Redox-Modulated Magnetic Transformations between Ferro- and

Nov 30, 2015 - In particular, the redox-induced magnetic reversal is easy to accomplish and exhibits promising application in the field of magnetic ma...
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Redox-Modulated Magnetic Transformations between Ferro- and Antiferromagnetism in Organic Systems: Rational Design of Magnetic Organic Molecular Switches Fengying Zhang, Xinyu Song,* and Yuxiang Bu School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, People’s Republic of China S Supporting Information *

ABSTRACT: Organic molecules with switchable magnetic properties have extensively technological applications due to the fact that magnetic conversion can be realized through diverse methods. In particular, the redox-induced magnetic reversal is easy to accomplish and exhibits promising application in the field of magnetic materials, and thus it is an imperative task to find magnetism-switchable systems. Herein, we computationally design two couples of nitroxy−pyrazinyl−nitroxy diradicals in which two nitroxy radical groups are connected to a redox-active pyrazinyl coupler in the para or meta modes. We find that the magnetic conversion can occur from ferromagnetic to antiferromagnetic exchange coupling or vice versa by means of the redox method in these designed magnetic organic molecules, and their magnetic exchange coupling constants are considerably large no matter for ferromagnetic or antiferromagnetic couplings, as evidenced at both the B3LYP and M06-2X levels of theory. Analyses indicate that redox-induced structural change of the coupler leads to conversion of its aromaticity and considerable spin delocalization from the π-conjugated structure and spin polarization from non-Kekule structure, which thus determine the spin coupling between two spin centers in the magnetic molecules. In addition, the spin alternation rule, singly occupied molecular orbital (SOMO) effect, and SOMO−SOMO energy splitting of triplet state are utilized to analyze the diradical characters of the molecules, suggesting effective tools for predicting molecular ground states (ferromagnetic, antiferromagnetic, or nonmagnetic). This work provides helpful information for the rational design of promising organic magnetic switches.

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INTRODUCTION Over the past two decades, the research of organic magnetic materials not only has generated a tremendous interest of the investigators but also increasingly becomes a focus of molecular science.1−5 Organic molecules with switchable spin states or magnetic properties have a wide range of applications in organic spintronics, molecular electronics, data storage devices, and so on, attributing to the unpaired electrons in their singly occupied molecular orbitals (SOMOs).6−10 Typical examples include the organometallic complexes with the spin switching11,12 and organic molecules with spin crossover in solid state13,14 or in solution.15,16 In the organic systems, the magnetic reversal phenomenon can be realized through proton-,17 temperature-,18,19 and light-induced20−22 methods as well as photoinduced photochromics.23−27 In particular, recently the redox-controllable magnetic switching of organic systems is attractive and likely to find extensively technological applications in the field of magnetic materials.18,28,29 In view of these, we design two new redox-modulated magnetic switching systems on the basis of the nitroxy−pyrazinyl−nitroxy diradical structures which can transform from ferromagnetic exchange coupling to antiferromagnetic coupling or vice versa depending on the redox reaction medium. We chose pyrazine as the coupler and redox reaction center unit, which is a well-known © 2015 American Chemical Society

organic compound and has been investigated early for its reduction reactivity in aqueous medium.30 Pyrazine and its derivatives are of great importance in the biological science, food chemistry, and photochemistry, etc.31−35 More importantly, as evidenced in many pyrazine derivatives, the pyrazine segment can serve as a redox active center to participate in many chemical reactions.30,36,37 We reasonably exploit this feature of pyrazine and successfully design the promising organic magnetic switches. To the best of our knowledge, there are several factors that can affect the spin coupling interaction. As demonstrated by Ali and Datta,38 spin delocalization as well as the length and aromaticity of the couplers would affect the magnetic coupling. Turek et al.39 revealed that spin polarization and molecular conformation could influence the spin coupling interaction as well by investigating a series of m-phenylene couplers. In this work, inspired by the mediating role of the m/p-phenylene couplers between the spin centers, we report a new strategy for realizing the spin state switching modulated by redox reaction. That is, two nitroxy groups (⟩N−O•) as the spin centers are Received: October 11, 2015 Revised: November 27, 2015 Published: November 30, 2015 27930

