Organic Magnetic Diradicals (RadicalâCouplerâRadical

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Organic Magnetic Diradicals (Radical-Coupler-Radical): Standardization of Couplers for Strong Ferromagnetism Daeheum Cho, Kyoung Chul Ko, and Jin Yong Lee J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 17 Jun 2014 Downloaded from http://pubs.acs.org on June 21, 2014

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The Journal of Physical Chemistry

Organic Magnetic Diradicals (Radical-Coupler-Radical): Standardization of Couplers for Strong Ferromagnetism Daeheum Cho, Kyoung Chul Ko, and Jin Yong Lee* Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea E-mail: [email protected]

RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to)

TITLE RUNNING HEAD. Strong ferromagnetic diradical molecules

CORRESPONDING AUTHOR FOOTNOTE. Jin Yong Lee Phone: +82-31-299-4560

Fax: +82-31-290-7075

e-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT. The intramolecular magnetic coupling constant (J) values of sets of diradicals linked with bis-DTDA, OVER and NN radicals (DTDA, OVER and NN groups) through an aromatic coupler were studied by unrestricted density functional theory calculations (UB3LYP/6-311++G(d,p). Among fifteen aromatic couplers, nine compounds with odd number of carbon atoms along its spin coupling path were found to give ferromagnetic interaction upon coupling with bisradicals while the other six couplers with even number of carbon atoms along its spin coupling path give rise to antiferromagnetic coupling. The overall trends in the strength of magnetic interactions of aromatic couplers were preserved for DTDA, OVER and NN groups so that the trend can be utilized as an index for the magnetic strength of a given coupler. It was found that the difference in nucleus independent chemical shift (NICS), bond order of connecting bonds and Mulliken atomic spin density at connected atoms between triplet and BS states are closely related to the intramolecular magnetic behavior. 2,4- and 2,5-phosphole couplers exhibit the strongest intramolecular ferromagnetic and antiferromagnetic interactions among fifteen aromatic couplers when linked with diverse bisradicals.

KEYWORDS

(Word

Style

“BG_Keywords”).

Diradical,

aromatic

coupler,

intramolecular

ferromagnetic interaction, intramolecular magnetic coupling constants, spin polarization, DFT calculations

BRIEFS (WORD Style “BH_Briefs”). A systematic study for various diradicals coupled via aromatic couplers proposed a strongly coupled ferromagnetic diradical with 2,4-phosphole coupler.


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1. Introduction Organic magnetic materials have been received considerable attention due to its superior properties such

as

lightness,1

magnetic

property,2

photomagnetic

behavior,3–5

spintronic

property,6,7

superconductivity,8,9 and so on. Especially, organic ferromagnetic materials can play an important role in spintronic applications. For example, graphene-based spintronics by means of their weak spin-orbit interaction, resulted in long spin-relaxation time.10,11 Since the discovery of the first pure organic magnet, β-crystal phase of p-nitrophenyl nitronyl nitroxide,12,13 many efforts have been made to understand the intra- and inter-molecular organic magnetic interactions14–18 and to develop strongly coupled pure organic magnets19–21. In a molecular point of view, intramolecular magnetic coupling constant governs the magnetic interaction within a molecule, and molecular crystal pattern, in turn, determines the intermolecular magnetic interaction. Although the material is an assembly of ferromagnetic molecules, only some of them can have magnetic behavior depending on the nature of molecular crystal. However, there is no objection to the fact that it is always beneficial to develop magnetic materials starting from the strong ferromagnetic molecular building blocks.

Figure 1. Structures of dithiadiazolyl (DTDA), carbon-connected 6-oxoverdazyl (OVER), and nitronyl nitroxide (NN) monoradicals.

In this context, diradicals which are the most elementary compounds containing intramolecular magnetic exchange interaction have been extensively investigated experimentally and theoretically for ACS Paragon Plus Environment

