Remarkable Magnetic Coupling Interactions in Multi-Beryllium

Apr 3, 2017 - Multi-beryllium-expanded small graphene-like molecules including oligoacenes (mBe-nA) and graphene patches (mBe-GP) are computationally ...
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Remarkable Magnetic Coupling Interactions in Multi-BerylliumExpanded Small Graphene-like Molecules with Well-Defined Polyradical Characters Meiyu Song, Xinyu Song,* and Yuxiang Bu School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, People’s Republic of China S Supporting Information *

ABSTRACT: Multi-beryllium-expanded small graphene-like molecules including oligoacenes (mBe-nA) and graphene patches (mBe-GP) are computationally designed through introducing two or three Be atoms into the specific benzenoid rings of the graphene-like molecules, leading to replacement of some C−C bonds by the C−Be−C linkages with elongated C···C distances of about 3.3 Å in them. As a result, the elongation of the C···C bonds and insertion of more Be atoms make the two radical moieties in each molecule relatively separated and their interaction relatively weak. Both density functional theory and CASSCF calculations indicate that all these multi-Be-expanded graphene-like molecules exhibit well-defined polyradical characters: an open-shell singlet diradical for all mBe-nA and an open-shell singlet diradical or quintet tetraradical for mBe-GP depending on the Be-insertion patterns of the patches. The main findings in this work are that (i) a switching from the parent graphene-like closed-shell molecules (e.g., linear oligoacenes and graphene patches) to the open-shell singlet (diradical) or quintet (tetraradical) ground states can be realized by introducing Be as linkers into the graphene-like molecules; (ii) more importantly, the spin-coupling interactions of such mBe-nA and mBe-GP are remarkably large; and (iii) in these Bemodified molecules the Be−C bonds exhibit considerable covalent character and the Be···Be distances are 2.67−2.84 Å, implying weak Be(s2)···Be(s2) metallophilic interaction. This work would open a new perspective for the rational design of perfect and stable singlet diradicals or polyradicals with large spin-coupling constants on the basis of small closed-shell graphene-like molecules by multimetal incorporation and also encourage experimentalists to pursue and realize these interesting structures with enhanced magnetic properties in the future. π conjugation throughout the entire carbon backbone.12−16 However, studies have also indicated that almost all linear oligoacenes possess the closed-shell (CS) singlet ground state, and only those larger than hexacene are thought to have diradical character in their ground states but which are still controversial and need further clarifying.13,17−19 Unfortunately, those acenes become less chemically stable with increasing their lengths, and the synthesis of longer, stable acenes is a difficult and challenging task because of their very low solubility, poor light and oxygen stability, and tendency to dimerize, as well as the difficult multistep synthetic approaches required. Consequently, for a long time, the experimental studies had been limited to oligomers up to pentacene. In order to allow graphene and its derivatives (oligoacene, small patches, and nanoribbons) a broader range of applications in organic materials, great efforts have been made to expand the graphene-like molecules and improve their stability and electronic properties.20−25 Cho et al. investigated the magnetic behaviors of pristine zigzag graphene nanoribbon with eight

1. INTRODUCTION Over the past several decades, the comprehensive discovery of graphene as a promising material has attracted enormous attention of both experimental and theoretical physicists and chemists owing to its unique electronic properties and potential applications.1−7 In particular, graphene and its derivatives with polyradical character as organic magnetic materials have been extensively studied.8−11 Graphene is a two-dimensional material with an extensive π-conjugated molecular framework that has the advantage of delivering magnetic exchange coupling through an sp2−pz carbon network due to its almost infinite spin-coupling pathways. Although graphene possesses a very broad development prospect, it is still poorly understood, especially in the spin or magnetic coupling aspects, and it even has some limitations or deficiencies. For example, small graphene patches usually do not have diradical character, and elongation of the zigzag edge results in an increase of diradical character. However, those with a long armchair edge have only weak or even do not present diradical character. Furthermore, linear oligoacenes, which are regarded as the simplest graphenelike molecules, have become a hot spot for research due to their fascinating electronic properties originating from their extended © XXXX American Chemical Society

Received: February 2, 2017

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DOI: 10.1021/acs.organomet.7b00082 Organometallics XXXX, XXX, XXX−XXX

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Organometallics

factors, as verified in our previous work.24,25 Undoubtedly, it is the key to realize a large separation of two target radical moieties for a graphene-like molecule without lowering its stability. As probed in our previous work, multi-Zn insertion into the C−C bonds of the benzenoid rings of oligoacenes and small graphene patches can justify this assertion because of the covalent character of the formed C−Zn bonds and the role of Zn d orbitals in mediating efficiently the spin coupling between the two spin moieties. However, the separation (e.g., the C···C distance in the C−Zn−C units) is so large that we only get mild spin couplings due to the large covalent radius of the Zn atoms. Thus, a slightly smaller separation of two target radical moieties would be required if one hopes to considerably enhance the spin coupling. Herein, we report a new computational design to realize the aim of further enhancing and improving intramolecular spin couplings of graphene-like molecules. That is, we introduce beryllium (Be) atoms into representative oligoacenes and graphene patches and separate two radical moieties through replacing the C−C bonds by C−Be−C linkages, thus considerably weakening the interaction between the two radical moieties and more possibly exhibiting diradical character or polyradical character. Over the past few years, the interaction of Be with graphitic compounds has frequently been investigated for various purposes.29−32 Besides, it is undoubtedly the toxicity of Be and the precautions required for its safe use that are the major difficulties that have historically limited the exploration of its chemistry, but studies of the preparation, structure, and properties of various organoberyllium compounds still have aroused the intense attention of chemists, both experimentally and theoretically.33−37 In this work, alkaline earth metal Be atoms instead of the transition metal Zn are chosen as the linkers to expand representative oligoacenes and small graphene patches. As expected, such Be-expanded graphenelike molecules exhibit diradical or tetraradical character with marked magnetic coupling characteristics (FM versus AFM). As an additional interesting finding, for the first time, we verify that the Be···Be unit exhibits weak metallophilic interaction with an s2···s2 mode instead of the d10···d10 mode observed in the transition metal compunds.24,25,38,39 This work would open a new perspective for the rational design of perfect and stable singlet diradicals or polyradicals using graphene-like molecules through non-transition-metal doping.