DOI: 10.1021/acs.jpcc.5b09939 J. Phys. Chem. C 2015, 119, 27930−27937

Article

The Journal of Physical Chemistry C attached to m- or p-pyrazinyl couplers with redox property, constructing two couples of the nitroxy−pyrazinyl−nitroxy molecular systems: nitroxy−p-pyrazinyl−nitroxy and nitroxy− m-pyrazinyl−nitroxy and their dihydrogenated counterparts. We mainly determine their ground states through comparing three possible low-lying states (closed-shell (CS) singlet state, broken-symmetry (BS) open-shell singlet state, and triplet (T) state) and discuss their different magnetic characters from the aspects of spin delocalization, spin polarization, the aromaticity of the couplers, and molecular conformation. As for molecular ground states, Borden et al. analyzed in detail the electronic states of the molecules including cyclobutaneteraone radical cation and radical anion, cyclopentadienyl radial, etc., employing diversified calculation methods.40,41 Our main findings are that the magnetic conversions (ferromagnetic ↔ antiferromagnetic) take place for each of the designed diradical structures upon reduction or oxidization. That is, the antiferromagnetic nitroxy−p-pyrazinyl−nitroxy can convert to a well-defined ferromagnetic counterpart upon reduction (dihydrogenation), while the well-defined ferromagnetic nitroxy−m-pyrazinyl− nitroxy converts to its well-defined antiferromagnetic counterpart upon reduction, thus leading to two pairs of redoxmodulated switches. The observed magnetic conversion phenomena and the nature of the corresponding ground states of such diradical molecules can be accounted for with the spin alternation rule,42,43 SOMO effect,44 and the SOMO−SOMO energy gaps in the triplet states of these compounds. In addition, the effect of steroisomerization is also analyzed. We hope the observed interesting magnetic switchable phenomenon in these newly designed magnetic organic molecules could be a basis for further design of the magnetism-controllable molecular switches and has promising applications.

devices. In this work, thereby we theoretically design and investigate two organic molecular switches each of which consists of two nitroxide groups and a redox-property-tunable coupler. That is two nitroxide radicals (⟩N−O•) are linked to the modified p/m-phenylene with conformational restriction, forming two nitroxide-based p/m-phenylene-like diradicals (1a and 2a, Figure 1). The modified p/m-phenylene couplers are

Figure 1. Schematic diagram of redox-modulated conversions of structures for the nitroxide-based radicals. The molecular segments within the black boxes are the redox-active units. They are pyrazines in 1a and 2a, while those in 1b and 2b are dihydropyrazine.

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DESIGN SCHEME AND COMPUTATIONAL DETAILS Design Scheme. The coupler and radicals are often indispensible in organic magnetic molecules. The development of couplers which can enhance the magnetic coupling effect between the radicals and switch the magnetic properties in a single organic molecule would contribute to opening up a promising area of the magnetic reversal materials.29 As known, m-phenylene is a coupler45 tending to support ferromagnetic interaction, while p-phenylene is that favoring antiferromagnetic coupling.43 Thus, it may be expected that attachment of two radical groups to either m-phenylene or p-phenylene could produce the diradicals with targeted magnetisms for further applications. Nitroxide-based radical is relatively stable because its unpaired electron is located in the antibonding π*-orbital over the N−O bond region, and further delocalization to the coupler or other conjugated molecular segments may stabilize the unpaired electron through decreasing the π*-orbital energy level (the singly occupied molecular orbital (SOMO)).8 Up to now, some nitroxide-based diradicals have been widely investigated both experimentally and theoretically, especially by Rajca and co-workers,46 and the magnetic switching phenomena were observed in them. More specially, Ali et al.29 designed a conformationally constrained nitroxy−mphenylene−nitroxy diradical and discussed its magnetic conversion from the ferromagnetic to antiferromagnetic coupling through a redox process. These findings stimulated our interest in searching for new organic diradical molecules that can display a prominent change in magnetic properties through certain methods and therefore can be useful in the design of magnetism-based molecular

