Reparametrization Approach of DFT Functionals Based on the

Article pubs.acs.org/JPCA

Reparametrization Approach of DFT Functionals Based on the Equilibrium Temperature of Spin-Crossover Compounds Ahmed Slimani,*,† Xuefang Yu,† Azusa Muraoka,‡ Kamel Boukheddaden,§ and Koichi Yamashita*,† †

Department of Chemical System Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan Department of Physics, Meiji University, 1-1-1 Higashi-Mita, Tama-Ku, Kawasaki-shi, Kanagawa 214-8571, Japan § Groupe d’Etude de la matière Condensée, CNRS-Université de Versailles 45, Avenue des Etats Unis, 78035 Versailles, Cedex, France ‡

ABSTRACT: The required approach to investigate the electronic properties of spin-crossover (SCO) compounds needs to be able to provide a reliable estimate of high-spin/low-spin (HS/LS) energy gaps while retaining an accurate and efficient computation of the ground-state energy. We propose a reparametrization approach of the density functional theory (DFT) functionals to adjust the exact exchange admixture that governs the HS/LS energy splitting. Through the investigation of the thermodynamic properties of two typical SCO compounds, we demonstrate that the computed equilibrium temperature depends linearly, like the HS/LS energy gap, on the coefficient of the exact exchange admixture. We show that by taking the experimental value of the equilibrium temperature of the studied SCO compound as a reference, different hybrid functionals converge to comparable and realistic HS/LS energy gaps as well as enthalpy and entropy differences that agree well with the prior experimental investigations. functionals to fit well the SCO compounds. We recall that the overwhelming majority of SCO compounds reported so far are based on Fe(II) complexes. Most of these SCO compounds are constituted by mononuclear species, among them the most extensively studied families with the general chemical formula Fe(L)2(NCS)2,20−29 where L stands for a ligand. For the purpose of this paper, we selected two representative SCO compounds termed as Fe(btr) 2 (NCS) 2 ·H 2 O and Fe(phen)2(NCS)2. In Fe(btr)2(NCS)2·H2O, btr means bistriazole with chemical formula C4N6H4 and NCS is the thiocyanate group. The corresponding molecular structure illustrated in Figure 1a shows an Fe atom bounded by btr ligands in the plane and NCS groups in the perpendicular direction. In Fe(phen)2(NCS)2, phen means 1.10-phenanthroline with chemical formula C12H8N2. The corresponding molecular structure is shown in Figure 1b and consists of an Fe atom surrounded by two phenanthroline groups and two thiocyanate groups. Indeed, these two systems are considered as archetypal SCO compounds because of their highly cooperative thermally induced spin transition. The Fe(btr)2(NCS)2 undergoes a sharp thermal spin transition from the HS state to the LS state at THS→LS ≈ 117 K and a reverse transition at TLS→HS ≈ 147 K,45 while Fe(phen)2(NCS)2 is well known by its abrupt spin transition centered at ∼176 K.30,31

1. INTRODUCTION The transition-metal molecular complexes, belonging to the d4−d7 electronic configuration, are known to exhibit a spin transition between the high-spin (HS) and low-spin (LS) states.1 Such a transition could be triggered by several parameters, such as temperature, pressure, light, magnetic field, and, as reported recently, an electric field.2−10 The bistable character of the spin-crossover (SCO) complexes depends on the intensity of the ligand field that splits the d orbitals into eg and t2g orbitals under octahedral symmetry. The LS state is characterized by a singlet multiplicity with a total spin quantum number S = 0, whereas the HS state has a quintet multiplicity with a total spin quantum number S = 2. Such molecular flexibility points to considerable capability and promising prospects for high technology applications such as high-density information storage, display devices, and microsensors. That is why the SCO compounds have and still stimulate much interest among scientists. Recently, the density functional theory (DFT) is introduced as a powerful tool for electronic structure investigation of SCO compounds.11−19 However, it is worth mentioning that with a much larger view covering all DFT investigations of the SCO compounds one can easily notice an important mismatch and divergence between their results. Such fact raises a question about the choice of the suitable DFT method to use. We should mention that several prior DFT studies of SCO compounds did not discuss the choice of the used functional, and they relied on anterior DFT investigations of different SCO compounds. As will be discussed further later, such a strategy is insufficient and could be misleading. We aim to overcome such a situation by establishing a new reparametrization approach of the DFT © XXXX American Chemical Society

