PSI - Issue 83

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

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implant like pure phosphate coatings? This issue should be given close attention, since peeling of coatings in the future for implants is observed quite often. We will investigate this question for silicon’s doping of TCP coating on titanium. The purpose of the investigation is to gain an understanding of the interactions between tricalcium phosphate coating, Ca 3 (PO 4 ) 2 , with titanium substrate and then between tricalcium silicon trioxide coating, Ca 3 (SiO 3 ) 2 , with titanium, to investigate whether the use of an additive makes improvements in the coating’s biocompatibility and adhesion strength (Dashevskiy et al., 2019).

2. Methods 2.1. Density Functional Theory

The object of the paper was to study the chemical reaction between the doped with silicon coating, Ca 3 (SiO 3 ) 2 and Ti substrate, and calculating their binding energy, and compare this with similar atomistic calculations for the pure phosphate coating, Ca 3 (PO 4 ) 2 , and Ti in our previous paper (Balueva et al., 2024):

Ti 2+ + Ca

3 (PO 4 ) 2

= Ti Ca 3 (PO 4 ) 2

(1.1)

Ti 2+ + Ca 3 (SiO 3 ) 2 = Ti Ca 3 (SiO 3 ) 2 This was determined by atomistic calculations ran using Gaussian09W and Gauss View. The optimization of the final products after chemical reaction between Ca 3 (SiO 3 ) 2 and Ti and calculation of their binding energy are obtained by Gaussian09W with the use of Density Functional Theory (DFT) as DFT has been used in previous research to study hydrogen bonds in biomolecules (e.g., Thanthiriwatte et al., 2010; Zangwill, 2014). Density Functional Theory was first introduced to the world in 1964 in Khon’s paper “Inhomogeneous Electron Gas” that he worked with Pierre C. Hohenberg (Hohenberg & Kohn, 1964). Density Functional Theory is an improved method of the Hartree Fock theory that finds the ground states of a many-electron systems by using the electronic density, where the electronic density is important because it can provide valuable information about the geometric and chemical properties of the system (Sherrill, 2020). The base of Density Functional Theory begins with Schrödinger’s equation as Schrödinger’s equation is used to describe the behavior of electrons by applying a Hamiltonian operator (1.1) to the wave function of a system - when the Hamiltonian operator, Ĥ , acts on the wave function, Ψ , of the system, it is proportional to the total energy, E, of the wave function of the system: ĤΨሺ ଵ , ଶ ,…, ே ሻൌȠΨሺ ଵ , ଶ ,…, ே ሻ (1.2) where the total energy of the system would have to consider the potential and kinetic energies of the nuclei and electrons in the system: Ĥൌܶ ൅ܸ (1.3) or Ĥൌܶ ௘௟௘௖ ሺ ሻ൅ܶ ௡௨௖ ሺ ሻ൅ܸ ௡௨௖ି ௘௟௘௖ ሺ , ሻ ൅ܸ ௡௨௖ି ௡௨௖ ሺ ሻ൅ܸ ௘௟௘௖ି ௘௟௘௖ ሺ ሻ (1.4) Then, the Density Functional Theory uses the Born – Oppenheimer approximation, that states that due to the fact, that electrons move much faster than nuclei, the nuclei can be considered as unmovable and their kinetic energy is 0, and then the potential energy of the nuclei is considered a fixed amount and can be treated as a constant. With the potential