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several decades.22–29 Among the various neutral radicals, dithiadiazolyl (DTDA), carbon-connected 6oxoverdazyl (OVER) and nitronyl nitroxide (NN) radicals have been particularly spotlighted due to their remarkable stability, synthetic simplicity and ability to generate the corporative magnetism (Figure 1).22,24,30–37 The DTDA radicals are a group of heterocyclic sulfur-nitrogen-containing free radicals that are well known as building blocks for organic magnets38 as well as super-conducting materials39,40. Variety of DTDA derivatives have been investigated since the first synthesis of phenyl-1,2,3,5dithiadiazolyl in 1980.41,42 The use of DTDA radical needs to be careful due to its strong propensity to form dimerization and various crystal structures.43 Verdazyl has become one of the largest families of stable radicals since its first synthesis and characterization by Kuhn and Trischmann in 1963.44 The oxoverdazyl is a famous branch of the verdazyl radicals. In this study we employ the carbon-connected 6-oxoverdazyl (OVER) in which the carbon atom is connected to another radical via a coupler. Since the discovery of first pure organic ferromagnet based on NN radical in 1991, NN is still believed to be the most promising neutral radical to generate very strong corporative magnetism and has been actively studied.16,17,22,26,28,45 Based on the density functional theory (DFT) calculations, diradicals consisting of aforementioned

free

radicals

were

confirmed

to

possibly

generate

pure

organic

ferromagnetism.16,23,26,46,47 The role of coupler linking two monoradicals through π-conjugation for the diradical is well known in magnetic exchange interaction.26–28 Generally, in conjugated diradical systems, the strength of the magnetic interaction reduces as the distance and dihedral angle between radicals and coupler increases.16,23,45,46 Introduction of heteroatom to coupler renders spin polarization through π-conjugation and produces two (or more) inequivalent spin coupling pathway of magnetic interaction48, making the prediction of magnetic exchange interaction more complicated. Ali and Datta examined the influence of various characteristics of a coupler on magnetic interaction such as bond order between radical and coupler and nucleus independent chemical shift (NICS)49 of an aromatic ring coupler.47 However, although many efforts have been made to understand the influence of coupler in magnetic coupling, to


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the best of our knowledge, there is no study to quantify and standardize the magnetic coupling strength of diverse couplers.

Scheme 1. Model systems used for standardization (I, II, and III) of the strength of the intramolecular magnetic interactions of the neutral radicals.

Recently, we developed model diradical systems (Models I, II, and III as depicted in Scheme 1) to standardize the strength of intramolecular magnetic interaction of diverse monoradicals.50 As shown in scheme 1, Models I and II have almost planar geometry and nearly equal coupler length. The model systems employ carbon-connected 6-oxoverdazyl (OVER) radical as a stationary reference to evaluate sole effect of diverse neutral radicals and to reduce steric repulsion with hydrogen atoms in benzene ring. Also, the ethynyl group was added to remove the repulsion between (m- or p-) benzene coupler and neutral radicals. These models exclude the influence of dihedral angle and coupler length and were successfully applied to standardize the strength of intramolecular magnetic interaction of diverse neutral radicals.51 Furthermore, on the basis of that result, we designed the strongly coupled ferromagnetic diradical materials as compared to known diradicals based on computational approach. As a result, we


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have shown that it is especially beneficial for designing ferromagnetically coupled diradicals and selecting radical moieties from the standardized set of monoradicals. In line with this, here we establish a strategy to evaluate a trend of the strength of intramolecular magnetic interactions for various aromatic couplers for efficient selection of coupler to design strongly coupled organic magnetic materials. To achieve this aim, magnetic coupling constant of a series of diradicals in three model systems (Scheme 2) were examined. In each system, the reference bisradicals were coupled via diverse aromatic couplers. Furthermore, we attempted to understand the trend of magnetic strength on the basis of the change in the nucleus independent chemical shift (NICS) of the aromatic couplers, bond order between coupler and radicals and atomic spin density distribution (spin polarization pattern).

2. Computational Details The magnetic exchange interactions between two magnetic centers 1 and 2 can be expressed by Heisenberg spin Hamiltonian

Hˆ = −2JSˆ1Sˆ2

(1)

Where Sˆ1 and Sˆ2 are the respective spin angular momentum operators and J is the magnetic exchange coupling constant. A positive sign of J indicates a ferromagnetic interaction while a negative indicates an antiferromagnetic interaction between the two spin moments. Larger absolute value of the J indicates stronger magnetic exchange interaction. For a diradical, J of eq 1 can be represented as E ( S = 1) − E ( S = 0) = − 2 J

(2)

Where E ( S = 1) and E ( S = 0) corresponds to the energies of the triplet and singlet states of a diradical molecule, respectively. So the magnetic coupling constant can be evaluated by simply determining correct triplet and singlet energy values. A number of calculations have been attempted to obtain