Special Issue: International Conference on Theoretical and High Performance Computational Chemistry Symposium Received: February 25, 2014 Revised: July 31, 2014

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dx.doi.org/10.1021/jp501943h | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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Figure 1. Molecular structure of Fe(btr)2(NCS)2 (a) and Fe(phen)2(NCS)2 (b) SCO compounds.

The present paper is organized as follows. In Section 2, we present the computational details; in Section 3, we report on a comparative study between several DFT functionals, and we describe the new reparametrization approach; in Section 4, we discuss the derived results based on a comparison with the experimental ones. Section 5 is the conclusion.

2. COMPUTATIONAL DETAILS To state more sufficiently the proposed reparametrization approach, we used a large number of DFT methods that provide diversity and covering different flavors in our investigations such as the popular B3LYP,32,33 the hybrid BPW91,34,35 PBEh1PBE,36 the recent new hybrid CAMB3LYP,37 the nonempirical GGA MPW1PW91,38 the pure PBEPBE,39 BLYP,33,34 B97D,40,41 and the dispersion-corrected WB97XD42 functionals. These methods were combined with the 6-31G(d) basis set, and the calculations were performed using the Gaussian 09 package.43 Indeed, the geometry optimization was carried out according to the free-molecule approximation that neglects any possible intermolecular interactions with anions or solvent. The geometries of the LS and HS states were taken from the experimental X-ray data.44−47 Indeed, the geometries of the HS and LS states are not the same because of the antibonding character of the eg orbitals that makes the metal ligand distance larger in the HS state. The HS/LS energy gap, ΔE, was calculated after fully geometry optimization. The energy of the LS state (S = 0), ELS, was obtained from the restricted Kohn−Sham (KS) calculation, and the energy of the HS state (S = 2), EHS, was obtained from the unrestricted KS calculation.

Figure 2. Energy difference between HS and LS states of the Fe(btr)2(NCS)2 SCO single molecule determined using different DFT methods.

that several DFT methods fail in the prediction of the LS state as ground state and favor the HS state. This is particularly true for the Hartree−Fock method, reported here for comparison. The latter method considers only the correlation between electrons of the same spin (Fermi correlation) while neglecting the correlation between electrons of opposite spin (Coulomb correlation). Consequently, the four unpaired electrons of Fe(II) are strongly avoided, which stabilizes the HS state, while the three paired electrons in the LS state cannot be avoided, which leads to an important Coulomb repulsion.48 Compared with the Hartree−Fock method, the other functionals gave a better estimation of the HS/LS energy gap due to the consideration of both Fermi and Coulomb correlations. However, as can be noted in Figure 2, the combination of the latter correlations is not balanced enough to give a consistent description. Such fact emphasizes once more the need for establishing a reliable reparametrization approach of DFT functionals able to provide a valid and credible description of SCO compounds. To reach this goal, we propose to rely on the intrinsic properties of SCO compounds, such as the equilibrium temperature, Teq, which is easily estimated from traditional experiments as magnetic or optical measurements. Before further proceeding, it is worthwhile to stress the potential role of the equilibrium temperature as an appropriate reference to reparametrize the DFT functionals. For that, let us briefly recall a simple thermodynamic model restricted for isolated SCO molecules49 where the fraction of molecules in

