Ferromagnetic Nature of Silicon-Substituted Meta-Xylylene

Article pubs.acs.org/JPCC

Ferromagnetic Nature of Silicon-Substituted Meta-Xylylene Polyradicals Shekhar Hansda, Arun K. Pal, and Sambhu N. Datta* Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India S Supporting Information *

ABSTRACT: Electronic and magnetic properties of silicon-substituted metaxylylene polyradicals containing meta-phenylene groups as couplers and silicon atoms in >Si−H groups as radical sites are quantum chemically investigated. The polyradicals are found to be stable with alternately periodic structure. They have high-spin ground states and show ferromagnetic interaction among all pairs of radical sites. The silicon sites are somewhat creased. A periodic calculation on the dimeric unit predicts the long-chain polyradical to be a one-dimensional ferromagnet. Band energy calculation gives a large gap between virtual and valence bands. The large energy gap owes its origin to the radical sites being out of plane of the phenylene rings, a twist between successive monomer units, and the difference between the pz orbital energy in carbon and silicon. The polyradical chains are electron insulators unlike substituted polysilene chains, though they are predicted to be good ferromagnets.

1. INTRODUCTION Polyradicals of organic origin have been the subjects of extensive research in recent years. This is because of a vast number of possible applications of these in the electronics industry, which arise from their conducting and semiconducting properties,1 magnetic nature,2,3 and spintronic characteristics.4,5 Organic radicals can be engineered to form 1-D polymers, 2-D networks, and 3-D solids with desirable properties. Organic polyradicals are high-spin polymers.6−9 Rajca and co-workers have synthesized organic high-spin polyradicals with ground-state spin as high as S ≈ 6000.6 The meta-phenylene unit is the most commonly used monomer fragment to form polyradicals. It has been studied experimentally as well as theoretically and proved to be one of the best ferromagnetic couplers.10−15 In an earlier work16 we investigated the polyradicals formed from substitution of organic radical moieties such as oxo-verdazyl on a polysilene chain and predicted these polymers to have spintronic properties. In this work, we have investigated the 1-D chain of meta-xylylene polyradicals where the linker carbon atom is replaced by a silicon atom as the radical center (shown in Figure 1). Quantum chemical calculations have been done by density functional theory (DFT) using the Becke 3-parameter exchange17 and Lee, Yang, and Parr correlation functional18 (B3LYP) with or without Grimme’s dispersion interaction.19 The results are in favor of a high-spin ground state in each case. A rationalization has been provided in the form of a spin alternation rule. This rule was initially put forward by Ovchinnikov20 in valence bond calculations. Later, it was deduced again in the context of unrestricted MO-SCF (USCF) formalism, which is practiced in most calculations (UHF and UKS).3,21,22 The Borden−Davidson nondisjoint singly occupied molecular orbital (SOMO) principle23 also supports the nature of ground-state spin. © XXXX American Chemical Society

Figure 1. Structures investigated in this work.

Magnetic exchange coupling constants between different pairs of radical centers have been estimated. These come out to be positive for each pair. Furthermore, periodic calculations have been done by using a truncated form of system 2 as the repeating unit. It is normally expected that branching radical sites in the meta position of phenylene groups would lead to a ferromagnetic coupling.3,10,12 The magnetic exchange coupling constants for the finite size polymers have an estimated asymptotic value of about 82 cm−1, and the periodic calculations yield a coupling constant around 96 cm−1. These are about half of the coupling constant for 2 and 2′. However, the band gap in the resulting 1-D periodic polymer has been found to be quite large. We predict that the 1-D polymer would be ferromagnetic with a moderate transition temperature of about 100 K and an electron insulator.

