Electronic and Steric Control of the Spin-Crossover ... - ACS Publications

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Electronic and Steric Control of the Spin-Crossover Behavior in [(CpR)2Mn] Manganocenes Jordi Cirera* and Eliseo Ruiz Departament de Química Inorgànica i Orgànica and Institut de Química Teòrica i Computacional, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain S Supporting Information *

ABSTRACT: A computational study of the spin-crossover behavior in the family [(CpR)2Mn] (R = Me, iPr, tBu) is presented. Using the OPBE functional, the different electronic and steric effects over the metal’s ligand field are studied, and trends in the spin-crossover-temperature (T1/2) behavior are presented in terms of the cyclopentadienyl (Cp) ligand functionalization. Our calculations outlined a delicate balance between both electronic and steric effects. While an increase in the number of electrondonating groups increases the spin-crossover temperature (T1/2) to the point that the transition is suppressed and only the low-spin state is observed, steric effects play an opposite role, increasing the distance between the Cp rings, which in turns shifts T1/2 to lower values, eventually stabilizing the high-spin state. Both effects can be rationalized by exploring the electronic structure of such systems in terms of the relevant d-based molecular orbitals.

1. INTRODUCTION Metallocenes are some of the most iconic molecules in organometallic chemistry. Since the discovery of ferrocene by Pauson and Miller,1,2 this type of sandwich compounds has been extensively studied3−5 and prepared with several first-row transition-metal ions such as vanadium,6 chromium,7 manganese,8 cobalt, and nickel.9,10 Although metallocenes are widely used in organic synthesis and catalytic cycles, with some derivatives showing activity in industrially relevant applications such as olefin polymerization,3 slightly less emphasis has been devoted to the study of electronically governed properties in such systems. Among them, spin crossover, a phenomenon in which the spin state of the metal center changes due to the action of an external stimuli,11 is of particular relevance due to the potential use of such systems as molecular level switches. Among the different metallocenes from the first row, d5 manganocene derivatives of general formula [(CpR)2Mn] have been widely studied.8 While some of these molecules are high-spin systems, such as the [(Cp 1,3,4‑tBu ) 2 Mn] molecule,12 with a magnetic moment of 5.9 μB, others have been reported to be low-spin systems, such as the [(Cp*)2Mn] molecule, with a temperature-independent magnetic moment of 2.18 μB.13 The possibility of accessing two alternative spin states points, therefore, to the potential design of manganocene molecules exhibiting spin crossover, and in fact this has been reported in the literature through the years.8,12,14 However, as also occurs for many other families of spin-crossover systems, the link between the chemical functionalization of the ligand and the physical properties of the system is buried under several competing effects. In fact, as was already introduced by Andersen and co-workers,12 two competing effects are in play for the [(CpR)2Mn] (R = Me, iPr, tBu) family. On one hand, © XXXX American Chemical Society

electron donor groups (i.e, methyl, isopropyl, tert-butyl, etc.) stabilize the low-spin state. However, too much steric congestion seems to have an opposite effect, stabilizing the high-spin state. To which extent each effect is at play remains not clear, and therefore, the rational design of manganocenes with selected spin-crossover properties is still elusive. In this paper, we present a computational approach to study spin-crossover in manganocenes of general formula [(CpR)2Mn] (R = Me, iPr, tBu). The computational methodology allows us to correctly model the spin-crossover behavior in such systems, as well as calculate with accuracy the corresponding spin-crossover temperatures when available. Moreover, by inspecting the underlying electronic structure of different members of this family, it is possible to determine the effect that ligand functionalization has on the spin-crossover temperature, and therefore on the spin-crossover behavior in such systems, much in the way that has been done for other families of spin-crossover molecules.15−17 This paper is organized as follows: first, we will present the computational methodology and the results for several members of the [(CpR)2Mn] family. Then a discussion of the data will be presented, and finally, the conclusions will be outlined.