the redox units in which two C−H fragments at the 2- and 5positions of phenylene are replaced by two nitrogen atoms,29 converting to the p/m-pyrazinyl couplers. Clearly, parent 1a and 2a can convert to 1b and 2b by undergoing a twoelectron−two-proton (2e−2H+) reduction (or dihydrogenation) process, respectively. The corresponding diradical structures and conversions are also shown in Figure 1. Further, we computationally explore the magnetic properties of these two pairs of nitroxy−pyrazinyl−nitroxy diradicals. Computational Details. All the molecular geometric optimizations and frequency analyses as well as energy calculations were performed at the (U)B3LYP/6-311++G(d,p) level of theory using which has been shown to successfully predict the molecular ground states. All optimized geometries were confirmed to be the minima on their potential energy surfaces, showing no imaginary frequency. The single-point calculations were done using a large basis set 6-311+ +G(3df,3pd). Besides, a more modern M06-2X function was adopted to verify the accuracy of some computational results, using the 6-311++G(d,p) basis set. In addition, the CASSCF(10,10)/6-311++G(d,p) method was used to measure the diradical character of 1a, 1b, 2a, and 2b through calculating the occupation numbers of their lowest unoccupied natural orbitals (LUNO). Since the nucleus-independent chemical shifts (NICS)47,48 have been widely applied to assessing aromaticity/antiaromaticity in which a negative NICS value denotes an aromatic molecule, while a positive NICS value suggests an 27931

DOI: 10.1021/acs.jpcc.5b09939 J. Phys. Chem. C 2015, 119, 27930−27937

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Table 1. Total Energies of the Open-Shell BS Singlet and Triplet States, Corresponding ⟨S2⟩ Values, Intramolecular Magnetic Exchange Coupling Constants (J, in cm−1) as Well as the Singlet−Triplet Energy Gaps (ΔEST, kcal/mol) Calculated at the (U)B3LYP/6-311++G(D,P) Level, and the J Values Calculated at the UM06-2X/6-311++G (D, P) Level Listed for Comparison E(T)/au (⟨S2⟩) 1a 1b 2a 2b

−757.8151405 −759.0170031 −757.8185563 −759.0066566

(2.008) (2.056) (2.031) (2.041)

E(BS)/au (⟨S2⟩) −757.8283139 −759.0139186 −757.8174271 −759.0178665

(0.644) (0.977) (0.985) (0.547)

J (B3LYP)

J (M06-2X)

ΔEST

−2117.9 626.9 236.7 −1645.4

−1917.1 520.2 237.9 −918.9

−12.15 3.68 1.37 −9.59

magnetic switching properties. In addition, the optimized geometries of all diradicals are displayed in Figures S1 and S2, and the bond lengths between nitrogen atom and oxygen atom and the adjacent atoms of radical centers as well as some dihedral angles between the coupler and two radical centers are also given. Moreover, we also find that the estimated |J| values for four pairs of diradicals are relatively high. As |J| is comparatively large in the ground state, the magnetic characteristics of these molecules are expected to have a great application.57 In addition, to help the understanding of the magnetic phenomena, the spin alternation rule and SOMO effect of these diradicals are taken into consideration, which have been proved to be a powerful tool for qualitative description of the ground state of the molecules.58 We also computed the energy gaps between two SOMOs in the triplet states for these molecules to further analyze the magnetic properties. In the following discussion, we mainly focus on the analyses of magnetic coupling interactions of the parent 1a and 2a and their reduced counterparts, 1b and 2b. Of course, the magnetic coupling interactions and switching phenomena are also roughly compared in their corresponding steroisomers, 1a′/1b′ and 2a′/2b′. Geometrical Character, Energetics, Magnetic Coupling, and Spin Density Distributions. As shown in Figures S1 and S2, the optimized molecular geometries indicate that in 1a two nitroxide radicals are coplanar with the p-pyrazinyl coupler, which is a typical Kekule structure, and the extensive πconjugation is developed between two ⟩NO• groups and the coupler, and therefore delocalization of the π-type unpaired electrons plays an essential role in determining the magnitude and sign of magnetic exchange couplings.38 A great fraction of spin density is delocalized from the two ⟩N−O• centers to the coupler, further suggesting the formation of the extended πconjugation (see 1a-BS in Figure 3), which potentially provides a feasible means of spin transport56 and facilitates a strong antiferromagnetic coupling. Although the coupler has aromaticity (the calculated NICS(0) and NICS(1) value at a point 1 Å above the center of coupling ring are 1.0607 and −3.5454 ppm, respectively), which is in favor of ferromagnetic coupling,38 delocalization of π-electrons is dominant in this conjugated system. As a logical consequence, the exchange coupling interaction is expectedly antiferromagnetic in 1a. The considerably large J value in Table 1 proves the authenticity of the result. Upon reduction of the molecule 1a to 1b, the good coplanarity between two nitroxide radicals and the coupler of phydropyrazinyl is somewhat removed, but the high πconjugation in 1a is greatly destroyed, which inhibits the extension of the π-conjugation and delocalization of πelectrons, being disadvantageous for the antiferromagnetic coupling, and then the conversion of magnetic character occurs although the coupler in 1b is antiaromatic (the calculated NICS(0) and NICS(1) are 3.8559 and 2.7574 ppm,