zigzag chains that are terminated with trimethylenemethane and 6-oxoverdazyl radicals, finding that the zigzag graphene nanoribbons with different terminating organic radical groups exhibit different magnetic properties.20 The doping effect on intramolecular magnetic exchange coupling of an edgeterminated zigzag graphene nanoribbon with organic radicals was studied by Nam and co-workers, demonstrating a possibility of reversible spin control of organic magnetic materials from antiferromagnetic (AFM) to ferromagnetic (FM) characteristics and vice versa by B or N doping and enhancement of the magnetic coupling strength of the edgeterminated zigzag graphene nanoribbons.21 On the other hand, oligoacenes mostly as the couplers were explored by designing novel, stable diradical oligoacene derivatives. For example, Bhattacharya et al. predicted the intramolecular exchange coupling constants for oxo- and thioxo-verdazyl-based high-spin ground-state diradicals with linear polyacene couplers of varying length.22 Ali et al. predicted the intramolecular magnetic exchange coupling constants for 11 nitronyl nitroxide diradicals with different linear and angular polyacene couplers from broken-symmetry (BS) density functional theory (DFT) treatment.23 To our knowledge, little attempt has been made to develop and improve the magnetic coupling interaction of linear oligoacenes through the modifications with variations of the benzenoid structures in oligoacenes, graphene patches, or other graphene-like molecules, especially the modifications through introducing a non-transition metal into their benzenoid rings. Clearly, it has been a formidable but meaningful task to seek or design new magnetic materials through modifying oligoacenes, graphene patches, or other graphene-like molecules. In recent years, our group is devoted continuously to the studies of graphene and graphene-like molecules.24−28 In particular, we theoretically designed multiZn-expanded oligoacenes (from benzene to pentacene, mZnnA, n = 1−5, m and n denote the number of Zn atoms and acenes, respectively) and multi-Zn-expanded graphene patches (mZn-GP) by introducing Zn arrays into oligoacenes and specific benzenoid rings of simple graphene patches in different ways, respectively, and explored their relevant electronic/ magnetic properties. Our results indicate that these multi-Znexpanded graphene-like molecules have open-shell singlet diradical ground states with well-defined diradical characters and AFM characteristics and that one of the mZn-GPs possesses a quintet ground state as a tetraradical.24,25 Although the designed multi-Zn-expanded graphene-like molecules in our previous works exhibit more significant radical character than their parent ones, we still struggle to find more appropriate atoms instead of Zn as dopant atoms to obtain greater enhancement in the magnetic coupling properties for graphene-like-based magnetic materials applications. As mentioned in our previous studies, our basic strategy for the radicalizing modification of graphene-like molecules is to make the cross-linking stabilization smaller than the delocalization stabilization of two target radical moieties in the molecules.24,25 Clearly, two modification schemes can realize this object: (i) enlarging the delocalization extent and thus increasing the delocalization stabilization of both or either of two radical moieties and (ii) enlarging the separation of two target radical moieties and thus decreasing the cross-linking stabilization. In addition, in general, it is easier to realize the above-mentioned change in large graphene patches than in small ones, but depending on more structural factors. Thus, the second scheme should be an efficient way, which depends on fewer structural

2. DESIGN SCHEME AND COMPUTIONAL DETAILS 2.1. Design Scheme. The coupler and radical units are often essential in organic magnetic molecules. In particular, the appropriate linkage of two radical moieties would influence the characteristics and strength of the magnetic coupling interaction in a single organic magnet. Seeking and designing an ideal coupler that can enhance or switch the magnetic properties of a molecule are always a concerned of many scientists. Thus, by considering more factors, we chose the transition metal Zn as the coupler to expand the graphene-like molecules in our previous studies and obtained the well-defined diradicals.24,25 However, by comparing Be with Zn and examining some of the Be-expanded oligoacenes, we surprisingly find that the Beexpanded analogues have more remarkable diradical character and magnetic properties than those of the Zn-expanded ones, although they both form divalent compounds with considerable covalent character for the Zn−C and Be−C bonds. As is well known, Be has a smaller covalent radius than Zn, and it is expected that the formed Be−C bond is shorter than the Zn−C bond; thus, the Be-expanded graphene-like molecules have a stronger spin coupling interaction or magnetism than the Zn-expanded ones. Undoubtedly, it is natural to B