2. METHODOLOGY Magnetic Coupling. The effective spin Hamiltonian is generally written in two main ways. First, the Heisenberg Received: November 10, 2014 Revised: January 28, 2015

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DOI: 10.1021/jp5112247 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C effective spin Hamiltonian gives an account of the isotropic interaction between the spins of relatively localized and unpaired electrons in a molecule

Once the magnetic couplings are known, the whole spectrum is known for the solution of the Ising Hamiltonian. The structures have been optimized again in ORCA 3.0.1 computation code.38 We have relied on UB3LYP methodology and 6-311G(d,p) basis set. Then single-point calculations on high-spin and broken symmetry states have been performed using B3LYP and its dispersion-corrected version (D3ZERO and D3BJ)19,39 with the 6-311++G(d,p) basis set. The coupling constants involved in the energy differences for vertical transition to different states of lower Sz have been calculated. The latter have been used to estimate the coupling constants between different radical centers. We have used the “FlipSpin” and “FinalMs” keywords in ORCA 3.0.1 to get the desired broken symmetry solutions. Periodic Calculation. Using the Ising Hamiltonian for a 1-D periodic system, one can easily obtain the energy difference of ferromagnetic and antiferromagnetic states per unit cell and write

N

Hex = −2J H ∑ Si·Sj (1)

iC−H radical site in lieu of >Si−H radical centers: the results will be published elsewhere. Overall Coupling Constant. Table 2 presents the singlepoint total energies of HS and BS states. Using this data, the vertical magnetic exchange coupling constants (J) are found from Yamaguchi eq 2. All J values are positive, as expected for a ferromagnetic coupling pattern. A smooth decreasing trend of JY with the number of phenylene rings (p) is evident. As the unpaired electrons are more delocalized in 2, species 2′ has a greater diradical character and a larger coupling constant (Table 2). However, the coupling constants are much less than the J values for the corresponding carbon analogues (which have J > 1000 cm−1).15 The decrease in J value owes its origin to a lesser through-bond coupling that arises from a difference in p-orbital energy between silicon and carbon and the distortion caused by the PJT effect.

Table 3. Single-Point High-Spin and Broken Symmetry Total Energy in Atomic Units, ⟨S2⟩ (in Parentheses), and Magnetic Exchange Coupling Constant J for Molecule 3, Calculated Using Basis Set 6-311++G(d,p) and the High-Spin Optimized Geometry in ORCA 3.0.1 B3LYP quartet ↑↑↑ BS1 ↑↑↓ BS2 ↑↓↑ BS3 ↓↑↑

−1564.134292 −1564.133600 −1564.132756 −1564.133444

(3.7759) (1.7680) (1.7587) (1.7663)

JY (cm−1) 75.7 167.1 92.6

B3LYP-D3ZERO −1564.166210 −1564.165553 −1564.164712 −1564.165366 D

(3.7750) (1.7674) (1.7584) (1.7662)

JY (cm−1) 71.8 163.0 92.3

B3LYP-D3BJ −1564.230956 −1564.230298 −1564.229459 −1564.230113

(3.7749) (1.7674) (1.7584) (1.7662)

JY (cm−1) 71.9 163.0 92.1


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The Journal of Physical Chemistry C

BS3, BS4, BS6, BS7, and BS9. The calculated data are shown in Table S4 in the Supporting Information. Assuming the approximate equalities J12 = J23 = J34 = Jn̅ n and J13 = J24 = Jn̅ nn, we get the average nearest-neighbor coupling constant as Jn̅ n = 160.8 cm−1 and the average next-nearest-neighbor coupling constant Jn̅ nn = 10.7 cm−1 while J14 = 10.4 cm−1. The Jn̅ n values for the nearest neighbors are close to that calculated for 3 (168.5 cm−1). The slightly smaller magnitude arises from our assumption of equality and also the slight difference in geometries (see Table S5, Supporting Information). The Jn̅ nn value for the next-nearest neighbors is again very small, though slightly higher than that for 3 (Table 4). Spin Density and SOMO plots. Figure 8 shows that indeed the major spin population resides on the silicon atoms

To estimate the intersite coupling constants, we use the relations E HS = E0 − Jr1r 2 /2 − Jr 2r 3 /2 − Jr1r 3 /2 E BS1 = E0 − Jr1r 2 /2 + Jr 2r 3 /2 + Jr1r 3 /2 E BS2 = E0 + Jr1r 2 /2 + Jr 2r 3 /2 − Jr1r 3 /2 E BS3 = E0 + Jr1r 2 /2 − Jr 2r 3 /2 + Jr1r 3 /2

(6)

for the triradical 3 in Figure 2 where r1, r2, and r3 refer to radical centers. The calculated Jr1r2, Jr2r3, and Jr1r3 are given in Table 4. Table 4. Magnetic Exchange Coupling Constant in cm−1 between Magnetic Centers in Triradicals, Calculated Using Basis Set 6-311++G(d,p) and the High-Spin Optimized Geometry in ORCA 3.0.1 functional