3. RESULTS AND ANALYSIS As a first step toward developing the new reparametrization approach of the DFT functionals, reference points are needed to estimate the accuracy of the proposed approach. For that, HS/LS energy gaps of the Fe(btr)2(NCS)2 SCO single molecule are computed using the previously described DFT methods. The results are summarized in Figure 2 and point out the main problems associated with the DFT methods when applied on the SCO compounds and include the following: (i) negative gaps leading to wrong ground state and (ii) even though the gaps are positive such as in the case of the BLYP, PBEPBE, and BPW91 functionals, the corresponding values are meaningless because there is no way to identify a unique HS/ LS energy gap. We should mention that these findings are not surprising because it is consistent with the prior DFT investigations on SCO compounds. Indeed, it is well known B



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Figure 3. HS/LS energy gap (top) and the equilibrium temperature Teq (bottom) plotted as a function of the amount of Hartree−Fock exchange, c, of the B3LYP functional in the case of Fe(btr)2(NCS)2 (a,b) and Fe(phen)2(NCS)2 (c,d), respectively.

EVWN and ELYP are the correlation functionals, and a, b, and c c c are semiempirical parameters with the following default values a = 0.72, b = 0.81, and c = 0.2. In fact, the failure of the B3LYP functional in predicting the ground state of the SCO was previously reported by Reiher et al. in ref 19. In the last cited reference, authors conducted several extensive DFT study on SCO compounds and assigned the failure of the B3LYP functional to the inadequacy of the admixture exact exchange. On the basis of investigations of the energy differences of states of different multiplicity, Reiher et al. suggest the reparametrization of the B3LYP method so as to reduce the admixture exact exchange through the adjustment of the semiempirical parameter c, and, consequently, the value c = 0.15 has been recommended. Since then, the latter reparametrized B3LYP functional was widely and still employed for the DFT investigations of the SCO compounds. Such value of parameter c was also used in our calculation, namely, B3LYP*(c = 0.15) in Figure 2; however, as can be seen, despite the improvement with respect to the default B3LYP functional, this reparametrization turns out to be insufficient because the HS/LS energy splitting is still negative where ΔEB3LYP*(c=0.15) = −6.86 kJ/mol. Nevertheless, we should mention that the latter result is suggestive to a further reduction in the admixture exact exchange. That is why a systematic investigation of smaller values of the semiempirical parameter c was carried out and reported in Figure 3a, showing the HS/LS energy gap of the Fe(btr)2(NCS)2 as a function of c. Such reparametrization clearly improves our results because it led to a positive HS/LS energy splitting that is linearly dependent on the c parameter in good agreement with the previous reports. One can easily notice that to obtain a positive HS/LS energy splitting the value of the semiempirical parameter c should be comprised in the interval [0, 0.14]. Despite these findings, the problem has not yet been solved because there is no criteria of selection of the appropriate value of the parameter c. This observation brings us

the HS state, nHS, is written as a function of Gibbs free energy and temperature: nHS = [1 + e(ΔG / kBT )]−1

(1)

T is the temperature, kB is the Boltzmann’s constant, and ΔG is the Gibbs free-energy difference between the HS and LS states and should vanish at the equilibrium temperature corresponding to equivalent fractions of HS and LS states (nHS = nLS). ΔG can be written as ΔG = ΔH − TΔS, where ΔH and ΔS are the enthalpy and the entropy differences, respectively. Thus, by setting ΔG = 0 the equilibrium temperature, Teq, can be expressed as

Teq =

ΔHeq ΔSeq

(2)

Indeed, the latter equation (eq 2) is a key step toward achieving our reparametrization approach of the DFT functionals, and that will be detailed in the following. a. Reparametrization of the B3LYP Functional. It can be seen from Figure 2 that the default B3LYP method fails in predicting the LS state as the ground state of the Fe(btr)2(NCS)2 SCO single molecule, where ΔEB3LYP = −35.76 kJ/mol. It should be noted that for the SCO compounds the latter functional is the most commonly used thanks to its semiempirical approach dependent on one or more adjustable parameters that could be tuned to fit the experimental results. Indeed, the exchange correlation energy of the B3LYP functional is defined as ExcB3LYP = ExLSDA + aExB88 + bEcLYP + (1 − b)EcVWN + c[Eex.ex − ExLSDA ]