antiaromatic molecule, to further illustrate the effect of the aromaticity of the coupler on molecular coupling interaction, the NICS values of the couplers in 1a, 1b, 2a, and 2b were estimated at the B3LYP/6-311++G(d,p) level using the GIAO methodology. Herein, theoretical estimates of magnetic exchange coupling constants were carried out employing the broken-symmetry (BS) approach of density functional theory (DFT) proposed by Noodleman et al.49,50 We calculated the magnetic exchange coupling constants (J) between two spin centers using a simple expression, which was developed by Yamaguchi and co-workers and regarded as the most applicable one for evaluating the J value.51,52 The expression is given as J = (EBS − ET)/(⟨S2⟩T − ⟨S2⟩BS), where EBS and ET refer to the energies of the BS open-shell singlet and triplet state, while ⟨S2⟩BS and ⟨S2⟩T denote the average spin square values of the two states, respectively. Ginsberg53 presented an expression of the energy gap between the pure singlet state and the triplet state (S−T energy gap), which was estimated as ΔEST = ⟨S2⟩T J (using the above-mentioned J, ΔEST = ES − ET). All of these DFT calculations were performed using the Gaussian 03 and 09 suites of program.54,55

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RESULTS AND DISCUSSION We theoretically design two conformationally constrained nitroxy−pyrazinyl−nitroxy diradicals, 1a and 2a, and they could undergo a 2e−2H+ reduction process to convert to 1b and 2b, respectively. The magnetic properties of these two pairs of diradical molecules are estimated and discussed in detail. Besides, to fully illustrate the accuracy of the calculated results and to examine the conformation effect, we also examine the stereoisomers of the parent diradicals 1a and 2a, namely 1a′ and 2a′, respectively. Similarly, after 2e−2H+ reduction, the stereoisomers 1a′ and 2a′ become the corresponding stereoisomers of 1b and 2b, namely 1b′ and 2b′, respectively (Figures S1 and S2). The calculated results indicate that the open-shell BS singlet is the ground state for 1a, 1a′, 2b, and 2b′, while the triplet is more stable for the corresponding 1b, 1b′, 2a, and 2a′. The detailed data including their energies of the closed-shell singlet (CS), open-shell BS singlet, and triplet (T) states, corresponding energy orders, energy gaps between the pure singlet state and triplet (ΔEST), and associated magnetic exchange coupling constants (J) calculated at the (U)B3LYP/6311++G(d,p) level56 are collected in Table 1, Table S1, and Table S2, respectively. In Table 1, the J values estimated at the UM06-2X/6-311++G(d,p) level are also presented for the purpose of comparison. The results show that the calculated J values are relatively accurate by employing two different functions and the magnetic conversions occur in the two couples of diradical molecules (1a ↔ 1b and 2a ↔ 2b). Besides, the results of single-point calculations for 1a, 1b, 2a, and 2b are listed as well in Table S3 to illustrate the reliability of the calculations using B3LYP function. Among them, some relevant data are used in the subsequent discussion about 27932