2. METHODOLOGY All density functional theory (DFT) calculations were carried out with the Gaussian 09 (revision D.01)18 electronic structure package with a 10−8 convergence criterion for the density matrix elements, using the hybrid GGA functional OPBE.19−22 This functional has been previously used to model spin-crossover processes in other Received: October 9, 2017

A

DOI: 10.1021/acs.inorgchem.7b02592 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. DFT Calculated Geometrical Parameters for the Studied Systems [(CpR)2Mn] (R = Me, iPr and tBu)a system

S

d(Mn−Cp1)

d(Mn−Cp2)

d(Mn−Cp)

α

τ

[(Cp1‑Me)2Mn] [(Cp1‑Me)2Mn] [(Cp1,3‑Me)2Mn] [(Cp1,3‑Me)2Mn] [(Cp1,3,4‑Me)2Mn] [(Cp1,3,4‑Me)2Mn] [(Cp1,2,3,4‑Me)2Mn] [(Cp1,2,3,4‑Me)2Mn] [(Cp1‑iPr)2Mn] [(Cp1‑iPr)2Mn] [(Cp1,3‑iPr)2Mn] [(Cp1,3‑iPr)2Mn] [(Cp1,3,4‑iPr)2Mn] [(Cp1,3,4‑iPr)2Mn] [(Cp1,2,3,4‑iPr)2Mn] [(Cp1,3,4‑iPr)2Mn] [(Cp1‑tBu)2Mn] [(Cp1‑tBu)2Mn] [(Cp1,3‑tBu)2Mn] [(Cp1,3‑tBu)2Mn] [(Cp1,3,4‑tBu)2Mn] [(Cp1,3,4‑tBu)2Mn]

1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2 1/2 5/2

1.692 2.051 1.695 2.051 1.702 2.051 1.707 2.048 1.695 2.053 1.716 2.064 1.751 2.111 1.790 2.141 1.703 2.061 1.728 2.071 1.774 2.123

1.693 2.050 1.698 2.043 1.702 2.050 1.707 2.049 1.694 2.056 1.719 2.059 1.747 2.143 1.784 2.138 1.703 2.061 1.732 2.071 1.774 2.128

1.693 2.051 1.697 2.047 1.702 2.051 1.707 2.049 1.695 2.055 1.718 2.062 1.749 2.127 1.787 2.140 1.703 2.061 1.730 2.071 1.774 2.126

178.98 162.91 178.92 163.24 179.19 163.48 177.63 177.63 177.78 163.95 175.23 159.59 177.15 170.31 175.59 172.05 180.00 180.00 174.72 161.77 177.01 172.95

9.16 28.72 2.62 45.78 2.73 31.55 0.42 31.55 4.88 8.68 10.44 5.86 11.88 48.06 75.86 50.41 35.98 36.11 12.99 16.92 8.78 6.17

a The average distance is indicated as d(Mn−Cp). All distances are given in Å. α is the angle for one Cp centroid, the manganese, and the other Cp centroid, and τ indicates the torsion angle between the Cp rings; both parameters are given in deg.

transition-metal compounds,23−30 and although we have been very successful in modeling SCO processes using the meta-hybrid TPSSh31,32 functional,15−17 for the particular case of [(CpR)2Mn] systems OPBE provides the correct ground state, while the TPSSh functional overstabilizes the high-spin state (see Table S3 in the Supporting Information). The fully optimized contracted triple-ζ allelectron Gaussian basis set developed by Ahlrichs and co-workers with polarization functions was employed for all of the elements.33 The studied systems have been fully optimized in both spin states (see section S1 in the Supporting Information for optimized structures), and a subsequent vibrational analysis was performed. These results can later be used, when possible, to compute thermochemical quantities from which one can extract the corresponding spincrossover temperature (T1/2), defined as the temperature in which equal populations of each spin state are observed.15 The spincrossover process can be described as a thermodynamic equilibrium, with the corresponding associated change in the free energy (ΔGSCO). Assuming an ideal system, in which the spin-crossover system is isolated, and due to the fact that the pressure-dependent term to the free enthalpy change is usually small, we can write the corresponding free energy changes for each process (ΔG) for the equilibrium expression of eq 1 as34,35

