First Principle Designing of Blatters Diradicals with Strong

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First Principle Designing of Blatter's Diradicals with Strong Ferromagnetic Exchange Interactions Ashima Bajaj, and Md. Ehesan Ali J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 09 May 2019 Downloaded from http://pubs.acs.org on May 9, 2019

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The Journal of Physical Chemistry

First Principle Designing of Blatter's Diradicals with Strong Ferromagnetic Exchange Interactions Ashima Bajaj and Md. Ehesan Ali∗ Institute of Nano Science and Technology, Phase 10, Sector-64, Mohali Punjab-160062, India E-mail: [email protected]

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ACS Paragon Plus Environment

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Abstract The stable organic diradicals that exhibit strong intramolecular ferromagnetic exchange interactions are suitable building blocks for organic magnetic materials (OMMs). Based on the ab initio calculations, here we report the electronic and magnetic properties of 1,2,4-benzotriazinyl based mono- and di-radicals (known as Blatter's radicals). The quantum mechanical calculations based on the density functional theory (DFT) reveals the merostability of the super stable Blatter's radicals. The stability could further be enhanced by tuning the spin-densities on the radical centers via the extended π-conjugation. The magnetic exchange interactions (2J) have been investigated for the Blatter's radical coupled to Nitronyl Nitroxide radical (i.e. Bl-NN) as the prototypical system that has recently been synthesized by Rajca et al. (J. Am. Chem. Soc. 2016, 138, 9377). The broken-symmetry (BS) approach within the standard DFT as well as constraint spin-density DFT (CDFT) methods are applied to compute the exchange interactions, while for wavefunction (WF) based multi-reference methods, the spin-symmetry adopted (e.g. CASSCF/NEVPT2) approach is applied. It is observed that the CBS-DFT provides much better 2J values as compared to the standard BS-DFT. The multi-reference calculations based on the minimal active space [i.e. CAS(2,2)] incorporating the delocalized magnetic orbitals provides quite reliable exchange interactions. After validating the applied computational methods, a number of ferromagnetically coupled hybrid diradicals are modelled by coupling the Blatter's mono-radical with various known stable organic radicals. A few of them are turned out to be quite promising candidates for the building block of OMMs.

1

Introduction

Organic magnetic materials (OMMs) are of current interest because of their potential applications in several disciplines that exploits their magnetic, 1,2 spintronic, 3–5 superconducting behaviour, 6,7 and photo-magnetic properties. 8–11 Easy and precise control over the structural and electronic properties of the organic molecules allow their precise fabrication into 2


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devices. 12 One of the persisting issues with OMMs is to obtain room temperature stable organic radicals with the desired electronic and magnetic properties. The development of such novel organic ferromagnetic materials exhibiting thermal stability as well as strong magnetic exchange interactions will replace the traditional magnetic materials in the near future. Such organic radicals would also play the central role in molecular spintronic applications and magnetic logic devices. 4,5,13 In organic diradicals two unpaired spins reside in the two singly occupied molecular orbitals (SOMOs) that are localized in the two spatially separated molecular regions. The non-magnetic molecular spacer bridges the radical centers and mediates the magnetic exchange interactions. It also plays a crucial role in controlling the coupling strength and nature of the coupling interactions. 14–16 In search of stable organic diradicals, over the last few decades, a number of stable organic diradicals have been reported. 17–20 Recently, Rajca and his co-workers succeeded in synthesizing couple of stable organic diradicals based on 1,2,4-Benzotriazinyl radical. 21,22 The later was first reported by Blatter and co-workers in 1968 and popularly known as Blatter’s radical in the literature. 23 Here onwards it will be referred as Blatter’s radical or Bl (see Fig. 1). Owing to the thermal stability of the radical with melting point 111-112°C and decomposition onset at 269°C, the radical was found to be super stable radical. 24 Despite the exceptional thermal and moisture stability, the radical remains relatively less explored for a long time due to its insufficient accessibility because of its difficulty in synthesis. Kountentis et al. over the last few years have established easy synthetic procedures for such super stable Blatter's radicals that opens up novel possibilities and regenerated interest for such radicals. 24–26 On the other hand over the last few decades, various organic radicals e.g. nitronyl nitroxide (NN), oxoverdazyl (OVER), dithiadiazolyl (DTDA), nitroxide (NO), phenoxyl (PO) and imino nitroxide (IN) radicals gained wide attentions for their stabilities and tunable magnetic properties. 16,27,28 Since the discovery of the pure organic ferromagnetic materials based on the NN radical in 1991, NN is still believed to be the most promising radical for gener-

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Figure 1: 1,2,4-Benzotriazinyl (Blatter's) radical with X= −CM e3 ,−H −CF3 . The benzene ring fused with the triazinyl ring is referred as the extended part of the radical where n corresponds to number of fused benzene rings. The phenyl ring connected to N1 is referred as coupler phenyl ring. ating strong magnetic properties. 28–31 Verdazyl has also become one of the largest families of stable radicals since its first synthesis and characterization by Kuhn and Trischmann in 1963. 32 The Oxoverdazyl is a famous branch of the Verdazyl radicals. 33 The DTDA radicals are a group of heterocyclic sulfur and nitrogen containing free radicals that are well known as building blocks for molecular conductor and switchable materials. 34,35 In this work we have computationally investigated the exceptional stability of the Blatter's radicals from the electronic and structural perspective and also explored its magnetic properties upon coupling the Blatter's mono-radical with one of the known stable radicals. The first-principle based computation of the magnetic exchange interaction is indeed a challenging task and a trustable blackbox method is yet to be developed. 36–38 In the current work we have adopted the recently developed spin-constraint density functional theory (CDFT) along with traditional density functional theory (DFT) to compute the magnetic exchange interactions. The computed exchange interactions in the density based methods are compared with the available experimental observations along with the multi-reference calculations.

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Theoretical background

The magnetic exchange interactions between the two spin centers, localized at two different sites, could be expressed by Heisenberg-Dirac-Van Vleck spin Hamiltonian

ˆ HDV V = −2JSˆ1 Sˆ2 H

(1)

where 2J is the magnetic exchange coupling constant which quantifies the strength of the magnetic interactions and Sˆ1 and Sˆ2 are the spin angular momentum operator on the two spin sites. The sign of 2J indicates the nature of the exchange interactions between the two spin centres with positive sign indicating ferromagnetic coupling whereas negative sign indicates an anti-ferromagnetic exchange interaction. For a diradical, 2J can be expressed as ES − ET = 2J,

(2)

where ES and ET are the energies of the singlet and the triplet spin-multiplets. For openshell diradical systems it becomes extremely difficult to obtain a symmetry adopted pure singlet state i.e. ES , from any single-determinant approach such as UDFT and UHF methods. It requires multi-configurational techniques such as CAS-CI, MCSCF, DDCI methods to represent a low spin-state wavefunction that inherently contains multi-determinant characteristics. Alternatively, the 2J values could still be obtained within the density functional theory (DFT) by using the broken-symmetry (BS) approximations as proposed by Noodleman. 39 The BS state is not a pure spin-state rather a mixed state comprising of the singlet and triplet wave functions. In the broken-symmetry approach the magnetic exchange interactions could be obtained as follows

2 ), 2J = 2(EBS − ET )/(1 + Sab

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(3)


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where EBS is energy of the broken-symmetry solution and Sab is the overlap integral between the two magnetic orbitals associated with sites a and b. The quantity ET stands for the energy of the triplet state formed from the BS orbitals. Depending on the extent of overlap between two magnetic sites, different expressions have been formulated to estimate the 2J values. 40–42 In this work we have adopted the recipe proposed by Ginsberg, 43 Noodleman 39 and Davidson 44 and is applicable when the overlap between the magnetic orbitals is sufficiently small. 2 2J = 2(EBS − ET )/Smax

(4)

The DFT based broken-symmetry approach generally reproduces the observed magnetic exchange interactions especially when the radical centers are coupled through a moderately conjugated spacers. In a recent work, we realized that for highly conjugated polyacene spacers the DFT broken-symmetry approach fail miserably to reproduce the exchange interactions. Obtaining an appropriate BS solution becomes difficult especially when the molecular structures are quite symmetric. However such difficulties could easily be tackled by applying the spin-constraint DFT (CDFT) approach. This is an alternative density based approach that allows total energy calculations subjected to the spatial constraint of spin-densities in the molecules. The 2J values could be extracted based on the CDFT energies for the BS and triplet states as of standard broken-symmetry methods. This is know as CBS-DFT approach. 45 The CBS-DFT method shown to provide an accurate exchange couplings for transition metal complexes. 46 Ali et al. applied the CBS, CEBS methods to obtain the exchange interactions for the iron-surf co-factors of the Rieske proteins. 47 To the best of our knowledge, this is the first report of CBS-DFT calculations to obtain the exchange interactions for organic diradicals. In addition to DFT based broken-symmetry method, the symmetry adopted method such as CASSCF and CASSCF-NEVPT2 48 calculations are also performed to compute the 2J values.

