**1. Introduction**

Fagopyrins are a group of compounds of natural origin found in plants of the genus Fagopyrum. Parts of these plants are commonly consumed by humans and animals throughout the world [1]. There are many species of Fagopyrum; however, the most consumed and studied are *Fagopyrum esculentum*, *F. tataricum*, and *F. cymosum* [2,3]. Parts of these plants provide a low-calorie, gluten-free food and a source of many elements and organic compounds of biological interest, such as rutin, quercetin, and fagopyrins [4–8].

Fagopyrins are anthraquinone derivatives characterized by a polycyclic system, which is interesting from the chemical point of view. The structure and intramolecular interactions of polycyclic compounds affect the physical and chemical properties and can influence potential applications of the compounds in pharmacy and medicine [9–12]. As shown in earlier work on hypericin [13] and sennidines [14], a highly substituted polycyclic system can exhibit a non-planar structure due to a variety of intramolecular interactions. At the time of writing this paper, data unambiguously define the spatial and electronic structures of fagopyrins. An explanation of this may be found in difficult and multi-stage processes needed to obtain the pure substance from plant material [15]. Additionally, the existence of unstable protofagopyrins [16,17] and the possibility of the existence of many derivatives [17,18] can be a problem.

**Citation:** Szyma ´nski, S.; Majerz, I. Theoretical Studies on the Structure and Intramolecular Interactions of Fagopyrins—Natural Photosensitizers of *Fagopyrum*. *Molecules* **2022**, *27*, 3689. https:// doi.org/10.3390/molecules27123689

Academic Editor: Miroslaw Jablonski

Received: 25 April 2022 Accepted: 4 June 2022 Published: 8 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The interest in fagopyrins is mainly due to their spectroscopic properties. They exhibit absorption of electromagnetic radiation in the wavelength range of the light around λmax 550 and 590 nm [15,19,20]. Upon excitation, they are able to transfer energy to the oxygen molecule, thereby producing reactive oxygen species (ROS) [21]. Singlet oxygen and other ROS are responsible for cell damage. Easy light activation of fagopyrin molecules shows the potential to be used in photodynamic therapy [20]. On the other hand, high consumption of the *Fagopyrum* plants can lead to the light sensitivity in animals, called fagopyrism [22]. Additionally, there are reports of the possible hepatotoxic effect of consumption of food rich in *Fagopyrum* plants on dogs [23]. Leaving aside the potential dangers of the photosensitizing properties of fagopyrins, their potential for pharmacological use appears to be high. Easy excitation with energy from the visible range, confirmed antifungal [24] and antimicrobial [25] properties, and natural origin are promising for use in targeted photodynamic therapy.

Although general studies on the structure of fagopyrins were undertaken [17], no crystal structures are available, given the current state of knowledge. Additionally, such a strongly substituted double anthrone moiety has many possibilities for intramolecular interactions. The introduction of piperidine and pyrrolidine substituents in the hypericin molecule that, in fact, forms fagopyrin allows for the appearance of new intramolecular interactions.

Considering the intramolecular interactions occurring in fagopyrins, the OHO hydrogen bond system formed by hydroxyl groups bound to carbonyl oxygen is the most characteristic. As the strength of the hydrogen bond is determined primarily by the electronegativity of the atoms with which the proton is bound [26], the hydrogen bond of the OHO type is the strongest. The strength of the hydrogen bond is expressed in changes in geometry, consisting in shortening the distance between the donor and the acceptor of the proton and the location of the proton close to the center of the distance between the donor and the acceptor [27]. The OHO hydrogen bond system in fagopyrin is additionally strengthened by the participation of the hydrogen bonds in closed bond cycles in which double and aromatic bonds are present [28]. However, in the case of fagopyrins containing the piperidine and pyrrolidine substituents with the nitrogen atom and the possibility of conformational changes of the molecules, the presence of weaker hydrogen bonds of OHN type should be taken into account.

Therefore, it seems necessary to investigate the possible intramolecular interactions and structure of fagopyrins and compare them with the present state of knowledge using the example of hypericin.

The purpose of this paper is to use in silico methods to determine the molecular structure and interactions of still unknown fagopyrin molecules. Conformational analysis is carried out to determine the probable spatial and electronic structure of fagopyrins and, importantly, the intramolecular interactions of substituents that determine the pharmacological properties of these natural compounds. The results calculated for the gas phase will provide valuable knowledge about these interesting derivatives and will contribute to the future exploration of the pharmacological properties of fagopyrins. The conformational analysis will determine the minimum energy structure and possible formation of the double-anthrone system in plant material.

### **2. Materials and Methods**

Determination of the spatial structure and conformational analysis of fagopyrin molecules were carried out using the Gaussian16 package [29]. Calculations were carried out using DFT/B3LYP/6-311++G(d,p) model with Grimme dispersion [30]. The optimized structures correspond to a minimum on local potential energy surfaces. QTAIM analysis was performed using the AIMALL program [31]. NCI analyses [32] were performed using the Multiwfn program [33]. NCI graphics were printed using the VMD program [34]. UV-VIS spectra and orbital analysis were performed with the ADF program [35].