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favor of the ferromagnetic coupling, and the spin transport is hampered between the two radical centers through the coupler, resulting in a small J value. This is in reasonable agreement with the idea that the strongly magnetic coupling is generally found to arise from spin delocalization. For 2a and 2b, the aromaticity of their spacer is largely responsible for control of the coupling interaction. This is also in good conformity with the opinion that the ferromagnetic trend increases as the aromaticity of the coupler increases or vice versa, but the aromaticity is disadvantageous to diradical character, thus giving rise to a small J value for 2a and a large |J| value for 2b. Besides, the nonKekule structure and spin polarization of the coupler are important factors for the ferromagnetic interaction in 2a, while as for 2b, a partially conjugated structure has a great influence on the antiferromagnetic interaction. We can conclude that strong antiferromagnetic coupling for 2b result from antiaromaticity of the coupler and delocalization of π-electrons. Furthermore, we note that each couple of the diradical molecules including 1a, 2a and 1b, 2b belong to positional isomers, while the differences of magnitude and sign of their J values are large. This observation demonstrates that molecular conformation plays a significant role in the control of the magnetic coupling. In addition, as for a further verification of our results, for the high-spin molecule, 2a, the calculated J value (236.7 cm−1) is very close to the J values (282.73 cm−1 (calcd) vs 140−280 cm−1 (expt)) of the reported high-spin nitroxide radical systems which were determined using the B3LYP method or experimental measurements,46,62−64 clearly demonstrating that the calculated results here are reliable. Besides, diradical characters of 1a, 1b, 2a, and 2b are measured quantitatively by the CASSCF(10,10)/6-311++G(d,p) method. The calculated occupation numbers of LUNO for 1a, 1b, 2a, and 2b are 0.502, 0.920, 0.911, and 0.402, respectively, suggesting that the amounts of diradical character are approximately 50.2%, 92.0%, 97.7%, and 40.2% for them. Clearly, these results are in good agreement with those estimated from the corresponding ⟨S2⟩ values (0.644, 0.977, 0.985, and 0.547), further confirming the accuracy of our computational results.56 As for the above-mentioned other two couples of diradical molecules, 1a′/1b′ and 2a′/2b′, their properties of magnetic couplings and magnetic transformations are exactly alike with their corresponding stereoisomer couples, 1a/1b and 2a/2b, and thus we will not discuss them. To further understand the magnetic properties and their relationship with molecular structures of these designed organic molecules, in the following sections, we analyze the magnetic characteristics from three aspects: spin alternation rule, SOMO effect, and SOMO− SOMO energy gap of the triplet state. Spin Alternation Rule. The spin alternation rule is a reliable guideline for predicting the nature of the ground state. Following this spin alternation rule, Ali and Datta reported that the sign of J is determined by the number of bonds in the spininteracting pathway through the coupler. If the number of bonds is odd, antiferromagnetism would arise and ferromagnetism happens when the number of bonds is even. Therefore, for the six-membered aromatic ring couplers, such as the couplers of p-phenylene, p-pyridine, and p-pyrazine, an antiferromagnetic coupling is supported, while a ferromagnetic coupling occurs for m-phenylene, m-pyridine, and m-pyrazine couplers according to this rule.65 Hence, 1a has a negative J value because the number of bonds in two coupling pathways are odd through the p-pyrazine coupler. 2a results in a positive J