DOI: 10.1021/acs.organomet.7b00082 Organometallics XXXX, XXX, XXX−XXX

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Organometallics make a detailed exploration of the Be-expanded graphene-like molecules for the design of and search for novel magnetic molecules. In fact, an oligoacene can be viewed as two parallel polyacetylene chains fused together. Each chain is a radical, and the unpaired electron delocalizes over the entire chain and thus is stabilized. However, a strong cross-linking interaction between the two radical chains leads to a CS ground state for oligoacenes, which is attributed to the fact that the cross-linking stabilization is over the delocalization stabilization along each chain in shorter oligoacenes. If the two radical chains do not directly contact with each other or stay away a considerable distance, the cross-linking stabilization will be far smaller than the delocalization stabilization; thus, the two radicals should be held as a diradical with considerable spin-coupling interaction. Clearly, to reach this objective, introduction of suitable covalent couplers into oligoacene would be a better choice. Inspired by alkyl metal compounds featuring C−M bonds and motivated by our metallization modification of organic conjugated molecules and DNA base pairs,40,41 we utilize two or three Be atoms to expand the representative graphene-like molecules (oligoacenes and graphene patches) and expect to obtain polyradical character (diradical versus tetraradical) and magnetism, as shown in Chart 1. For the multi-Be-expanded oligoacenes (mBe-nA, n = 1−5, m and n denote the number of Be atoms and acenes, respectively), two polyacetylene chains can be viewed as two radical moieties bound together by more cross-linking C−Be−C bonds. Compared with parent oligoacenes, the interchain distance in mBe-nA greatly increases due to the introduction of Be, and more importantly all mBe-nA exhibit well-defined diradical character. This indicates that introduction of a Be array into a short oligoacene can assign the expanded oligoacene an open-shell singlet diradical character and considerably large magnetic coupling interaction. Clearly, this examination further confirms that multi-Be modification should be a reliable way to realize polyradicalization of graphene-like molecules. We thus use Be atoms as the couplers to expand oligoacenes (from benzene to pentacene) and three representative graphene patches (pyrene/Pyr, anthanthrene/Ant, and benzo[ghi]perylene/Bpe, Chart 1). In fact, much more organic Be compounds have been synthesized and structurally characterized up to now,33−35 although their corresponding applications are relatively unexplored compared to that of its neighboring element compounds. Be is a metallic divalent element and possesses the ability to form strong covalent bonds. The empty 2p orbitals are energetically close to the occupied 2s one, forming sp hybrid orbitals. For this reason, and having two valence electrons only, the Be atom is able to form two covalent bonds that are collinear. Besides, the empty p orbitals of Be benefit magnetic coupling through p−π conjugation (mentioned below). Because of their 1s22s2 electronic structure, adjacent Be does not form metal−metal multiple bonds, thus avoiding the formation of short Be−Be covalent bonds, which can distort the graphene-like molecular structures. In addition, it should be noted that similar to the d 10 ···d 10 metallophilic interaction,24,25,38,39 the s2···s2 interaction has been also observed, e.g., strong CS s2···s2 interactions in the TlI···TlI unit,42,43 the PbII··· PbII unit,42,44−46 and the M−···M− structures for M = K and Rb in their crown ether compounds.42,47 Thus, it is expected that two adjacent Be could form the CS s2···s2 interaction. This interaction ensures that two adjacent C−Be−C units are not mutually repulsive, thus not distorting the structures. In short, mBe-nA and multi-Be-expanded graphene patches (mBeGP) are computationally designed through introducing Be as linkers. As shown in Chart 1, mBe-nA include two types: (i) the longitudinal insertion ((n+1)Be-nA, n = 1, 2) [2Be-expanded benzene (2Be-1A), 3Be-expanded naphthalene (3Be-2A)] and (ii) the quasi-transverse insertion at the middle benzenoid ring [2Be-expanded oligoacenes (2Be-nA, n = 1−5, nA denote benzene, naphthalene, anthracene, tetracene, and pentacene, respectively)], while mBe-GP include 3Beexpanded pyrene (3Be-Pyr), 3Be-expanded anthanthrene (3Be-Ant), and 3Be-expanded benzo[ghi]perylene (3Be-Bpe). 2.2. Computational Details. Given the successful application of DFT in predicting all kinds of chemical and physical properties which may not be easy to realize through experiments and its extensive use in

Chart 1. Topological Representation of Acenes and Their Polyradicaloid Character and Schemes of Multi-BeExpanded Acenes (mBe-nA, m and n Denote the Number of Be Atoms and Acenes, Respectively) in Two Patterns ((n +1)Be-nA (n = 1, 2) and 2Be-nA (n = 1−5)) and Multi-BeExpanded Graphene Patches (mBe-GP including 3Be-Pyr, 3Be-Ant, and 3Be-Bpe)a

a

Note: nA, Pyr, Ant, and Bpe denote the parent acenes, pyrene, anthanthrene, and benzo[ghi]perylene, respectively.

characterizing electronic properties of oligoacenes and graphene nanoribbons,10,13,20,21,48 herein, we chose it as our main research method to obtain a basic understanding of the geometric structures and electronic properties of the multi-Be-expanded graphene-like molecules. The geometries of all the designed molecules (mBe-nA and mBeGP) were fully optimized at the (U)B3LYP/6-311++G(d,p) level of theory. Subsequently, frequency analyses were also performed to confirm the minima on the potential energy surfaces, revealing no imaginary frequency. The relevant energy quantities including the singlet−triplet energy gaps and the energy gaps between the highest occupied molecular orbital (HOMO) and lowest unoccupied C

DOI: 10.1021/acs.organomet.7b00082 Organometallics XXXX, XXX, XXX−XXX

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Organometallics molecular orbital (LUMO) were determined. Further, adiabatic/ vertical ionization potentials (IPs) and electron affinities (EAs) of mBe-nA were calculated at the B3LYP/6-311G(d,p) level of theory to check the redox stability. In addition, the CASSCF(10,10)/6-31G(d) method was also used to measure the diradical character of all the molecules through calculating the occupation numbers of their LUMOs. To calculate the magnetic coupling constants (J), the following formula, which was established unambiguously by Yamaguchi and co-workers,49−51 was employed: J = (EBS − ET)/ (⟨S2⟩T − ⟨S2⟩BS), where EBS and ET denote the energies of the BS open-shell singlet and triplet (T) states and ⟨S2⟩T and ⟨S2⟩BS represent the corresponding average spin-square values in the T and BS states, respectively. A positive J value denotes the FM coupling, whereas a negative value indicates the AFM coupling. To obtain the open-shell BS singlet solution, the “guess = mix” keyword is used within the unrestricted formalism. All the calculations were carried out using the Gaussian 03 and 09 quantum chemical packages.52,53

