representative VB structures illustrated in Scheme 2 (see also Section 3 for theoretical details). The weights were calculated from the VB structure coefficients and the overlap integrals between VB structures, using the Coulson–Chirgwin formula [28]. A noteworthy observation from the table is that VBSCF-calculated W

_{1}consistently demonstrates the largest weight of Φ

_{1}(68.39% in model I, 69.26% in model II, and 50.25% in model III) (Table 1a). In model I, W

_{2}is the second largest and significantly larger than the W

_{3}and W

_{4}values. These results suggest that σ donation prevails over π backdonation in this model. In model II, W

_{2}decreases while W

_{3}and W

_{4}increase compared to their corresponding weights in model I, indicating that the proximal HS

^{–}ligand attenuates σ donation while enhancing π backdonation. The attenuation of σ donation and the enhancement of π backdonation are even more pronounced in model III, where W

_{2}–W

_{4}exhibit similar values (8.59, 8.52, and 8.53%, respectively), underscoring the role of equatorial ligands in promoting π backdonation. Another intriguing finding for model III is the relatively large values of W

_{5}and W

_{6}(9.27%), indicating that states concurrently involving one Heitler–London (HL) bonding pair for σ donation and one for π backdonation emerge as significant contributors to the overall wave function. Breathing orbital valence bond (BOVB) calculations produced results qualitatively similar to those obtained from VBSCF calculations (Table 1b). However, the BOVB decreased the weights of Φ

_{1}while increasing the weights of Φ

_{2}–Φ

_{4}, suggesting that the orbital breathing effect enhances CT in both directions. W

_{7}and W

_{8}were found to be very small in both the VBSCF and BOVB calculations.

_{2}value when transitioning from model II to model III (Table 1), the W(σ) value for model III surpasses that of model II (Table 2). This outcome stems from the heightened contribution of the VB structures simultaneously involving both σ and π bonds, specifically Φ

_{5}and Φ

_{6}. Once again, the BOVB calculations yielded qualitatively similar results to the VBSCF calculations, albeit with elevated values for W(σ) and W(π).

#### 2.2. Energy Analysis: Resonance between VB Structures

_{1}, the most dominant VB structure, using the following equation:

_{x}π

_{y}in the case of VB(all) calculations, but other states from deactivated VB calculations, such as VB(σ), can also be used as X. It is important to note that a more positive value of RE indicates a larger resonance stabilization effect. Table 3a provides a summary of the VBSCF-calculated RE values for different states. When we compare the RE(σ), RE(π

_{x}), and RE(π

_{y}) values for model I, which gauge the energetic stabilization attributable to respective CT processes, it becomes evident that σ donation plays a notably more substantial role in stabilizing the system compared to π backdonation. However, in model II, the relative significance of σ donation and π backdonation undergoes a notable change. Here, the RE(σ) value decreases from 26.98 kcal/mol (model I) to 17.49 kcal/mol (model II), whereas the RE(π

_{x}) and RE(π

_{y}) values increase from 4.03 kcal/mol (model I) to 7.84–7.86 kcal/mol (model II). This trend becomes even more pronounced in the case of model III, which exhibits RE(σ), RE(π

_{x}), and RE(π

_{y}) values of 15.77, 12.91, and 12.94 kcal/mol, respectively. Thus, the energetic stabilization for each of these CT routes in model III is of similar magnitude. These results highlight the critical roles played by proximal and equatorial ligands in energetically modulating both the σ-donation and π-backdonation effects, which can be attributed to alterations in the stability of the involved d-orbitals within distinct ligand fields [29].

_{3}ligands, which would further accentuate the equatorial ligand effect on π backdonation. In fact, our earlier DFT study indicated that in a porphine-based P450 model, π backdonation was approximately twice as significant as σ donation in terms of energetic stabilization [10,11], instead of the approximately 1.6-fold ratio observed in model III.

_{x}), RE(σπ

_{y}), and RE(π

_{x}π

_{y}) values consistently surpass the corresponding RE values for one of their constituent CT routes, i.e., RE(σ), RE(π

_{x}), or RE(π

_{y}). In addition, the RE(σπ

_{x}π

_{y}) value exceeds the values of RE(σπ

_{x}), RE(σπ

_{y}), and RE(π

_{x}π

_{y}). These findings illustrate the stabilizing influence that results from the mixing of a larger number of VB structures.