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Computational strategy

The molecular geometries of all the radical species are optimized applying the B3LYP 49 hybrid functional and def2-TZVP basis set. 50 The open-shell molecular species are treated using the spin-unrestricted Kohn-Sham (UKS) method within the DFT framework. Resolution of the Identity (RI) approximation along with the auxiliary basis set def2/J has been used. 51 Chain of spheres (COSX) numerical integration are used for the Hartree-Fock exchange to speed up the calculations without losing its accuracy. Tight convergence limits and increased integration grids (grid5) are used throughout. To compute the magnetic exchange interactions, two different density based approaches namely broken-symmetry DFT (BS-DFT) and spin-constraint broken-symmetry DFT (CBSDFT) are adopted. The details of CBS-DFT method could be obtained in one of the authors previous work. 47,52 The magnetic exchange interactions (2J) are computed in BS-DFT approach using the B3LYP/def2-TZVP method in ORCA 53 quantum chemical code . Since, the magnetic exchange interactions do not depend significantly on the basis set, 54 thus all the BS-DFT calculations are performed with def2-TZVP basis set. While for CBS-DFT the adopted methodology is B3LYP/6-31G(d) due to the limitation of the former quality of basis sets in the NWChem 55 quantum chemical code especially for the constraint spindensity DFT calculations. The detailed criteria followed for zone selection and constraining appropriate amount of magnetic moment on the selected zones for CBS-DFT is provided in SI. The magnetic coupling constants are extracted for the density based approaches using Eq. 4 from the respective energy differences between the high-spin and broken-symmetry state. To obtain the 2J values in the symmetry-adopted multi-configurational methods, the complete active space configuration interactions (CAS-CI) calculations are performed. 37 Starting from the minimal active space that contains the two unpaired electrons in two magnetic orbitals i.e. CAS(2,2), the active spaces were extended upto CAS(10,10) to in-

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dentify its role on the computed exchange interactions. 56,57 The energy gaps between LS and HS states for the designed diradicals are calculated using CASSCF/def2-TZVP methodology on the optimized geometries. CASSCF calculation accounts the large extent of the static electronic correlation. The dynamical correlation is further included in a perturbative treatment with n-electron valence state perturbation theory (NEVPT2) method. 58 The unrestricted natural orbitals (UNO) 59,60 are chosen as the initial orbitals for CASSCF and for CASSCF-NEVPT2, the CASSCF optimized orbitals are considered. The value of 2J is calculated using Eq. 2.

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Results and Discussion

The unique spin distribution of the Blatter's mono-radical among the three nitrogen atoms within the triazinyl ring makes the radical as super stable in nature. In the following subsection we will discuss how to acquire additional stability for Blatter's mono-radical moieties based on the ab initio studies. Followed by a comprehensive discussion, validation of the adopted computational methods and techniques to compute the magnetic exchange interactions (2J) are provided. The predicted magnetic properties of the designed Blatter's based diradicals and the factors that control their magnetic properties are discussed in the subsequent subsections.

4.1

Tuning the spin-delocalization of Blatter's mono-radical: Merostabilisation

The two main strategies are generally adopted for enhancing the stability of organic radicals. 61 One is the topological protection of the spin centres i.e. screening the spin bearing atom with the bulky substituents and the other one is the delocalization of unpaired electrons over a large part of atomic skeleton. 62,63 The stability of Blatter’s radical is rationalized in terms of merostabilisation i.e. the radicals are stabilized by resonance and steric hindrance. 8


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The introduction of three endocyclic nitrogen atoms in to a carbon backbone gives rise to a distribution where spin-density is highly localized on the three N-atoms of the triazinyl ring. The delocalization of spin-density is further facilitated by the extended part of the radical i.e. fused benzene ring, which being coplanar with triazinyl moiety provides an easy pathway for spin delocalization in the heterocyclic radical (see Fig. 1). Thus, the stability of radical is owed to the extensive delocalization of spin-density on both the benzene ring as well as endocyclic N-atoms. The stability of the radical is further enhanced by modifying the molecular framework by extended conjugation i.e. on increasing the number of coplanar fused benzene rings. The Löwdin spin-density on three nitrogen atoms along with the total spin-density on the triazinyl ring with the increasing number of rings is tabulated in Table 1. Table 1: Löwdin spin-density on N-atoms and triazinyl ring of Blatter's monoradical with increasing number of fused benzene rings using B3LYP/def2-TZVP method for −CM e3 . No. of rings (n) µN1 µN2 µN4 µNi Total(triazinyl)a 1 0.220 0.240 0.235 0.695 0.791 2 0.201 0.250 0.221 0.672 0.719 3 0.198 0.256 0.210 0.664 0.690 4 0.188 0.254 0.205 0.647 0.660 P Total triazinyl ring spin-densities are obtained as (µNi + µCi (triazinyl)) P

a

The decrease in spin-density on the triazinyl ring with the increase of n clearly indicates the delocalization of spin-densities from the radical centers to the extended part of the radical. Thus, the enhanced spin delocalization and hence merostabilisation is accelerated through extended conjugation of molecular structure.

4.2

Magnetic Exchange Interactions in Blatter’s Diradicals

Rajca et al. recently synthesized two stable diradicals by coupling the Blatter's radical with nitronyl nitroxide (NN) and imino nitroxide(IN). 21 We will refer these, here onwards, as Bl-NN and Bl-IN respectively (see Fig. 2 & Fig. 5). The authors scholarly investigated the 9



exchange interactions through quantitative EPR spectroscopy and also compared the experimental observations through the standard DFT calculations within the broken-symmetry approach (BS-DFT). 21 An exchange interaction of 162.53 cm−1 was observed for Bl-NN. However the computed 2J value adopting the BS-DFT(B3LYP/6-31G(d,p)) method was 489 cm−1 . This indicates the overestimation of the exchange interactions in the standard BS-DFT methods. Even with the hybrid functionals, the overestimation of 2J is well known in literature. 64–67 Furthermore, in a much recent study, the authors probe the exchange interactions through SQUID magnetometry which renders them with 2J value of of 175±7 cm−1 . 22

Figure 2: Blatter's coupled with NN (Bl-NN), n corresponds to number of fused benzene rings, φ1 and φ2 are the dihedral angles which the central phenyl ring makes with NN and Blatter's radical respectively.