3. RESULTS AND DISCUSSION We computationally designed and characterized three series of the multi-Be-expanded graphene-like molecules ((n+1)Be-nA (n = 1, 2), 2Be-nA (n = 1−5), and mBe-GP), and their magnetic properties were determined. All calculated results including the energies of their CS, BS, and T states, relative stability, ⟨S2⟩ values, and associated J values at the (U)B3LYP/ 6-311++G(d,p) level are gathered in Table 1 and Table S1 in

Figure 1. Geometries of 3Be-expanded and 2Be-expanded naphthalene (3Be-2A and 2Be-2A) and the corresponding Zn-expanded analogues (3Zn-2A and 2Zn-2A) and their parent naphthalene with indicated bond lengths (Å) and adjacent Be−Be distances (Å) optimized at the UB3LYP/6-311++G** level.

polyacetylene chains or two small conjugated fragments are connected by a mediating Be array instead of direct C(sp2)− C(sp2) bonds.13 Like their parent naphthalene, 3Be-2A and 2Be-2A are both planar. Similarly, all of the other mBe-nA are also planar. The salient feature of these oligoacene derivatives is that multi-Be insertion does not give rise to any significant structural distortions except for elongation of the cross-linking C···C bonds. In order to describe the characteristics of mBe-nA more intuitively, Figure 1 shows the interatomic distances of the cross-linking C−Be−C units and other main bond lengths associated with the polyacetylene chains. Other optimized geometries of mBe-nA with indicated bond lengths and adjacent Be···Be distances are shown in Figure S1 (in the SI). It is clear that the Be···Be distances range from 2.67 to 2.85 Å for all cases considered here, indicating that no covalent bonds between two adjacent Be formed, and the Be···Be contacts could be attributed to weak CS s2···s2 interaction, which is similar to the d10···d10 metallophilic interaction. These characteristic distances are slightly longer than and also close to those (2.43−2.50 Å) between two parallel opposite edges in each benzenoid ring unit of the parent acenes.24 That is also one of the foremost reasons that mBe-nA with the elongated C···C bonds can still maintain the parallel orientations of all the C−Be−C units and all the atoms still are in the same plane like their parent oligoacenes. In the following, we focus on the elongated cross-linking C···C distances and C−Be bonds. In detail, as shown in Figure 2, two electrons of Be occupy appropriate sp hybrid orbitals caused by the mixing of the occupied 2s and a low-lying unoccupied 2p orbital of Be, and the two singly occupied sp hybrid orbitals interact with two singly occupied sp2 hybrid orbitals of two C in the two

Table 1. Energies (kcal/mol) for the Singlet−Triplet Gaps (ΔE(T‑BS)), Differences between Open-Shell BS Singlet and CS Singlet, ΔE(BS−CS), and ⟨S2⟩ Values for the Open-Shell Singlet and the Corresponding Energy Orders, and Intramolecular Magnetic Exchange Coupling Constants (J in cm−1) at the (U)B3LYP/6-311++G(d,p) Level for the MultiBe-Expanded Oligoacenes and Graphene Patches (n+1)BenA

⟨S2⟩BS

ΔE(T‑BS)

ΔE(BS‑CS)

energy order

J (cm−1)

2Be-1A 3Be-2A 2Be-nA

0.801 5.13 0.730 5.71 ⟨S2⟩BS ΔE(T‑BS)

−5.97 −3.38 ΔE(BS‑CS)

E(BS) < E(T) < E(CS) E(BS) < E(CS) < E(T) energy order

−1438.9 −1484.6 J (cm−1)

2Be-1A 2Be-2A 2Be-3A 2Be-4A 2Be-5A 3Be-GP

0.801 0.858 0.963 1.014 1.050 ⟨S2⟩BS

5.13 3.68 1.67 0.92 0.43 ΔE(T‑BS)

−5.97 −6.78 −9.16 −11.25 −13.72 ΔE(BS‑CS)

E(BS) < E(T) < E(CS) E(BS) < E(T) < E(CS) E(BS) < E(T) < E(CS) E(BS) < E(T) < E(CS) E(BS) < E(T) < E(CS) energy order

−1438.9 −1082.1 −540.9 −312.1 −149.5 J (cm−1)

3Be-Ant 3Be-Bpe

0.975 0.785

1.55 4.57

−7.95 −4.31

E(BS) < E(T) < E(CS) E(BS) < E(CS) < E(T)

−503.6 −1250.6

the Supporting Information (SI). The main results will be analyzed as follows. The optimized structure features are mentioned in Section 3.1, and Section 3.2 discusses relevant results about the diradical character and magnetism of these multi-Be-expanded graphene-like molecules. Additionally, a special analysis about how to quantify the quintet tetraradical for 3Be-Pyr is given in Section 3.3. The redox stability of mBenA and the stability of mBe-GP are discussed in Section 3.4. 3.1. Structural Features. First, the optimized structures of mBe-nA are analyzed. Two representatives (3Be-2A and 2Be2A, the naphthalene derivatives multi-Be-modified in different ways: insertion along longitudinal (long axis) and quasitransverse directions of acenes) of two mBe-nA series in their ground states are shown in Figure 1, together with the corresponding parent naphthalene and the multi-Zn-expanded analogues24 for comparison. Obviously, two resembling

Figure 2. Schematic representation of the formation of the C−Be bonds and the p−π conjugation in the C−Be−C units. D

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Figure 3. Geometries of the multi-Be-expanded graphene patches in three different patterns (3Be-Pyr, 3Be-Ant, and 3Be-Bpe) with indicated bond lengths (Å) and adjacent Be−Be distances (Å) optimized at the UB3LYP/6-311++G** level.