respectively) which is unfavorable to ferromagnetic coupling. Consequently, the magnetic coupling interaction in 1b becomes relatively weaker compared with 1a and the conclusion is confirmed by the moderately positive J value as shown in Table 1. Besides, we have also visualized the spin density distributions of 1b shown in Figure 3, from which we can evidently observe that spin orientations of two unpaired electrons are parallel, that is the molecule is of ferromagnetic coupling.56 Especially, the energies and magnetic measurement provide solid evidence for the ferromagnetic coupling between two nitroxide radical centers through the coupler. Fortunately, geometric optimization of 2a as shown in Figure S1 presents a similar case to 1a, indicating that two nitroxide radicals and the spacer also approach coplanar. The dihedral angles of both two −NO• radicals and the coupler plane are less than 2°. Nevertheless, the magnetic exchange coupling interactions between 2a and 1a are dramatically different from each other. The reason is attributed to 2a which belongs to non-Kekule organic molecule, unfavoring the antiferromagnetic coupling. The results have also corroborated that the spin sources bridged by a non-Kekule coupler would offer possible ferromagnetic coupling.59 Additionally, the spacer, possessing six electrons, is aromatic (the calculated NICS(0) and NICS(1) are −3.8869 and −6.9687 ppm, respectively). In general, a triplet ground state would be expected when the spacer has aromaticity. Besides, perhaps spin polarization is another source of the ferromagnetic coupling in the m-pyrazinyl-based diradical, which is analogous to the m-phenylene-based diradicals.59 In a word, non-Kekule structure of the molecule in combination with the aromaticity and spin polarization of the coupler plays a synergetic role in determining the ferromagnetic interaction for 2a. However, a sharp drop in the magnitude of magnetic coupling constant occurs for 2a compared with 1a. These observations should be ascribed to the aromaticity of the coupler because the aromaticity can cause a decrease of the diradical properties which does not favor the magnetic coupling interaction, therefore leading to a small J value.60 With respect to 2b, through 2e−2H+ reduction of 2a, the magnetic reversal takes place as well. The reason may be that the coupler is an eight-π-electron system, which is composed by two nitrogen atoms together with two double bonds both donating four electrons. The aromaticity of the spacer disappears in this organic molecule; that is to say, it is antiaromatic (the calculated NICS(0) and NICS(1) are 2.5728 and 2.0765 ppm, respectively), and hence the antiferromagnetic coupling is more beneficial naturally. On the other hand, in Figure S2, we have noticed that partial conjugated structure is formed between two radical groups and the coupler, which creates a profitable condition for the magnetic coupling interaction between the radicals, leading to a considerably strong antiferromagnetic interaction. Besides, as mentioned above, an antiaromatic coupler can facilitate the diradical character, thus contributing to a large |J| value. Moreover, the presence of N−H fragment instead of nitrogen atom increases the steric hindrance of the coupler, and hence the direct exchange is inhibited between two nitroxide radicals compared with 2a. Whereas the direct exchange usually enhances the ferromagnetic coupling according to the Hund’s rule,61 thereby for 2b antiferromagnetic coupling is normally expected. On the whole, for 1a, its π-conjugated Kekule structure has made a great contribution to the antiferromagnetic coupling, enhancing the coupling interaction, and led to a considerably large |J| value. However, for 1b, a nonconjugated structure is in 27933

DOI: 10.1021/acs.jpcc.5b09939 J. Phys. Chem. C 2015, 119, 27930−27937

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The Journal of Physical Chemistry C value due to two even spin-interacting pathways through the mpyrazine coupler. In the case of 1b and 2b, at first glance, we regard 1b as antiferromagnetism because of two odd coupling pathways and 2b as ferromagnetism due to two even coupling pathways. But in combination our calculations, the scheme of spin alteration (Figure 2), and spin density plots (Figure 3), we