ELSDA x

(1)

EB88 x

where denotes the Slater exchange, is the Becke’s gradient correction to the local spin density approximation (LSDA) for the exchange, Eex.ex is the exact exchange energy, C



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Figure 4. HS/LS energy gap (top) and the equilibrium temperature Teq (bottom) plotted as a function of the amount of Hartree−Fock exchange, c0, of the PBE0 functional in the case of Fe(btr)2(NCS)2 (a,b) and Fe(phen)2(NCS)2 (c,d), respectively.

the latter compound is well known as Teq = 176 K. By taking this value of Teq as a reference, we found that the appropriate coefficient of admixture exact exchange corresponds to c = 0.153, leading to ΔEB3LYP*(c=0.153) = 11.13 kJ/mol as energy gap. In this stage, we should mention that the HS/LS energy gaps of both SCO single molecules derived from the proposed reparametrization approach here are quite plausible and reasonable because they agree well with prior investigations and that will be discussed further in the next section. b. Reparametrization of the PBE0 Functional. For the sake of comparison and potential expanse of our reparametrization approach to the others DFT methods, additional calculations were performed using the PBE0 functional50 obtained combining the so-called PBE-generalized gradient functional with a predefined amount of exact exchange. Indeed, in the default description of the PBE0 functional, 25% of the PBE exchange energy was replaced by the Hartree−Fock exchange appointed as c0 in the corresponding energy:

to the main aim of the present paper. We propose to take the equilibrium temperature of the considered SCO compound as a reference to match the B3LYP functional to the studied SCO compound. The proposed strategy is simple and consists of the following steps: (i) optimization of the HS and LS geometries for different exact exchange admixture, (ii) starting from the optimized geometry, performance of thermochemistry calculations at the experimental value of equilibrium temperature of considered SCO compound, (iii) using eq 2, calculation of the theoretical value of Teq where ΔHeq and ΔSeq will be derived from the previous step, and, finally, (iv) identification of the semiempirical parameter c that leads to the experimental value of Teq. In doing so, the equilibrium temperature of Fe(btr)2(NCS)2 was calculated and reported in Figure 3b as a function of the parameter c. The latter Figure points out a remarkable feature; that is, Teq also depends linearly on the coefficient of exact exchange admixture but with a different slope when compared with the linear trend of the HS/LS energy gap (∼10 order of magnitude). The experimental equilibrium temperature of Fe(btr)2(NCS)2 SCO compound could be estimated from magnetic measurement as the arithmetic mean value of THS→LS and TLS→HS: Teq = ((TLS→HS + THS→LS)/2) = 132 K. Accordingly, one can easily deduce from Figure 3b that to obtain this experimental value of Teq the parameter c should be 0.115, which is a satisfactory value because it belongs to the interval determined from Figure 3a, leading to an LS state as ground state, and, most importantly, the latter value of c leads to reasonable HS/LS energy gap estimated as ΔEB3LYP*(c=0.115) = 16.33 kJ/mol. It is interesting at this juncture to also investigate the HS/LS energy gap of the Fe(phen)2(NCS)2 SCO single molecule. Thus, by following the same procedure previously described, we reparametrized the B3LYP, and results are summarized in Figure 3c,d. The equilibrium temperature of

ExcPBE0 = ExcPBE + c0[ExHF − ExPBE]

(3)

To validate the proposed reparametrization approach based on the equilibrium temperature, we adjusted the parameter c0 in the PBE0 functional for the both compounds Fe(btr)2(NCS)2 (Figure 4a,b) and Fe(phen)2(NCS)2 (Figure 4 c,d). It can be seen from Figure 4a,c that the default PBE0 functional with 25% of Hartree−Fock exchange is not satisfactory for both SCO compounds and it needs to be reparametrized. Indeed, we can notice from Figure 4b−d that to obtain the experimental values of the equilibrium temperature, reductions in the amount of Hartree−Fock exchange are also needed for the PBE0 functional. Thus, using the same reasoning as in the case of the B3LYP functional, we found that the appropriate coefficients of Hartree−Fock exchange and the corresponding D



