Tuning the Spin-Crossover Properties of the [(Cp 1-R ) 2 Mn] Metallocenes

In this work, we present a computational study using density functional theory (DFT) on how the single functionalization of the cyclopentadienyl ligand in [(Cp 1-R ) 2 Mn] systems can be used to tune the spin-crossover properties in such systems. Using the OLYP functional, accurate values for the transition temperature ( T 1/2 ) can be obtained, and our DFT methodology can be used to explore the effect that different substituents have on tuning such quantity. In particular, we show that the electronic structure of the [(Cp 1-R ) 2 Mn] can be tuned via the R group, allowing for a fine-tuning degree of the T 1/2 that expands between 0 and 400 K. Our results allow for a rational design of new manganocene based systems with tailored SCO properties.


Introduction
Spin-crossover (SCO) systems are molecules or materials that can switch between two alternative spin-states, thus exhibiting switching behaviour. [1][2][3][4] The transition from the low-to the high-spin state can be triggered using an external stimulus, commonly temperature, and with the spin-state change there are profound changes in the physical properties of the system. This duality is very appealing from the technological point of view, because one can envision harvesting such materials for molecular level devices or spintronic applications. [5][6][7][8] The SCO phenomenon, firstly reported nearly a century ago, 9 has grown at the interface between physics and chemistry, and the number of compounds exhibiting SCO behaviour has vastly increased over the last years.
Despite the large development of the field, the vast majority of systems exhibiting SCO behaviour contain an Fe II (d 6 ) metal center, [10][11][12][13][14] and there is an increasing interest on expanding the set of compounds with other metals and oxidation states exhibiting this behaviour. 15 Similarly, while coordination chemistry has proven to be key in the design of ligands that generate the right splitting among the d-based molecular orbitals for the molecule to exhibit SCO, organometallic molecules usually have a larger ligand-field splitting that leads to low-spin states, and very few examples have been reported. 16,17 Among the few organometallic SCO systems reported, the manganocene family ([Mn(Cp R ) 2 ]) has provided several examples of functionalized molecules exhibiting such behaviour. [17][18][19][20] More relevant is the fact that the transition temperature (T 1/2 ), defined as the temperature with equal populations of both spin-states and a key physical property in SCO systems, can be modulated in such families via the R group.
The interplay between steric and electronic effects in tuning T 1/2 for the alkyl substituted manganocenes of general formula [Mn(Cp n-R ) 2 ] (n = 1 to 5 and R = Me, i Pr or the ligand field around the Mn II ion can be increased by adding more electron-donor groups, such as methyl, but that bulky substituents, such as iso-propyl or tert-butyl, can have the opposite effect due to the steric hindrance that they introduce in the molecule, which pushes the Cp rings away from the metal center. However, the effect of the functionalization of the cyclopentadienyl ligand with other groups than methyl in order to control the SCO properties of the [Mn(Cp 1-R ) 2 ] family has not been explored.
In this work, we used electronic structure calculations at the density functional theory (DFT) level to evaluate the effect that different R groups have over the transition temperature (T 1/2 ). By changing the R group we will show that a fine degree of tuning over T 1/2 can be achieved, allowing for the modulation of such value in a wide range of temperatures. The presented results open the door to in silico design of new metallocenes with selected SCO properties, thus providing experimental chemists a powerful tool for the rational design of new molecules with specific transition temperatures. cessing scripts were used (see Supporting Information). The n-electron valence perturbation theory (NEVPT2) 25 calculations were performed with the Orca 4.0 code. 26 In these calculations, we employed the def2TZVPP basis set, including the corresponding auxiliary basis set for the correlation and Coulomb fitting. The active space contains the 5 d-orbitals of the metal and 4 electrons, and the ab initio ligand-field theory (AILFT) approach was employed to extract the related orbitals. 27