(3) Equation 3 can be recast so that the molar fraction of the high-spin state depends on the change in the free energy at each temperature as (4) where R is the gas constant and T the temperature. Thus, the temperature that provides a molar fraction γHS = 0.5 will correspond to the spin-crossover temperature (T1/2). Given that equal populations of both spin states will mean that ΔGSCO = 0, by fitting the ΔGSCO vs T data, one can extract the corresponding spincrossover temperatures (T1/2) for each calculated system. All the fitting parameters together with the corresponding correlation coefficient can be found in Table S4 in the Supporting Information. All time-dependent density functional theory (TD-DFT)36 calculations were performed on the low-spin optimized molecules. It is well-known that, although DFT methods provide relatively accurate energy gaps, more reliable energies for this quantity can be obtained using TD-DFT, which accounts for electron relaxation.37

3. RESULTS In this work, we have analyzed three different families of manganocenes, in which the cyclopentadienyl ring was being functionalized with the methyl (Me), isopropyl (iPr) and tertbutyl (tBu) groups. For each one of these compounds, we have fully optimized both the low- and high-spin states in order to study their potential spin-crossover behavior. In Table 1, the most relevant geometric parameters for each of the studied compounds can be found (see Scheme 1). As can be seen from these data, the functionalization of the Cp− with methyl groups has almost no effect in the cyclopentadienyl to manganese bond lengths in the low-spin state, with ring centroid to metal distances ranging from 1.693 to 1.702 Å (an overall increase in the bond lengths of only 0.53%). On the other hand, the functionalization of the ligands with isopropyl or tert-butyl has

(1) where (2) is the Gibbs free energy associated with spin state i at a given temperature. In eq 2, the enthalpy term (Hi) includes both electronic (Eiel) and vibrational (Eivib) contributions. For molecular complexes, Eivib can be properly estimated by using the harmonic approximation, while the term Eiel, describing the electronic energy of spin state i, can be obtained directly from ab initio calculations (in our case, using DFT with the OPBE functional). The entropy contribution to the free energy (Si) can also be properly estimated using the harmonic approximation. Since ΔGSCO can be related to the equilibrium constant, we can rewrite eq 1 in terms of the relative populations of both high-spin (γHS) and low-spin (γLS) states, as can be seen in eq 3: B

DOI: 10.1021/acs.inorgchem.7b02592 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Scheme 1. Definition of the Geometrical Parameters (α and τ) for the Studied Systems [(CpR)2Mn] (R = Me, iPr and t Bu), As Indicated in Table 1a

Table 2. Energy Differences between the High- and LowSpin States (in kcal/mol, Positive Value Indicates Low-Spin Ground State) for the Studied Systems [(CpR)2Mn] (R = Me, iPr and tBu), with the Corresponding Spin-Crossover Temperatures (T1/2, in K) and Energy Gaps between Nonbonding and Antibonding Orbitals (in cm−1)a system [(Cp)2Mn] [(Cp1‑Me)2Mn] [(Cp1,3‑Me)2Mn] [(Cp1,3,4‑Me)2Mn] [(Cp1,2,3,4‑Me)2Mn] [(Cp1‑iPr)2Mn] [(Cp1,3‑iPr)2Mn] [(Cp1,3,4‑iPr)2Mn] [(Cp1,2,3,4‑iPr)2Mn] [(Cp1‑tBu)2Mn] [(Cp1,3‑tBu)2Mn] [(Cp1,3,4‑tBu)2Mn]

α is the angle for one Cp centroid, the manganese, and the other Cp centroid. τ indicates the torsion angle between the Cp rings.