Jr1r2

Jr2r3

Jr1r3

E0 (au)

B3LYP B3LYP-D3ZERO B3LYP-D3BJ

185.7 185.0 184.6

151.4 144.0 144.0

0.44 0.44 0.44

−1564.133523 −1564.165460 −1564.230206

All three J values remain almost the same for all three functionals, around 185, 146, and 0.44 cm−1, respectively. Different fragments in the tetraradical are illustrated in Figure 7. The net charge and spin population on different fragments

Figure 8. Spin density plots in ground states obtained at the UB3LYP/ 6-311++G(d,p) level.

Figure 7. Division of fragments in system 4 into radical centers r1−r4 and couplers C1−C4.

in the high-spin ground state. The ground-state spin distribution follows the spin alternation rule in UKS.3,21,22 The singly occupied molecular orbital (SOMO) plots for the BS2 (↑↓↑) solution of system 3 are given in Figure 9. The SOMO principle proposed by Borden and Davidson23 for a diradical states that nondisjoint SOMOs, that is, SOMOs which have

are given in Table 5. Each radical center together with the meta-phenylene group attached to it on the right side is almost neutral in charge, revealing a repetition of neutral units. Charge polarization tells a different story. The first repeating unit from the left is largely nonpolar, while all other repeating units have a large polarization of charge. This increases the ionicity and significantly decreases the spin population on all other phenylene rings. As the intermediate meta-phenylene groups serve as couplers, Jr1r2 is greater than Jr2r3 in the triradical. There is an obvious reason for Jr1r3 to be far smaller than Jr1r2 and Jr2r3. The larger distance between the radical sites weakens the magnetic interaction.54 The calculated Jr1r3 is too small, and it does not give any significant contribution to the ferromagnetic nature of spin coupling. An attempt to calculate J values for system 4 has been made. Unfortunately, the required BS calculations converged only for

Figure 9. SOMO plots for system 3 in the broken-symmetry state (BS2, ↑↓↑) obtained at the UB3LYP/6-311++G(d,p) level.

Table 5. B3LYP/6-311++G(d,p) Level Net Charge and Spin Populations on the Fragments of 1−4 in the High-Spin State 1 r1 C1 r2 C2 r3 C3 r4 C4

2

3

4

charge

spin

charge

spin

charge

spin

charge

spin

0.088 −0.088

0.910 0.090

0.101 −0.144 0.295 −0.253

0.892 0.187 0.928 −0.006

0.104 −0.088 0.382 −0.465 0.331 −0.263

0.890 0.166 0.917 0.124 0.916 −0.013

0.106 −0.088 0.394 −0.419 0.440 −0.499 0.335 −0.268

0.889 0.167 0.920 0.090 0.918 0.113 0.921 −0.019

E


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optimized by the UB3LYP/TZVP method, and the state Sz =1 per unit has been found to be more stable than the spin state Sz = 0. The total energy of the optimized unit cells and Sz values are given in Table 6. These values along with z = 2, N = 2, and Sz = 1/2 have been used to calculate the Ising coupling constant (JI) in the long-chain polymer from eq 4: 187.1 cm−1 (B3LYP) and 197.0 cm−1 (B3LYP-D). The corresponding JY (JH) for the polymer is determined from eq 5 with N = 2. We get JH of about 93.6 cm−1 (B3LYP) and 98.5 cm−1 (B3LYP-D). These values match the decreasing trend of JY with increasing length as shown in Table 2. To make this point more apparent, the trend is also illustrated in Figure 11, where we have used JY for 2′, 2, 3, and 4 corresponding to the number of phenylene rings p = 1, 2, 3, and 4, respectively. The trend follows an equation of the form

Figure 10. Unit cell for periodic calculations in this work.