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reliable J.28,46,52 Despite of its simplicity, accurate computation of J is still challenging. For example, the use of unrestricted Hartree-Fock (UHF) method introduces spin contamination, which is an artificial mixing of different spin states, in singlet diradical calculations, resulting in poor description of the energy of singlet spin state.50 The use of multiconfigurational methods, which yield pure singlet spin states but are computationally heavy, is not allowed for systems containing a large number of atoms.48 An alternative approach is the broken symmetry (BS) formalism proposed by Ginsberg and Noodleman so as to obtain proper description of the lowest spin state, singlet state in a diradical, with less computational cost.53–55 BS approach have been successfully applied to diradical systems to compute reliable magnetic coupling constant J by many authors independently.37,50–52,56–59 BS solution is not an eigenfunction of Heisenberg spin Hamiltonian, but is an admixture of the singlet and triplet states. Based on the BS formalism, the magnetic coupling constant can be written as

J=

where

( EBS − ET ' ) 1 + Sab 2

(3)

S ab is the overlap integral between the two magnetic orbitals a and b. EBS and ET’ are the energy

of the BS solution for the singlet state and the energy of the triplet state using the BS orbitals. ET’ could be approximated by the energy of triplet state ( ET ' ≈ ET ) which is obtained by unrestricted density functional theory (UDFT) calculation due to its small spin contamination in the high spin state. In contrast to triplet state, the BS state is often spin contaminated so that requires proper spin projection procedure. Depending on the overlap integral Sab2, there are many different spin projection schemes. Among them, Yamaguchi et al.60 proposed an elegant way of spin projection by replacing overlap integral as average spin square values of each spin states. According to Yamaguchi’s projection scheme, the magnetic coupling constant J is given by


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J=

2

( EBS − ET ) < S 2 >T − < S 2 >BS

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(4)

2

where < S >T and < S >BS are average spin square values for corresponding triplet and BS states. Magnetic coupling constants reported in this study were computed by using this projection scheme. All the calculations were carried out by using a suite of Gaussian 09 programs.61 The unrestricted B3LYP (Becke 3-parameter exchange, Lee-Yang-Parr correlation)62 hybrid functional was used in combination with the 6-311++G(d,p) basis set for all geometry optimizations. Since an approximate exchange-correlation functional is used in DFT calculations, discrepancy between calculated and experimental J values might be inevitable. It is well known that DFT calculations often provide overestimated J values. B3LYP functional, however, have been proved to give qualitatively correct prediction of J.26,50,52 Frequency calculations were performed to make sure that the optimized geometries are true local minima on the potential energy surface and to obtain zero-point vibrational energy corrections. In order to obtain BS open-shell singlet solution, firstly, single point calculation was performed with “stable = opt” (ensuring the stability of the initial wavefunction) and “guess = mix” (enabling BS formalism) keywords, then geometry optimization was carried out only with “guess = mix” keyword. To understand the influence of aromaticity of the coupler on the magnetic interaction, the nucleus independent chemical shift (NICS) values were calculated at the center of the aromatic ring by means of GIAO-B3LYP/6-311++G(d,p) method. Wiberg indices of connecting bonds linking two monoradicals through a coupler (See Figure 1) were calculated by using natural bond orbital (NBO)63 analysis to study the effect of bonding nature of the diradicals on the magnetic exchange interaction.

3. Results and discussion


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Scheme 2. Diradical groups used for standardization of the strength of the intramolecular magnetic interactions of the aromatic couplers

As already mentioned in the introduction, magnetic interaction is significantly affected by the length of a coupler and dihedral angle. For a conjugated diradical, the strength of magnetic interaction decreases with the increase of coupler length and dihedral angle between coupler and radicals. Even ground-state spin crossover from triplet to singlet can occur by changing the dihedral angle.50 To this end, eliminating the effect of dihedral angle is necessary to evaluate the sole effect of a coupler on the magnetic interactions, while the spacer length is an intrinsic character of a coupler. On the other hand, we need to consider at least several groups of radicals to attenuate the characteristic behavior of a certain radicals on magnetic interaction. Thus, we carefully designed series of diradical model systems where stationary reference bisradicals are coupled through various couplers that satisfy above conditions. As seen in Scheme 2, DTDA, OVER and NN bisradicals were linked via fifteen aromatic couplers (see also Figure 2 for the selected couplers). The use of DTDA and OVER have the advantages of almost planar geometries (dihedral angle ranges from 0 to 7.6 o , and see Supporting Information, Table S4 and S5) due to less steric repulsion at contact between the radicals and coupler so as not to introduce dihedral angle effect. Additionally, NN based bisradicals were used to confirm the applicability of the predicted trend of the strength of intramolecular magnetic interaction where the dihedral angle between ACS Paragon Plus Environment

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bisradicals and coupler ranges from 0 to 34 o (see Supporting Information, Table S6).