a

a much larger effect on the metal−ligand bond lengths. Adding isopropyl groups increases the Cp−Mn bond length from 1.695 to 1.749 Å (an increase of 3.2%) and tert-butyl enlarges the metal−ligand bond length from 1.703 to 1.774 Å (an increase of 4.2%). Moreover, when these bond lengths are compared with those of [(Cp)2Mn] in the low-spin state, the methyl-functionalized systems remain quite close to the naked manganocene geometry, while the isopropyl and tert-butyl systems suffer progressive increases in their metal−ligand bond lengths. The computed values are in in good agreement with the available experimental information (see Table S2 in the Supporting Information), with an average deviation for the Cp−Mn bond length of 1.6%. From the above data, it is clear that the functionalization of the cyclopentadienyl ring with methyl groups does not play a significant steric effect; rather, any change in the electronic properties of the studied systems will derive from the electrondonating character that the methyl groups will have over the aromatic rings. Opposite to that, the functionalization of the ligands with iPr and tBu groups has a much larger steric component, and thus, it is expected that changes in the spincrossover behavior of such systems can be traced back to this steric component. We must stress here that, due to the molecular nature of the presented calculations, only intramolecular steric effects are accounted for, which will obviously have an effect on the molecular geometry and therefore on the properties, but we are neglecting the effect of neighboring complexes and cooperativity (intermolecular elastic interactions), which may also play a role in modulating the spincrossover temperature, and not necessarily in the same direction, as will be discussed for the particular case of the [(Cp1‑tBu)2Mn] and [(Cp1,3‑tBu)2Mn] complexes in section 4. For all studied systems, the corresponding spin-crossover temperature has been computed by fitting the thermal dependence of the Gibbs free energy. The corresponding results as well as energy differences between both spin states and the approximated energy gap between orbitals can be found in Table 2. The first result that can be outlined from Table 2 is the different electron donor characters of the H, Me, iPr, and tBu groups. The single functionalization of the cyclopentadienyl ligand with each one of these substituents has the expected effect over the orbital splitting due to the increasing electron donor character of these substituents. This effect can be better observed by plotting the energy gap between nonbonding and antibonding orbitals as a function of the Taft equation σ* value, a parameter that measures the field and inductive effects of the substituent (Figure 1). However, bulkier substituents

ΔEHS‑LS/kcal·mol−1 7.40 9.10 10.56 11.56 12.31 8.71 6.84 0.71 −14.35 7.08 5.07 −3.75

Δ/cm−1

T1/2/K 38

345 (152) 449 (303)39 529 551 629 430 306 − (370)40,41 − 353 (266)12 260 (241)12 −

16504 16707 16888 17124 17221 16757 16155 15405 14448 16854 16056 14844

a

Values in parentheses correspond to experimental data (with references).

such as iPr and tBu groups already show the competitive effect that sterics has over the electronic effects. By plotting the energy gap between the high-spin and low-spin states against the same σ* value, one can observe that, if indeed this energy gap increases with the Me functionalization, inclusion of iPr and tBu groups leads to smaller energy differences, which in turns leads to smaller spin-crossover temperatures. These results highlight the subtle equilibrium between both effects in terms of tuning the T1/2 in the family of [(CpR)2Mn] compounds. The results in Table 2 can be correlated with the geometrical parameters for the studied systems to gain further insight into the different effects at play in the spin-crossover behavior of the studied molecules. As can be seen in Figure 2, two different regimes can be observed, depending on whether the functionalization is done with methyl groups or whether the functionalization is done with isopropyl or tert-butyl groups: that is, if the spin-crossover behavior is modulated by electronic effects or by steric effects, as will be discussed later. Figure 2 illustrates the electron donor nature of the methyl substitution into the cyclopentadienyl ring. As can be seen from Figure 2 and Table 1, there is very little influence over the Mn−Cp bond length in the low-spin state with an increasing number of methyl groups added to the cyclopentadienyl ligand (bond lengths between 1.69 and 1.71 Å). However, a significant increase in the energy gap between the nonbonding and antibonding orbitals can be observed, as well as a systematic increase in the corresponding computed spincrossover temperatures as a result of the electron donor effect of the methyl groups (see Table 2). This effect can be also observed when the systems [(Cp)2Mn] and [(Cp1‑Me)2Mn] are compared. While in both cases the geometrical parameters are almost identical in terms of bond lengths, a significant increase in the energy gap is observed just by adding one methyl group to the Cp ligand. Moreover, this chemical modification comes with a significant increase in the estimated T1/2 between both systems (see Table 2). In contrast, isopropyl and tert-butyl functionalization of the Cp ligand leads to a progressive decrease in the calculated T1/2. Although both groups are also electron donors, like the methyl group, C

DOI: 10.1021/acs.inorgchem.7b02592 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. (left) Energy gap between nonbonding and antibonding orbitals as a function of the Taft σ* value for the [(Cp1‑R)2Mn] (R = H, Me, iPr, t Bu) family. (right) Energy gap between the high- and low-spin states for the same systems as a function of σ*.

