PSI - Issue 23

Alla V. Balueva et al. / Procedia Structural Integrity 23 (2019) 173–178 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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(Figures 4-6) demonstrate the optimized geometry of the reactants and products. For all final geometric structures after the reaction, electron density distributions, and ground state energies were obtained, along with the equilibrium angles and lengths of the Ti – O bonds. The bond energies between individual constituents of HAp and Ti were calculated.

(a) (b) Fig. 4. Optimized geometry of the Ti (II) interaction with oxygen (a) in the Ti (OH) PO 4 complex. Binding energy is 2.03 a.u. (b) in the Ti (OH) 2 PO 4 complex. Binding energy is 2.09 a.u. (Ti – grey atom, O – red atom, P – orange atom) From Fig. 4a, we can see that [Ti (OH) PO 4 ] 2- has a quasi-chair structure. It has a mechanically stable structure. When compared to the standard vibrational behavior of phosphate, the increase in frequency between the titanium and oxygen interaction suggests a higher energy in the structure. Additionally, the bond lengths between titanium and oxygen have shortened, also suggesting a more favorable binding energy. The next complex, [Ti (OH) 2 PO 4 ] 3- , is a good demonstration of how susceptible Ti(II) is to gaining electron density throughout every variation of the polyatomic structures (Fig. 4b). Titanium consistently gains electron density more than the phosphorus atom and, in later complexes, more than Ca (Fig. 5-6). The phosphorus atom is gaining electron density from the oxygen atoms, but not as dramatically as the titanium atom. This is a consistent trend throughout the structures as they grow in complexity. The length of the bond connecting the hydroxide ions to titani um is approximately 1.73 Å. The binding energy is 2.09 a.u. (atomic units). 3- , and hydroxide, OH - , as the polyatomic complexes of the hydroxyapatite, to investigate their interaction/attraction and electron exchange during the reaction on the HAp – Ti surface. The next step, we added a positive Ca 2+ , for a more complete exploration of the interaction of Ti and HAp constituents on the surface. Now, the Phosphorus (orange atom in Fig. 6) and Ti (grey atom) ions, are complemented by another positively charged Ca atom (green atom). Earlier in this investigation, it was found that the [Ti PO 4 ] - complex demonstrated a very high electron density towards the Ti atom ’s orbital. Titanium’s charge was changed from 2+ to about 0.124+. The phosphorous atom (orange atom in Fig. 5a) received significantly less gain in electron density, deeming it much less influenced than titanium. However, with the addition of Ca 2+ (Fig. 5a, b), there is more orbital space available. Naturally, this will result in a more positive charge for the titanium, phosphorous, and calcium. We can still anticipate titanium being the most influenced. The ground state energy of Ti 2+ is approximately -844.42 a.u. and Ca 2+ + PO 4 3- has a ground state energy of about -1319.896 a.u., and Ti 2+ + Ca 2+ + PO 4 3 has a ground state energy of -2169.1466 a.u., so their binding energy is about 4.8306 a.u. In Fig. 5b, once again, we can see that Ti(II) electron density is considerably more influenced than the phosphorous or calcium electron density. Note however, despite the fact that there is additional orbital space with the arrival of yet another calcium atom, that the electron density of titanium and phosphorous has increased since the variant in Fig. 5a. This suggests that the calcium atom will become the most electronically independent throughout the various structures. Ti(II) has a ground state energy of approximately -844.42 a.u. and 2Ca 2+ + PO 4 3- has a ground state energy of -1997.396 a.u., while Ti 2+ + 2Ca 2+ +PO 4 3- has a ground state energy of 4.2406 a.u. 3.2. Binding energy of Tricalcium Phosphate Ca 3 (PO 4 ) 2 and Titanium In our calculations, we first modeled interactions of a Ti 2+ cation and the anions phosphate, PO 4