more favorable than the corresponding CS singlet and triplet states (see Table 1 and Table S1 of the SI). The spin contaminations for their singlet states are also very stable with an almost constant value close to 1.0 (⟨S2⟩ = 0.73−1.05), which clearly indicates that the singlet state is a mixture of pure singlet (⟨S2⟩ = 0.0) and pure triplet state (⟨S2⟩ = 2.0). It should be especially noted that the spin contaminations for 3Be-2A (⟨S2⟩BS = 0.730) and 3Be-Bpe (⟨S2⟩BS = 0.785) are close to the ideal ⟨S2⟩ value (0.750) of a monoradical with doublet spin state, but these ⟨S2⟩BS values denote the degree of mixture of pure singlet and pure low-lying triplet state for these two diradical systems and are different from the ideal ⟨S2⟩ value of a monoradical. What is more, large values of ΔE(T‑BS) and ΔE(BS‑CS) for mBe-nA and mBe-GP (3Be-Ant and 3Be-Bpe) reflect the advantage of the open-shell singlet over the corresponding triplet and CS singlet ones (see Table 1 and Table S1 of the SI). Moreover, the magnetic coupling interactions of these molecules are characterized through the calculated magnetic exchange constants (J). The J values are much more negative or the |J| values are considerably larger for these molecules in their ground states, indicating that they possess strong AFM characteristics and thus are expected to have many more potential applications.54 In addition, the J values change from −1438.9 to −149.5 cm−1 for the 2Be-nA series, exhibiting a tunable magnetic coupling tendency. Clearly, this tendency should be attributed to the fact that the unpaired electrons become more delocalized and the spin coupling interaction becomes weaker as the number of fused benzenoid rings increases. Overall, all these mBe-nA and mBe-GP (excluding 3Be-Pyr) show prominent diradical character, in contrast with the parent oligoacenes (from benzene to pentacene) and graphene patches (anthanthrene and benzo[ghi]perylene) that have the CS ground states and are not radicals. More importantly, the magnetic coupling interactions of these mBe-nA and mBe-GP considered here are about 1.6 times stronger than those of the corresponding multi-Znexpanded analogues.24,25 To make a more intuitive comparison, the calculated J values (JBe) of mBe-nA and mBe-GP versus those (JZn) of the corresponding multi-Zn-expanded analogues are given in Figure 4, and relevant data are given in Table S2 (in the SI). All these results present a highly linear correlation, and the correlation slope is about 1.6. Clearly, this observation further confirms the conclusion that the magnetic coupling strength increases when the spacer length decreases.22,55 Hence, the shorter C···C distances in mBe-nA and mBe-GP than their corresponding Zn systems are conducive to enhancing the magnetic coupling interaction. Besides, we also

polyacetylene chains, forming the C−Be−C linkage. In these mBe-nA molecules, the C−Be bond lengths are about 1.65− 1.68 Å. Compared with the parent acenes, the cross-linking C··· C distances in mBe-nA are largely elongated by 1.8 Å from ∼1.5 Å (in the parent acenes) to ∼3.3 Å due to the introduction of Be atoms. Clearly, it is rational to predict that two radical polyacetylene chains become relatively separated and their interactions should become relatively weak when these crosslinking C−C units are replaced by C−Be−C with such an elongation (∼3.3 Å) for the C···C distances. As a consequence, two unpaired electrons on two polyacetylene radical chains become weakly coupled, inducing a change from the CS singlet ground state of the parent linear oligoacenes to the open-shell singlet diradical ground states for mBe-nA. In contrast, the cross-linked C···C distances in mBe-nA are about 0.6 Å shorter than those (about 3.9 Å) in the multi-Zn-expanded analogues.24 The shorter C−Be bond could be attributed to the far shorter covalent radius of Be (∼0.90 Å) than that (∼1.22 Å) of Zn. The optimized structures of mBe-GP with the marked bond lengths and adjacent Be···Be distances are given in Figure 3. At the same time, the corresponding multi-Zn-expanded analogues24 are given in Figure S2 (the SI) for comparison. The structure features of mBe-GP are similar to those of mBe-nA. That is, multi-Be insertion does not induce any significant structural distortions for the nanosized graphene patches except for the elongation of the middle cross-linking C···C distances. Like mBe-nA, the Be···Be distances of mBe-GP are about 2.64− 2.66 Å and the C−Be bonds are about 1.66−1.68 Å. The former is closer to the C···C distance (2.43−2.50 Å) between two approximately parallel C−Be−C units. The unpaired electrons on two conjugated fragments become weakly coupled as the two conjugated fragments in mBe-GP become relatively separated and their interaction becomes weak, leading to polyradical character for mBe-GP like that for mBe-nA, depending on the structures of the graphene patches. A general regularity is that the larger the radical fragments, the more delocalized the spin electrons and the weaker the interaction between them. 3.2. Diradical Characters and Magnetism. The calculations also indicate that almost all linear oligoacenes possess the CS singlet ground state, and only those larger than hexacene are expected to have diradical character in their ground states but which are still controversial and need further verification.13,17−19 However, surprisingly enough, our DFT calculations show that all mBe-nA have open-shell singlet ground states with the well-defined diradical character, implying that their open-shell singlet ground states are energetically E