Figure 2. Fifteen aromatic couplers (i-xv) investigated (R = DTDA, OVER, and NN).

Figure 2 shows the selected aromatic couplers and corresponding model systems investigated in this study (See also Scheme 2). Aromatic five- or six-membered ring couplers with broad range of aromaticity (NICS values of −5 ~ −17) including phosphole, benzene, thiophene, pyridine, furan, azulene, pyrrole and triazole were studied. We exclude linear couplers such as ethylene, butadiene and hexatriene for simplicity of analysis. We considered different topological arrangement between radicals and coupler, for example, 2,4-phosphole based bisradical (i) and 2,5-phosphole based bisradical (xv), because they give different strength and type of intramolecular magnetic exchange interaction according to spin alternation rule.23,26 According to this rule, for example, NN-m-benzene-NN diradical is expected to have triplet ground state (ferromagnetic), while NN-p-benzene-NN has singlet ground state (antiferromagnetic).26


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Table 1. Calculated intramolecular magnetic coupling constants (J in cm-1) of various couplers (i-xv) for DTDA, OVER, and NN groups. Couplers 2,4-phosphole based bisradical (i) 1,3-phenylene based bisradical (ii) 2,4-thiophene based bisradical (iii) 3,5-pyridine based bisradical (iv) 2,6-pyridine based bisradical (v) 2,4-furan based bisradical (vi) 1,3-azulene based bisradical (vii) 2,4-pyrrole based bisradical (viii) 1,2,4-triazole based bisradical (ix) 2,5-pyridine based bisradical (x) 1,4-phenylene based bisradical (xi) 2,5-pyrrole based bisradical (xii) 2,5-furan based bisradical (xiii) 2,5-thiophene based bisradical (xiv) 2,5-phosphole based bisradical (xv)

(a)

DTDA 48.2 33.6 29.9 31.7 24.5 24.5 22.0 15.5 14.4 -56.0 -56.7 -77.1 -89.3 -85.5 -123.2

OVER 61.5 53.8 41.0 39.7 24.4 32.7 31.1 23.4 8.3 -63.4 -67.2 -72.8 -91.9 -92.4 -132.4

(b)

(c)

200

200

100

100

NN 128.7 48.3 69.7 53.2 27.2 56.2 34.5 17.7 0.0 -158.5 -202.9 -322.0 -373.9 -395.1 -543.1

40

0

-40

-80

-120

-160

-1

-1

The J values of NN group (cm )

-1


80

The J values of OVER group (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 -100 -200 -300 -400 -500 -600

-120

-80

-40

0

40 -1

The J values of DTDA group (cm )

0 -100 -200 -300 -400 -500 -600

-120

-80

-40

0

40 -1


-120

-80

-40

0

40

80 -1


Figure 3. Correlation between calculated J values of each bisradical groups. (a) DTDA and OVER groups, (b) DTDA and NN groups, and (c) OVER and NN groups.

The calculated J values of each set of bisradicals were listed in Table 1 (See Supporting Information Table S1, S2 and S3 for zero-point corrected energies and spin square values for triplet and BS states). Interestingly, the same trend in the magnitude of J values through (i) to (xv) couplers is observed in different radicals (DTDA, OVER and NN groups) except for a few cases such as (iii) of DTDA group,


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(v) of OVER group, and (ii) of NN group. Figure 3 represents correlation among calculated J values of each set of radical group: (a) DTDA and OVER groups, (b) DTDA and NN groups, and (c) OVER and NN groups. The linear correlations indicate that the trends of magnetic strength of aromatic couplers are maintained for three different radical groups. It implies that the trend obtained by using our standardization scheme can be utilized as an index for the strength of magnetic interactions of couplers when it is coupled with variety of radical species. Among fifteen couplers of each group, 2,4-phosphole (i) gave the largest positive J, i.e., the strongest ferromagnetic coupling, while 2,5-phosphole (xv) resulted in the largest negative J, i.e., the strongest antiferromagnetic coupling. The magnitude of the absolute J value with 2,5-phosphole (xv) is twice to four times larger than that with 2,4-phosphole (i). Hence we can conclude that 2,4-phosphole (i) and 2,5-phosphole (xv) couplers can be utilized to make strong ferromagnetic and antiferromagnetic bisradicals, respectively. On the other aspect, nine couplers (i-ix) resulting in positive J (ferromagnetic interaction) and the other six couplers (x-xv) resulting in negative J values (antiferromagnetic interaction) can act as ferromagnetic and antiferromagnetic coupler upon coupling with bisradicals. We compared the J values of bisradicals with aromatic couplers to those with ethylene coupler which is considered to be the strongest magnetic coupler. Compared to our previous results for magnetic coupling constant J of bisradicals with ethylene coupler, the absolute J values of NN-2,5-phosphole-NN (-543.1 cm-1) and OVER-2,5-phosphole-OVER (-132.4 cm-1) are smaller than that of NN-ethylene-NN50 (-842.1 cm-1) and OVER-ethylene-OVER51 (-218.6 cm-1), respectively. Thus, 2,5-phosphole coupler gives a weaker magnetic interaction between

