Systematic Approach To Design Organic Magnetic Molecules

Jun 4, 2012 - rule. 1. INTRODUCTION. Organic high-spin molecules1 have been extensively ..... coupler due to an inducement of almost planar geometry f...
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Systematic Approach To Design Organic Magnetic Molecules: Strongly Coupled Diradicals with Ethylene Coupler Kyoung Chul Ko,† Daeheum Cho,† and Jin Yong Lee*,†,‡ †

Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea Supercomputing Center, Korea Institute of Science and Technology Information, Yuseong, Daejeon 305-806, Korea

‡

S Supporting Information *

ABSTRACT: The intramolecular magnetic coupling constant (J) values of diradical systems linked with two monoradicals through a coupler (para-substituted phenyl acetylene (Model I), meta-substituted phenyl acetylene (Model II), ethylene (Model III)) were investigated by unrestricted density functional theory calculations. We divided eight monoradicals into α-group and β-group according to Mulliken spin density values of the connected atoms. The overall trends in the strength of magnetic interactions of diradicals were found to be identical in three different model systems. The diradicals with para-substituted phenyl acetylene coupler resulted in almost twice stronger intramolecular magnetic coupling interactions of the corresponding diradicals as compared to the meta-substituted one with opposite magnetism. NNEthylene-PO (nitronyl nitroxide radical coupled to phenoxyl radical via ethylene coupler) was calculated to have the strongest magnetic coupling constant with ferromagnetism, and to be even stronger (more than twice) than NN-ethylene-NN (nitronyl nitroxide diradical with ethylene coupler), which was reported to have strong antiferromagnetic interactions in a previous experiment. It was found that the spin density values of the connected atoms are closely related to the determination of magnetic interactions and J values. The spin states of the ground state in diradical systems were explained by means of the spin alternation rule. investigated theoretically and experimentally.12,13 Most of these studies focused on finding the diradical molecules that result in large intramolecular magnetic interactions and that are synthetically affordable. In diradical systems, it was well-known that the magnetic interactions between two radical sites can be influenced by bond distances and dihedral angles between radicals and coupler. For conjugated system, magnetic interactions generally decrease as the bond distance or spacer length increases.12,14 For example, in ferromagnetic coupling systems, the geometrical distortion induced by dihedral angles was reported to reduce J values.12,15 Moreover, a spin crossover occurs from triplet to singlet upon torsion; that is, the spin state of the ground state was changed. For antiferromagnetic coupling cases, the changes of magnetic coupling constants show more complicated behavior depending on the electronic structure in the course of twisting between either spin source, as shown in a previous theoretical study.15 A number of diradical molecules were comprehensively studied in density functional theory (DFT) framework with the consideration of length of coupler

1. INTRODUCTION Organic high-spin molecules1 have been extensively studied due to their potential applications using their magnetic property,2 superconductivity,3 spintronic property,4 and photomagnetic behavior5 and so on. Generally, in the solid state, the overall magnetic properties of molecular-based materials can be controlled by intramolecular as well as intermolecular magnetic interactions depending on the structures and features of molecular crystal.6 Recently, quantum chemical methods successfully described the magnetic properties of molecularbased magnetic materials using state-of-the-art theoretical calculations.7 Those methods used the First-Principles Bottom-Up procedure,8 which starts from the evaluation of radical−radical pair interactions to predict the macroscopic magnetic properties. Many theoretical studies predicted and reproduced the available experimental data in a wide variety of molecular-based magnets.9 In this context, for diradical-based magnets, estimating the intramolecular magnetic interactions is a priority task for designing and synthesizing a potential magnetic material that retains an appropriate spin−spin interaction.10 A variety of organic stable neutral radicals have been used as spin sources and building blocks to generate magnetic interactions (J) in diradical systems.11 Also, diverse couplers that link the two radicals ferromagnetically (or antiferromagnetically) were © 2012 American Chemical Society