In this work we have computed the magnetic exchange interactions adopting the BS-DFT approach and using the B3LYP/def2-TZVP method that results in 2J value of 397.80 cm−1 for Bl-NN. The computed 2J values are similar to the previous DFT calculations reported by Rajca et al., 21 and it largely overestimates the experimental value of 175±7 cm−1 . 22 Generally DFT functionals tends to strongly delocalize the magnetic orbitals especially for highly 10


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conjugated molecules. Such spurious delocalization of the magnetic orbitals results in quite strong exchange interactions between the magnetic sites, which often leads to the overprediction of the 2J values. 65–68 One of the remedy to these shortcomings is spin-constraint density functional theory (CDFT) in which the spin-density could be localized in the specified spatial regions. 69 The exchange interactions could be extracted as of BS-DFT method using the CDFT total energies. This method is known as CBS or CBS-DFT. 45 In CBS technique, the spin magnetic moment is confined in two zones which are localized on two radical centers i.e. Bl and NN (shown in Figure S5 in SI). Due to natural delocalization of spin-density from Blatter's triazinyl ring to fused benzene ring, as anticipated in Section 4.1, only 0.765 units of spin moment is confined on the triazinyl ring . Thus, allowing the remaining 0.235 of the moment to delocalize on the fused benzene ring. However,for NN radical, in order to prevent the apparent delocaliztion of spin-density, the magnetic moment confined on the selected zone is kept fixed to one unit. Adopting this recipe of the constrained brokensymmetry DFT calculations, the computed exchange interactions for Bl-NN are found to be 219.40 cm−1 (see Table 2 and Fig. 4). Thus, CBS-DFT remarkably improves the exchange interactions as compared to the standard broken-symmetry approaches. Furthermore, to obtain an intriguing understanding of the computed exchange interactions from the spin symmetry-broken density based technique, the symmetry adopted wave function theory (WFT) based multi-configurational methods are also adopted. The multiconfigurations self-consistent field (MCSCF) calculations are performed accounting both the static as well as dynamic electronic correlations. 25,70 The choice of the active space [i.e. n active electrons in m active orbitals CAS(n,m)] requires rigorous observations of the MOs and strong chemical intuitions. 71 In this work, the active spaces are selected based on the unrestricted natural orbitals (UNO) 59,60 that was obtained from the UKS optimized orbitals. In CASSCF calculations, the selected initial active space orbitals are further optimized and the optimized CAS orbitals are also meticulously analysed to understand their role in the exchange interactions. To do so, various active spaces i.e. from the minimal active space

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CAS(2,2) to CAS(10,10) are examined.

Figure 3: Selected active space orbitals for CASSCF. The two magnetic orbitals (SOMOs) incorporated in CAS(2,2) space are shown in red enclosure. The additional orbitals included in CAS(4,4)and CAS(6,6) space are shown in green and blue enclosures respectively. In case of minimal active space i.e. CAS(2,2) the two magnetic orbitals, which contain the unpaired electrons in the radical centers are chosen (see Fig.3). Incidentally these orbitals are basically the singly occupied natural orbitals SONOs (SOMOs.) The computed exchange interactions using CASSCF(2,2) is 96.56 cm−1 . With the inclusion of dynamical electronic correlations, CASSCF(2,2)-NEVPT2 calculation yeilds us with exchange coupling of 177.77 cm−1 , which resembles very closely to the recent experimental results obtained with SQUID magnetometry i.e. 175.10 cm−1 . 22 The magnetic orbitals involved are mainly localized both on the Bl as well as on NN. However one of the SOMOs is indeed delocalized over the central phenyl ring connecting both the radical centers (see Fig.3). Quite promising results with minimal CAS can be attributed to the SOMOs that has taken into account the radical 12


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centers as well as the coupler.

Figure 4: Computed magnetic exchange coupling constants (2J ) for Bl-NN with different DFT and ab initio based methods. The black dotted line represents the experimental exchange coupling. 21 To incorporate the correlation effects of the π-orbitals stemming from the conjugated spacer the CAS(4,4), CAS(6,6), CAS(8,8) and CAS(10,10) active spaces are incorporated in the MCSCF calculations. The computed exchange interactions are tabulated in Table 2. In CASSCF calculations, the 2J values indeed depend on the CAS space, however the dependency is not linear with the size of the active space (see Fig. 4), though the total energy decreases with the increase of electronic degrees of freedom. The computed exchange interactions for Bl-NN in the minimal active space is 96.56 cm−1 , while maximum value 177.77 cm−1 is obtained for CASSCF(6,6). The lowest energy solutions i.e. highest active space i.e.CAS(10,10) provides a value of 131.36 cm−1 . The inclusion of dynamical correlations through a similar approach to the second order Møler-Plesset perturbation theory, the NEVPT2 58 on the respective CASSCF optimized orbitals reveals a quite consistent 2J values 13



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for all the active orbitals considered except CAS(10,10) (See Table 2 and Fig. 4). The largest (10,10) active space strongly overestimate the exchange interactions. This is due to the overestimation of the electron correlations of larger number of unoccupied orbitals. Considering a good match between the theory and experimental exchange interactions and role of dynamical and non-dynamical contributions to exchange interactions, the CASSCF(2,2)-NEVPT2 calculations are found to be quite promising. Hereafter, we will stick to this method to compute the magnetic exchange interactions from the WFT using the minimal active space. Table 2: Computed magnetic coupling constants (2J) and spin-states energies for Bl-NN at different density functional theory and ab initio methods. Energy(Eh) HS LS BS-DFT -1586.74819 -1586.74728a CBS-DFT -1587.13946 -1587.13896a CASSCF(2,2) -1577.56828 -1577.56784 CASSCF(4,4) -1577.58252 -1577.58213 CASSCF(6,6) -1577.62865 -1577.62784 CASSCF(8,8) -1577.65545 -1577.65479 CASSCF(10,10) -1577.66511 -1577.66451 CASSCF(2,2)-NEVPT2 -1584.48586 -1584.48505 CASSCF(4,4)-NEVPT2 -1584.46724 -1584.46641 CASSCF(6,6)-NEVPT2 -1584.47128 -1584.47036 CASSCF(8,8)-NEVPT2 -1584.47373 -1584.47285 CASSCF(10,10)-NEVPT2 -1584.47081 -1584.46939 exp. 22 Method

a

2J (cm−1 ) 397.80 219.47 96.56 85.59 177.77 144.85 131.68 177.77 182.16 201.91 193.13 311.65 175±7

Instead of LS state energy the total energy of the broken-symmetry (BS) state is

provided.

4.3

Designed Blatter’s Coupled Diradicals

Gaining insights into the electron-density and wavefunction based methods in computations of the magnetic exchange interactions (2J) for Bl-NN, we have modelled several stable organic diradicals based on the Blatter’s radical. Here we aim to design strong ferromagnetically coupled diradicals. The popular stable organic radicals e.g. OVER, DTDA, IN, NO and 14


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PO are coupled with the super stable Blatter's radical. The resulting hybrid diradicals are denoted as Bl-OVER, Bl-DTDA, Bl-IN, Bl-NO and Bl-PO respectively. Fig. 5 depicts the molecular structure of the modelled diradicals. The ferromagnetic exchange interactions in the modelled diradicals are nourished upon considering the appropriate molecular topology i.e. para and meta substitutions. The OVER, DTDA and IN monoradicals are attached at the para position of the coupler phenyl ring of the Blatter's radical. However NO and PO are attached at the meta positions to coroborate with the spin-alternation rules. 72,73

Bl-OVER

Bl-DTDA

Bl-NO

Bl-IN

Bl-PO

Figure 5: Modelled diradicals by coupling Blatter's radical with OVER (Bl-OVER), DTDA (Bl-DTDA), IN (Bl-IN), NO (Bl-NO) and PO(Bl-PO) The exchange interactions for all the modelled diradicals are computed using the aforementioned BS-DFT, CBS-DFT, CASSCF(2,2) and CASSCF(2,2)-NEVPT2 and the results are tabulated in Table 3. A comparison of the estimated 2J values obtained from the various methods are given in Fig. 6. Based on the theoretically pronounced method i.e. CASSCF(2,2)-NEVPT2, it is evident that the experimentally synthesized Bl-NN is still the best candidate for organic magnetic materials with strong ferromagnetic exchange interactions. The next best candidate for OMMs is Bl-OVER with the exchange coupling constant of 160.21 cm−1 . In fact Bl-PO and Bl-NO are also quite promising candidates for OMMs, 15



with 2J values of 138.26 and 98.76 cm−1 respectively. Table 3: Comparison of calculated magnetic exchange coupling constants for modelled Blatter based diradicals using BS-DFT, CBS-DFT, CASSCF(2,2), CASSCF(2,2)-NEVPT2 2J(cm−1 ) BS-DFT CBS-DFT CASSCF(2,2) CASSCF(2,2)-NEVPT2 Bl-OVER 312.44 254.51 94.37 160.21 Bl-DTDA 150.38 109.73 37.31 65.84 Bl-IN 130.74 87.78 9.47 39.50 Bl-NO 159.08 140.46 35.11 98.76 Bl-PO 287.24 258.98 120.71 138.26 Bl-IN is another experimentally synthesized diradical by Rajca et al., 21 but authors were not able to predict the ground state of this diradical with certainty. However,quite large ferromagnetic exchange interaction with 2J=209.9 cm−1 was predicted by them using BSDFT approach. Our BS-DFT calculations also predicts exchange interaction 130.74 cm−1 . But, CASSCF(2,2) provides a value of only 9.47 cm−1 , which further increases to 39.50 cm−1 on incorporating dynamical correlation. Thus large overestimation in the exchange interactions is observed using the BS-DFT methods irrespective of the adopted exchange correlation functionals. However , the computed exchange interactions from CASSCF(2,2) indicates that spin interactions are very weak in case of Bl-IN. Along with Bl-IN, this overestimation of exchange interactions by BS-DFT is observed in all the modelled diradicals. This indicates that the CBS-DFT method is indeed a better choice for wide variety of the organic diradicals.