radicals

connected at both ends than ethylene coupler. On the other hand, 2,4-phosphole coupler has spin coupling path through odd number of carbon atoms and generates intramolecular ferromagnetic interaction when coupled with bisradicals pair, while ethylene coupler has spin coupling path through even number of carbon atoms with antiferromagnetic interaction. Generally, couplers consisting of spin coupling path through even number of conjugated carbon atoms yield intramolecular ferromagnetic coupling only when coupled with hetero-diradicals. Considering the synthetic difficulty of hetero-


12

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diradicals,64 2,4-phosphole have advantage to generate ferromagnetically coupled bisradicals. Moreover, slopes of the graph in Figure 3 imply the ratios among the magnitudes of J for different radicals. From the values of the slopes, 1.12, 3.64, and 3.20 for Figure 3(a), (b), and (c), respectively, we know that the magnitude of magnetic coupling strength of NN group is about three times that of DTDA and OVER groups, while the magnitude of magnetic coupling strength of OVER group is almost equivalent to that of DTDA group. Hence, the strength of magnetic interaction of the radical groups studied here is in the order of NN > OVER ~ DTDA, which is fully consistent with our previous study on standardization of the magnetic strength of diverse organic radical species.50 In order to further understand the influence of coupler on intramolecular magnetic coupling constant (J), we analyzed isotropic nucleus independent chemical shift (NICS(0)iso) of all the aromatic rings, Wiberg bond indices of connecting bonds, and Mulliken atomic spin density at connected atoms in each bisradicals. We more focused on the difference of these values between triplet and BS states, because the nature of magnetic interaction is determined by relative stability of the two spin states.

Nucleus Independent Chemical Shift (NICS). NICS is well-known measure of aromaticity for diverse cyclic compounds based on their ring currents.65–67 The effect of aromaticity on intramolecular magnetic interaction has already been discussed.47,65 Higher loss of aromaticity upon coupling with radical moieties is thought to be due to the strong participation of the π-electrons in the magnetic exchange polarization.47 In most of the previous study, they didn’t consider the NICS values of both triplet and BS spin states of diradicals. However, the change in the aromaticity between triplet and BS states would be more critical for magnetic behavior. Thus, the difference between the NICS(0)iso values of triplet and BS state (∆NICST-BS = NICS(0)iso,T – NICS(0)iso,BS) is calculated and reported in Table 2 (see Supporting Information for the NICS values of corresponding parent aromatic couplers). Since NICS values of aromatic ring is negative and become positive upon loss of aromaticity, positive values of ∆NICST-BS indicates the higher degree of aromaticity loss (strong spin polarization) in triplet state


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and vice versa. As shown in Table 2, positive ∆NICST-BS values were found in bisradicals (i)-(ix) with positive J, and negative values in bisradicals (x)-(xv) with negative J. Moreover, Figure 4 indicates that there is a linear correlation between ∆NICST-BS and J values. This finding strongly supports the statement that higher loss of aromaticity corresponds to strong spin polarization. However, we cannot find any notable relationship between NICS value of parent aromatic coupler and J values of bisradicals (See Supporting Information Figure S1, S2 and S3). We can recognize that the difference in the NICS values between triplet and BS state is directly related to the J values of bisradicals not NICS values of parent coupler.

Table 2. The difference between the NICS(0)iso values of triplet and BS state (∆NICST-BS) and J values (in cm-1) of various couplers for each bisradical groups.

Couplers

DTDA J (cm-1) ∆NICST-BS

(i) 0.0393 48.2 (ii) 0.0805 33.6 (iii) 0.0642 29.9 0.0810 31.7 (iv) (v) 0.0454 24.5 0.0536 24.5 (vi) (vii) 0.0422 22.0 0.0727 15.5 (viii) (ix) 0.0099 14.4 -0.0778 -56.0 (x) (xi) -0.0775 -56.7 (xii) -0.0313 -77.1 (xiii) -0.0697 -89.3 (xiv) -0.0717 -85.5 (xv) -0.2037 -123.2 a not displayed in the linear regression.

