Theoretical Study of the Mechanism of Valence Tautomerism in Cobalt

16 Nov 2010 - Valence tautomerism is studied in the [CoII-HS(sq)2(bpy)]/[CoIII-LS(sq)(cat)(bpy)] mononuclear cobalt complex by using DFT methods (HS, ...
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Theoretical Study of the Mechanism of Valence Tautomerism in Cobalt Complexes Daisuke Sato, Yoshihito Shiota, Gergely Juha´sz, and Kazunari Yoshizawa* Institute for Materials Chemistry and Engineering, and International Research Center for Molecular Systems, Kyushu UniVersity, Fukuoka 819-0395, Japan ReceiVed: August 6, 2010; ReVised Manuscript ReceiVed: October 7, 2010

Valence tautomerism is studied in the [CoII-HS(sq)2(bpy)]/[CoIII-LS(sq)(cat)(bpy)] mononuclear cobalt complex by using DFT methods (HS, high spin; LS, low spin; cat, catecholate; sq, semiquinone; bpy, 2,2′-bipyridine). Calculations at the B3LYP* level of theory reproduce well the energy gap between the CoII-HS and CoIII-LS forms giving an energy gap of 4.4 kcal/mol, which is comparable to the experimental value of 8.9 kcal/mol. Potential energy surfaces and crossing seams of the electronic states of the doublet, quartet, and sextet spin states are calculated along minimum energy paths connecting the energy minima corresponding to the different spin states. The calculated minimum energy crossing points (MECPs) are located at 8.8 kcal/mol in the doublet/ sextet surfaces, at 10.2 kcal/mol in the doublet/quartet surfaces, and at 8.4 kcal/mol in the quartet/sextet surfaces relative to the doublet ground state. Considering the energy of the three spin states and the crossing points, the one-step relaxation mechanism between the CoII-HS and CoIII-LS forms is the most probable. This research shows that mapping MECPs can be a useful strategy to analyze the potential energy surfaces of systems with complex deformation modes. SCHEME 1

Introduction Valence tautomeric (VT) complexes have attracted much attention recently because of their possible application in new molecular devices like memory or display devices.1 VT complexes show a ligand-metal electron transfer coupled with a spin change on the central metal ion, which can be switched by external stimuli like light, heat, or pressure.2 Different valence states of VT complexes have significantly different charge and spin distributions and, consequently, different optical, electric, and magnetic properties.3,4 The changes in spin multiplicity or valence state are induced through a reversible intramolecular electron transfer involving a metal ion and redox active ligands in a mechanism analogous to that observed in Prussian blue.5 Valence tautomerism has also been observed in enzymes like copper dependent amine oxidases,6 between quiononoid cofactors and copper active center assisting oxygen activation. The most well-known VT systems are the cobalt dioxolene complexes, where the electron transfer takes place between the central cobalt ion and semiquinonate (sq)/cathecholate (cat)type ligands. At low temperature the cobalt ion is in a diamagnetic CoIII state; at higher temperature an electron from ligands can reduce the metal to a high-spin CoII state. The mechanism of VT and the relaxation between the valence states have been studied on several complexes,2,7-9 and the theory of nonadiabatic multiphonon relaxation10 is considered to be an adequate framework for the description of the process. The relationship between the rate of thermal relaxation between valence states and structural factors is still an open problem.11,12 The analysis of potential energy surfaces (PESs) of the relevant electronic states can lead us to better understanding the mechanism of this relaxation process. Such an understanding is essential to create novel materials with better switching properties. A schematic representation of low-lying PESs is shown in Scheme 1 along the nuclear coordinate associated with VT. * To whom correspondence should be addressed. E-mail: kazunari@ ms.ifoc.kyushu-u.ac.jp.

The relaxation and excitation processes between the ground lowspin state and the high-spin state are associated with a metalto-ligand charge transfer (MLCT) or a ligand-to-metal charge transfer (LMCT) via a weak electronic coupling between these different spin states. The charge transfer also couples with spin inversion on the metal ion. For an analysis of the potential energy surfaces, however, it is difficult to identify the relevant normal modes that describe the geometrical changes between different valence states. In spin-crossover (SCO) systems, where only the spin state of the metal ion changes, such an analysis is generally adopted along a single total symmetric mode.13 Even in SCO systems the single-mode approach has limitations. Recently we proposed a different approach: following minimum energy pathways and finding the minimum energy crossing points (MECPs) between different electronic states would give a good insight to the mutual position of these PESs.14 One can reasonably assume that the relaxation of an excited state is going along close to the gradient path and funnels around MECPs, which play a central role in the intersystem crossing. Geometrical changes associated with the VT transition are expected to be more complex than the spin crossover15 for several reasons. While in SCO complexes the average M-L