4.4

Interplay between stability of the organic radicals and the magnetic exchange interactions

It has been realized that the stability of the Blatter’s radical could be enhanced by attaching the additional coplanar fused benzene rings, which facilitates the delocalization of spin-densities from the radical sites. Do this enhanced stability of Blatter's coupled dirad16


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Figure 6: Comparison of Calculated Exchange Coupling Constant using BS-DFT, CBSDFT, CASSCF(2,2), CASSCF(2,2)-NEVPT2 for modelled diradicals icals affect the magnetic exchange interactions? To find an answer, we have investigated the magnetic exchange interactions of Bl-NN diradicals by increasing the number of fused benzene rings of the Blatter's radical (see Fig. 2). The results are tabulated in Table 4. As we increase the number of the rings, we observed the significant decrease in the (2J ) values. This negative correlation between number of rings and (2J ) is reflected in the four different methods including CBS-DFT and CASSCF-NEVPT2 methods. The single-point energies along with values and calculated magnetic exchange coupling constant (2J ) with aforementioned methods are provided in SI (Table in SI). As the number of the benzene rings increases from n=1 to 4, along with the exchange coupling, the dihedral angle which the central phenyl ring makes with the Blatter’s radical and NN radical also found to change significantly. The dihedral angles φ1 and φ2 (shown in Fig.2 are listed in Table 4. The strength of the magnetic exchange couplings indeed strongly depends on the dihedral angles. 74 Elimination of the contributions of the dihedral angle is necessary to evaluate the sole effect of the merostabilising the radical on the magnetic 17



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interactions. Table 4: Comparison of calculated magnetic exchange coupling constants for Bl-NN using BS-DFT, CBS-DFT ,CASSCF(2,2), CASSCF(2,2)-NEVPT2 with corresponding Dihedral Angles φ1 and φ2 No. of Rings 1 2 3 4

2J(cm−1 ) BS-DFT CBS-DFT CASSCF(2,2) CASSCF(2,2)-NEVPT2 397.80 219.47 96.56 177.77 285.58 263.36 70.23 149.24 134.38 122.90 32.92 74.62 146.82 136.07 37.31 79.01

φ1 and φ2 21.3/46.2 14.6/59.2 21.8/67.2 21.4/65.4

To do so, we have constrained both the dihedral angles to zero, making the configuration planar. The inset of Fig. 7 shows the computed exchange interactions for the constrained geometries using BS-DFT at B3LYP/def2-TZVP level. The computed total energies along with values for constrained geometry are provided in SI. Due to the more effective overlap of the magnetic molecular orbitals, the planar configuration results in enhanced 2J values and with a continuous decrease in coupling constants with the increasing number of the rings. Thus, spin delocalization plays a major role in controlling the exchange coupling constant. With increasing number of rings and hence spin delocalization, the stability of diradical is increasing but at the cost of reduced magnetic exchange interactions.

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BS-DFT CBS-DFT CASSCF(2,2) CASSCF(2,2)-NEVPT2

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-1

2J (cm )

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600

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1

2

3

4

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0

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2

3

No. of Rings (n)

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Figure 7: Graph showing the variation of exchange coupling constant 2J (cm−1 ) with increasing number of fused benzene rings (n). The inset of the graph shows the variation of 2J with n for constrained geometry using BS-DFT, B3LYP/def2-TZVP level.

5

Conclusions

Adopting the density functional theory as well as wavefunction based multi-configurational methods we have investigated the magnetic exchange interactions of a recently synthesized diradical i.e. Blatter's radical coupled to the Nitronyl Nitroxide (Bl-NN) diradical. The standard broken-symmetry (BS-DFT) calculations strongly overestimate the exchange interactions. However, the constrained spin-density based broken-symmetry approach (CBSDFT) is found to be highly promising method for computations of the exchange interactions. Theoretically pronounced spin-symmetry adopted multi-configurational techniques such as CASSCF and CASSCF-NEVPT2 methods are also adopted to compute the magnetic exchange interactions. The later method includes both the static as well as dynamical electron correlation effects into the exchange interactions and remarkably produces the 2J value of 177.7 cm−1 , for which Rajca et al. observed 175±7 cm−1 . It has been realized that the minimal active spaces i.e. 2 unpaired electrons in the 2 magnetic orbitals, CAS(2,2), are

19



quite reasonable choice here for the Blatter'coupled diradicals in computing the exchange interactions. The 2J values indeed depends on the active spaces, however it becomes worse especially for the perturbative evaluation of the dynamical correlations when a large number of virtual orbitals are taken into considerations in the CASSCF calculations. Within the density-based approach CBS-DFT should be the preferred method however the wavefunction based multi-reference calculations even with the minimal active space could reproduce the experimental coupling constants, hence a much better choice than any density based approach. However, additional care and precautions must be taken for the spin-density localizations in CBS-DFT and appropriate selection of the CAS space for the multi-reference calculations. Upon validation of the applied computational methods, exchange interactions were computed for designed hybrid Blatter's based diradicals. Based on the prominent CASSCF(2,2)NEVPT2 method, Bl-OVER and Bl-PO were found to exhibit strong exchange interactions of 160.21 and 138.26 cm−1 respectively. Thus, along with Bl-NN, Bl-OVER and Bl-PO are equally good candidates for magnetically robust triplet ground state diradicals. Further, the unique stability of the super stable Blatter's radical is investigated and is owed to extensive delocalization of spin-density on the three N-atoms of the triazinyl ring and coplanar fused benzene ring which provides an explicit pathway for delocalization of spin-density. The stability can further be enhanced by attaching additional coplanar fused benzene rings which indeed decreases the exchange interactions. Thus, it is very likely that with the appropriate modifications in the molecular structure of the radical, strong ferromagnetic interactions with increased stability could be realized.

Acknowledgement This work has been dedicated to Prof. Sambhu N. Datta, on the occasion of his 70th Birthday. Financial support from Department of Science and Technology through SERB-ECR

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project No. ECR/2016/000362, Indo-Sweden joint project No. DST/INT/SWD/VR/P01/2016 and computational resources obtained from CDAC-Pune are gratefully acknowledged. Supporting Information Available: Computed total energies, Löwdin spin density analysis, selection of the active space for CASSCF calculations and radical merostability. This material is available free of charge via the Internet at http:// pubs.acs.org.

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First Principle Designing of Blatter's Diradicals with Strong Ferromagnetic Exchange Interactions Ashima Bajaj and Md. Ehesan Ali∗ Institute of Nano Science and Technology, Phase 10, Sector-64, Mohali Punjab-160062, India E-mail: [email protected]

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Abstract The stable organic diradicals that exhibit strong intramolecular ferromagnetic exchange interactions are suitable building blocks for organic magnetic materials (OMMs). Based on the ab initio calculations, here we report the electronic and magnetic properties of 1,2,4-benzotriazinyl based mono- and di-radicals (known as Blatter's radicals). The quantum mechanical calculations based on the density functional theory (DFT) reveals the merostability of the super stable Blatter's radicals. The stability could further be enhanced by tuning the spin-densities on the radical centers via the extended π-conjugation. The magnetic exchange interactions (2J) have been investigated for the Blatter's radical coupled to Nitronyl Nitroxide radical (i.e. Bl-NN) as the prototypical system that has recently been synthesized by Rajca et al. (J. Am. Chem. Soc. 2016, 138, 9377). The broken-symmetry (BS) approach within the standard DFT as well as constraint spin-density DFT (CDFT) methods are applied to compute the exchange interactions, while for wavefunction (WF) based multi-reference methods, the spin-symmetry adopted (e.g. CASSCF/NEVPT2) approach is applied. It is observed that the CBS-DFT provides much better 2J values as compared to the standard BS-DFT. The multi-reference calculations based on the minimal active space [i.e. CAS(2,2)] incorporating the delocalized magnetic orbitals provides quite reliable exchange interactions. After validating the applied computational methods, a number of ferromagnetically coupled hybrid diradicals are modelled by coupling the Blatter's mono-radical with various known stable organic radicals. A few of them are turned out to be quite promising candidates for the building block of OMMs.