Figure 2. Correlation between the average distance CpR−Mn (R = Me, iPr, tBu), measured as the Mn to centroid distance, and the energy gap between nonbonding and antibonding orbitals.

to be high spin above 0 K (see section S1 in the Supporting Information).

the steric contribution takes over and, as can be seen from Figure 2 and Table 2, a progressive increase in the Mn−Cp bond length is observed, which leads to smaller energy gaps between the sets of d-based orbitals and ultimately to the suppression of the SCO behavior. In fact, the [(Cp1,3,4‑tBu)2Mn] system has already an S = 5/2 ground state,12 as a result of the significant metal to ligand bond length enlargement, which generates a sufficiently small ligand field such as to favor the high-spin state. A close inspection of the generated data also allows us to extract the limiting Mn−Cp bond length value for which one should expect spin crossover to occur, and the corresponding associated ligand field. This value has been estimated to be around 1.755 Å (measured as the Mn to the Cp ring centroid distance), with a corresponding ligand field of approximately 15305 cm−1 (see Table S5 in the Supporting Information). This means that any functionalization performed on the ring that forces the low-spin state to have a metal to ligand bond length larger than this cutoff value should not exhibit spincrossover behavior and, rather, remain in the high-spin state at all temperatures. This effect can be verified by analyzing some other functionalized systems such as the [(Cp1,2,3,4‑iPr)2Mn] and the [(Cp1,2,3‑tBu)(Cp1,3‑tBu)Mn] molecules, both computed

4. DISCUSSION A useful starting point to discuss the interplay between electronic and steric effects in the fine tuning of the spincrossover temperature in [(CpR)2Mn] systems is the molecular orbital (MO) diagram for the simplest member of this family: that is, the manganocene itself. Even though this molecule has been extensively studied, and it is well-known that its crystal structure is a polymeric chain42 and its magnetic moment is only compatible with a high-spin (S = 5/2) situation,43 we can model the molecule as an isolated entity in both spin states using computational tools and use its MO diagrams as a starting point to analyze the different effects that ring functionalization will have over the spin-crossover behavior. A schematic molecular orbital diagram for the [(Cp)2Mn] system is shown in Figure 3. From Figure 3, the first thing that can be observed is that in both spin states there are two sets of orbitals that can be clearly distinguished: the set of nonbonding orbitals, composed by the dxy, dx2−y2, and dz2 orbitals, and the set of antibonding orbitals, composed by the dxz and dyz orbitals. This means that the D

DOI: 10.1021/acs.inorgchem.7b02592 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 3. Schematic molecular orbital diagram for the [Mn(Cp)2] system in high-spin (left) and low-spin (right) states.

control of the energy gap between this two sets of orbitals, and by extension the spin-crossover properties of these systems, is going to be controlled by the interaction between the frontier molecular orbitals of the cyclopentadienyl ligand and the dxz and dyz orbitals. The set of nonbonding orbitals is going to remain as it is, regardless of whatever functionalization occurs on the Cp ligand, due to the lack of interaction between the frontier molecular orbitals of the metal and the ligand (the orbitals are purely nonbonding), and its effect on tuning the SCO properties is going to be negligible. Functionalization of the Cp ligand with methyl groups, an electron-donating group, increases the localization of the ligand’s frontier molecular orbitals and raises its energy, as can be seen from Table 2 and Figure 2. Also, in Figure 4 we show an schematic representation of the MO diagram for the [(Cpn‑Me)2Mn] family (n = 1−4), reflecting the increase in energy of the dxz and dyz orbitals as a result of the methyl functionalization on the Cp ligands. However, such functionalization minimizes possible steric congestions between both