OVER ∆NICST-BS 0.0498 0.1135 0.0819 0.1071 0.0640 0.0693 0.0710 0.0901 0.0062 -0.0950 -0.1069 -0.0161 -0.0657 -0.0801 -0.5775a

NN -1

J (cm ) 61.5 53.8 41.0 39.7 24.4 32.7 31.1 23.4 8.3 -63.4 -67.2 -72.8 -91.9 -92.4 -132.4


∆NICST-BS 0.1239 0.1274 0.1318 0.1252 0.0641 0.1076 -0.0010 0.0773 0.0087 -0.2149 -0.2435 -0.3047 -0.2814 -0.3324 -0.2120a

J (cm-1) 128.7 48.3 69.7 53.2 27.2 56.2 34.5 17.7 0.0 -158.5 -202.9 -322.0 -373.9 -395.1 -543.1

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(a)

(b)

(c)

100

200

60 80

0 -20 -40 -60 -80 -100 -120 -140 -160 -0.25

-0.20

-0.15

-0.10

-0.05

0.00

∆NICST-BS of DTDA group

0.05

0.10

100 60

-1

-1

20


40


-1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40 20 0 -20 -40 -60 -80 -100

0 -100 -200 -300 -400 -500

-120 -0.15

-0.12

-0.09

-0.06

-0.03

0.00

0.03

0.06

0.09

0.12

∆NICST-BS of OVER group

0.15

-600 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00

0.05

0.10

0.15

0.20

∆NICST-BS of NN group

Figure 4. Correlation between ∆NICST-BS and J values of (a) DTDA, (b) OVER and (c) NN groups.

Bond Order. Bond order is a typical parameter representing the degree of interaction between coupler and radical moiety in diradicals.47 As illustrated in Figure 1, the atoms of radical moieties marked with open triangle were connected to a coupler and were named as “connecting atom”, and the bonds linking coupler and connected atom were named as “connecting bond”. Each diradicals has two connected atoms and connecting bonds since there are two radical moieties in the diradical. Wiberg bond indices of the two connecting bonds in triplet and BS state were calculated and the averaged values were denoted as BOT and BOBS, respectively. It is widely accepted that a coupler extensively conjugated with monoradical moieties can generate a strong magnetic interaction between the two radical sites.5,35,47,68,69 However, we here emphasize that the difference in bond orders between triplet and BS state is more intimately related with intramolecular magnetic coupling constant (J). The difference in the average bond orders between triplet and BS state (∆BOT-BS = BOT - BOBS) of fifteen bisradicals were listed in Table 3. As expected, bisradicals with larger positive J value exhibit more positive ∆BOT-BS values, indicating stronger interaction between coupler and radical moieties in triplet state resulting in ferromagnetic interaction. Therefore, we can deduce that effective coupling between radical moieties through a coupler in the triplet state allows significant spin polarization arising from the interactions within radical pairs, making triplet state to be lower in energy than BS state (for discussions about spin polarization, see also next section). As shown in Figure 5, we can observe linear correlation between ∆BOT-BS and magnetic coupling constant J in DTDA, OVER, and NN groups (A few exceptions such


15


as (iv) and (x) of NN group are not displayed for the linear regression). However, we cannot find any correlation between the absolute bond orders of triplet (or BS) state and J (See Supporting Information, Figure S4, S5, and S6).

Table 3. The difference of average Wiberg bond indices of connecting bonds between triplet and BS states (∆BOT-BS) and J values for DTDA, OVER, and NN groups. DTDA J (cm-1) ∆BOT-BS

OVER -1 ∆BOT-BS J (cm )