1

Introduction

Organic magnetic materials (OMMs) are of current interest because of their potential applications in several disciplines that exploits their magnetic, 1,2 spintronic, 3–5 superconducting behaviour, 6,7 and photo-magnetic properties. 8–11 Easy and precise control over the structural and electronic properties of the organic molecules allow their precise fabrication into 2


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devices. 12 One of the persisting issues with OMMs is to obtain room temperature stable organic radicals with the desired electronic and magnetic properties. The development of such novel organic ferromagnetic materials exhibiting thermal stability as well as strong magnetic exchange interactions will replace the traditional magnetic materials in the near future. Such organic radicals would also play the central role in molecular spintronic applications and magnetic logic devices. 4,5,13 In organic diradicals two unpaired spins reside in the two singly occupied molecular orbitals (SOMOs) that are localized in the two spatially separated molecular regions. The non-magnetic molecular spacer bridges the radical centers and mediates the magnetic exchange interactions. It also plays a crucial role in controlling the coupling strength and nature of the coupling interactions. 14–16 In search of stable organic diradicals, over the last few decades, a number of stable organic diradicals have been reported. 17–20 Recently, Rajca and his co-workers succeeded in synthesizing couple of stable organic diradicals based on 1,2,4-Benzotriazinyl radical. 21,22 The later was first reported by Blatter and co-workers in 1968 and popularly known as Blatter’s radical in the literature. 23 Here onwards it will be referred as Blatter’s radical or Bl (see Fig. 1). Owing to the thermal stability of the radical with melting point 111-112°C and decomposition onset at 269°C, the radical was found to be super stable radical. 24 Despite the exceptional thermal and moisture stability, the radical remains relatively less explored for a long time due to its insufficient accessibility because of its difficulty in synthesis. Kountentis et al. over the last few years have established easy synthetic procedures for such super stable Blatter's radicals that opens up novel possibilities and regenerated interest for such radicals. 24–26 On the other hand over the last few decades, various organic radicals e.g. nitronyl nitroxide (NN), oxoverdazyl (OVER), dithiadiazolyl (DTDA), nitroxide (NO), phenoxyl (PO) and imino nitroxide (IN) radicals gained wide attentions for their stabilities and tunable magnetic properties. 16,27,28 Since the discovery of the pure organic ferromagnetic materials based on the NN radical in 1991, NN is still believed to be the most promising radical for gener-

3



Figure 1: 1,2,4-Benzotriazinyl (Blatter's) radical with X= −CM e3 ,−H −CF3 . The benzene ring fused with the triazinyl ring is referred as the extended part of the radical where n corresponds to number of fused benzene rings. The phenyl ring connected to N1 is referred as coupler phenyl ring. ating strong magnetic properties. 28–31 Verdazyl has also become one of the largest families of stable radicals since its first synthesis and characterization by Kuhn and Trischmann in 1963. 32 The Oxoverdazyl is a famous branch of the Verdazyl radicals. 33 The DTDA radicals are a group of heterocyclic sulfur and nitrogen containing free radicals that are well known as building blocks for molecular conductor and switchable materials. 34,35 In this work we have computationally investigated the exceptional stability of the Blatter's radicals from the electronic and structural perspective and also explored its magnetic properties upon coupling the Blatter's mono-radical with one of the known stable radicals. The first-principle based computation of the magnetic exchange interaction is indeed a challenging task and a trustable blackbox method is yet to be developed. 36–38 In the current work we have adopted the recently developed spin-constraint density functional theory (CDFT) along with traditional density functional theory (DFT) to compute the magnetic exchange interactions. The computed exchange interactions in the density based methods are compared with the available experimental observations along with the multi-reference calculations.

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2

Theoretical background

The magnetic exchange interactions between the two spin centers, localized at two different sites, could be expressed by Heisenberg-Dirac-Van Vleck spin Hamiltonian

ˆ HDV V = −2JSˆ1 Sˆ2 H

(1)

where 2J is the magnetic exchange coupling constant which quantifies the strength of the magnetic interactions and Sˆ1 and Sˆ2 are the spin angular momentum operator on the two spin sites. The sign of 2J indicates the nature of the exchange interactions between the two spin centres with positive sign indicating ferromagnetic coupling whereas negative sign indicates an anti-ferromagnetic exchange interaction. For a diradical, 2J can be expressed as ES − ET = 2J,

(2)

where ES and ET are the energies of the singlet and the triplet spin-multiplets. For openshell diradical systems it becomes extremely difficult to obtain a symmetry adopted pure singlet state i.e. ES , from any single-determinant approach such as UDFT and UHF methods. It requires multi-configurational techniques such as CAS-CI, MCSCF, DDCI methods to represent a low spin-state wavefunction that inherently contains multi-determinant characteristics. Alternatively, the 2J values could still be obtained within the density functional theory (DFT) by using the broken-symmetry (BS) approximations as proposed by Noodleman. 39 The BS state is not a pure spin-state rather a mixed state comprising of the singlet and triplet wave functions. In the broken-symmetry approach the magnetic exchange interactions could be obtained as follows

2 ), 2J = 2(EBS − ET )/(1 + Sab

5


(3)


Page 36 of 60

where EBS is energy of the broken-symmetry solution and Sab is the overlap integral between the two magnetic orbitals associated with sites a and b. The quantity ET stands for the energy of the triplet state formed from the BS orbitals. Depending on the extent of overlap between two magnetic sites, different expressions have been formulated to estimate the 2J values. 40–42 In this work we have adopted the recipe proposed by Ginsberg, 43 Noodleman 39 and Davidson 44 and is applicable when the overlap between the magnetic orbitals is sufficiently small. 2 2J = 2(EBS − ET )/Smax

(4)

The DFT based broken-symmetry approach generally reproduces the observed magnetic exchange interactions especially when the radical centers are coupled through a moderately conjugated spacers. In a recent work, we realized that for highly conjugated polyacene spacers the DFT broken-symmetry approach fail miserably to reproduce the exchange interactions. Obtaining an appropriate BS solution becomes difficult especially when the molecular structures are quite symmetric. However such difficulties could easily be tackled by applying the spin-constraint DFT (CDFT) approach. This is an alternative density based approach that allows total energy calculations subjected to the spatial constraint of spin-densities in the molecules. The 2J values could be extracted based on the CDFT energies for the BS and triplet states as of standard broken-symmetry methods. This is know as CBS-DFT approach. 45 The CBS-DFT method shown to provide an accurate exchange couplings for transition metal complexes. 46 Ali et al. applied the CBS, CEBS methods to obtain the exchange interactions for the iron-surf co-factors of the Rieske proteins. 47 To the best of our knowledge, this is the first report of CBS-DFT calculations to obtain the exchange interactions for organic diradicals. In addition to DFT based broken-symmetry method, the symmetry adopted method such as CASSCF and CASSCF-NEVPT2 48 calculations are also performed to compute the 2J values.

