## 1 Introduction  
Rapid industrial growth has increased the need for more efficient methods to address water and air pollution [1, 2, 3, 4]. Organic dyes, such as methylene blue and rhodamine B, pose significant health risks due to their toxic effects, including skin and respiratory irritation [5, 6]. Traditional methods, like adsorption and filtration, are effective, but they come with limited capacity and high energy requirements, diminishing their efficiency [7, 8]. Photocatalysis offers significant advantages, particularly in environmental applications. It effectively degrades organic pollutants, neutralizes harmful substances, and eliminates microorganisms, making it a key water and air purification method [9, 10, 11]. Among photocatalysts, titanium dioxide (TiO\({}_{2}\)) is the most widely used due to its stability and effectiveness [12, 13, 14]. However, its practical application is constrained by its ability to absorb light mainly in the UV range, which constitutes just 5% of sunlight [15; 16; 17]. To overcome this limitation, current research focuses on modifying TiO\({}_{2}\) or the creation of TiO\({}_{2}\)-based materials capable of absorbing visible light, thereby enhancing their efficiency and applicability [18; 19; 20]. Titanium-oxo complexes (TOCs) are an important research direction for modifying TiO\({}_{2}\)-based materials. These compounds are characterized by stable structures in which the {Ti\({}_{4}\)O\({}_{6}\)} core can be stabilized by various organic ligands, e.g., alkoxide and carboxylate [21; 22; 23; 24; 25; 26]. Coordination of appropriate ligands reduces the HOMO-LUMO gap, causing radiation absorption in a wider range. An example is the study by [PERSON] et al., who investigated TOCs with {Ti\({}_{10}\)O\({}_{12}\)} cores stabilized by benzoic acid derivatives. They exhibited that using 4-methoxybenzoate ligands significantly enhanced the photocatalytic efficiency of these complexes against rhodamine B [27]. This effect was attributed to a reduction in the gap from 3.34 eV to 2.47 eV. The proposed mechanism of photocatalytic activity was related to the ligand-to-metal charge transfer (LMCT), which facilitated the generation of reactive oxygen species (ROS) responsible for degrading the dyes into H\({}_{2}\)O and CO\({}_{2}\)[28; 29]. The structure of the {Ti\({}_{4}\)O\({}_{6}\)} core can also influence the photocatalytic activity of TOCs. Results of our work on oxo complexes with core structures {Ti\({}_{6}\)O\({}_{6}\)}, {Ti\({}_{4}\)O\({}_{2}\)}, {Ti\({}_{3}\)O}, and {Ti\({}_{6}\)O\({}_{4}\)}, stabilized by 9-fluoreencarboxylate ligands, confirm this effect. Systems containing {Ti\({}_{6}\)O\({}_{4}\)} and {Ti\({}_{6}\)O\({}_{6}\)} cores tended to shift the absorption maximum toward the UV range, whereas simpler units ({Ti\({}_{3}\)O} and {Ti\({}_{4}\)O\({}_{2}\)}) shifted it toward visible light [30]. Continuing this line of research, we replaced carboxylate ligands with \(\alpha\)-hydroxy carboxylate ligands (i.e., with 9-OH-9-fluoreencarboxylate [31] and mandelate ligands [32]). Our aim was to stabilize the structures of oxo complexes using new ligands, synthesize complexes with novel core structures, and evaluate the impact of these factors on their photocatalytic activity. While analyzing the possibilities of modifying TiO\({}_{2}\)-based materials, we became interested in a method to enhance their photocatalytic activity through doping with ruthenium complexes [33; 34; 35; 36; 37; 38]. In recent years, the electrocatalytic and photocatalytic activity of single Ru atoms was investigated [39]. However, ruthenium(II) tris(bipyridine) complexes are regarded as benchmark photocatalysts due to their strong light absorption and long excited-state lifetimes [40; 41; 42]. Relatively few reports address the photocatalytic activity of Ru(III) complexes, although they have gained attention in recent years [43; 44; 45]. This led us to investigate the effects of ruthenium(III) complexes on organic dye degradation and compare their performance with oxo-Ti(IV) complexes.