rings and leads to geometries in which the metal−ligand bond length is almost unaltered. Therefore, the result for the SCO behavior in such a family is that, by increasing the number of methyl groups added to the Cp ligand, we progressively favor the low-spin state, thus increasing the expected spin-crossover temperature and moving from a SCO system, [(Cp1‑Me)2Mn], to a low-spin molecule, [(Cp*)2Mn]. A comparison with experimental data is complicated, due to the lack of data for several members of the [(Cpn‑Me)2Mn] family. Regardless, in Table 2 we provide the computed T1/2 values for the studied systems. As can be seen, functionalization of the manganocene with one methyl yields to an increase in the spin-crossover temperature of around 90 K, value that is properly reproduced by the calculations. The systematic bias toward higher values when the OPBE functional is used can be estimated as a mean average error of 119 K, or alternatively 0.24 kcal/mol, an error that lies below the 1 kcal/mol error acceptable for calculations at the density functional theory level. As a matter of fact, the computed spin-crossover temperatures can be plotted against the number of substituents, providing a nice correlation between the degree of functionalization of the Cp ring and T1/2. A similar effect therefore should be expected when other electron-donating groups are added, such as isopropyl and tertbutyl, and as a matter of fact, this is what happens in both [(Cp1‑iPr)2Mn] and [(Cp1‑tBu)2Mn] when the energy splitting between nonbonding and antibonding orbitals with the same energy gap for the naked [(Cp)2Mn] is compared (see Table 2). However, as soon as we add more substituents of such types to the Cp ligand, the steric congestion forces the rings to move apart, thus reducing the interaction between the Cp frontier molecular orbitals and the dxz and dyz orbitals. Thus, the energy of those orbitals goes down, and the progressive functionalization of the [(Cpn‑iPr)2Mn] and [(Cpn‑tBu)2Mn] families moves us from SCO molecules to high-spin systems. Indeed, the [(Cp1,2,3,4‑iPr)2Mn] system has been characterized as a high-spin system.40,41 Although the computed values agree

Figure 4. Computed spin-crossover temperatures (T1/2) vs the number of methyl groups in the [(Cpn‑Me)2Mn] family. E

DOI: 10.1021/acs.inorgchem.7b02592 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 5. (left) Walsh diagram for the [(Cpn‑Me)2Mn] family, showing the limiting cases ([(Cp1‑Me)2Mn] and [(Cp1,2,3,4‑Me)2Mn]). (right) Walsh diagram for the [(Cpn‑tBu)2Mn] family, showing the limiting cases ([(Cp1‑tBu)2Mn] and the [(Cp1,2,3,4‑tBu)2Mn]).

From an electronic structure point of view, the control of the spin-crossover temperature as well as the stabilization of the high-spin state or the low-spin state can be fully rationalized by analyzing the underlying electronic structure of the studied systems using a molecular orbital depiction. All studied systems have two sets of d-based molecular orbitals, the nonbonding set, formed by the dxy, dx2−y2 and dz2 orbitals, and the set of antibonding orbitals, which includes the low remaining d-based molecular orbitals, dxz and dyz. The degree of antibonding character in the latter is going to be key in controlling the spin-crossover properties of such systems. Electron-donating groups, such as methyl, isopropyl, and tertbutyl, can be used to functionalize the cyclopentadienyl ring. This functionalization increases the energy gap between nonbonding and antibonding orbitals, thus leading to higher spin-crossover temperatures. Addition of more than one methyl group keeps increasing the spin-crossover temperature, to the point that, beyond the [(Cp1,3,4‑Me)2Mn] system, the molecules become low-spin systems due to the energetic penalty cost that has the occupation of the pair of antibonding orbitals dxz and dyz. However, by adding two or three isopropyl or tert-butyl groups, the opposite behavior appears, and a progressive decrease in the spin-crossover temperature leads to a high-spin situation for both [(Cp 1,3,4‑iPr ) 2 Mn] and [(Cp1,3,4‑tBu)2Mn] systems. This can be explained because of the progressive loss of antibonding character experienced by the dxz and dyz pair of orbitals as a result of the steric congestion imposed by the alkane substituents, which pushes the cyclopentadienyl rings away from each other, increasing the metal−ligand bond length and therefore reducing the energy gap between both sets of orbitals. It is important to stress that we estimated the critical bond length to be around 1.754−1.756 Å within the statistical error of the computed values, meaning that any functionalization on the Cp rings which leads to similar or larger bond lengths should also suppress the SCO behavior in favor of a high-spin system. Obviously, this limiting value has been extracted from our calculations and omits crystal-packing effects that can be, as has been explained above, important in some cases. An important point outlined from the presented calculations is the delicate interplay between steric and electronic effects in terms of tuning the spin-crossover temperature in mangano-