6


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3

Computational strategy

The molecular geometries of all the radical species are optimized applying the B3LYP 49 hybrid functional and def2-TZVP basis set. 50 The open-shell molecular species are treated using the spin-unrestricted Kohn-Sham (UKS) method within the DFT framework. Resolution of the Identity (RI) approximation along with the auxiliary basis set def2/J has been used. 51 Chain of spheres (COSX) numerical integration are used for the Hartree-Fock exchange to speed up the calculations without losing its accuracy. Tight convergence limits and increased integration grids (grid5) are used throughout. To compute the magnetic exchange interactions, two different density based approaches namely broken-symmetry DFT (BS-DFT) and spin-constraint broken-symmetry DFT (CBSDFT) are adopted. The details of CBS-DFT method could be obtained in one of the authors previous work. 47,52 The magnetic exchange interactions (2J) are computed in BS-DFT approach using the B3LYP/def2-TZVP method in ORCA 53 quantum chemical code . Since, the magnetic exchange interactions do not depend significantly on the basis set, 54 thus all the BS-DFT calculations are performed with def2-TZVP basis set. While for CBS-DFT the adopted methodology is B3LYP/6-31G(d) due to the limitation of the former quality of basis sets in the NWChem 55 quantum chemical code especially for the constraint spindensity DFT calculations. The detailed criteria followed for zone selection and constraining appropriate amount of magnetic moment on the selected zones for CBS-DFT is provided in SI. The magnetic coupling constants are extracted for the density based approaches using Eq. 4 from the respective energy differences between the high-spin and broken-symmetry state. To obtain the 2J values in the symmetry-adopted multi-configurational methods, the complete active space configuration interactions (CAS-CI) calculations are performed. 37 Starting from the minimal active space that contains the two unpaired electrons in two magnetic orbitals i.e. CAS(2,2), the active spaces were extended upto CAS(10,10) to in-

7



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dentify its role on the computed exchange interactions. 56,57 The energy gaps between LS and HS states for the designed diradicals are calculated using CASSCF/def2-TZVP methodology on the optimized geometries. CASSCF calculation accounts the large extent of the static electronic correlation. The dynamical correlation is further included in a perturbative treatment with n-electron valence state perturbation theory (NEVPT2) method. 58 The unrestricted natural orbitals (UNO) 59,60 are chosen as the initial orbitals for CASSCF and for CASSCF-NEVPT2, the CASSCF optimized orbitals are considered. The value of 2J is calculated using Eq. 2.

4

Results and Discussion

The unique spin distribution of the Blatter's mono-radical among the three nitrogen atoms within the triazinyl ring makes the radical as super stable in nature. In the following subsection we will discuss how to acquire additional stability for Blatter's mono-radical moieties based on the ab initio studies. Followed by a comprehensive discussion, validation of the adopted computational methods and techniques to compute the magnetic exchange interactions (2J) are provided. The predicted magnetic properties of the designed Blatter's based diradicals and the factors that control their magnetic properties are discussed in the subsequent subsections.

4.1

Tuning the spin-delocalization of Blatter's mono-radical: Merostabilisation

The two main strategies are generally adopted for enhancing the stability of organic radicals. 61 One is the topological protection of the spin centres i.e. screening the spin bearing atom with the bulky substituents and the other one is the delocalization of unpaired electrons over a large part of atomic skeleton. 62,63 The stability of Blatter’s radical is rationalized in terms of merostabilisation i.e. the radicals are stabilized by resonance and steric hindrance. 8


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The introduction of three endocyclic nitrogen atoms in to a carbon backbone gives rise to a distribution where spin-density is highly localized on the three N-atoms of the triazinyl ring. The delocalization of spin-density is further facilitated by the extended part of the radical i.e. fused benzene ring, which being coplanar with triazinyl moiety provides an easy pathway for spin delocalization in the heterocyclic radical (see Fig. 1). Thus, the stability of radical is owed to the extensive delocalization of spin-density on both the benzene ring as well as endocyclic N-atoms. The stability of the radical is further enhanced by modifying the molecular framework by extended conjugation i.e. on increasing the number of coplanar fused benzene rings. The Löwdin spin-density on three nitrogen atoms along with the total spin-density on the triazinyl ring with the increasing number of rings is tabulated in Table 1. Table 1: Löwdin spin-density on N-atoms and triazinyl ring of Blatter's monoradical with increasing number of fused benzene rings using B3LYP/def2-TZVP method for −CM e3 . No. of rings (n) µN1 µN2 µN4 µNi Total(triazinyl)a 1 0.220 0.240 0.235 0.695 0.791 2 0.201 0.250 0.221 0.672 0.719 3 0.198 0.256 0.210 0.664 0.690 4 0.188 0.254 0.205 0.647 0.660 P Total triazinyl ring spin-densities are obtained as (µNi + µCi (triazinyl)) P

a

The decrease in spin-density on the triazinyl ring with the increase of n clearly indicates the delocalization of spin-densities from the radical centers to the extended part of the radical. Thus, the enhanced spin delocalization and hence merostabilisation is accelerated through extended conjugation of molecular structure.

4.2

Magnetic Exchange Interactions in Blatter’s Diradicals

Rajca et al. recently synthesized two stable diradicals by coupling the Blatter's radical with nitronyl nitroxide (NN) and imino nitroxide(IN). 21 We will refer these, here onwards, as Bl-NN and Bl-IN respectively (see Fig. 2 & Fig. 5). The authors scholarly investigated the 9



exchange interactions through quantitative EPR spectroscopy and also compared the experimental observations through the standard DFT calculations within the broken-symmetry approach (BS-DFT). 21 An exchange interaction of 162.53 cm−1 was observed for Bl-NN. However the computed 2J value adopting the BS-DFT(B3LYP/6-31G(d,p)) method was 489 cm−1 . This indicates the overestimation of the exchange interactions in the standard BS-DFT methods. Even with the hybrid functionals, the overestimation of 2J is well known in literature. 64–67 Furthermore, in a much recent study, the authors probe the exchange interactions through SQUID magnetometry which renders them with 2J value of of 175±7 cm−1 . 22

Figure 2: Blatter's coupled with NN (Bl-NN), n corresponds to number of fused benzene rings, φ1 and φ2 are the dihedral angles which the central phenyl ring makes with NN and Blatter's radical respectively.

In this work we have computed the magnetic exchange interactions adopting the BS-DFT approach and using the B3LYP/def2-TZVP method that results in 2J value of 397.80 cm−1 for Bl-NN. The computed 2J values are similar to the previous DFT calculations reported by Rajca et al., 21 and it largely overestimates the experimental value of 175±7 cm−1 . 22 Generally DFT functionals tends to strongly delocalize the magnetic orbitals especially for highly 10


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conjugated molecules. Such spurious delocalization of the magnetic orbitals results in quite strong exchange interactions between the magnetic sites, which often leads to the overprediction of the 2J values. 65–68 One of the remedy to these shortcomings is spin-constraint density functional theory (CDFT) in which the spin-density could be localized in the specified spatial regions. 69 The exchange interactions could be extracted as of BS-DFT method using the CDFT total energies. This method is known as CBS or CBS-DFT. 45 In CBS technique, the spin magnetic moment is confined in two zones which are localized on two radical centers i.e. Bl and NN (shown in Figure S5 in SI). Due to natural delocalization of spin-density from Blatter's triazinyl ring to fused benzene ring, as anticipated in Section 4.1, only 0.765 units of spin moment is confined on the triazinyl ring . Thus, allowing the remaining 0.235 of the moment to delocalize on the fused benzene ring. However,for NN radical, in order to prevent the apparent delocaliztion of spin-density, the magnetic moment confined on the selected zone is kept fixed to one unit. Adopting this recipe of the constrained brokensymmetry DFT calculations, the computed exchange interactions for Bl-NN are found to be 219.40 cm−1 (see Table 2 and Fig. 4). Thus, CBS-DFT remarkably improves the exchange interactions as compared to the standard broken-symmetry approaches. Furthermore, to obtain an intriguing understanding of the computed exchange interactions from the spin symmetry-broken density based technique, the symmetry adopted wave function theory (WFT) based multi-configurational methods are also adopted. The multiconfigurations self-consistent field (MCSCF) calculations are performed accounting both the static as well as dynamic electronic correlations. 25,70 The choice of the active space [i.e. n active electrons in m active orbitals CAS(n,m)] requires rigorous observations of the MOs and strong chemical intuitions. 71 In this work, the active spaces are selected based on the unrestricted natural orbitals (UNO) 59,60 that was obtained from the UKS optimized orbitals. In CASSCF calculations, the selected initial active space orbitals are further optimized and the optimized CAS orbitals are also meticulously analysed to understand their role in the exchange interactions. To do so, various active spaces i.e. from the minimal active space

11



CAS(2,2) to CAS(10,10) are examined.

