One of the ways to improve and accelerate osseointegration of a surgical implant with bone is application of biocompatible coatings, in particular, hydroxyapatite (HAp). Since the cases of delamination of the coating take place in dental practice, it is very important to estimate the adhesive strength of HAp with the implant. A measure of the coating-to-substrate bond strength is the energy of this bond. In this research, quantum chemistry is used to calculate the binding energy of functional groups (anions) of hydroxyapatite and titanium 2+, which is a standard implant material. First, using Density Functional Theory with Becke three-parameter Lee-Yang-Parr hybrid exchange-correlation functional, the lowest potential energy surface is calculated. Then, by ab initio molecular dynamics, the reaction path, the reaction products, frequencies of oscillations, the activation energies and binding energies between various combinations of component anions of HAp and Ti(II) are calculated.