Received: November 22, 2011 Revised: May 26, 2012 Published: June 4, 2012 6837

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However, those approaches also have constraint to correlation corrections for large molecules and require a heavy computational cost. Thus, in this study, we used the broken symmetry (BS) formalism proposed by Noodleman to describe the singlet diradical as a compromise method.17 Basically, the BS solution is not the pure eigenstate of the singlet diradical, but the mixed state of singlet and triplet spin states. To evaluate the reliable magnetic exchange coupling constant J, the energy value should be refined by spin projection method to eliminate the spin contamination. The J value can be obtained by diverse spinprojected methods depending on the extent of overlap between magnetically active orbitals.18 Among them, the most appropriate and popular one for evaluating the magnetic coupling constants is the following formalism, which was proposed by Yamaguchi and co-workers.19 The coupling constant J is given by

and dihedral angle effect between radicals and couplers by Ali and Datta.14 Recently, we introduced a way to standardize the strength of magnetic coupling for any spin source based on Models I and II as depicted in Scheme 1.16 As seen in Scheme 1, Models I and Scheme 1. Model Systems Used for Standardization (I,II) and Confirmation (III) of the Strength of the Intramolecular Magnetic Interactions of the Neutral Radicals

J=

⟨S2⟩T − ⟨S2⟩BS

(3)

where EBS/ET and ⟨S2̂ ⟩BS/⟨S2⟩T are the energy and average spin square values of the BS/triplet state, respectively. To evaluate the intramolecular magnetic interactions of the series of radical, we calculated the magnetic exchange coupling constants by using the DFT method. All of the calculations were performed using a suite of Gaussian 03 programs.20 Geometry optimizations were carried out with unrestricted spin polarized density functional theory, UB3LYP/6-311++G(d,p) level. In our previous study, it was found that the basis set dependence of J values is not critical to the trend of the magnetic interactions.16 Generally, the results calculated by adding more polarization and diffuse functions may give more accurate values. Thus, we choose an adequately large basis set (6-311++G(d,p)) considering our computational resources and time. First, the triplet diradical systems were optimized. Next, the BS state diradical systems were optimized on the basis of those geometries. In BS state calculations, to generate the appropriate BS wave functions, we used both “stable=opt” and “guess=mix” keywords. A command “stable=opt” allows one to reoptimize the wave function to the lowest energy solution of the SCF equations until any instability was not found. 21 The “guess=mix” keyword allows the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) to be mixed, and this removes the α,β spatial symmetries and generates a new initial guess.20 By using this symmetry broken initial guess, we obtained the BS solutions. All of the molecules of BS states and triplet states have been fully optimized. We then evaluated the intramolecular magnetic coupling constants J values by using the obtained energy values. Subsequently, the frequency calculations of triplet and BS states have been performed to confirm the minima on the potential energy surfaces and to make a correction for the zero-point vibrational energies. To classify the radical moieties, we also carried out the calculations for the eight monoradicals.

II have the advantages of almost planar geometries (dihedral angles of θ1 and θ2 ≈ 0°) and nearly equivalent coupler lengths. In both models, we used the oxoverdazyl (o-VER(C)) radical as a stationary reference radical, which cannot induce the repulsion with hydrogen atoms in benzene ring. Also, the ethynyl group as a coupler was added to remove the steric repulsion between the benzene and diverse radicals so as not to induce the torsion angles. These models exclude the influence of the coupler length and dihedral angle on the intrinsic magnetic coupling constant and were successfully applied to standardize the strength of the intramolecular magnetic interactions.16 Herein, we further developed this strategy as a quantitative approach to make a trend of strength of intramolecular magnetic interactions for diverse radicals. Moreover, we intended to design strong ferromagnetic diradical molecules based on systematic study and classification of the radical moieties regarding the intrinsic magnetic interactions.