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projections on the HS/LS energy gap are c0 = 0.095, ΔEPBE0(c=0.095) = 16.09 kJ/mol, and c0 = 0.129, ΔEPBE0(c=0.129) = 17.37 kJ/mol for Fe(btr)2(NCS)2 and Fe(phen)2(NCS)2 SCO single molecules, respectively. Such values are much better than the default PBE0 results and are in good agreement with the reparametrized B3LYP method. The latter reparametrization points out another interesting feature, that is, the HS/ LS energy gap, and the equilibrium temperature responds linearly to the change in the amount of the Hartree−Fock exchange, c0. We should mention that such behavior is consistent with the observations with the B3LYP functional, and it is considered to be relatively new in the case of the PBE0, although, as previously stated, the same trend was observed with the B3LYP method.

Table 2. Computed Thermodynamic Properties Using the Reparametrized DFT Functionals Fe(btr)2(NCS)2

ΔHeq (kJ/mol) ΔSeq (J/mol/K)

Table 1. Summary and Comparison of Results Derived from the Reparametrized DFT Functionals, DFT+U Method, and Experiment Fe(btr)2(NCS)2

B3LYP* PBE0* DFT+U52 experiment51

Fe(phen)2(NCS)2

HS/LS energy splitting (kJ/mol)

exact exchange admixture

HS/LS energy splitting (kJ/mol)

0.115 0.095

16.33 16.09 16.5

0.153 0.129

11.13 17.37 13.6 12.1

PBE0* c0 = 0.095

B3LYP* c = 0.153

PBE0* c0 = 0.129

10.54 79.83

9.85 74.68

9.81 69.75

9.77 74.06

= 8.03 kJ/mol (ΔHheating = 8.94 kJ/mol) and entropy difference ΔScooling = 68.0 J/mol/K (ΔSheating = 58.7 J/mol/K),53 while for Fe(phen)2(NCS)2, the corresponding enthalpy and entropy differences are ΔH = 8.60 kJ/mol and ΔS = 48.78 J/mol/K. The difference observed between the computed and experimental values of entropy could be attributed to the approximation of free molecule used in our calculation that allows free motions to the single molecule unlike the solid state, which is constrained. Throughout this work, we have assumed that the SCO single molecules have the same equilibrium temperature as the bulky systems. Of course, such assumption neglects the effects of the intermolecular interactions that sensitively influence the thermal transition of the SCO compounds. Indeed, with respect to the latter point, we admit that it is of particular relevance to apply such reparametrization approach on the DFT+U method because it describes well bulky systems from where the equilibrium temperature is derived. This issue will be considered in coming work. Besides, it is easily seen that the proposed reparametrization approach is simple to implement in hybrid DFT functionals unlike pure ones, where further investigations will be needed to reach this goal. We have checked the effect of the basis set on the estimation of the HS/ LS energy gap of the Fe(btr)2(NCS)2 SCO single molecule, where the LANL2DZ basis set was used with B3LYP functional instead of 6-31G(d) basis set. We noted that the former basis set did not significantly change the HS/LS energy gap or the semiempirical parameter c in the exchange correlation energy of the B3LYP method, where the corresponding value was 18.45 kJ/mol for c ≈ 0.102. We should mention that the method used here for the estimation of the equilibrium temperature fits well less cooperative SCO systems where the thermal spin transition occurs without hysteresis and gives a direct access to the equilibrium temperature. With regard to the latter point, the abrupt thermal spin transition of Fe(phen)2(NCS)2 is of special interest in our analysis because it disambiguates the definition of the equilibrium temperature of cooperative SCO systems. In fact, we admit that for Fe(btr)2(NCS)2 the definition of Teq as an arithmetic mean value was approximated and can be slightly shifted depending on the experimental conditions. Indeed, the crystalline quality of the SCO compounds influences their thermal behavior, and there is experimental evidence that the equilibrium temperatures of SCO powder and single crystal are slightly different. Additionally, we should mention that the size and the shape of the hysteresis loop are sensitive to the thermal kinetic, and a thermal hysteresis loop may be purely kinetic if the interaction parameter is below some threshold value, and the temperature sweep rate is appreciably high. Another point of interest that deserves comment is related to the nature of the thermal spin transition. Indeed, some SCO compounds undergo an incomplete transition to the LS or HS state. Such situation would be challenging to the proposed reparametrization approach if the incomplete transition is not well identified