_{1}) is identical in our VBSCF and BOVB calculations, and the variational space is broader in BOVB for other states. Hence, the RE values calculated using BOVB necessarily exceeded their corresponding VBSCF counterparts, as shown in Table 3b. In essence, this trend signifies that the VB structures involving CT experience greater stabilization in the BOVB framework as a result of the orbital breathing effect. Overall, while the enhancement of the RE values in BOVB compared to the VBSCF values is not particularly substantial, relatively significant increases are observed when π

_{x}and π

_{y}VB structures were simultaneously included in the wave function in model III. It is also noteworthy that both VBSCF and BOVB yield similar enhancements or reductions in RE values when transitioning from model I to model III. For instance, in the case of RE(π

_{x}), the enhancement factor is approximately 3.2 in both VBSCF and BOVB results.

_{x}), as defined in Equation (4), assesses the resonance stabilization arising from the combination of the σ and π

_{x}VB structures.

_{x}) and ∆RE(σπ

_{y})) holds notable energetic significance. This observation underscores the existence of a synergistic CT (sCT) effect arising from the interplay between σ donation and π backdonation. The sCT effect does not straightforwardly align with the additive and separate consideration of σ donation and π backdonation, and it cannot be solely explained through ligand-field arguments. Notably, in the case of model III, which most closely mimics a real P450, ∆RE(σπ

_{x}) and ∆RE(σπ

_{y}) display the highest magnitude among all models, indicating that the proximal and equatorial ligands play a prominent role in promoting σ–π resonance. It should also be noted that there are two distinct sets of σ–π resonance interactions (σ–π

_{x}and σ–π

_{y}) due to the presence of two π-backdonation orbital-interaction pairs (Figure 1). Comparatively, many other ligands, unlike CO, can only form a single π-backdonation orbital-interaction pair, resulting in just one set of σ–π resonance. This inherent disparity in sCT leads to a relatively heightened level of energetic stabilization in the ferrous heme–CO complex, distinguishing it from other complexes in terms of its bonding characteristics.

_{x}π

_{y}) values exhibit near-zero values across all models. The data indicate that the contribution of π–π resonance to the overall energetic stabilization is notably smaller than that of σ–π resonance. Nevertheless, in BOVB calculations, there is a significant enhancement of π–π resonance (∆RE(π

_{x}π

_{y}) = 4.03 kcal/mol in model III) compared to the VBSCF value (0.47 kcal/mol). This enhanced π–π resonance contributes to the additional stabilization in ferrous heme–CO bonding. This is especially relevant as many other ligands possess only one π-backdonation orbital-interaction pair and therefore cannot establish any π–π resonance. Consequently, the sCT effect resulting from π–π resonance also contributes to the additional energetic stabilization of ferrous heme–CO bonding. For comparison, we also computed the ∆RE(π

_{x}π

_{y}) value for acetylene, yielding values of 13.41 kcal/mol (VBSCF) and 13.63 kcal/mol (BOVB) (Table S2). Thus, the energetic significance of π–π resonance is more pronounced in the case of acetylene. This finding also suggests that resonance between different bonding modes may be a widespread phenomenon extending beyond coordination complexes.

## 3. Materials and Methods

^{–}ligands at the B3LYP-D3BJ/def2-TZVP(6D,10F) level of theory [30,31,32,33,34,35,36]. To better align with the conventional notation of d-orbitals in chemistry such as ${d}_{{z}^{2}}$ and ${d}_{xz}$, we reorientated the optimized geometry such that Fe was placed at the origin, with Fe and the C atom of CO aligned along the z axis and one of the equatorial N atoms situated within the xz plane. For this purpose, we selected the N atom with the smallest magnitude of the N–Fe–S–H dihedral angle. The resultant model is referred to as model 0. However, applying VB calculations to model 0 was deemed computationally intensive. Therefore, we built three simplified models (I–III) based on model 0, as outlined in Scheme 1. These models retained the essential influence of proximal and equatorial ligands on the iron center while being computationally more manageable. The simplest model, model I, lacked any proximal or equatorial ligands, model II included a proximal HS

^{–}ligand, and model III featured both proximal and equatorial ligands (HS

^{–}and NH

_{3}). The atomic positions for models I and II were directly derived from model 0. We followed a similar procedure for constructing model III, but we optimized the positions of the hydrogen atoms within the NH

_{3}ligands at the B3LYP-D3BJ/def2-TZVP(6D,10F) level using Gaussian 16 [37], while keeping all other atoms fixed.