10.1021/jp107391x  2010 American Chemical Society Published on Web 11/16/2010

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bond lengths can generally represent well the totally symmetric breathing modes and can describe the main geometry distortion associated with SCO, it is not true for VT complexes. VT systems often contain two geometrically inequivalent ligands, in which the totally symmetric modes during the transition cannot be expected. Therefore the valence tautomerism induces a redox reaction of the ligands resulting in a new type of lowsymmetry distortions of the complex. Analyzing the PES along several normal modes is not preferred, as it is computationally very expensive. In this manuscript we would like to show how one can map the low energy states of a realistic VT complex finding the relevant minimum energy crossing points (MECPs). Since a PES has 3N - 6 degrees of freedom in a molecular system of N atoms, crossing seams between the high- and lowspin states are described by 3N - 7 degrees of freedom under the boundary condition of Ehigh spin ) Elow spin. The transition probability in the vicinity of a crossing seam provides a new selection rule for a dominant pathway involving a state-to-state transfer reaction, and therefore a MECP can be identified as a transition state for a nonadiabatic transition.16-19 Thus, we expect that spin-transition phenomena like valence tautomerism or spin crossover can occur in the vicinity of a MECP. In this study we use a model for the cobalt bis(quinone) complex [CoIII(3,5-dbcat)(3,5-dbsq)(bpy)] (Scheme 2), which was first reported by Buchanan and Pierpont in 1980,20,21 where 3,5-dbcat, 3,5-dbsq, and bpy are 3,5-di-tert-butyl-1,2-catecholate, 3,5-di-tert-butyl-1,2- semiquinone, and 2,2′-bipyridine, respectively. The complex is in the CoIII-LS/SQ form (doublet spin state) below 273 K, and the population of the CoII-HS/2SQ form (sextet spin state) starts with increasing temperature. In solution, the equilibrium can be induced by the variation of temperature and monitored by magnetic measurements and spectroscopic techniques such as UV/vis, NMR, and EPR spectroscopy.22 Adams et al.23,24 also reported from measurements of electric absorption spectrum that the [CoIII(3,5-dbcat)(3,5-dbsq)(bpy)] complex in CH2Cl2 solution at low temperatures shows a 600 nm band characteristic of the CoIII-LS complex. An increase of temperature promotes intramolecular electron transfer, resulting in the formation of CoII ion, and at the same time a cat ligand is oxidized to a sq ligand. As a consequence, the intensity of the 600 nm band decreases while the intensity of a 770 nm band characteristic of the CoII-HS tautomer increases. The [CoIII(3,6-dbcat)(3,6-dbsq)(py2O)] complex has a hysteresis of 230 K by measurements of magnetic moment although repeated traces show a gradual breakdown in the hysteresis,25 where 3,6-dbcat, 3,6-dbsq, and py2O are 3,6-di-tert-butyl-1,2catecholate, 3,6-di-tert-butyl-1,2- semiquinone, and 2,2′-bis(pyridine) ether, respectively. Sato et al.26 reported photoinduced

VT observed in [CoII-HS(3,5-dbsq)2(tmeda)] (tmeda: N,N,N′,N′tetramethylethylenediamine). In this complex, illumination induces the electron transfer from a 3,5-dbsq to CoIII-LS to yield CoII-HS while the magnetization µeff is increased from 1.7 to 2.3 µB. The lifetime of the photoinduced metastable state at 5 K is 175 min. They reported that [CoII-HS(3,5-dbsq)2(phen)] (phen: phenanthroline) also shows photoinduced VT.8 When the lowspin-state complex is excited by 532 nm light at 5 K, µeff is increased from 1.7 to 2.7 µB in 1 min and then saturated during illumination. This rapid response to light irradiation of this complex is applicable to optical switching devices. Roux et al.9 reported from X-ray absorption fine structure (EXAFS) assignment that the thermal and pressure-induced VT interconversion between high- and low-spin states directly occurs via no intermediate spin state. Although many experimental studies have been made on VT of the cobalt dioxolene system, little is known about the VT mechanism. Adams, Noodleman, and Hendrickson23 carried out DFT calculations to estimate the relative energies of the [CoIII-LS(cat)(sq)(phen)] complex in the high-spin, intermediate-spin, and low-spin states. They reported the optimized structures in these spin states and qualitative analysis using the X-R and the BP86 methods. In this paper, we report a detailed analysis of low-lying PESs and MECPs to elucidate the thermal valence-tautometric mechanism in the [CoIII-LS(sq)(cat)(bpy)] complex. Method of Calculation Energy calculations for the [CoII-HS(sq)2(bpy)] and [CoIIILS(sq)(cat)(bpy)] complexes in the doublet, quartet, and sextet spin states were carried out by using unrestricted density functional theory (UDFT) implemented in the program packages Gaussian 0327 and GAMESS.28,29 For the Co atom the (14s9p5d)/ [9s5p3d] primitive set of Wachters-Hay30,31 with one polarization f-function (R ) 1.117)25 and for the H, C, N, and O the 6-311G** basis set32,33 were used. While the relative energies of different spin states play a significant role in the analysis of crossing seams, it is well-known that DFT methods are less accurate in predicting small energy gaps between different spin states. The B3LYP functional34,35 is often used for predicting geometry and spectroscopic properties of systems containing transition metals; however, it tends to overestimate the stability of the high-spin state.36 On the other hand, calculations with the BP86 functional (a combination of the Becke’s37 exchange functional and the Perdew’s correlation functional38) tend to overestimate the stability of the low-spin state. The OPBE functional,39-41 a combination of the PBE correlation functional and the newly developed OPTX exchange functional, gives