Results
Previous work on the computational modeling of T 1/2 in [Mn(Cp R ) 2 ] (R = Me, i Pr or t Bu) showed that DFT methods (OPBE in particular) were able to correctly model the SCO behaviour in such systems. 21 However, we decide to pursue a systematic benchmark of different DFT methods aiming to be as quantitative as possible towards the calculation of the transition temperature. With that goal, we choose as a benchmark model the [Mn(Cp 1-Me ) 2 ] system for its simplicity, which allows the testing of multiple functionals and basis set schemes, and also because there is structural information in gas phase (d(Mn-C) = 2.433 Å and 2.144 Å for high-and low-spin respectively), 28 as well as a proper characterization of its T 1/2 (303 K), 17 data that will allow us to properly calibrate the computational method of choice.
Several DFT methods were tested for the [Mn(Cp 1-Me ) 2 ] system, including TPSSh, 29,30 OPBE, 31,32 OLYP, 31,33 M06L, 34 B3LYP, 35 B3LYP* 36 and SCAN. 37 A full optimization in both high-and low-spin state using BS3 was done, followed by the corresponding vibrational analysis to ensure its minimum nature. The corresponding spin-state energy differences as well as relevant geometric parameters and the calculated T 1/2 (where meaningful) are given in table 1.   Table 3. In Figure 1, we plotted the computed T 1/2 against the  p Hammett parameter 40 for all the [Mn(Cp 1-R ) 2 ] systems in Table 3. As can be seen in the figure, a trend with the electron donating (or electron withdrawing) character of the R group can be observed.
In general, a decrease in the T 1/2 is observed with increasingly withdrawing character of the R group. Although this trend in the computed T 1/2 spans on a 500 K range, the geometries of the computed systems remains almost identical, as can be observed using the average Mn-Cp centroid-distance. For all systems in Table 3 Results for such calculations are summarized in Table 4. . For Mn II , there is a large change in the total spin between high-spin and low-spin states (S HS = 5/2, S LS = 1/2), but for Cr II , the situation is much softer. Actually, the computed S elec for Mn II and Cr II are, respectively, 5.96 and 3.31 cal K −1 mol −1 . Because T 1/2 = H/S, for the chromium systems, the reduction of the spin-state energy gap is largely compensated by the decrease in the entropy change due to the Cr II electron configuration. Nevertheless, if we can reduce the H even more for a [Cr(Cp 1-R ) 2 ] system, it should, potentially, exhibit SCO behaviour.
Following this idea, we introduced a second NO 2 substituent, and computed the spinstate energy gap for the [Cr(Cp 1,3-NO 2 ) 2 ] molecule. For that molecule, H=3.62 kcal mol −1 and S = 10.0 cal K −1 mol −1 , thus making its T 1/2 = 362 K, a value that makes it a potential candidate for exhibiting SCO behaviour.

Discussion
Our working hypothesis is that, in principle, one can tune the ligand field around the metal center by making the ring more negatively charged, as is experimentally ob- We can thus see that the use of the Hammett parameters to describe the electron-donating character of the substituents and its effect on tuning T 1/2 holds to a great extent, but some points are clearly out of the trend. To understand the origin of such deviations, we collected more data on the low-spin state systems. In particular, NEVPT2 calculations analyzed using the ab initio ligand field theory (AILFT) framework were used to get the energies of the five d-based molecular orbitals, and a Hirshfeld charge analysis was done to calculate the total charge of the Cp 1-R rings for each R. Numerical data can be found in the SI. Let's first analyze the Cp 1-R ring charge. A correlation can be found between the  p Hammett parameter and the total charge of the ring (R 2 = 0.74, see SI). However, a close inspection of the numerical data shows that SiMe 3 produces an unusually positive charge on the ligand, falling off the expected trend. In fact, removing that point greatly increases the correlation between charge and  p (R 2 = 0.85). This result shows that the Hammett parameter is mostly reflecting the total charge of the ring and its effect on the splitting of the d-based molecular orbitals, but may be missing other orbital effects that can be at play. In fact, the numerical data for the outliers shows that they tend to have smaller ligand-field splitting energy gaps than expected. To further analyze the orbital effect, we compared the frontier molecular orbitals of a pure donor ligand (R=CH 3 ) with the ones from R = SO 2 Cl, CCPh, (CH)NOH, B(OH) 2 and PCl 2 . The possibility of extending the -system of the ligand over the R group reduces the antibonding character of the d xy (or d yx ) orbitals, thus lowering its energy and producing HOMO-LUMO gaps smaller than expected.

Conclusions
In this work, we presented a robust computational methodology to study the spin-