_{K}} within the total wave function Ψ:

_{K}} are VB structures. For all VB calculations, we utilized the XMVB 3.1 software in both the Xiamen Atomistic Computing Suite (XACS) cloud environment and an installed version [40,41,42]. Additionally, to enhance our understanding of the resonance stabilization in the ferrous heme–CO complex models, we applied VB calculations to acetylene. Orbitals were plotted using Multiwfn and IQmol [43,44].

_{x}) and the yz plane (π

_{y}), respectively. The fourth group was dedicated solely to ${d}_{xy}$ AOs, which were used to describe a non-bonding electron pair on the ferrous ion.

_{1}, which corresponds to the “dormant state,” the active electrons do not participate in any covalent bonding. In contrast, Φ

_{2}–Φ

_{4}each involve a single HL-type covalent bond, established either in the σ or the π framework, thus incorporating CT across fragments. Φ

_{5}–Φ

_{7}also involve CT but uniquely entail the formation of two HL-type bonding pairs. In Φ

_{8}, CT transpires across all σ-donation or π-backdonation routes. Electrons that were not treated explicitly by VB were described in a doubly occupied MO fashion, utilizing hybrid AOs. For models II and III, we adhered to essentially the same AO grouping approach, treating Fe and its proximal and equatorial ligands as one fragment. More details of VB orbital specification can be found in the Supplementary Materials (Figure S1). The VB calculation involving all possible VB structures and six active electrons is referred to as VB(all).

_{2}molecule, which include the left–right electron correlation for the bond [46]. Alternatively, when we prohibited σ donation, we focused on VB structures associated with the orbitals in the π frameworks (i.e., VB(π

_{x}π

_{y})). In terms of electron correlation, VB(π

_{x}π

_{y}) in VBSCF captures a larger portion of non-dynamical correlation than VB(π

_{x}) or VB(π

_{y}). The initial guess for these calculations was derived from the preceding VB(all) calculation. This deactivation approach allowed us to evaluate the extent of stabilization attained through the resonance mixing of different VB structures for different CT routes. It should be noted that the contribution of the two-electron-transferred state (e.g., the third structure in Scheme 3 in the case of VB(σ)), was typically very small.

_{x}), and VB(π

_{y}) calculations with BOVB, we considered three distinct VB structures within their respective σ or π routes (see Scheme 3). Meanwhile, the VB(σπ

_{x}), VB(σπ

_{y}), and VB(π

_{x}π

_{y}) calculations comprised 9 (=3 × 3) VB structures each, and VB(σπ

_{x}π

_{y}) calculations encompassed a total of 27 (=3 × 3 × 3) VB structures.

## 4. Conclusions

## Supplementary Materials

_{x}, and (c) π

_{y}frameworks, obtained through the VBSCF-VB(all) calculation of model I; Figure S3: VB orbitals in the (a) σ, (b) π

_{x}, and (c) π

_{y}frameworks, obtained through the VBSCF-VB(all) calculation of model II; Figure S4: VB orbitals in the (a) σ, (b) π

_{x}, and (c) π

_{y}frameworks, obtained through the VBSCF-VB(all) calculation of C

_{2}H

_{2}; Table S1. Total energies (in hartrees) obtained from (a) VBSCF and (b) BOVB calculations; Table S2. ∆RE values (in kcal/mol), obtained from (a) VBSCF and (b) BOVB calculations; Figure S5; Frontier orbitals and their energy levels (in hartrees), obtained through B3LYP-D3BJ/def2-TZVP(6D,10F) calculations for models I-III, after removing the CO ligand; Table S3: XYZ coordinates (Å).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic illustration of one σ-donation and two π-backdonation orbital-interaction pairs for CT in ferrous heme–CO bonding.

**Scheme 1.**Models I–III for VB analysis, constructed utilizing the previously optimized geometry of a P450 model [10].

**Figure 2.**VB orbitals in the (

**a**) σ, (

**b**) π

_{x}, and (

**c**) π

_{y}frameworks, obtained through the VBSCF-VB(all) calculation for model III.

