PSI - Issue 42

Alla V. Balueva et al. / Procedia Structural Integrity 42 (2022) 9–17 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

12

4

⃐⃑ ̂ ( ⃑, ⃑ ) = ( ⃑ ) ⃐⃑

(2.3)

and taking into account the normalization of wave functions, this expression can be rewritten as ⃐⃑ ̂ ( ⃑, ⃑ ) = ( ⃑ ) ⃐⃑ and taking into account the normalization of wave functions, this expression can be rewritten as ⃐ ⃑⃑ ̂ ( ⃑, ⃑ ) = (2.5) which means the minimization of quadratic functional with respect to ⃐⃑ will give us the true energy minimum, . In this paper Density Functional Theory is used to determine the ground state energies of polyatomic complexes in the TiO 2 – tricalcium phosphate system. The goal is the theoretical calculation of the binding energy of the tricalciun phosphate coating and TiO 2 after their reaction, that was calculated by subtracting the sum of ground state energies of the constituent molecules before the reaction from the ground state energy of the cohesive, whole, combined molecule after the reaction occurred: W bon = / TP Ti TP Ti E E E   (2.1) 3. Results: Binding energy and Stable Configurations of different Tricalcium Phosphate Constituents with Titanium 3.1 Method Figures 2 – 11 represents molecules of the products and the reactants optimized in Gaussian09. We calculated the ground-state energy, the charge of the titanium as it varies with increasingly complex molecule configurations, about the TiO 2 bond length, the TiO 2 bond angle, and the binding energy. Then we set up the constituents of tricalcium phosphate, Ca 3 (PO 4 ) 2, which are phosphate (PO 4 ) and calcium Ca , in stable position of a global minimum on the potential energy surface, and calculated their initial ground state energies. Using Gaussian09, we were modeling chemical reactions of TiO 2 with the constituents (PO 4 ) and Ca, and finally with tricalcium phosphate Ca 3 (PO 4 ) 2 itself, to calculate ground state energies of the products and reactants, based on that binding energies were calculated as final products. We used the B3LYP and 6-31G basis set to perform calculations. Phosphate (PO 4 ) , Calcium (Ca) , Titanium dioxide (TiO 2 ) The calculation converged as all the frequencies of oscillations were real. Phosphate PO 4 (see its optimized structure on Figures 2) has a ground-state energy of -641.9 a.u. After optimization calcium has a ground-state energy of -677.5 a.u. (2.4)