4. DISCUSSION To shed light on the consistency of the reparametrization approach based on the equilibrium temperature of the SCO compounds, we summarize in Table 1 the derived values of

exact exchange admixture

Fe(phen)2(NCS)2

B3LYP* c = 0.115

HS/LS energy splitting obtained from the proposed approach here. Additionally, for the sake of comparison, we also incorporated anterior HS/LS energy gaps determined experimentally via calorimetric analysis51 and theoretically by DFT +U method taking explicitly into account the periodicity of the crystal.52 It worth mentioning that in the DFT+U analysis previously cited the value of U was chosen so as to reproduce the experimental HS/LS energy gap determined by the calorimetric investigations. In view of the previous results, the proposed reparametrization approach based on the equilibrium temperature of the SCO compounds seems very satisfactory because it reduces the dispersion in results between the different methods. Indeed, one can easily notice that the derived HS/LS energy splitting converges to comparable values that agree well with the prior theoretical and experimental investigations on solid-state systems. This is an interesting point because the HS/LS energy gap of a SCO single molecule remains so far unexplored and the derived values from the reparametrized functionals arise as plausible first approximations. In this stage, we should mention that the equilibrium thermodynamic properties such as the enthalpy and the entropy leading to the calculation of the equilibrium temperature are not discussed in detail in the previously described study. Therefore, we report the latter parameters in Table 2. As can be seen, the different DFT functionals provide consistent values, and, most importantly, they are in good agreement with the experimental investigations on SCO powder. Indeed, for Fe(btr)2(NCS)2 SCO compound, the recent calorimetric measurements in cooling (heating) mode lead to following enthalpy difference ΔHcooling E



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strated that the computed equilibrium temperature of the SCO compounds is linearly dependent on the exact exchange admixture as the HS/LS energy gap. The central idea behind the proposed reparametrization approach was to use the experimental equilibrium temperature of the studied SCO system as a reference to identify the appropriate amount of exact exchange admixture. On the basis of such strategy, significant and clear improvements were obtained, and our main results include the following: (i) the reparametrized DFT functionals succeed in their description of the ground state of the considered SCO systems, (ii) different DFT methods converge to comparable and realistic HS/LS energy gaps that agree well with the prior experimental study, and (iii) the derived HS/LS energy gap and the thermodynamic properties seem to be a first good approximation in the case of the SCO single molecule. We believe that the proposed reparametrization approach of the DFT functionals based on the equilibrium temperature of SCO compounds is simple, but it will be very helpful for future DFT investigations because it allows adapting the considered DFT functional to the studied SCO compound.

as whether it occurs in the molecule itself or is a mixture of fully HS and LS molecules. For the sake of completeness of the previous study, the configuration coordinate diagram of Fe(btr)2(NCS)2 that depicts the total energy as a function of the iron-ligand distance, rFe−L, was also calculated using the reparametrized B3LYP*(c = 0.115) functional. (See Figure 5.) The diagram

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Figure 5. Configuration coordinate diagram of Fe(btr)2(NCS)2 computed with B3LYP* (c = 0.115) within the 6-31G(d) basis set. The zero of energy is taken as the energy minima of the LS state.