**Scheme 2.**Schematic drawings of representative VB structures. Black, red, and blue colors are used for electrons involved in σ donation, π backdonation in the xz plane, and π backdonation in the yz plane, respectively.

**Figure 3.**The energy levels of the ten MOs around the frontier orbitals (B3LYP-D3BJ/def2-TZVP(6D,10F)) for models I–III without the CO ligand. The bars for occupied and unoccupied MOs are colored red and blue, respectively.

**Figure 4.**∆RE values (in kcal/mol) for models I–III, obtained from VBSCF (green) and BOVB (red) calculations.

**Scheme 3.**Schematic illustration of the sCT effect, arising from the resonance interaction between different sets of VB structures.

**Table 1.**Weights of Φ

_{1}–Φ

_{8}(in %) for models I–III, obtained by (

**a**) VBSCF-VB(all) and (

**b**) BOVB-VB(all) calculations

^{a}.

(a) VBSCF | ||||||||
---|---|---|---|---|---|---|---|---|

Model | W_{1} | W_{2} | W_{3} | W_{4} | W_{5} | W_{6} | W_{7} | W_{8} |

I | 68.39 | 20.68 | 1.23 | 1.23 | 2.89 | 2.89 | −0.03 | 0.03 |

II | 69.26 | 12.31 | 3.60 | 3.61 | 4.05 | 4.06 | −0.08 | 0.13 |

III | 50.25 | 8.59 | 8.52 | 8.53 | 9.27 | 9.27 | −0.15 | 0.75 |

(b) BOVB | ||||||||

I | 60.22 | 25.81 | 2.40 | 2.40 | 3.81 | 3.81 | −0.03 | 0.16 |

II | 58.12 | 18.52 | 5.83 | 5.84 | 5.03 | 5.05 | −0.08 | 0.43 |

III | 37.22 | 14.24 | 12.74 | 12.76 | 9.50 | 9.52 | −0.20 | 1.84 |

^{a}The total numbers of VB structures in VB(all) calculations with VBSCF and BOVB are 175 and 27, respectively.

**Table 2.**Effective weights (in %) of σ and π characters, determined via the VBSCF method. Values in parentheses are from BOVB calculations.

Model | W(σ) | W(π) |
---|---|---|

I | 23.6 (29.7) | 5.3 (8.7) |

II | 16.4 (23.7) | 11.3 (16.9) |

III | 18.1 (24.4) | 26.7 (36.0) |

**Table 3.**RE values (in kcal/mol) for various states, obtained from (

**a**) VBSCF and (

**b**) BOVB calculations.

(a) | |||||||
---|---|---|---|---|---|---|---|

Model | σ | π_{x} | π_{y} | σπ_{x} | σπ_{y} | π_{x}π_{y} | σπ_{x}π_{y} |

I | 26.98 | 4.03 | 4.03 | 38.12 | 38.12 | 8.11 | 49.08 |

II | 17.49 | 7.84 | 7.86 | 33.63 | 33.65 | 15.79 | 49.07 |

III | 15.77 | 12.91 | 12.94 | 41.91 | 41.93 | 26.32 | 65.80 |

(b) | |||||||

I | 28.53 | 4.85 | 4.85 | 39.45 | 39.45 | 11.04 | 51.07 |

II | 18.91 | 9.36 | 9.38 | 34.43 | 34.46 | 21.18 | 51.48 |

III | 17.12 | 15.52 | 15.55 | 45.20 | 45.17 | 35.11 | 72.93 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, E.; Hirao, H.
Synergistic Charge Transfer Effect in Ferrous Heme–CO Bonding within Cytochrome P450. *Molecules* **2024**, *29*, 873.
https://doi.org/10.3390/molecules29040873

**AMA Style**

Zhang E, Hirao H.
Synergistic Charge Transfer Effect in Ferrous Heme–CO Bonding within Cytochrome P450. *Molecules*. 2024; 29(4):873.
https://doi.org/10.3390/molecules29040873

**Chicago/Turabian Style**

Zhang, Enhua, and Hajime Hirao.
2024. "Synergistic Charge Transfer Effect in Ferrous Heme–CO Bonding within Cytochrome P450" *Molecules* 29, no. 4: 873.
https://doi.org/10.3390/molecules29040873