DOI: 10.1021/acs.organomet.7b00082 Organometallics XXXX, XXX, XXX−XXX

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Organometallics

extension to Be is due to the small energy difference between the Be empty p orbitals and SOMOs of two Be-linked molecular fragments. That is, the partially conjugated structures could be described as the p−π conjugation of the empty pz orbitals of the Be couplers with the π orbitals of their linked molecular fragments due to symmetry matching and their comparable energy levels, leading to a considerably strong AFM interaction. Clearly, the coupling interaction between two radicals has not changed much in the (n+1)Be-nA (n = 1, 2) series, while that in the 2Be-nA (n = 1−5) series gradually decreases toward zero from 2Be-1A to 2Be-5A. This difference between the two series could be attributed to their different Be-doping modes, which causes two aspects of differences in the structures and properties and thus produces different effects on their J values. (1) The distances between the two radical centers (or their reduced centers) remain unchanged for (n+1)Be-nA but become elongated gradually as n increases for 2Be-nA.24 (2) As a major reason, as shown in Figure 5 and Figure S3 (in the SI), the two unpaired electrons are distributed uniformly throughout two parallel chains of polyacetylene for (n+1)BenA, keeping the total relative distance unchanged. However, for 2Be-nA, two single electrons are mainly distributed in the Belinked regions, respectively, and a part of spin density can spread to other benzenoid rings of 2Be-nA due to the πconjugation effect; this could ultimately make the total relative distances between the two spin single electrons increase along with the increase of the number of the fused benzene rings. As a result, the strength of the coupling interaction decreases along with the increase of n for 2Be-nA. Usually, the shapes of SOMOs play a major role in determining the magnetic properties of diradicals and could reflect the diradical character qualitatively and vividly. Here, the shapes of SOMOs (Figures 5, 6, and S3 of the SI) are further taken into account to characterize the diradicals quantitatively. As proposed by Borden and Davidson,56 a triplet state is the ground state when two SOMOs of a molecule are nondisjointed (atoms are common), while a molecule with disjointed shapes (atoms are not common) in two SOMOs would show a BS singlet ground state. We find that the shapes of SOMOs are disjointed for mBe-nA and 3Be-Ant and 3BeBpe of mBe-GP, and thus the ground states are an open-shell BS singlet with a strong AFM. The shapes of SOMOs in mBenA are very similar to the singly occupied orbitals of decacene with an open-shell singlet ground state, studied by Bendikov and co-workers.13 That is, the shapes of SOMOs show strong evidence for their remarkable diradical character. Generally, a perfect diradical is characterized by the occupation numbers of 1.0 in the HOMO and LUMO, whereas a perfect CS molecule possesses the occupation numbers of 2.0 and 0.0 in the HOMO and LUMO, respectively. To further explore the diradical character and depict the diradical character quantitatively, we performed CASSCF(10,10) calculations to obtain the occupation numbers of the LUMO as a measure of the amount of diradical character for these designed molecules.57,58 As shown in Table S3 (in the SI), the LUMO occupation numbers are 0.648 (⟨S2⟩BS = 0.80) and 0.563 (⟨S2⟩BS = 0.73) for 2Be-1A and 3Be-2A in the (n +1)Be-nA series, indicating their 65% and 56% diradical character percentages, respectively. For the 2Be-nA series, the LUMO occupation numbers range from 0.648 (⟨S2⟩BS = 0.80) to 0.884 (⟨S2⟩BS = 1.05), and the amounts of diradical character are 65−88%, respectively. For all mBe-nA, the diradical

Figure 4. Linear relationship of J values of the multi-Be-expanded oligoacenes and graphene patches with the multi-Zn-expanded analogues (calculated at the UB3LYP/6-31G**(C,H)/SDD(Zn) level), where M denotes Be or Zn.

show the singly occupied molecular orbitals (SOMOs) in Figures 5 and 6, and we notice that partial conjugation is

Figure 5. Singly occupied molecular orbitals (SOMO) of open-shell singlet multi-Be-expanded naphthalene (3Be-2A and 2Be-2A, isovalue = 0.02) and their corresponding spin density maps (isovalue = 0.004).

Figure 6. Singly occupied molecular orbitals (SOMOs) of open-shell singlet 3Be-Ant and 3Be-Bpe (isovalue = 0.02) and their corresponding spin density maps (isovalue = 0.004).

formed between two radical moieties and the coupler Be, which creates a beneficial condition for the magnetic coupling interaction between the two radical moieties. This conjugation F

DOI: 10.1021/acs.organomet.7b00082 Organometallics XXXX, XXX, XXX−XXX

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we also compared the HOMO−LUMO gaps for CS states of the Be-expanded and Zn-expanded oligoacenes and parent oligoacenes and graphene patches (Table S5 of the SI). The variation trend of the HOMO−LUMO gaps of parent oligoacenes and 2Be-nA as examples is given in Figure 8 for

character percentages are far larger than those (6−21%) of their parent acenes (the so-called CS molecules). Besides, the LUMO occupation numbers of 3Be-Ant and 3Be-Bpe in the mBe-GP series are 0.834 (⟨S2⟩BS = 0.97) and 0.612 (⟨S2⟩BS = 0.78), and consequently the diradical character percentages are estimated to be 83.4% and 61.2%, respectively. These results clearly confirm much more enhanced diradical character for mBe-nA and mBe-GP compared with their corresponding parent graphene-like molecules. Meanwhile, the results of LUMO occupation numbers are in good agreement with those estimated from the corresponding ⟨S2⟩BS values, further proving the accuracy of our computational results. The singlet−triplet gaps (Table S4 of the SI) and HOMO− LUMO gaps (Table S5 of the SI) of mBe-nA and mBe-GP were calculated in order to explore a favorable energetic basis that prompts mBe-nA and mBe-GP to exhibit perfect diradical characters. Taking 2Be-nA as examples, a succinct graphic is used for a more detailed and direct display of the differences of the singlet−triplet gaps between mBe-nA and their parent oligoacenes for a more intuitive comparison. In particular, just as shown in Figure 7 and Table S4 (in the SI), for 2Be-nA (n =

Figure 8. Variation trend of the HOMO−LUMO energy gaps for the CS states of oligoacenes and their corresponding 2Be-expanded oligoacene analogues (2Be-nA, n = 1−5).

