## 3 Results and Discussion
### Spin Crossover  
Generally, molecules with different spin states have different structures. On the other hand, we could rearrange the electrons by varying structures to tune the spin state. For example, it has been shown that we can modulate the coordination field of metal ions by changing the molecular structure, such as stretch and rotation, and can achieve the SCO [17; 43; 44]. We can use a similar strategy to achieve spin transformation in this vein. In the current study, we investigate the SCO materials with \(d^{4}-d^{7}\) complexes, including PMnCp, PFeCp, and PCoCp, whose structures are shown in Figure 2. It is observed that the main differences between the structures lie in the folds of the porphyrin plane, the distance between the metal and the porphyrin center, and the bond length between the carbon atoms in the Cp ring and the metal. In particular, the changes of the first two are much smaller than those of the latter, so we suspect that the Cp ring may be the key to controlling the molecular spin states. When the Cp ring is rotated and stretched by some means, porphyrins and metal ions also move, which correspondingly modifies the coordination field of metal ions (as shown in Figure 3), leading to the SCO. In our calculation, PMnCp may have three spin states, among which the quintet is the molecular ground state and the triplet state is 0.15 eV higher than the ground state, which is very close to it. In contrast, the energy of the singlet is 1.16 eV higher than the ground state. It is difficult to realize the SCO if the energy difference is too large. Therefore, only the SCO from the quintet to the triplet is analyzed here. Sextet (Fe-HS, high-spin) is the ground state of PFeCp, which is 0.15 eV lower than the quartet (Fe-IS, intermediate-spin) and 0.43 eV lower than the doublet (Fe-LS, low-spin). The singlet (Co-LS) of PCoCp is the ground state, which is 0.24 eV lower than the triplet (Co-IS) and 0.54 eV lower than the quintet (Co-HS). With these energy differences, the SCO occurs easily, and it is possible to achieve the tri-stable switching. To describe the spin transition between these spin states, we calculate the total electronic energies of PMnCp, PFeCp, and PCoCp complexes as a function of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multirow{2}{*}{**Spin State**} & \multirow{2}{*}{
\begin{tabular}{c} **Relative** \\ **Energy (eV)** \\ \end{tabular} } & \multirow{2}{*}{\(\mathbf{M_{TM}}\) (\(\mu\)B)**} & \multirow{2}{*}{**Sandwich (Y/N)**} & \multirow{2}{*}{\(\mathbf{d_{TM-Cp}}\) (\(\mathbf{\AA}\))} & \multirow{2}{*}{\(\mathbf{d_{TM-P}}\) (\(\mathbf{\AA}\))} \\ \hline \multirow{2}{*}{Sc} & singlet & 0 & 0.00 & Y & 2.217 & 0.830 \\  & triplet & 1.81 & 0.01 & Y & 2.215 & 0.814 \\ \hline \multirow{2}{*}{Ti} & doublet & 0 & 1.01 & Y & 2.097 & 0.782 \\  & quartet & 1.85 & 1.03 & Y & 2.096 & 0.773 \\ \hline \multirow{2}{*}{V} & singlet & 0.82 & 0.00 & Y & 1.955 & 0.757 \\  & triplet & 0 & 2.05 & Y & 2.062 & 0.767 \\  & quintet & 1.82 & 2.07 & Y & 2.063 & 0.759 \\ \hline \multirow{2}{*}{Cr} & doublet & 0.86 & 1.00 & Y & 1.938 & 0.757 \\  & quartet & 0 & 3.22 & N & 2.972 & 0.291 \\  & sextet & 0.65 & 3.92 & N & 3.713 & 0.048 \\ \hline \multirow{2}{*}{Mn} & singlet & 1.16 & 0.00 & Y & 1.912 & 0.758 \\  & triplet & 0.15 & 2.25 & N & 2.960 & 0.270 \\  & quintet & 0 & 3.72 & N & 2.703 & 0.370 \\ \hline \multirow{2}{*}{Fe} & doublet & 0.43 & 2.07 & N & 3.383 & 0.078 \\  & quartet & 0.15 & 2.40 & N & 3.090 & 0.225 \\  & sextet & 0 & 4.07 & Y & 2.202 & 0.676 \\ \hline \multirow{2}{*}{Co} & singlet & 0 & 0.00 & N & 2.963 & 0.176 \\  & quartet & 0.24 & 1.09 & N & 3.383 & 0.066 \\ \cline{1-1}  & quintet & 0.54 & 2.75 & N & 3.690 & 0.065 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data of PTMCp (TM = Sc \(-\) Co). Spin state marked in blue is molecular ground state. Ground-state energy of molecule is zero as reference. \(\mathbf{M_{TM}}\): magnetic moment of TM ion, obtained by mulliken population. Sandwich (Y/N): whether structure is sandwich type (Yes or No).