A common feature of spin-crossover molecules deposited on a substrate is the presence of a residual proportion of high-spin (HS) molecules at low temperature, instead of the pure low-spin (LS) phase observed in the bulk. In this work, we analyse by means of periodic rPBE calculations, the deposition of a monolayer of an Fe(II) spin-crossover [Fe((3,5-(CH₃)₂Pz)₃BH)₂] complex on a Au(111) substrate, with different proportions of HS/LS molecules. Our results indicate that there exist both thermodynamic and kinetic factors favoring the presence of a mixed HS/LS state at low temperature. The pure LS phase and a mixed spin state with 1/3 of HS molecules are close in energy, and the transition from this mixed spin state to the pure LS is hindered by the highest activation barrier in the transition from the HS to LS phase. The presence of the surrounding molecules of the 2D superstructure facilitates the transition from the LS to HS state and the interaction between the molecular layer and the surface increases with the proportion of HS molecules, in line with the epitaxial growth of the monolayer and its similarities with the (01) plane of the HS bulk molecular crystal. The density of states resulting from the rPBE calculations is used to simulate STM images. An excellent agreement is found between the simulated STM images for the mixed state with 1/3 of HS molecules and the images acquired at a constant height for a submonolayer of this Fe(II) complex on Au(111).