a clear comparison. In detail, for the 2Be-nA series, the calculated HOMO−LUMO gaps decrease from 1.79 eV (2Be1A) to 0.83 eV (2Be-5A). In addition, the HOMO−LUMO gaps of 3Be-Ant and 3Be-Bpe are 1.15 and 1.47 eV, respectively. In comparison to those (from 6.79 eV/benzene to 2.21 eV/pentacene) of their parent acenes and parent graphene patches (2.87 eV/anthanthrene and 3.48 eV/ benzo[ghi]perylene), the HOMO−LUMO gaps of mBe-nA and mBe-GP are small enough so that they could allow the promotion of an electron from the HOMO to the LUMO to give diradical character more easily.59 On the other hand, we find the HOMO−LUMO gaps of mBe-nA are about 1 eV smaller than those of the Zn-expanded analogues.24 This could provide a favorable energetic basis for the stronger strength of the magnetic coupling interactions in mBe-nA compared with the Zn-expanded analogues. However, for 3Be-Ant and 3BeBpe in the mBe-GP series, their J couplings and the CS state HOMO−LUMO gaps do not obey the above relationship. The same is true for the corresponding Zn-containing analogues.25 Clearly, the differences should be attributed to their different structures, electronic properties, and molecular orbital topologies. But, as shown in Figure 4, a highly linear correlation of the J couplings between all these Be-expanded species and their corresponding Zn-containing analogues indicates that the Beexpanded and corresponding Zn-expanded graphene-like molecules follow the same regularity. Overall, these results further confirm the above conclusion that these multi-Beexpanded graphene-like molecules have open-shell singlet ground states and can be viewed as well-defined diradicals with considerably large magnetic couplings. 3.3. Tetraradical Character. It is worth noting that we obtain 3Be-Pyr with a quintet ground state when three Be are introduced into pyrene. An unrestricted BS UB3LYP/6-311+ +G** calculation indicates that 3Be-Pyr possesses tetraradical character in its ground state and first excited state (SOMOs and spin density map given in Figure S4 of the SI). To confirm the radical characters of its quintet ground state and open-shell BS

Figure 7. Dependences of singlet−triplet state energy gaps of acenes and their corresponding multi-Be-expanded oligoacenes (the 2Be-nA series, n = 1−5). The data in parentheses are the ⟨S2⟩ values of the corresponding species.

1−5), the gaps ΔE(T‑BS) rapidly decrease from 5.1 (2Be-1A) to 0.4 kcal/mol (2Be-5A). From this trend, we can predict that the gap would be gradually close to zero if the number of benzenoid units increases, even more probably leading to a triplet ground state. More importantly, the singlet−triplet gaps for two mBe-nA series are considerably smaller than those of their parent acenes especially of the shorter acenes (from benzene to pentacene). They are close to and even smaller than those (about 5.5 kcal/mol) of higher acenes with perfect diradical characters. The singlet−triplet gaps of higher acenes are shown in Table S4. On the other hand, the singlet−triplet gaps (ΔE(T−BS)) of 3Be-Ant (1.55 kcal/mol) and 3Be-Bpe (4.57 kcal/mol) in the mBe-GP series are also considerably small. In brief, these observations indicate that multi-Be introduction into some C−C bonds of the graphene-like molecules can produce Be-modified graphene-like derivatives with considerably small singlet−triplet gaps and also imply that multi-Be modification of the graphene-like molecules can provide a favorable energetic basis for the appearance of diradical character in the Be-modified graphene-like derivatives. Further, G

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diradicals through a multi-Be coupler, yielding a quintet tetraradical. 3.4. Stability of These Multi-Be-Modified Graphene Derivatives. In view of possible practical applications of these multi-Be-modified graphene-like molecules (mBe-nA and mBeGP), it is necessary to examine their stability including the redox stability of mBe-nA and bond dissociation energies of mBe-GP. Here, the redox stability of mBe-nA was examined through comparing their IPs and EAs and those of the corresponding oligoacenes and the multi-Zn-expanded analogues. For all mBe-nA, IPs (Table S6 of the SI) are slightly smaller than those of their corresponding parent oligoacenes, and the differences between the Be-expanded acenes and parent acenes decrease from 2.20 eV (2Be-1A) to 0.59 eV (2Be-5A). More importantly, IPs (5.54−6.89 eV) of these mBe-nA are still larger than that (e.g., IP = 5.19 eV for decacene) of higher acenes featuring diradical character and high redox reactivity, although Be introduction can cause a slight lowering of IPs compared with the corresponding parent acenes. Similar variation trends are also observed in EAs (Table S7 of the SI). Especially, the results indicate that IPs (5.54−6.89 eV) of these mBe-nA are closer to those (6.13−9.09 eV) of the corresponding parent acenes than those of multi-Zn-expanded analogues (5.28−6.39 eV), proving that the redox stability of mBe-nA is larger than those of the multi-Zn-expanded analogues that we studied before. Overall, both IPs and EAs indicate that mBe-nA possess enough redox stability. In addition, we calculated the bond dissociation energies of mBe-GP to measure their C−Be−C bond strength. Meanwhile, that of a dimethylberyllium (H3C−Be−CH3) compound that has linear, two-coordinate structures in the vapor phase was also calculated for comparison. The dissociation pattern is (−C−Be−C−)n → (−C−Be)n + (C−)n, where C denotes the linked carbon atoms of molecular fragments, as defined in Figure S6 of the SI. Results indicate that the dissociation energies of these mBe-GP are 293.59 (3Be-Ant), 294.85 (3BeBpe), and 297.03 (3Be-Pyr) kcal/mol, respectively, with average values of about 97.9, 98.3, and 99.0 kcal/mol for each C−Be−C in three 3Be-expanded graphene patches, respectively. The average bond dissociation energy of a single C−Be−C linkage is not only almost equivalent to that (94.4 kcal/mol) of H3C−Be−CH3, which was already synthesized experimentally, but also close to the bond dissociation energy (95.2 kcal/mol) of the Be complexes synthesized and calculated by Arrowsmith and co-workers.33 In short, for these designed mBe-expanded graphene-like derivatives, it is reasonable to predict that all of them should be thermodynamically stable and may be expected to be synthesized.

