PSI - Issue 83

Alla V. Balueva et al. / Procedia Structural Integrity 83 (2026) 196–207

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energy is calculated by taking the different of the energy of the complete compound (or product) and the sum of the energies of the individual reactants [Balueva et al., 2025]: ݁ ݎ ݕ ൌ ௥௘௔௖௧௔௡௧௦ െ ௣௥௢ௗ௨௖௧ To calculate the binding energy of the compounds, TiCa 3 (PO 4 ) 2 and TiCa 3 (SiO 3 ) 2 , the ground state energy of each reactant of the compound needed to be calculated, thus the compound was built step by step as shown in Fig. 3 - 5. In order to calculate the binding energy of the final compounds, TiCa 3 (PO 4 ) 2 and TiCa 3 (SiO 3 ) 2 compounds, we started by calculating the optimization of phosphate [PO 4 ] 3- and silicon trioxide [SiO 3 ] 2- as the ground state energies of these compounds would be used to calculate the binding energy of larger, more complex molecular structures, such as TiCa 3 (PO 4 ) 2 and TiCa 3 (SiO 3 ) 2 . Optimization calculations were obtained using Gaussian09 optimization calculations, calculation setting was Ground state, DFT, default spin, B3LYP, for the methods and the basis set: 6 31G + (d, p). 3.2. Density Functional Theory Optimization of Phosphate PO 4 and silicon trioxide SiO 3

Stable interaction configuration of the Si 2- interaction with oxygen in the complex [SiO 3 ] 2- (Si – dark grey atom, O - red atoms) (b)

Stable interaction configuration of the P 3- interaction with oxygen in the complex [PO 4 ] 3- (P - orange atom, O - red atoms) (a)

Fig. 3. A comparison of stable configuration of products after the reaction of phosphate (a) and the reaction of silicon trioxide (b).

The ground state energy for [PO 4 ]

3- and [SiO

3 ] 2- were calculated to be -642.119 a.u and -515.06 a.u,

respectively.

3.3. Reactions of Ti 2+ with [PO 4 ] 3 - and Ti 2+ with [SiO 4 ] 2 In Fig. 4, the structures modeled a chemical reaction between pure titanium Ti and phosphate [PO 4 ]

3- (Figure 4a)

and silicon trioxide [SiO 4 ]

2- (Figure 4b). The products of the structures for both [TiPO 4 ]

- and [TiSiO

4 ]

- were optimized

using Gaussian09. The ground state energy of [TiPO 4 ]

- (Figure 4a) was calculated to be -1491.79 a.u. and the charge