with the experimentally observed trend in solution, for some systems the solid-state data provide spin-crossover temperatures that move in the opposite direction. Experimentally, the functionalization from [(Cp1‑tBu)2Mn] to [(Cp1,3‑tBu)2Mn] leads to a decrease in the spin-crossover temperature when measurements are done in solution, but the opposite trend (an increase of the T1/2) is observed for solid-state data. This behavior can be explained by crystal packing effects, which produce a contraction of the Cp−Mn bond length with increasing functionalization,12 thus leading to behavior opposite to that observed in solution and predicted by the calculations (see Tables S2 and S3 in the Supporting Information), increasing such parameters and stressing one more time the delicate balance between electronic and steric effects that are at play in these systems. Similarly, the only member of the [(Cpn‑iPr)2Mn] family with a reported spincrossover temperature, the [(Cp1,3,4‑iPr)2Mn] system, has an unusually high T1/2 (370 K), while our calculations predict such a system to be a high-spin system. However, the lack of experimental data for this family makes it difficult to trace back the origin of such a discrepancy. The only clue here is the fact that the [(Cp1,2,3,4‑iPr)2Mn] system behaves as a high-spin system, and its Cp−Mn bond lengths are slightly greater (see Table 2) than for [(Cp1,3,4‑iPr)2Mn], thus suggesting one more time that crystal-packing effects are at play. Figure 5 gives a schematic MO diagram for such families, showing the progressive decrease in energy due to the loss of antibonding character of the dxz and dyz pair of orbitals.

5. CONCLUSIONS In this work, a computational study of the spin-crossover properties in manganocene systems of general formula [(CpR)2Mn] (R = Me, iPr, tBu) has been presented. Using the OPBE functional with a triple-ζ basis set with polarization functions on all atoms, the experimental behavior of such systems is correctly reproduced. More importantly, our calculations allow us to gain insight into the delicate equilibrium between electronic and steric effects, which are at play in controlling the spin-crossover behavior in such systems. F

DOI: 10.1021/acs.inorgchem.7b02592 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry cene systems. Even though at first glance one might expect to increase the spin-crossover temperature by adding electrondonating groups, sterics can counterbalance this effect and eventually lead to the opposite situation, which once again points out how difficult it can be to foresee the effect of a given chemical modification over the SCO behavior in a given system and reinforces the idea that theoretical modeling can provide trends in such behavior, trends that can be of great help in the rational design of new molecules with tailored properties.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02592. Cartesian coordinates with the corresponding energy and first frequency for every computed geometry in all spin states, comparison with available geometric data, results with TPPSh functional vs the OPBE functional and fitting values, and determination of the limiting value for SCO to occur (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail for J.C.: [email protected]. ORCID

Jordi Cirera: 0000-0002-9564-9819 Eliseo Ruiz: 0000-0001-9097-8499 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research reported here was supported by the Spanish Ministerio de Economiá y Competitividad (grant CTQ201564579-C3-1-P, MINECO/FEDER, UE). E.R. thanks the Generalitat de Catalunya for an ICREA Academia award. We gratefully acknowledge the computer resources of the Consorci Serveis Universitaris de Catalunya (CSUC).

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DOI: 10.1021/acs.inorgchem.7b02592 Inorg. Chem. XXXX, XXX, XXX−XXX