2. COMPUTATIONAL DETAILS If there are two magnetic sites 1 and 2 in a system, the magnetic exchange interactions can be expressed by phenomenological Heisenberg spin Hamiltonian: Ĥ = −2JS1̂ S2̂ (1) where Ŝ1 and S2̂ are the respective spin angular momentum operators and J is the magnetic exchange coupling constant. The constant of J indicates the magnitude and type of interaction. The positive and negative J values represent the ferromagnetic and antiferromagnetic interactions between the spin moments, respectively. For a diradical system, the electronic states of the singlet and triplet would be eigenstates of the Heisenberg Hamiltonian. Also, it is possible to demonstrate that J values of eq 1 can be computed as E(S = 1) − E(S = 0) = −2J

(E BS − E T)

(2)

where E(S = 0) and E(S = 1) are the energies of the singlet and triplet states of a magnetic molecule, respectively. Despite using the unrestricted formalism based on a single determinant wave function, we cannot truly describe the pure singlet state of diradicals. This introduces spin contamination in such calculations. Thus, multiconfigurational methods have been implied to obtain the proper energy of singlet diradicals.

3. RESULTS AND DISCUSSION Figure 1 shows the selected radical systems investigated in this study. In Figure 1, the atoms marked by the open triangle were connected to the coupler as shown in Scheme 1 and were named as “connected atoms”. The nitroxide (NO), phenoxyl 6838

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have positive (α) spin density, and they are classified as αgroup. On the other hand, NN, o-VER(C), DTDA, and IN have negative (β) spin density at the connected atoms and are classified as β-group. The largest positive spin density locates at a radical dot of molecules, which was marked in Figure 1 for most of the monoradicals except PO. Those eight neutral radicals (NO, PO, o-VER(N), IA, NN, o-VER(C), DTDA, and IN) were connected to the coupler in three models (Scheme 1). Phenyl acetylene was used as a coupler for Model I and Model II, and ethylene as a coupler for Model III. o-VER(C) was as a reference radical connected to one end of the coupler for Model I and Model II, and NN as a reference radical for Model III. As mentioned above, the optimized structures of Models I and II have almost planar geometries with small dihedral angles (0° ≤ θ1 ≤ 4.6°, 0° ≤ θ2 ≤ 5.5°; see the Supporting Information for details, Table S1). The calculated magnetic coupling constants of those model systems are listed in Table 1 (see also Table S3). It was found

Figure 1. Classification of the selected eight radicals into α-group and β-group.

Table 1. Calculated Magnetic Coupling Constants for Models I−III and the Mulliken Atomic Spin Density Values of the Connected Atom of Monoradicals Using UB3LYP/6311++G(d,p)

(PO), oxoverdazyl (o-VER), nitronyl nitroxide (NN), dithiadiazolyl (DTDA), and imino nitroxide (IN) are wellknown neutral radicals due to their remarkable stabilities. They have been commonly used as a building block to generate ferromagnetic and antiferromagnetic couplings in magnetic materials.22 The oxoverdazyl radicals denoted as o-VER(N) and o-VER(C) are different in the connectivity; the carbon atom/nitrogen atom is connected to another radical via coupler.12a Indolinic aminoxyl (IA) was found in a previous organic synthesis study by chance.23 It must be stressed that IA may not have enough stability as compared to other stable neutral radicals. Figure 2 shows the Mulliken atomic spin densities. Depending on the spin of the connected atoms, we classified the radicals into two groups: α-group and β-group. If the connected atom of a radical has α-spin (positive spin density), it is classified as α-group; otherwise, it is β-group as shown in Figure 2. Filled and empty circles denote the positive (α) and negative (β) spin density, respectively (see Figures S1, S2 for values). The connected atoms of NO, PO, o-VER(N), and IA

neutral radical

J value of Model I (cm−1)

J value of Model II (cm−1)

J value of Model III (cm−1)

Mulliken atomic spin density of the connected atom

NO PO o-VER(N) IA NN o-VER(C) DTDA IN

−116.4 −102.8 −55.2 −36.1 40.4 20.2 18.7 14.8

232.8 219.9 114.1 71.7 −83.2 −40.7 −38.1 −30.0

1694.6 1880.1 1005.4 598.4 −842.1 −391.8 −365.9 −324.1

0.459 0.396 0.176 0.152 −0.245 −0.173 −0.148 −0.136

that α-group and β-group radicals clearly show the opposite sign of magnetic coupling constants for each diradical system. For radicals belonging to α-group, the calculated magnetic coupling constants of meta-substituted compounds are negative