Figure 3: Selected active space orbitals for CASSCF. The two magnetic orbitals (SOMOs) incorporated in CAS(2,2) space are shown in red enclosure. The additional orbitals included in CAS(4,4)and CAS(6,6) space are shown in green and blue enclosures respectively. In case of minimal active space i.e. CAS(2,2) the two magnetic orbitals, which contain the unpaired electrons in the radical centers are chosen (see Fig.3). Incidentally these orbitals are basically the singly occupied natural orbitals SONOs (SOMOs.) The computed exchange interactions using CASSCF(2,2) is 96.56 cm−1 . With the inclusion of dynamical electronic correlations, CASSCF(2,2)-NEVPT2 calculation yeilds us with exchange coupling of 177.77 cm−1 , which resembles very closely to the recent experimental results obtained with SQUID magnetometry i.e. 175.10 cm−1 . 22 The magnetic orbitals involved are mainly localized both on the Bl as well as on NN. However one of the SOMOs is indeed delocalized over the central phenyl ring connecting both the radical centers (see Fig.3). Quite promising results with minimal CAS can be attributed to the SOMOs that has taken into account the radical 12


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centers as well as the coupler.

Figure 4: Computed magnetic exchange coupling constants (2J ) for Bl-NN with different DFT and ab initio based methods. The black dotted line represents the experimental exchange coupling. 21 To incorporate the correlation effects of the π-orbitals stemming from the conjugated spacer the CAS(4,4), CAS(6,6), CAS(8,8) and CAS(10,10) active spaces are incorporated in the MCSCF calculations. The computed exchange interactions are tabulated in Table 2. In CASSCF calculations, the 2J values indeed depend on the CAS space, however the dependency is not linear with the size of the active space (see Fig. 4), though the total energy decreases with the increase of electronic degrees of freedom. The computed exchange interactions for Bl-NN in the minimal active space is 96.56 cm−1 , while maximum value 177.77 cm−1 is obtained for CASSCF(6,6). The lowest energy solutions i.e. highest active space i.e.CAS(10,10) provides a value of 131.36 cm−1 . The inclusion of dynamical correlations through a similar approach to the second order Møler-Plesset perturbation theory, the NEVPT2 58 on the respective CASSCF optimized orbitals reveals a quite consistent 2J values 13



Page 44 of 60

for all the active orbitals considered except CAS(10,10) (See Table 2 and Fig. 4). The largest (10,10) active space strongly overestimate the exchange interactions. This is due to the overestimation of the electron correlations of larger number of unoccupied orbitals. Considering a good match between the theory and experimental exchange interactions and role of dynamical and non-dynamical contributions to exchange interactions, the CASSCF(2,2)-NEVPT2 calculations are found to be quite promising. Hereafter, we will stick to this method to compute the magnetic exchange interactions from the WFT using the minimal active space. Table 2: Computed magnetic coupling constants (2J) and spin-states energies for Bl-NN at different density functional theory and ab initio methods. Energy(Eh) HS LS BS-DFT -1586.74819 -1586.74728a CBS-DFT -1587.13946 -1587.13896a CASSCF(2,2) -1577.56828 -1577.56784 CASSCF(4,4) -1577.58252 -1577.58213 CASSCF(6,6) -1577.62865 -1577.62784 CASSCF(8,8) -1577.65545 -1577.65479 CASSCF(10,10) -1577.66511 -1577.66451 CASSCF(2,2)-NEVPT2 -1584.48586 -1584.48505 CASSCF(4,4)-NEVPT2 -1584.46724 -1584.46641 CASSCF(6,6)-NEVPT2 -1584.47128 -1584.47036 CASSCF(8,8)-NEVPT2 -1584.47373 -1584.47285 CASSCF(10,10)-NEVPT2 -1584.47081 -1584.46939 exp. 22 Method

a

2J (cm−1 ) 397.80 219.47 96.56 85.59 177.77 144.85 131.68 177.77 182.16 201.91 193.13 311.65 175±7

Instead of LS state energy the total energy of the broken-symmetry (BS) state is

provided.

4.3

Designed Blatter’s Coupled Diradicals

Gaining insights into the electron-density and wavefunction based methods in computations of the magnetic exchange interactions (2J) for Bl-NN, we have modelled several stable organic diradicals based on the Blatter’s radical. Here we aim to design strong ferromagnetically coupled diradicals. The popular stable organic radicals e.g. OVER, DTDA, IN, NO and 14


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PO are coupled with the super stable Blatter's radical. The resulting hybrid diradicals are denoted as Bl-OVER, Bl-DTDA, Bl-IN, Bl-NO and Bl-PO respectively. Fig. 5 depicts the molecular structure of the modelled diradicals. The ferromagnetic exchange interactions in the modelled diradicals are nourished upon considering the appropriate molecular topology i.e. para and meta substitutions. The OVER, DTDA and IN monoradicals are attached at the para position of the coupler phenyl ring of the Blatter's radical. However NO and PO are attached at the meta positions to coroborate with the spin-alternation rules. 72,73

Bl-OVER

Bl-DTDA

Bl-NO

Bl-IN

Bl-PO

Figure 5: Modelled diradicals by coupling Blatter's radical with OVER (Bl-OVER), DTDA (Bl-DTDA), IN (Bl-IN), NO (Bl-NO) and PO(Bl-PO) The exchange interactions for all the modelled diradicals are computed using the aforementioned BS-DFT, CBS-DFT, CASSCF(2,2) and CASSCF(2,2)-NEVPT2 and the results are tabulated in Table 3. A comparison of the estimated 2J values obtained from the various methods are given in Fig. 6. Based on the theoretically pronounced method i.e. CASSCF(2,2)-NEVPT2, it is evident that the experimentally synthesized Bl-NN is still the best candidate for organic magnetic materials with strong ferromagnetic exchange interactions. The next best candidate for OMMs is Bl-OVER with the exchange coupling constant of 160.21 cm−1 . In fact Bl-PO and Bl-NO are also quite promising candidates for OMMs, 15



with 2J values of 138.26 and 98.76 cm−1 respectively. Table 3: Comparison of calculated magnetic exchange coupling constants for modelled Blatter based diradicals using BS-DFT, CBS-DFT, CASSCF(2,2), CASSCF(2,2)-NEVPT2 2J(cm−1 ) BS-DFT CBS-DFT CASSCF(2,2) CASSCF(2,2)-NEVPT2 Bl-OVER 312.44 254.51 94.37 160.21 Bl-DTDA 150.38 109.73 37.31 65.84 Bl-IN 130.74 87.78 9.47 39.50 Bl-NO 159.08 140.46 35.11 98.76 Bl-PO 287.24 258.98 120.71 138.26 Bl-IN is another experimentally synthesized diradical by Rajca et al., 21 but authors were not able to predict the ground state of this diradical with certainty. However,quite large ferromagnetic exchange interaction with 2J=209.9 cm−1 was predicted by them using BSDFT approach. Our BS-DFT calculations also predicts exchange interaction 130.74 cm−1 . But, CASSCF(2,2) provides a value of only 9.47 cm−1 , which further increases to 39.50 cm−1 on incorporating dynamical correlation. Thus large overestimation in the exchange interactions is observed using the BS-DFT methods irrespective of the adopted exchange correlation functionals. However , the computed exchange interactions from CASSCF(2,2) indicates that spin interactions are very weak in case of Bl-IN. Along with Bl-IN, this overestimation of exchange interactions by BS-DFT is observed in all the modelled diradicals. This indicates that the CBS-DFT method is indeed a better choice for wide variety of the organic diradicals.

