We present an atomistic approach, based on the x-ray diffraction structure, to model cooperative spin-transition phenomena in the [Fe(pyrazine)] [Ni(CN)4] spin-crossover compound. The vibronic coupling is described through a double-well potential along the totally symmetric Fe-ligand stretching mode, whereas the elastic interactions between the Fe centers are considered by an additional spin-state-dependent two-body potential. The model is then investigated through molecular dynamics simulations in the isothermal-isobaric ensemble. This approach provides a real-time spatiotemporal description of the spin transition, from the atomic movements to the nanoscale behavior, removing in this way some ad hoc assumptions used in state-of-the-art atomistic models, while keeping the computational cost affordable. This work is separated into two papers. In the present Part I, we report on the methodology used to describe the electron-lattice interaction to simulate the spin transition in the bulk material within a realistic molecular structure. Part II [S. Mi et al., Phys. Rev. B 109, 054104 (2024)] will address the spatiotemporal dynamics (nucleation and growth) of the spin transition in a bilayer actuator, correlating the buildup of elastic stresses and the resulting deformation of the nanoscale object using the atomistic approach developed here.