Figure 2. Mulliken atomic spin density distributions of monoradicals. 6839

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Figure 3. Comparison of J values (cm−1) of Model I and Model II for α-group (a) and β-group (b) radicals.

opposite sign. The slopes of Figure 3a and b are −2.07 and −2.08, which means the magnitude of magnetic coupling strength of Model II is almost twice that of Model I. In other words, the magnetic coupling constant of the diradical systems at para-positions is almost twice that at meta-positions regardless of the type of radical groups, although the signs of J values are opposite. This finding demonstrates that the parasubstituted diradcal systems that use a phenyl acetylene coupler are better suited for inducing strong magnetic coupling interactions than are meta-substituted ones. In addition, we propose that both J values of Model I and Model II can be utilized as an index for the strength of magnetic interactions of different radicals due to their linear relationship. The overall trends in the strength of magnetic interactions of α-group and β-group were shown to be in the order of NO > PO > o-VER(N) > IA and NN > o-VER(C) > DTDA > IN, respectively. Considering the absolute J values for each of radical groups, we expect that NO, PO, o-VER(N), and NN can be used as a potential spin source that could generate strong intramolecular magnetic interactions in diradical systems. To the best of our knowledge, a linear relationship between the intramolecular magnetic interactions in two different coupler systems for diverse radicals was confirmed for the first time. Especially, dividing the radical groups into αand β-group was also newly attempted. We thought that a fundamental understanding about the strength of intrinsic magnetic interactions for each of radicals needed to be preceded for designing diradical molecules that carry a strong magnetic coupling constant. To confirm the above trends of intramolecular magnetic interactions for radical moiety of each groups, we investigated the magnetic exchange coupling constant of another model system (Model III). We also tried to explore the diradical molecules that could carry strong intrinsic magnetic interactions. Thus, in this system, we used NN as the stationary reference radical, which belongs to β-group and shows the strongest magnetic interactions in β-group, because it was known to be a stable radical and make a bond with other radicals via π-conjugation.11 The ethylene was adopted as a coupler due to an inducement of almost planar geometry for diradical systems with small dihedral angles. In particular, it is well-known that the ethylene coupler provides strong intramolecular magnetic interactions in diradical systems due to short coupler length.

causing antiferromagnetic coupling, while those of the parasubstituted ones are positive causing ferromagnetic coupling. Oppositely, for β-group radicals, the calculated magnetic coupling constants of meta-substituted compounds are positive, while those of para-substituted ones are negative. These results indicate that the geometrical topology (meta- and para-) of benzene coupler as well as the types of radical group (α- and βgroups) can determine the ferromagnetic or antiferromagnetic interactions for the diradical systems. Those changes of magnetic interaction imply that the above two factors (geometrical topology and the types of radical group) were strongly related to the alternating pattern of spin distribution, which can be helpful to determine a favorable type of magnetic coupling for diradical molecules. More details will be discussed later. Various experimental and theoretical results elucidated that meta- and para-substituted positions can decide the types of magnetic interactions in benzene-bridged diradical systems.12,13 For biradical systems that are composed of two identical radicals and a benzene coupler, meta-substituted compounds generally show the ferromagnetic coupling, whereas parasubstituted compounds show the antiferromagnetic coupling. In our results, considering o-VER(C) is a β-group radical, it can be concluded from the calculations that the diradicals, when βgroup radicals are coupled with each other via meta-substituted phenyl acetylene, generally generate ferromagnetism consistently with experiment. Regardless of the models (i.e., regardless of the couplers), the calculated magnetic coupling constants for the α-group show the opposite sign to those for the β-group. It is very interesting to note that the coupling types (ferromagnetic or antiferromagnetic) are determined not only by the types of coupler but by the types of radicals (α- or β-group). Also, α-group radicals generally show stronger magnetic interactions than do β-group radicals for three models as noted in Table 1. Furthermore, our systematic study gives more general tendency to determine the ferromagnetic or antiferromagnetic coupling depending on the types of coupler and spin sources. Figure 3 shows the relationship between the calculated J values of Model I and Model II for α- and β-group radicals. Very interestingly, there are almost linear relationships between the magnetic coupling constants of Models I and II for both radical groups. As seen Table 1 and Figure 1, α-group radicals result in negative J values in Model I, and positive J values in Model II and Model III, while β-group radicals result in the 6840