NN

Couplers J (cm-1) ∆BOT-BS (i) 0.0016 48.2 0.0020 61.5 0.0055 128.7 (ii) 0.0006 33.6 0.0012 53.8 0.0028 48.3 (iii) 0.0009 29.9 0.0013 41.0 0.0028 69.7 b (iv) 53.2 0.0006 31.7 0.0009 39.7 -0.2465 (v) 0.0005 24.5 0.0010 24.4 0.0019 27.2 a (vi) 0.0008 24.5 0.0010 32.7 56.2 (vii) 0.0005 22.0 0.0011 31.1 0.0037 34.5 a (viii) 0.0004 15.5 0.0006 23.4 17.7 (ix) 0.0003 14.4 0.0007 8.3 0.0006 0.0 b (x) -0.0019 -56.0 -0.0024 -63.4 0.0439 -158.5 (xi) -0.0017 -56.7 -0.0027 -67.2 -0.0057 -202.9 (xii) -0.0028 -77.1 -0.0034 -72.8 -0.0127 -322.0 (xiii) -0.0032 -89.3 -0.0040 -91.9 -0.0171 -373.9 (xiv) -0.0032 -85.5 -0.0036 -92.4 -0.0196 -395.1 (xv) -0.0052 -123.2 -0.0059 -132.4 -0.0262 -543.1 a b unable to obtain Wiberg bond indices by NBO analysis. not displayed in the linear regression.

(a) 60

(c)

100

200

0 -20 -40 -60 -80 -100 -120 -140

100

60

-1


-1

20

-160 -0.006

(b) 80

40


-1


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40 20 0 -20 -40 -60 -80 -100 -120 -140 -160

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

∆BOT-BS of DTDA group

0.001

0.002

-0.006

-0.004

-0.002

0.000

0.002

∆BOT-BS of OVER group

0 -100 -200 -300 -400 -500 -600 -0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

∆BOT-BS of NN group

Figure 5. Correlation between ∆BOT-BS and J (in cm-1) of (a) DTDA group, (b) OVER group and (c) NN group. ACS Paragon Plus Environment

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Mulliken atomic spin density. In the previous study, we found a close relationship between the Mulliken atomic spin density at the connecting atom of radical moiety and the strength of the magnetic interaction of diradical systems.50 We observed that a diradical with higher spin density at connected atom exhibits stronger intramolecular magnetic exchange interaction (and consequently larger J). Mulliken atomic spin densities at the connecting atom of diverse monoradicals that are coupled with a reference oxoverdazyl-m(or p)-benzene-coupler were calculated and used as an index for the strength of intramolecular magnetic interaction of the given radical moiety. On the other hand, atomic spin density distribution pattern in the diradical also allows us to predict the ground spin state as per the rule of spin alternation.23,26,27 To evaluate the strength of magnetic interaction of aromatic couplers, we analyze the trend of spin density at connecting atoms of diradicals in which reference bisradicals (DTDA, OVER and NN) are linked via a coupler. The differences in the Mulliken atomic spin densities between triplet and BS state (ρ(T-BS) = ρ(T)-ρ(BS)) at connecting atoms were calculated for the series of bisradicals. Surprisingly, linear correlations between ∆ρ(T-BS) and the magnetic coupling constant (J) were observed for the three groups of bisradicals (Table 4 and Figure 6). In association with the relationship among bond order, Mulliken spin density, and magnetic coupling constant J, we argue that considerable interaction between monoradicals through a coupler in triplet state opens up the possibility for strong spin polarization in triplet states leading to strong intramolecular ferromagnetic interaction. Indeed, for bisradicals with positive J (i-ix), spin polarization in triplet state is dominant over BS state (see Supporting Information Figure S7, S8 and S9 for all the Mulliken atomic spin density distributions of bisradicals).48,70–73

Table 4. The difference of average spin densities of connecting atoms between triplet and BS states (∆ρ(T-BS)) for DTDA, OVER, and NN groups. DTDA Couplers

∆ρ(T-BS)

-1

J (cm )

OVER J (cm-1) ∆ρ(T-BS)


∆ρ(T-BS)

NN J (cm-1) 17


(i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii) (xiv) (xv)

0.0075 0.0110 0.0040 0.0070 0.0130 0.0040 0.0040 0.0030 0.0015 -0.0080 -0.0100 -0.0090 -0.0090 -0.0130 -0.0170

48.2 33.6 29.9 31.7 24.5 24.5 22.0 15.5 14.4 -56.0 -56.7 -77.1 -89.3 -85.5 -123.2

(a) 60

61.5 53.8 41.0 39.7 24.4 32.7 31.1 23.4 8.3 -63.4 -67.2 -72.8 -91.9 -92.4 -132.4

0.0115 0.0040 0.0085 0.0050 0.0020 0.0045 0.0020 0.0060 0.0005 -0.0035 -0.0070 -0.0070 -0.0130 -0.0110 -0.0185

(b)

(c)

100

200

20

128.7 48.3 69.7 53.2 27.2 56.2 34.5 17.7 0.0 -158.5 -202.9 -322.0 -373.9 -395.1 -543.1