to their corresponding spin density plots and the signs of the calculated coupling constants. SOMO Effect. Here, we further take into account the SOMO effect of eight diradicals (see Figure 3 and Figure S3) to predict their ground states. As proposed by Borden and Davidson,44 a triplet is the ground state when two SOMOs of a molecule are nondisjoint, while the molecule with disjoint shape in two SOMOs would show singlet ground state. In addition, the shape of the SOMOs could affect the S−T energy gap of the molecule When the disjoint character of SOMOs appears, the overlapped region of atomic orbitals occupied by two electrons is small, and hence the repulsion of two electrons is correspondingly weak, leading to nearly degenerate ground states and naturally small S−T energy gap.59 While for the nondisjoint shape of SOMOs, intense repulsion between two electrons in atomic orbitals is considerably large and spin parallel orientation is favorable, contributing to the triplet ground state and a large S−T energy gap. Careful examinations of our results reveal the disjoint character of SOMO plots of 1a, 1a′, 2b, and 2b′, which imply that 1a, 1a′, 2b, and 2b′ have open-shell singlet ground states and have small S−T energy gaps. Nonetheless, for 1b, 1b′, 2a, and 2a′, their SOMOs are noticeably nondisjoint, leading to triplet ground states and large S−T energy gaps. Clearly, the above SOMO analyses are in good agreement with the conclusions from the evaluated J values and S−T energy gaps given in Table 1. SOMO−SOMO Energy Level Splitting. Hoffmann66 suggested that if the energy difference between two consecutive SOMOs (ΔESS) is less than 1.5 eV, the two nonbonding electrons would occupy different degenerate orbitals in order to minimize their electrostatic repulsion with spin-parallel orientation, thus resulting in a triplet ground state. Meanwhile, Constantinides et al.59 found that molecules are clearly singlet ground states when ΔESS > 1.3 eV based on the calculations of a series of linear and angular polyheteroacenes. Zhang et al.67 demonstrated that the critical values of ΔESS are different for different m-phenylene-based diradical systems. In this respect, molecules 1a and 2b with relatively larger SOMO−SOMO energy gaps are known to possess antiferromagnetic coupling, corresponding to 1.39 and 1.06 eV (ΔESS), respectively. In particular, it is distinctly borne out that 1a is singlet ground state, whose ΔESS is more than 1.3 eV. While ΔESS for 1b and 2a are much smaller, with ΔESS of 0.67 and 0.65 eV, respectively, leading to ferromagnetic coupling. Clearly, our results are well consistent with the analyses described above. Simultaneously, we notice that the S−T energy gap and SOMO−SOMO energy gap have a close relationship. That is the molecule with a large ΔESS gives rise to a small or negative ΔEST, while the molecule with a small ΔESS tends to have a highly positive ΔEST, although the linear correlation is fair between ΔESS and ΔEST in our estimation (see Figure S4). In other words, for singlet molecules (1a and 2b), large ΔESS contribute to negative ΔEST, while for the triplet state 1b and 2a, small ΔE SS leads to positive ΔE ST , obeying the aforementioned relationship between ΔESS and ΔEST very well. However, slightly large ΔESS instead causes relatively high S−T energy gap for 1b compared with 2a, which belongs to the triplet ground state as well. The deviation could be attributed to such a fact that electronic delocalization in spin density for 1b is smaller than that of 2a (Figure S5), and thus strong repulsion of electrons contributes to a large S−T energy gap.67 Besides, the relationship between ΔESS and ΔEST also holds for 1a′, 1b′, 2a′, and 2b′. The energies of consecutive SOMOs for the

Figure 2. Scheme of spin alteration for 1a, 1b, 2a, and 2b.

Figure 3. SOMOs (isovalue = 0.02) and spin density maps (isovalue = 0.004) for the BS states of 1a and 2b and T states of 1b and 2a calculated at the (U)B3LYP/6-311++G (d, p) level.

find that each of two nitrogen atoms in the coupler can provide two π-electrons, which is the equivalent of a chemical bond, and thus two spin-interaction pathways become even in 1b and odd in 2b, corresponding to ferromagnetic coupling and antiferromagnetic coupling, respectively. Clearly, this analysis is completely opposite to the above direct prediction using the spin alternation rule and thus can be viewed as an expansion of the spin alternation rule.38,65 Naturally, the modified spin alternation rule can be equally applied to 1a′, 2a′, 1b′, and 2b′ as well, and their coupling pathways are in good accordance with our calculations. In a word, all these conclusions coincide 27934

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has been demonstrated that spin delocalization from the πconjugated structure, spin polarization from non-Kekule structure of the molecules, the aromaticity of spacers, and molecular conformation all play a remarkably significant role in controlling the magnetic coupling interaction. More importantly, the spin alternation rule, SOMO effect, and SOMO− SOMO energy gaps of the triplet states of these molecules are all the helpful tools for describing the ground states of the molecules. Of course, for the specific reduction processes of the parent molecules 1a and 2a, we still need to make great attempts to explore the conversion mechanisms.