4.4

Interplay between stability of the organic radicals and the magnetic exchange interactions

It has been realized that the stability of the Blatter’s radical could be enhanced by attaching the additional coplanar fused benzene rings, which facilitates the delocalization of spin-densities from the radical sites. Do this enhanced stability of Blatter's coupled dirad16


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Figure 6: Comparison of Calculated Exchange Coupling Constant using BS-DFT, CBSDFT, CASSCF(2,2), CASSCF(2,2)-NEVPT2 for modelled diradicals icals affect the magnetic exchange interactions? To find an answer, we have investigated the magnetic exchange interactions of Bl-NN diradicals by increasing the number of fused benzene rings of the Blatter's radical (see Fig. 2). The results are tabulated in Table 4. As we increase the number of the rings, we observed the significant decrease in the (2J ) values. This negative correlation between number of rings and (2J ) is reflected in the four different methods including CBS-DFT and CASSCF-NEVPT2 methods. The single-point energies along with values and calculated magnetic exchange coupling constant (2J ) with aforementioned methods are provided in SI (Table in SI). As the number of the benzene rings increases from n=1 to 4, along with the exchange coupling, the dihedral angle which the central phenyl ring makes with the Blatter’s radical and NN radical also found to change significantly. The dihedral angles φ1 and φ2 (shown in Fig.2 are listed in Table 4. The strength of the magnetic exchange couplings indeed strongly depends on the dihedral angles. 74 Elimination of the contributions of the dihedral angle is necessary to evaluate the sole effect of the merostabilising the radical on the magnetic 17



Page 48 of 60

interactions. Table 4: Comparison of calculated magnetic exchange coupling constants for Bl-NN using BS-DFT, CBS-DFT ,CASSCF(2,2), CASSCF(2,2)-NEVPT2 with corresponding Dihedral Angles φ1 and φ2 No. of Rings 1 2 3 4

2J(cm−1 ) BS-DFT CBS-DFT CASSCF(2,2) CASSCF(2,2)-NEVPT2 397.80 219.47 96.56 177.77 285.58 263.36 70.23 149.24 134.38 122.90 32.92 74.62 146.82 136.07 37.31 79.01

φ1 and φ2 21.3/46.2 14.6/59.2 21.8/67.2 21.4/65.4

To do so, we have constrained both the dihedral angles to zero, making the configuration planar. The inset of Fig. 7 shows the computed exchange interactions for the constrained geometries using BS-DFT at B3LYP/def2-TZVP level. The computed total energies along with values for constrained geometry are provided in SI. Due to the more effective overlap of the magnetic molecular orbitals, the planar configuration results in enhanced 2J values and with a continuous decrease in coupling constants with the increasing number of the rings. Thus, spin delocalization plays a major role in controlling the exchange coupling constant. With increasing number of rings and hence spin delocalization, the stability of diradical is increasing but at the cost of reduced magnetic exchange interactions.

18


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BS-DFT CBS-DFT CASSCF(2,2) CASSCF(2,2)-NEVPT2

400

800

300

700

-1

2J (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


600

200

500

1

2

3

4

100

0

1

2

3

No. of Rings (n)

4

Figure 7: Graph showing the variation of exchange coupling constant 2J (cm−1 ) with increasing number of fused benzene rings (n). The inset of the graph shows the variation of 2J with n for constrained geometry using BS-DFT, B3LYP/def2-TZVP level .

5

Conclusions

Adopting the density functional theory as well as wavefunction based multi-configurational methods we have investigated the magnetic exchange interactions of a recently synthesized diradical i.e. Blatter's radical coupled to the Nitronyl Nitroxide (Bl-NN) diradical. The standard broken-symmetry (BS-DFT) calculations strongly overestimate the exchange interactions. However, the constrained spin-density based broken-symmetry approach (CBSDFT) is found to be highly promising method for computations of the exchange interactions. Theoretically pronounced spin-symmetry adopted multi-configurational techniques such as CASSCF and CASSCF-NEVPT2 methods are also adopted to compute the magnetic exchange interactions. The later method includes both the static as well as dynamical electron correlation effects into the exchange interactions and remarkably produces the 2J value of 177.7 cm−1 , for which Rajca et al. observed 175±7 cm−1 . It has been realized that the minimal active spaces i.e. 2 unpaired electrons in the 2 magnetic orbitals, CAS(2,2), are 19



quite reasonable choice here for the Blatter'coupled diradicals in computing the exchange interactions. The 2J values indeed depends on the active spaces, however it becomes worse especially for the perturbative evaluation of the dynamical correlations when a large number of virtual orbitals are taken into considerations in the CASSCF calculations. Within the density-based approach CBS-DFT should be the preferred method however the wavefunction based multi-reference calculations even with the minimal active space could reproduce the experimental coupling constants, hence a much better choice than any density based approach. However, additional care and precautions must be taken for the spin-density localizations in CBS-DFT and appropriate selection of the CAS space for the multi-reference calculations. Upon validation of the applied computational methods, exchange interactions were computed for designed hybrid Blatter's based diradicals. Based on the prominent CASSCF(2,2)NEVPT2 method, Bl-OVER and Bl-PO were found to exhibit strong exchange interactions of 160.21 and 138.26 cm−1 respectively. Thus, along with Bl-NN, Bl-OVER and Bl-PO are equally good candidates for magnetically robust triplet ground state diradicals. Further, the unique stability of the super stable Blatter's radical is investigated and is owed to extensive delocalization of spin-density on the three N-atoms of the triazinyl ring and coplanar fused benzene ring which provides an explicit pathway for delocalization of spin-density. The stability can further be enhanced by attaching additional coplanar fused benzene rings which indeed decreases the exchange interactions. Thus, it is very likely that with the appropriate modifications in the molecular structure of the radical, strong ferromagnetic interactions with increased stability could be realized.

Acknowledgement This work has been dedicated to Prof. Sambhu N. Datta, on the occasion of his 70th Birthday. Financial support from Department of Science and Technology through SERB-ECR

20


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project No. ECR/2016/000362, Indo-Sweden joint project No. DST/INT/SWD/VR/P01/2016 and computational resources obtained from CDAC-Pune are gratefully acknowledged. Supporting Information Available: Computed total energies, Löwdin spin density analysis, selection of the active space for CASSCF calculations and radical merostability. This material is available free of charge via the Internet at http:// pubs.acs.org.

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(8) Matsuda, K.; Matsuo, M.; Irie, M. Photoswitching of intramolecular magnetic interaction using diarylethene with oligothiophene conjugated chain. J. Org. Chem. 2001, 66, 8799–8803. (9) Tanifuji, N.; Irie, M.; Matsuda, K. New photoswitching unit for magnetic interaction: diarylethene with 2, 5-bis (arylethynyl)-3-thienyl group. J. Am. Chem. Soc. 2005, 127, 13344–13353. (10) Bhattacharya, D.; Shil, S.; Misra, A.; Bytautas, L.; Klein, D. J. Photomagnetic and nonlinear optical properties in cis-trans green fluoroprotein chromophore coupled bisimino nitroxide diradicals. Int. J. Quantum Chem. 2015, 115, 1561–1572. (11) Irie, M.; Fukaminato, T.; Matsuda, K.; Kobatake, S. Photochromism of diarylethene molecules and crystals: memories, switches, and actuators. Chem. Rev. 2014, 114, 12174–12277. (12) Di, C.; Zhang, F.; Zhu, D. Multi-functional integration of organic field-effect transistors (OFETs): Advances and perspectives. Adv. Mater. 2013, 25, 313–330. (13) Casu, M. B. Nanoscale studies of organic radicals: Surface, interface, and spinterface. Acc. Chem. Res. 2018, 51, 753–760. (14) Song, M.; Song, X.; Bu, Y. Core-modified porphyrin diradicals with a C=C unit: Redoxdriven magnetic switching. J. Phys. Chem. C 2017, 121, 21231–21243. (15) Ko, K. C.; Cho, D.; Lee, J. Y. Systematic approach to design organic magnetic molecules: Strongly coupled diradicals with ethylene coupler. J. Phys. Chem. A 2012, 116, 6837–6844. (16) Cho, D.; Ko, K. C.; Lee, J. Y. Organic magnetic diradicals (radical–coupler–radical): Standardization of couplers for strong ferromagnetism. J. Phys. Chem. A 2014, 118, 5112–5121. 22


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First Principle Designing of Blatters Diradicals with Strong

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