singlet excited state, we performed a CASSCF(10,10)/631G(d) calculation for the open-shell BS singlet state and obtained occupation numbers of LUMO+1 (0.674), LUMO (0.627), HOMO (1.330), and HOMO−1 (1.374), respectively, which clearly indicate tetraradical character.57,60 Further, we analyzed how to quantify the open-shell BS singlet tetraradical. For a system that possesses four unpaired electrons, the openshell BS singlet tetraradical could be achieved by linking two singlets or two triplets.60 As shown in Figure 9, a three-Be array

Figure 9. Model for four radical centers in 3Be-expanded pyrene (3BePyr). Jintra (6.3 kcal/mol) and Jinter (4.0 kcal/mol) denote the intrafragment and interfragment spin couplings, respectively.

divides pyrene into two semistructures, and each semistructure has been proved to possess a triplet ground state and thus be a triplet diradical. In general, there are two coupling modes for the two semistructures: ↑↑···↑↑, yielding a quintet state, and ↑↑ ···↓↓, yielding an open-shell singlet state, as shown in Figure S5. Examination indicates that 3Be-Pyr possesses a quintet ground state and thus is a high-spin tetraradical (↑↑···↑↑). To clarify the spin coupling degree, for the present system, two kinds of magnetic couplings are checked: the intrafragment direct coupling (Jintra) in each semistructure and the interfragment Be-mediated cross-coupling (Jinter) between the two semistructures. The intrafragment direct coupling (Jintra) in each semistructure coincides with the corresponding singlet−triplet energy gap, while the interfragment Be-mediated cross coupling (Jinter) is an intuitive measure of the coupling and electronic communication between the two semistructure radicals. In the calculations, the semistructure is directly extracted from the optimized 3Be-Pyr by cutting and hydrogen-saturating the C− Be bonds as the initial configuration, and single-point calculations are carried out at the B3LYP/6-311++G(d,p) level for the BS and T states. The calculated results (EBS = −309.6544777, ⟨S2⟩ = 1.013 and ET = −309.6645019, ⟨S2⟩ = 2.066) indicate the ground state to be triplet and Jintra is 6.3 kcal/mol using the Yamaguchi scheme.49−51 According to Figure S5, the interfragment coupling constant is 4.0 kcal/mol (Jinter = EBS − EQ, the energy difference between the BS and quintet states of 3Be-Pyr). These indicate that the intrafragment direct coupling is stronger than the interfragment Bemediated coupling, due to a better conjugative effect in the former. In addition, the calculated positive intrafragment coupling (Jintra) in each semistructure of pyrene is a direct evidence for a triplet ground state diradical, and the calculated positive Jinter value proves that the Be-mediated coupling of two triplet diradical fragments is also not too strong and has a ↑↑···↑ ↑ high-spin mode instead of a ↑↑···↓↓ low-spin mode. Clearly, this is direct evidence of the coupling between two triplet

4. CONCLUSIONS In summary, we theoretically designed mBe-nA in two series ((n+1)Be-nA, n = 1, 2, and 2Be-nA, n = 1−5), according to different ways of introducing two or three Be atoms to oligoacenes, and three mBe-GP (3Be-Pyr, 3Be-Ant, and 3BeBpe). The structures and electronic properties as well as magnetic coupling interaction of these Be-expanded molecules were explored and analyzed systematically and comprehensively. Both the unrestricted DFT and CASSCF calculations predict that all the mBe-expanded graphene-like molecules except 3Be-Pyr possess open-shell BS singlet ground states as diradicals, while 3Be-Pyr possesses a quintet ground state as a tetraradical with an open-shell BS singlet excited state (also a tetraradical). The calculated spin exchange coupling constants H

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(J) indicate that these molecules except for 3Be-Pyr possess strong AFM character, and especially the 2Be-nA (n = 1−5) series exhibit a tunable magnetic property. The more interesting finding in this work is the realization of magnetic switching from the nonmagnetic parent oligoacenes and graphene patches with the CS singlet ground states to the magnetic multi-Be-expanded graphene-like derivatives with an open-shell BS singlet ground state (AFM diradicals) or quintet ground state (tetraradical) by introducing Be as the linkers. More importantly, the magnetic coupling strength of these multi-Be-expanded graphene-like derivatives is considerably enhanced compared with that of the multi-Zn-expanded analogues. In addition, because of the covalent characteristics of the formed Be−C bonds, there is no repulsion between two adjacent Be atoms; instead there is a weak s2···s2 metallophiliclike interaction between them, as evidenced by approximately parallel C−Be−C linkages in each molecule. On the whole, this work provides a new strategy for the design of magnetic material molecules with significantly enhanced magnetic properties on the basis of the graphene-like molecules. Clearly, this strategy could be also applied to other graphene-like molecular systems for obtaining expected polyradical structures with tunable magnetic coupling characteristics through choosing the structural shapes and Be-modification modes of the target graphene-like molecules. Besides, this theoretical study also contributes to the growing field of structural chemistry of Be compounds and hopefully can encourage experimentalists to pursue and realize interesting structures with enhanced spin-coupling properties.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.7b00082. Calculated data and figures including energies of the CS singlet, open-shell BS singlet, and T states, geometrical parameters, magnetic coupling constants; SOMOs and spin density maps; occupation numbers of LUMO and diradical percentages; singlet−triplet energy gaps; HOMO−LUMO energy gaps, IPs, EAs, and others (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86-531-88363670. ORCID

Xinyu Song: 0000-0002-7486-9388 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by NSFC (21373123, 21573128, and 20973101) and NSF (ZR2013BM027) of Shandong Province. All calculations were carried out at the National Supercomputer Center in Jinan, the National Supercomputer Center in Shenzhen, and the High-Performance Supercomputer Center at SDU-Chem. I

DOI: 10.1021/acs.organomet.7b00082 Organometallics XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.organomet.7b00082 Organometallics XXXX, XXX, XXX−XXX