triplet states and the SOMO−SOMO energy gaps of 1a, 1b, 2a, and 2b and their corresponding stereoisomers 1a′, 1b′, 2a′, and 2b′ are given in Table 2, together with the S−T energy gaps for the purposes of comparison. Table 2. SOMO Energies of the Triplet States, SOMO− SOMO Energy Gaps, and Singlet−Triplet Energy Gaps Calculated at the (U)B3LYP/6-311++G (D, P) Level 1

ES (au)

1a 1b 2a 2b 1a′ 1b′ 2a′ 2b′

−0.23799 −0.17681 −0.22287 −0.19215 −0.23811 −0.17644 −0.22293 −0.19284

ES (au)

ΔESS (eV)

ΔEST (kcal/mol)

−0.18694 −0.15213 −0.19901 −0.15317 −0.15317 −0.15148 −0.19907 −0.15903

1.39 0.67 0.65 1.06 1.39 0.68 0.65 0.92

−12.15 3.68 1.37 −9.59 −12.17 3.77 1.38 −9.04

2

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b09939. All calculated data and figures calculated at the (U)B3LYP/6-311++G (d, p) level including the energies for the close-shell singlet, broken-symmetry open-shell singlet and triplet, the corresponding energy orders, ⟨S2⟩ values, intramolecular magnetic exchange coupling constants as well as singlet−triplet energy gaps for all designed diradical molecules; optimized geometries of all diradical molecules and those with N−O bond lengths as well as the bond lengths of the adjacent atoms of radical centers and relevant dihedral angles between the coupler and two radical groups; SOMOs and spin density distributions; the correlation plot between SOMO− SOMO energy gaps of triplet states and S−T energy gaps (PDF)

From what has been discussed above, we have understood the fundamental principles about the magnetic transformations of 1a ↔ 1b, 2a ↔ 2b, 1a′ ↔ 1b′ and 2a′ ↔ 2b′, but with regard to their applications in device design, we still need to make greater efforts for an in-depth understanding. The magnetic reversal of the materials is crucial in molecular magnetism and closely linked to magnetic data storage. Brokensymmetry singlet−triplet energy difference equals 2J, i.e., E(S = 0) − E(S = 1) = 2J. If the 2J value is large, the diradical, which possesses a good coplanarity with the coupler, could exist in solution or in solid state.46 Moreover, the small dihedral angles shown in Figure S2 provide sufficient evidence for the coplanarity between the coupler and two radical centers. In this work, 2J values of all the molecules are comparatively large, and thus we can make full use of these molecules to design magnetic switches in solution matrix, in which the high-spin states of 1b, 1b′, 2a, and 2a′ (i.e., triplet ground state) can store magnetic information as an “ON” states and the low-spin states of 1a, 1a′, 2b, and 2b′ (open-shell singlet) can also store magnetic information as an “OFF” states. Thus, the information can be processed and then be transferred in the device. For the above-mentioned magnetic switch, the operating principle is distinctly different from that of the classical switch in which two magnetic states are blocked by energy barrier between two molecules, such as photoinduced or temperature-induced magnetic switch. In these newly designed switches, the molecular magnetic states could be present directly by regulating the medium and need not surmount the energy barrier between two molecules. Of course, these conceptually manufactured magnetic molecules may be applied in spintronics, magnetic sensing, conducting, and semiconducting magnetic materials, etc. That is to say, we hope these molecules would have diverse applications in the near future and could pave a road for the design of organic magnetic switches. Certainly, further studies are still needed for practical applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (X.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by NSFC (21373123, 20633060, and 20973101) and NSF (ZR2013BM027) of Shandong Province. A part of the calculations were carried out at National Supercomputer Center in Jinan, Shanghai Supercomputer Center, and High-Performance Supercomputer Center at SDU-Chem.

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REFERENCES

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CONCLUSIONS In summary, what we mainly concentrate on this work is to theoretically design two pairs of organic magnetic material molecules, whose magnetic exchange coupling constants (J) have a pronounced variation accompanied by a transformation from ferromagnetic coupling to antiferromagnetic coupling or vice versa through the redox-modulation method. Moreover, it 27935

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