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better-balanced results in general. Swart et al.42 tested the OPBE functional on seven FeII spin-crossover complexes and found a good agreement between calculated and experimental energy gaps between the singlet and quintet spin states in these systems. The other promising candidate for calculating relative spin energies is a reparametrized version of B3LYP developed by Reiher and co-workers: the B3LYP* functional with 15% Hartree-Fock exchange instead of 20%.43-45 Geometry optimizations were performed with the B3LYP, B3LYP*, BLYP, BP86, and OPBE methods. The stability of optimized geometries was confirmed with vibrational analyses, and no imaginary frequency was found. In distorted octahedral ligand field, the lowest-lying quartet and sextet spin states are approximately threefold degenerate corresponding to the occupation of the t2g orbitals in the CoII and CoIII states. According to the DFT calculations, the energy splitting between these pseudodegenerate levels of the quartet and sextet spin states is less than 1 kcal/mol at the B3LYP*/6-311G** level of theory. Through this study we assume that the three pseudodegenerate levels are essentially equivalent; therefore, we focused only on the most stable state of each spin and valence states and restricted the discussion for the crossing seam between these states. The 〈s2〉 values of the optimized structures at the B3YP* level were calculated to be 0.7500 in the doublet spin state, 3.7506 in the quartet spin state, and 8.7502 in the sextet spin state. The calculations of crossing seams of different two spin states, A and B, were carried out in the following three steps: (1) from the optimized geometry of the A state, an approximate steepestdescent path was followed to the equilibrium geometry of the B state by using simple geometry optimization; (2) single-point calculations in all the three spin states were performed along this approximate steepest-descent path in order to monitor the relative energies; (3) the crossing points of potential energy surfaces were found where the energy of two spin states became equal. Using these crossing points as starting geometries, the minimum energy crossing points (MECPs) were found using the improved gradient-based algorithm developed by Farazdel and Dupuis.16 Results and Discussion Comparison of DFT Methods. Reiher and co-workers43-45 compared several DFT methods for their accuracy of estimating the energy gap between the high-spin and low-spin states, ∆EQS ) Equintet - Esinglet, in FeII spin-crossover systems. Only using accurate calculation of energy splitting between the quintet- and singlet-spin states can give meaningful discussion of the crossing seams between two PESs. To test the validity of our calculation technique, we compared the energy gap between the doublet and the sextet spin states in the [CoIII-LS(sq)(cat)(bpy)] and [CoIIHS(sq)2(bpy)] complexes calculated with five different types of density functional on a complex [CoIII-LS(sq)(cat)(bpy)], a simple model of complex [CoIII-LS(3,5-dbsq)(3,5-dbcat)(bpy)]. Calculated energy gaps and geometrical parameters are summarized in Table 1 and compared with experimental values. Magnetic property measurements of the [CoIII-LS(3,5-dbsq)(3,5dbcat)(bpy)] complex revealed that the doublet spin state is the stable spin state at low temperature.11 The spin multiplicity of the ground state was correctly predicted by the BP86, OPBE, BLYP, and B3LYP* methods, whereas the B3LYP method overestimates the stability of the sextet spin state with a calculated energy of -4.0 kcal/mol relative to the doublet spin state. Computed energy gaps of 24.2 kcal/mol at the BP86 level and 18.9 kcal/mol at the BLYP level are overestimated

Sato et al. TABLE 1: Energy Gaps between the High- and Low-Spin States (kcal/mol) and Average Co-Ligand Distances (Å) in the [CoIII-LS(sq)(cat)(bpy)] and [CoII-HS(sq)2(bpy)] Complexes BP86

OPBE BLYP B3LYP B3LYP* exptla

∆E 24.2 10.6 18.9 -4.0 r(CoIII-LS-L)ave 1.897 1.885 1.922 1.908 r(CoII-HS-L)ave 2.047 2.052 2.072 2.094 b