0 -20 -40 -60 -80 -100 -120

100

60

-1


-1 -1

40

-140 -0.020

0.0040 0.0130 0.0025 0.0040 0.0090 0.0025 0.0020 0.0020 0.0025 -0.0085 -0.0090 -0.0100 -0.0100 -0.0100 -0.0140

80

The J values of OVER group (cm ) )

-1


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40 20 0 -20 -40 -60 -80 -100 -120

0 -100 -200 -300 -400 -500

-140 -600

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

∆ρ(T-BS) of OVER group

∆ρ(T-BS) of DTDA group

0.020

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

∆ρ(T-BS) of NN group

Figure 6. Correlation between Mulliken atomic spin density at connecting atoms and J values (in cm-1) of (a) DTDA, (b) OVER and (c) NN groups.

We tried to understand the ground spin states of bisradicals by analyzing the spin density distributions in terms of spin alternation rule. The rule states that the adjacent atomic center in π-conjugated system prefers opposite spins, in other word, α- and β-spin alternatively. Figure 7 shows the plots of spin density distributions of triplet and BS states of (i) and (xv) in DTDA, VER, and NN group bisradicals (see Supporting Information Figure S10 through S15 for all the spin density distributions of bisradicals). It is worth to note that the spin polarization of (i) in BS state and (xv) in triplet state are blocked (black solid line) for all three groups of bisradicals. It is well known that ground spin state follows the spin


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alternation pattern through the coupler, while energetically unfavorable spin state has a mismatching of spin polarization.50 By means of this rule, we can predict that ferromagnetic and antiferromagnetic couplings are favored in (i) and (xv) bisradicals, respectively, and this prediction is consistent with our computational results. Hence, we can notice that the similarity in the magnetic behaviors of three different classes of bisradicals, DTDA, VER, and NN, originates from the similarity of spin polarization pattern and also that magnetic behaviors of diverse bisradicals can be qualitatively estimated by spin alternation rule.

Figure 7. Spin density distributions of triplet (T) and BS states of (i) and (xv) for DTDA, VER, and NN group bisradicals. Blue and green colors represent the α- and β-spin, respectively. Black solid line indicates the mismatching of the spin polarization.

4. Conclusions We investigated the trend of strength of intramolecular magnetic coupling constants (J) of series of bisradicals (DTDA, OVER and NN groups) coupled with an aromatic coupler based on the unrestricted DFT calculations with B3LYP/6-311++G(d,p) basis sets. The calculated sets of aromatic couplers include phosphole, thiophene, pyrrole, benzene, pyridine, furan, azulene and triazole which possess broad range of NICS values (-5~-17). Interestingly, the trend of the strength of magnetic interaction of couplers was preserved in DTDA, OVER and NN groups. Furthermore, calculated J values of DTDA, ACS Paragon Plus Environment

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OVER and NN groups have linear relationship so that those values can be used as an index parameter to estimate the strength of magnetic interactions of a given coupler. The trend of the strength of magnetic interactions of bisradicals were explained based on the analysis of nucleus independent chemical shift (NICS), bond order and Mulliken atomic spin density distribution. Among fifteen aromatic couplers, we found 2,4- and 2,5-phosphole couplers gave the strongest intramolecular ferromagnetic and antiferromagnetic interaction, respectively, when those couplers are connected with bisradicals. The strength of magnetic interaction of 2,5-phosphole coupler is comparable to that of ethylene coupler which is known to be the strongest organic coupler to date. 2,4-phosphole coupler based bisradicals exhibit intramolecular ferromagnetic interactions while ethylene based bisradicals are supposed to be antiferromagnetic depending on the number of carbon atoms along its spin coupling path as per the spin alternation rule. Considering the synthetic difficulty of heterodiradicals, 2,4-phosphole coupler is promising to make strongly coupled intramolecular ferromagnetic bisradicals (homodiradicals). Our results can be utilized in designing organic magnetic materials based on the diradical approach. ACKNOWLEDGMENT. The authors would like to acknowledge the support from KISTI supercomputing center through the strategic support program for the supercomputing application research [No. KSC-2013-C2-028].

SURPPORTING INFORMATION AVAILABLES. Calculated zero-point corrected total energies, dihedral angles between a coupler and radical moieties, NICS(0)iso values, bond orders of connecting bonds, Mulliken atomic spin density distributions. This material is available free of charge via the Internet at http://pub.acs.org.

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Organic Magnetic Diradicals (RadicalâCouplerâRadical

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