  Density functional theory (DFT) including van der Waals weak interaction in
conjunction with the so called rotational invariant DFT+U, where $U$ is the
Hubbard interaction of the iron site, is used to show that the fluorinated spin
crossover Fe(phen$)_{2}$(NCS$)_{2}$ molecule whether in the gas phase or
adsorbed on Cu(001) surface switches from the original low spin state to the
high spin state. Using Bader electron density analysis, this inversion of the
spin-crossover is explained in terms of electron doping of the Fe-octahedron
cage which led to an increase of the Fe-N bond lengths. Consequently, the
ligand-field splitting is drastically reduced, making the high-spin ground
state more stable than the low-spin state. The calculated scanning tunneling
microscopy (STM) images in the Tersoff-Hamann approximation show a clear
distinction between the fluorinated and the unfluorinated molecule. This
theoretical prediction is awaiting future STM experimental confirmation.