4.4 1.905 2.081

8.9c 1.904d 2.078e

a Experimental values of the [CoIII-LS(3,5-dbsq)(3,5-dbcat)(bpy)] complex and the [CoII-HS(3,5-dbsq)2(bpy)] complex. b ∆E ) Edoublet - Esextet. c Reference 24a. d Reference 20. e Reference 24b.

compared to the experimental value of 8.9 kcal/mol.15 As it was expected, the two methods that reproduced the energy gap closest to the experimental value are the OPBE and B3LYP* methods with a sextet spin state energy of 10.6 and 4.4 kcal/ mol, respectively. Finally, we also checked the relative energy of the intermediate spin quartet state with these two methods. The OPBE method predicts that the quartet state is below the sextet state with 1.3 kcal/mol, whereas the B3LYP* method predicts that the energy of the quartet state is 3.0 kcal/mol higher than the sextet state. Since experimentally the intermediate-spin quartet state is above the high-spin sextet state, the B3LYP* method is the best choice for the calculation of the PESs and crossing seams in the CoII VT system as well as FeII spincrossover systems.43-45,14 In contrast to the calculated energy gaps, there are no significant differences in the optimized geometries obtained by using different functionals. In the doublet spin state, computed average distances of the Co-ligand bonds are 1.897 Å in the BP86 method, 1.885 Å in the OPBE method, 1.922 Å in the BLYP method, 1.908 Å in the B3LYP method, and 1.905 Å in the B3LYP* method, as shown in Table 1. In the sextet spin state, average Co-ligand distances are 2.047 Å in the BP86 method, 2.052 Å in the OPBE method, 2.072 Å in the BLYP method, 2.094 Å in the B3LYP method, and 2.081 Å in the B3LYP* method. In the experimental values, average Co-ligand bond distances are 1.904 Å in the doublet state and 2.078 Å in the sextet spin state. The optimized structures by the B3LYP and B3LYP* methods are in good agreement with the X-ray structure, and therefore we used the later for further analysis of the system. Optimized Structures and Electronic States. As the second step of this study, we considered detailed structures of the Co complexes in the three spin states. In addition to the doublet ground state and the sextet state, we considered two possible electronic structures with intermediate (quartet) spin state corresponding to [CoII-IS(sq)2(bpy)] and [CoI1I-IS(cat)(sq)(bpy)]. Calculations showed that the lowest-lying quartet spin state is [CoII-IS(sq)2(bpy)], and [CoI1I-IS(cat)(sq)(bpy)] corresponds to the first excited quartet spin state. Optimized structures of the ground doublet spin state (1), the low-lying quartet spin state (2), the first excited quartet state (2′), and the low-lying sextet spin state (3) are shown in Figure 1. The distances of the Co-ligand bonds strongly depend on the valence state and spin multiplicity. The low-spin state (the high-valence state) tends to have a short cobalt-ligand distance, while the high-spin state (the lowvalence state) tends to have a large distance. Calculated Co-ligand bond lengths in 1 are between 1.874 and 1.952 Å. The C-O bond lengths of sq are 1.318 and 1.325 Å. In 2, however, the bond distances of Co-O1 and Co-O3 elongated to 2.145 Å in 2 from 1.889 Å in those of 1, while the Co-O2, Co-O4, Co-N1, and Co-N2 bond lengths remain unchanged. As a result, 2 undergoes a significant axial distortion to relax

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Figure 1. Optimized structures of the doublet spin state (1), the low-lying quartet spin state (2), the first excited quartet spin state (2′), and the sextet spin state (3). Values in parentheses are the optimized geometry of 2′. Units are in Å; B3LYP*/6-311G** level of theory.

TABLE 2: Computed Energies (kcal/mol) and Mulliken Spin Densities of 1, 2, 2′, and 3 entry 1 2 2′ 3