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Figure 4. Comparison of J values (cm−1) of Model II and Model III for α-group (a) and β-group (b) radicals.

obtained from broken symmetry approach with B3LYP functional for other diradical systems. This discrepancy between calculated results and experimental ones is perhaps not surprising, because DFT methods use the approximate exchange-correlation functional (including the B3LYP functional), instead of the exact exchange-correlation functional, to describe the magnetic states.27 Furthermore, the DFT calculations, which applied the approximate exchange-correlation potentials, inherently suffer from the self-interaction error.28 Recently, a variety of investigations have been performed to find a more accurate approximate exchangecorrelation functional for describing magnetic couplings in molecular systems, such as hybrid density functionals with the different amount of Hartree−Fock exchange,29 a new suite of hybrid meta GGA functionals,26b range-separated hybrid functionals,30 LDA+U functionals, GGA+U functionals,31 double-hybrid density functionals,32 and so on. Despite the above efforts, more investigation is still required to make a new functional standard. It seems hard to justify the accuracy of a functional due to limited experimental data in each study. In this context, instead of developing a new functional, we suggest a scaling factor as a practical tool to estimate the magnetic coupling constant by using B3LYP functional. For example, once the calculated J values of NN-ethylene-NN are scaled by a factor of 0.416 (=350/842.1), we expect that we could obtain the magnetic coupling constants that can be compared to experiment directly. Afterward, we tried to use this scaling factor to the J values of seven diverse organic biradical molecules, which contain the benzene, ethylene, pyridine, and thiophene as a coupler. Consequently, we found that the calculated J values scaled are in excellent agreement with experiment. To obtain more accurate J values, we tried to analyze the J values obtained from the zero-point corrected total energy (sum of electronic and zero-point vibrational energies) for each of the model systems (Table S5). Consequently, it was found that the J values and the trends of J values for each radical group are not significantly changed by zero-point vibrational energy correction. Thus, it is expected that the overestimation of calculated J values may not be caused by the zero-point vibrational energies, which may reflect the geometrical difference between BS state and triplet state. Moreover, our expectations about the trends of magnetic coupling interactions also might be not changed. Considering the experimental procedure, we obtained the J values by using the molecular

Analyzing the optimized structures of Model III, the two dihedral angles (θ1 and θ2) were very small ( PO > o-VER(N) > IA and NN > o-VER(C) > DTDA > IN. Also, it was demonstrated that the calculated J values of Models I and II have almost linear relationships, and those values could be used for an index parameter to estimate magnetic interactions. The magnetic exchange coupling constants of another diradical system (Model III) were also consistent with the other models, and hence confirm the trend. Thus, once the values are scaled with known experimental values, we could obtain a quantitative magnetic coupling constant for any diradical systems after careful calibration. NN-ethylene-PO was calculated to have the stronger magnetic coupling constant than any other diradical systems. In particular, the calculated magnetic interaction of NN-ethylene-PO was much stronger (more than twice) than that of NN-ethylene-NN, which was reported to have strong antiferromagnetic interactions in a previous experiment by Ziessel et al. Considering that our calculation also predicted NN-ethylene-NN to be antiferromagnetic, NN-ethylene-PO is expected to have very strong ferromagnetic interactions. It was found that the spin density values of the connected atoms are closely related to the determination of magnetic interactions and J values. The spin states of the ground state in diradical systems were explained by means of the spin alternation rule. Our results will be helpful in designing organic magnetic materials incorporated with diradical molecules.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Calculated Mulliken atomic spin density values of monoradicals, dihedral angles, intramolecular magnetic coupling constants, spin density distributions, zero-point vibrational energy corrections to the calculated J values, and the log files from all 48 calculations for Models I−III. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +82-31-299-4560. Fax: +82-31-290-7075. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the NRF Grant (no. 20070056343) funded by the Korean Government (MEST). We would like to acknowledge support from the KISTI supercomputing center through the strategic support program for supercomputing application research [no. KSC-2011-C2-54]. 6843

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