JpY = J∞ + (J1Y − J∞)exp[−β(p − 1)]

(7)

with JY1 = 243.0 cm−1. A least-squares fitting gives the exponent β as 0.3915 and 0.4185 for B3LYP [Figure 11a] and B3LYP-D [Figure 11b], respectively. The rmsd values are small at 9.2 and 10.5, respectively. The asymptotic limit J∞ is found as 77 (B3LYP) and 86 (B3LYP-D) in cm−1. The exponential dependence on length (p) is well-known from our previous work54,55 and the work of Matsuda et al.57,58 on phenylene chains. The infinite chain with periodicity has a finite JH value, about 95 cm−1, to identify the polymer as a moderately strong ferromagnet. The estimated J∞ is a little smaller than JH. This happens as the individual finite polymers have geometries deviating from the periodic geometries. The deviation increases with p, and it weakens the π-conjugation thereby lowering the strength of magnetic coupling. The energy band diagram is obtained for the unit cell at the UB3LYP/TZVP level (Figure 12). For α-electrons, the highest valence band has energy maximum at −0.1652 au, and

Figure 11. Plot showing trend of JY with respect to p: calculated JY from (a) B3LYP [red] and (b) B3LYP-D [blue]. The periodic results are shown by squares.

nonvanishing coefficient on common atoms, can have parallel spin on these atoms. This contributes to the exchange energy, thereby making the HS state lower in energy. The same principle can be rationalized for polyradicals. The SOMOs shown in Figure 9 for the BS solution together are not disjoint, turning the HS state into the ground state. Periodic Calculation. Crystal09 computational code has been adopted for the periodic calculation on the 1-D chain using the unit cell in Figure 10, as explained earlier. Geometries of both spin states Sz = 1 and Sz = 0 per unit have been

Table 6. Total Energy of the Optimized Unit Cell and Magnetic Exchange Coupling Constant (J) Using Basis TZVP (CRYSTAL09) B3LYP FM AFM

B3LYP-D

Sz per unit

E (au)

JI (cm−1)

JH (cm−1)

E (au)

JI (cm−1)

JH (cm−1)

1 0

−1041.8434143 −1041.8417093

187.1

93.6

−1041.8779472 −1041.8761523

197.0

98.5

Figure 12. Band diagram (a) for alpha electrons and (b) for beta electrons. F



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the lowest virtual band has an energy minimum at −0.0058 au as shown in Figure 12a. For β-electrons, the highest valence band has an energy maximum at −0.2362 au, and the lowest virtual band has an energy minimum at −0.0805 au (Figure 12b). The calculated band gaps are 4.34 eV for α-electrons and 4.24 for β-electrons, both being quite large. So, the polymer formed would be an electron insulator or, at most, a wide gap semiconductor. To compare, the verdazyl-substituted polysilene chains were found to be weakly ferromagnetic but conductors or semiconductors.16

ASSOCIATED CONTENT

S Supporting Information *

Total energy and ⟨S2⟩ value of optimized geometries (Table S1), dihedral angles of optimized geometry for other spin states (Table S2), optimized geometry of the singlet state of system 4 (Figure S1), ORCA single-point energies of 2′ and 2 (Table S3), ORCA single-point energies of 4 with the B3LYP functional (Table S4), and dihedral angles in optimized geometry of 4 (Table S5). Full Gaussian09 ref 37 and output files. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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5. CONCLUSIONS In this work, we have investigated electronic and magnetic properties of the silicon-substituted 1-D chain of metaphenylene polyradicals. The analysis shows that these systems have high-spin ground states with moderately large magnetic exchange coupling constants (J). However, the J values are quite smaller than the J values for the carbon analogues. The reason for this is the nonplanarity of optimized geometries caused by the pseudo Jahn−Teller effect and the difference between the energies of the pz orbitals on carbon and silicon atoms. However, these systems have periodic character like the carbon analogues: the alternatively placed phenylene moieties are parallel to each other. The intersite coupling constants calculated are affected by the increased polarity of the repeating units on the right side. The coupling constants between nearest neighbors on this side are smaller in magnitude. Spin density data show that the spin is mainly centered on Si atoms. The spin alternation rule and SOMO plots for the triradical 3 support the high-spin ground state. The overall J values calculated for different p-mers show a decreasing trend with an increasing number of phenylene rings (p). The band energy diagram is indicative of the polymer having a wide band gap. Therefore, the polymer is predicted to be ferromagnetic with a moderate transition temperature (∼100 K) but an electron insulator.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-22-2576 7156. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support of this work by Department of Science and Technology and thank I.I.T. Bombay computer centre for their generous support. S.H. acknowledges University Grants Commission for a fellowship. G


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