electronic state III

Co doublet CoII quartet CoIII quartet CoII sextet

energy

Co

sq

cat

bpy

0.0 7.4 7.7 4.4

0.06 1.10 1.27 2.80

0.47 0.99 1.01 1.07

0.47 0.99 0.69 1.07

0.00 -0.08 0.03 0.07

structure constraint. The Co-ligand bonds in 3 range from 2.055 to 2.128 Å, and the Co-O1 and Co-O3 bonds are 2.055 and 2.055 Å. To gain a better understanding of different equilibrium geometries associated with the different spin states, we considered their electronic structures. Table 2 shows the relative energies and calculated spin densities in each electronic configuration. Since the spin density is 0.06 in the cobalt atom of 1, the cobalt atom is in a diamagnetic state corresponding to the cobalt(III) low-spin state. On the other hand, each of the two dioxolene ligands have a Mulliken spin density of 0.47. Thus, both ligands carry spin, and there are no distinguishable catecholate (cat) and semiquinonate (sq) ligands. Experimentally, however, the unpaired spin is localized on one of the dioxolane ligands, and the cat and sq ligands can be distinguished in the X-ray crystallographic structure.16 One possible explanation of the cat/sq delocalization in the calculated structure is that intermolecular interactions are responsible for the localization of the unpaired electron in the doublet spin state. As our calculations are performed without considering the molecular environment, such intermolecular interactions are not included in our model. According to our calculations, the lowest-lying quartet spin state 2 is the [CoII-IS(sq)2(bpy)] valence state with d7 electron configuration on the CoII ion and the two sq radical species as ligands. This assignment of 2 is fully consistent with calculated spin densities of 1.10 on the Co atom and 0.99 on sq. In contrast, the [CoI1I-IS(cat)(sq)(bpy)] valence state, 2′, has d6 electrons in the CoIII atom and the radical sq and cat ligands. Calculated spin densities in 2′ are 1.27 in the Co atom, 1.01 in sq, and 0.69 in cat. The calculated energies of [CoII-IS(sq)2(bpy)] and [CoI1I-IS(cat)(sq)(bpy)] are 7.4 and 7.7 kcal/mol, respectively. Thus, in the initial state of [CoI1I-LS(cat)(sq)(bpy)] the LMCT is likely to occur compared to the spin inversion with electron transfer from the t2g orbitals to the e2g orbitals, leading to the formation of the [CoII-IS(sq)2(bpy)] complex as the low-lying quartet state. In 3 the spin densities of the cobalt atom and the two dioxolane ligands are 2.80, 1.07, and 1.07, respectively. The SOMO, LUMO, and d orbitals of 1 are shown in Figure 2. The SOMO and LUMO, which are identical in all the valence

states, correspond to a sq ligand orbital and a bpy ligand orbital, respectively. The geometrical differences between the doublet 1 and quartet 2 states can be explained by considering the electron transfer from a cat π* orbital to the d4 orbital associated with the valence tautomerism. The other electron transfer from the d3 orbital to the d4 orbital leads to the formation of 2′ in the quartet state. In 2 the d4 orbital is singly occupied, while the d5 orbital is unoccupied. In general, the t2g and eg orbitals in the octahedral ligand field correspond to nonbonding and antibonding interactions, respectively, with respect to the metal and ligands. Thus, the expansion of the Co-ligand distances is reasonable in 3 compared to 1. Potential Energy Surfaces of the Doublet, Quartet, and Sextet Spin States. Let us next look at the potential energy surfaces of the Co complexes along deformation coordinates that connect local minima. Table 3 shows the relative energies of 1, 2, and 3 at the B3LYP*/6-311G** level of theory. The doublet spin state in the equilibrium geometry 1 is the most stable electronic configuration, and therefore we set here the zero energy level to compare the relative energies of the other states. As a result of single-point calculations, relative energies of 1 are 0.0 kcal/mol in the doublet state, 23.9 kcal/mol in the quartet state, and 34.7 kcal/ mol in the sextet state; relative energies of 2 are 21.7 kcal/mol in the doublet state, 7.4 kcal/mol in the quartet state, and 17.5 kcal/ mol in the sextet state. Therefore, the quartet state is the ground state. The geometrical changes from 1 to 2 induces surface crossing in which spin inversion occurs; therefore, we expect two crossing seams (doublet/quartet and doublet/sextet). On the other hand, relative energies of 3 are 31.7 kcal/mol in the doublet state, 17.2 kcal/mol in the quartet state, and 4.4 kcal/mol in the sextet state. The geometrical change from 1 to 3 as well as the 1 to 2 change is responsible for surface crossings; therefore, we can expect at least three crossing points (doublet/quartet, doublet/sextet, and quartet/sextet) based on the topological behavior. These results suggest that structures and energies of surface crossings provide significant information about the VT conversion of the Co complex. We traced the potential energy surfaces to find the crossing points between different spin states using the gradient from optimization procedure. The energy plots of the three spin states along geometric distortions are summarized in Figure 3. The horizontal axis displacement dk for step k is given by the following equation: k

dk )

∑ √|ri - ri-1|2 i)1

(1)

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Figure 2. (a) Co d orbitals, SOMO, and LUMO of 1. (b) Orbital diagrams of 1 (doublet), 2 (quartet), and 3 (sextet) valence states.

TABLE 3: Relative Energies of the Optimized Structures 1 (Doublet), 2 (Quartet), and 3 (Sextet) at the B3LYP*/ 6-311G** Level of Theorya doublet quartet sextet a

1

2

3

0 23.9 34.7

21.7 7.4 17.5

31.7 17.2 4.4

Units are in kcal/mol.