Corresponding Authors

*A.S.: E-mail: [email protected]. *K.Y.: E-mail: [email protected]. Tel: 03-58417286.

clearly shows that the ground state is the LS with an energy gap ΔEB3LYP *(c=0.115), as expected, and it also reveals that a transition el from the LS state to the HS state may occur by rising the iron− ligand distance at rFe−L ≈ 2 Å. It is instructive at this point to examine the computed potential energy curves of the HS and LS states. Indeed, in a single configuration coordinate diagram in which we neglect the higher-order spin orbit coupling and assume the harmonic limit, the respective potential energy ULS and UHS of the LS and HS states can be written as U LS =

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by a grant from JSPS KAKENHI (no. 21245004) and from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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1 LS 1 LS 2 HS HS 2 K (rFe − L − rFe = K HS(rFe − L − rFe − L) and U − L) + ΔE 2 2

(4)

REFERENCES

(1) Gütlich, P.; Goodwin, H. A. Spin Crossover in Transition Metal Compounds I-III. In Topics in Current Chemistry; Springer: Berlin, 2004. (2) Gütlich, P. Spin Crossover in Iron(II) Complexes. Struct. Bonding (Berlin, Ger.) 1981, 44, 83−195. (3) Gütlich, P.; Hauser, A.; Spiering, H. Thermal and Optical Switching of Iron (II) Complexes. Angew. Chem., Int. Ed. Engl. 1994, 33, 2024−2054. (4) König, E. Nature and Dynamics of the Spin-State Interconversion in Metal Complexes. Struct. Bonding (Berlin, Ger.) 1991, 76, 51−152. (5) Kahn, O.; Martinez, C. J. Spin-Transition Polymers: From Molecular Materials Toward Memory Devices. Science 1998, 279, 44− 48. (6) Bousseksou, A.; Boukheddaden, K.; Goiran, M.; Conséjo, C.; Boillot, M. L.; Tuchagues, J. P. Dynamic Response of the SpinCrossover Solid Co(H2(fsa)2en)(py)2 to a Pulsed Magnetic Field. Phys. Rev. B 2002, 65, 172412. (7) Kosaka, W.; Nomura, K.; Hashimoto, K.; Ohkoshi, S. Observation of an Fe(II) Spin-Crossover in a Cesium Iron Hexacyanochromate. J. Am. Chem. Soc. 2005, 127, 8590−8591. (8) Papanikolaou, D.; Kosaka, W.; Margadonna, S.; Kagi, H.; Ohkoshi, S.; Prassides, K. Piezomagnetic Behavior of the Spin Crossover Prussian Blue Analogue CsFe[Cr(CN)6]. J. Phys. Chem. C 2007, 111, 8086−8091. (9) Prins, F.; Monrabal-Capilla, M.; Osorio, E. A.; Coronado, E.; van der Zant, H. S. J. Room-Temperature Electrical Addressing of a Bistable Spin-Crossover Molecular System. Adv. Mater. 2011, 23, 1545−1549.

where the elastic constants in the LS and HS states are defined, respectively, as KLS = MwLS2 and KHS = MwHS2, where M is the ionic mass, wLS and wHS are the characteristic vibrational frequencies for LS and HS states, respectively, and ΔE is the HS/LS energy gap. Both configuration coordinate diagrams were fitted using the equations in 4 and lead to the following frequencies, wLS = 94.93 cm−1 for the LS state and wHS = 74.11 cm−1 for the HS state. From such frequencies, it is easily seen that the assumption of a soft HS state with lower vibrational frequency than the LS state is verified. In addition, the ratio (wLS/wHS) ≈ 1.3 is in good agreement with the experimental ratios of LS and HS Debye temperatures.

5. CONCLUSIONS In the present study, we accentuated the need to a new reparametrization approach of the DFT functionals to improve their description of the SCO compounds as well as to provide a consistent estimation of the HS/LS energy gap. Such aspects are fundamental for accurate ab initio investigations. Thus, we proposed a new reparametrization approach, which involves the hybrid exchange approximation embodied in the B3LYP and PBE0 functionals based on the equilibrium temperature of the SCO systems. In doing so, we investigated the thermodynamic properties of two archetype Fe(II) SCO compounds for a different amount of exact exchange admixture. We demonF



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Reparametrization Approach of DFT Functionals Based on the

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