In eq 1, ri is the ith coordinate in the optimized step. Note that displacement dk corresponds to geometric distortions along the steepest descent path including all geometry changes, rather than mapping only changes in the Co-ligand bond length. The energies of the valence states as a function of displacement, d, are shown in Figure 3. We found six crossing points, DS1, DQ1, QS1, DS2, DQ2, and QS2. Figure 3a shows the energy plots along the deformation coordinate that connects 1 and 3. When the geometry changes from 1 to 3, the energy of the doublet spin state rises, while the energy of the sextet spin state declines. These changes in energies of three spin states can be interpreted on the basis of electronic configuration of the Co atom and two dioxolane ligands. In the doublet spin state, d4 and d5 orbitals are unoccupied, the semiquinone ligand orbitals are singly occupied, and the highest occupied catecholate ligand orbital is doubly occupied. On the other hand, in the sextet spin state, d4 and d5 orbitals are singly occupied, and the semiquinone ligands orbitals are singly occupied. In the sextet spin state, these orbital energies decline through the bond elongations of Co-ligand induced by the geometry change, while orbital energies rise in the doublet spin state. The quartet PES has a local minimum at d ) 0.639, in which the energy is 14.9 kcal/ mol because the molecular structure is the closest to the optimized quartet at this point. The doublet and sextet spinstate energy crosses at DS1. The PESs of the doublet and quartet spin states have a crossing point DQ1 at d ) 0.888, and the energy is 16.0 kcal/mol. The PESs of the quartet and sextet spin states have a crossing point QS1, in which d ) 0.721, and the energy is 14.3 kcal/mol. We found the three energy crossing points along the 1-3 geometrical changes. Figure 3b shows the energy plots along the deformation coordinate that connects 1 and 2 as a function of d. The starting point of the plot represents the optimized structure of the doublet

spin state, and the end of plot represents that of the quartet spin state. In Figure 3b, calculated energies of the doublet spin state rise, while the energy of the quartet spin state declines. The sextet PES has a local minimum at d ) 0.919, in which the energy is 13.0 kcal/mol. At the end of plot as the optimized quartet, the displacement value is 1.362, and this is the smallest among the other plots because the difference of geometry is small between the optimized doublet and the optimized quartet. The potential energy surface along the 1-2 geometrical change has two energy crossing points. The doublet and quartet spinstate energy crosses at DQ2, d ) 0.574, the energy at this point being 10.4 kcal/mol. The PESs of the doublet and sextet spin states have a crossing point DS2 at d ) 0.663 with an energy of 13.6 kcal/mol. Figure 3c represents the energy plots along the deformation coordinate; the starting point of the energy plots corresponds to 2 and the end of plots corresponds to 3. During the geometry changes from the optimized quartet to the optimized sextet, the energies in the quartet (sextet) state were increased (decreased). Thus the two potential energy surfaces cross at d ) 0.375, and the energy of QS2 is 9.4 kcal/mol. The doublet potential energy surface has a local maximum at d ) 1.042 with an energy of 35.1 kcal/mol. The energy change around the end of plot is moderate in all energy plots. Minimum Energy Crossing Points. Although we are particular interested in the crossing points between different spin states, these points are not minima. We next consider the MECP corresponding to the “transition state” of the nonadiabatic transition from one spin state to another spin state. To gain a better understanding of PESs and spin-transition mechanism, Farazdel and Dupuis developed the method to calculate the MECP.46 They introduced the constraint that the energies on different PESs are equal (EA ) EB). Then, the problem is the following

{

minimize f(x) ≡ cAEA(x) + cBEB(x) subject to c(x) ≡ EA(x) - EB(x) ) 0

(2)

where f(x) is the objective function, c(x) is the constraint function defining the crossing seam, cA and cB are fixed arbitrary finite quantities (excluding the obvious case of cA ) cB ) 0), and x

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Figure 3. Energy plots of the three spin states along the geometric distortions (a) from 1 to 3, (b) from 1 to 2, and (c) from 2 to 3.

Figure 4. Optimized structures of the doublet/sextet MECP (DSM), the doublet/quartet MECP (DQM), and the quartet/sextet MECP (QSM). Units are in Å.

) {x1, x2,.. ., xn} is the nuclear degrees of freedom. In this case, both f(x) and c(x) are assumed to be twice differentiable with bounded Hessians (second derivatives). Under these conditions, they used the Lagrange method of undetermined multiplier and configured undetermined multiplier as in eq 2

L(y) ) f(x) - λc(x) ) cAEA(x) + cBEB(x) - λ[EA(x) - EB(x)]

(3)

where λ is the Lagrange multiplier that guarantees the EA ) EB condition of the seam and y ≡ (x, λ)T. If the value of cA + cB is 1, on the crossing seam the equation L ) EA ) EB consists. This constraint reduces the problem to find the minimum point y* ≡ (x*, λ*)T of L(y). This can be accomplished by using a variety of methods for unconstrained minimization to the ones used for geometry optimization calculation.47 According to this procedure, we optimized MECPs starting from the crossing points in Figure 3 and obtained three MECPs in Figure 4; DSM is a MECP with respect to the doublet/sextet PESs; DQM is a MECP with respect to the doublet/quartet PESs; QSM is a MECP with respect to the quartet/sextet PESs. Calculated energies of DSM, DQM, and QSM are 8.8, 10.2, and 8.4 kcal/mol, respectively. DSM is optimized from the crossing point DS1 (10.5 kcal/mol) in Figure 3. We can expect symmetric structure of DSM because the 1-3 geometrical changes retain a Cs symmetry structure. However, DSM has an asymmetric structure and lies 1.7 kcal/mol below DS1. Therefore, the relaxation path leading to DSM involves an asymmetric deformation, which must play an important role in the energy changes of the minimum crossing point between the doublet and sextet states. The B3LYP* results indicate that small differences between DSM and 1 in the cobalt-ligand bonds are in a range from 0.049 to 0.127 Å. The Co-N bond lengths, 2.059 and 2.079 Å, are close to that of the sextet optimized structure (3) rather than the doublet optimized structure (1). Consequently,

DSM is located at the midpoint of 1 and 3. DQM is obtained by optimization from DQ1, which is the crossing point between the doublet and the quartet spin state at 16.0 kcal/mol. The cobalt-ligand bond lengths are longer than the optimized quartet spin-state structure (2) in some bonds. In the geometry DQM, the two Co-N bond lengths are 2.077 and 2.087 Å while that of the geometry 2 are 1.927 and 1.926 Å, and in 1, both Co-N bond lengths are 1.952 Å. The Co-O4 bond length is 2.001 Å, and this is longer than the quartet one. The other Co-O bond lengths are in a range from 1.950 to 1.975 Å, and these are shorter than 2. The geometry DQM has a longer Co-ligand bond than the geometry 1, while O-C bond lengths are in a range from 1.292 to 1.305 Å, which are intermediate between the geometries 1 and 2. The geometry DQM is close to the geometry 2 rather than the optimized doublet geometry 1 although the geometry DSM has some bonds that partially look like the geometry 3. The quartet/sextet MECP (QSM) is obtained by optimization from QS2, which is the crossing point between the quartet and the sextet spin state at 9.4 kcal/mol. The energy is 8.4 kcal/mol. The Co-O1 and the Co-O3 bonds are longer than other cobalt-ligand bonds. The MECP QSM and the optimized quartet geometry 2 have similar axial distortion, due to the single electron on the eg-like orbitals. However, the other cobalt-ligand bond lengths of the geometry QSM are shorter than the optimized sextet geometry (3) and the same as the optimized quartet geometry (2). The O-C bond lengths are in a range from 1.275 to 1.292 Å. Finally we consider a one-step mechanism and a two-step mechanism of valence tautomerism as shown in Scheme 3. In the one-step mechanism, the electronic excitation from the doublet ground state to the excited sextet spin state occurs concomitant with two electron transfers. In the two-step mechanism, this path involves an intermediate complex in the quartet spin state. First, the electron transfer occurs from the catecholate ligand to the CoIII ion, resulting in the formation of

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SCHEME 3

the semiquinonate and the CoII ion. Second, one-electron excitation from t2g orbitals to eg orbitals occurs in the cobalt atom. As mentioned above, we found the three MECPs of DSM (8.8 kcal/mol), DQM (10.2 kcal/mol), and QSM (8.4 kcal/mol). Since DSM lies 2.0 kcal/mol below DQM, the one-step mechanism is energetically favored in the VT conversion. In the reverse VT conversion the two-step mechanism is comparable, due to small energy difference between QSM and DSM. The analysis of PESs and MECPs leads us to conclude that a onestep mechanism is more likely for valence tautomerism in both directions. However, we should note that the close proximity of the quartet states may result in strong coupling with the doublet and sextet states through spin-orbit coupling. Concluding remarks We have investigated the valence tautomerism of the [CoIIHS(sq)2(bpy)] complex using DFT calculations. We characterized the potential energy surfaces (PESs) and the minimum energy crossing points (MECPs) in the low-spin doublet state, the intermediate-spin quartet state, and the high-spin sextet state. The BP86, OPBE, BLYP, B3LYP, and B3LYP* methods were compared for the estimation of the energy gap between the lowspin doublet state and the high-spin sextet state. Consequently, the B3LYP*/6-311G** level of theory gave reasonable results fully consistent with experiment. The comparison of the DFT methods is implemented by using the [CoII-HS(3,5-dbsq)2(bpy)] complex, and the analyses of PESs and MECPs are done using the [CoII-HS(sq)2(bpy)] complex for simplicity and saving calculation costs. Detailed energy analysis of the crossing seams between the pairs of valence states gives a better understanding of the mechanism of valence tautomerism. The calculations show that the ground state is doublet spin state and that energies of the low-lying points are 4.4 kcal/mol in the sextet spin state (2) and 7.4 kcal/mol in the quartet spin state (3) relative to the optimized point of the doublet state (1). PESs were followed along minimum energy pathway between the optimal geometries of valence states. The coordinate of pathways represents molecular deformation from 1. In geometry 1, the energies of the doublet, quartet, and sextet spin states are 0.0, 23.9, and 34.7 kcal/mol, respectively. Similarly in geometry 2, the energies of the doublet, quartet, and sextet spin states are 21.7, 7.4, and 17.5 kcal/mol, and in geometry 3, the energies of the doublet, quartet, and sextet spin states are 31.7, 17.2, and 4.4 kcal/mol, respectively. We determined the doublet/sextet MECP of 8.8 kcal/mol. The doublet/quartet MECP and the quartet/sextet

MECP were calculated to be 10.2 and 8.4 kcal/mol, respectively. Considering calculated energies in MECPs, the one-step mechanism for valence tautomerism in the [CoII-HS(sq)2(bpy)] complex is energetically favored, which is fully consistent with experimental observation. Such an analysis using only normal mode scans would be difficult in a system where the relationship of different valence states can be described only with complex combination of modes. In the VT systems, both the symmetric and asymmetric distortions of the coordination environment around the CoII/III center and the deformation of the redox-active dioxoloene ligands are pronounced. Our approach of using MECPs can be a useful tool for analysis in systems where several complex deformations play an important role. Acknowledgment. We thank Grants-in-Aid for Scientific Research (Nos. 18GS0207, 21750063, and 22245028) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), the Kyushu University Global COE Project, the Nanotechnology Support Project, the MEXT Project of Integrated Research on Chemical Synthesis, and CREST of the Japan Science and Technology Cooperation. Supporting Information Available: Complete ref 27 and atomic Cartesian coordinates for all the structures optimized in the present study. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Gu¨tlich, P.; Garcia, Y.; Woike, T. Coord. Chem. ReV. 2001, 219, 839. (b) Kahn, O.; Launay, J. P. Chemtronics 1988, 3, 140. (c) Hauser, A. Coord. Chem. ReV. 1991, 111, 275. (2) (a) Pierpont, C. G.; Buchanan, R. M. Coord. Chem. ReV. 1981, 38, 45. (b) Evangelio, E.; Molina, D. R. Eur. J. Inorg. 2005, 2005, 2957. (c) Sato, O.; Cui, A.; Matsuda, R.; Tao, J.; Hayami, S. Acc. Chem. Res. 2007, 40, 361. (d) Evangelio, E.; Molina, D. R. C. R. Chim. 2008, 11, 1137. (e) Wang, M.-S.; Xu, Gang.; Zhang, Z.-J.; Guo, G.-C. Chem. Commun. 2010, 46, 361. (3) Hendrickson, D. N.; Pierpont, C. G. Top. Curr. Chem. 2004, 234, 63. (4) Sato, O.; Tao, J.; Zhang, Y.-Z. Angew. Chem., Int. Ed. 2007, 46, 2152. (5) (a) Miller, J. S. AdV. Mater. 1994, 6, 217. (b) Entley, W. R.; Girolami, G. S. Science 1995, 268, 397. (c) Ferlay, S.; Mallah, T.; Ouahes, R.; Veillet, P.; Verdaguer, M. Nature 1995, 378, 701. (d) Mallah, T.; Thiebaut, S.; Verdaguer, M.; Veillet, P. Science 1993, 262, 1554. (e) Sato, O.; Iyoda, T.; Fujishima, A.; Hashimoto, K. Science 1996, 271, 49. (6) (a) Kaim, W.; Rall, J. Angew. Chem., Int. Ed. 1996, 35, 43. (b) Dooley, D. M.; McGuirl, M. A.; Brown, D. E.; Turowski, P. N.; McIntire, W. S.; Knowles, P. F. Nature 1991, 349, 262. (c) Rall, J.; Wanner, M.; Albrecht, M.; Hornung, F. M.; Kaim, W. Chem.sEur. J. 1999, 5 (10), 2802.

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