Article pubs.acs.org/JPCC
Theoretical Investigation of Magnetic and Conducting Properties of Substituted Silicon Chains. I. Hydrogen and Oxo-Verdazyl Ligands Shekhar Hansda, Iqbal A. Latif, and Sambhu N. Datta* Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai − 400 076, India S Supporting Information *
ABSTRACT: In this work, we investigate the magnetic and conducting properties of polysilene chains attached to the stable free radical oxo-Verdazyl (o-VER) via C-linkage, by using quantum chemical and solid state methods. Calculations are first carried out on 39 possible monomers in their triplet and broken symmetry states following the density functional methodology UB3LYP and using Gaussian 03 and 09 codes. The magnetic exchange coupling constant (J) is calculated for each species. Here, the magnetic exchange coupling constant J equals the negative of the ratio of the energy difference and difference between the low-spin and the high-spin ground states, in accordance with the Heisenberg spin exchange Hamiltonian. Geometry is optimized using the 6-31G(d) basis set. Single-point calculations on the triplet and broken symmetry states are performed with the optimized geometries and 6-311G(d,p) basis set. Calculations on three series of molecules of interest are finally done by employing the 6-311++G(d,p) basis set. Planar silicon chains having o-VER groups at alternative positions have intramolecular ferromagnetic (FM) interaction (with positive J). The nonalternative arrangement shows antiferromagnetic (AFM) coupling (with negative J). These results directly agree with the spin alternation rule. However, alternatively placed o-VER groups that are arranged as a stack perpendicular to the axis of the silicon chain show from weak AFM to weak FM intramolecular interaction. Negative J values are calculated for distorted as well as exactly parallel stacks of o-VER without methyl groups. We find positive J values for distorted stacks and negative J for parallel stacks, both with methyl groups retained in o-VER. These observations for the stacked radicals are rationalized in terms of a competition between through-chain FM and through-space AFM spin interactions. In the second step, solid state calculations are performed on the planar FM polymer (without methyl groups in o-VER) and two AFM chains with o-VER groups stacked in parallel (without and with methyl groups) by using the CRYSTAL09 code. These are based on the UB3LYP methodology and 6-21G(d) basis set. From these calculations, we predict the first polymer, with estimated J of the order of 30 cm−1, to be a semiconductor with band gap 1.27 eV. The stacked two, both antiferromagnetic with J = −27 and −35 cm−1, are predicted to be, respectively, a conductor and a semiconductor, the latter with a band gap of only 0.57 eV. The distorted stack version of the third polymer is likely to be ferromagnetic and a semiconductor, like the first polymer, though they considerably differ in structural geometry. consequent electronic delocalization within the σ-bonded backbone which leads to a good semiconducting property.1,2 Recently, Deepak et al. have found that polysilane has greater electron conductivity than hole conductivity.3 Various organosilicon polymers with a conjugated chain have attracted considerable attention because of their possible application as semiconducting materials.4 As part of our ongoing work on magnetic molecules of organic origin, we explore here possible silicon polymers that may simultaneously exhibit ferromagnetism and semiconducting nature. In our previous work, we have studied a variety of organic diradicals prepared from the stable monoradical centers like nitronyl nitroxide (NN), oxo-verdazyl (o-VER), and
I. INTRODUCTION Silicon is well-known for its abundance and semiconducting properties. The latter can be easily manipulated by doping silicon with impurities, thereby changing the band gaps. Compounds of silicon with C, N, and O are quite common and have wide applications. Silicon carbide, silicone, siloxane, and silicon nitride constitute a few examples. The chemistry of forming Si−C, Si−N, or Si−O bonds is well-known, but the formation of Si−Si bonds to yield a specific polymeric chain is in the process of continual development. Silicon has the property of catenation and can form a stable long linear chain. In fact, polysilane and polysilene are chains containing only silicon in the backbone. Stable polymers with a silicon backbone and containing up to 40 000 monomer units have been synthesized.1 Cyclic and acyclic silicon catenates are significantly different in properties from their carbon analogues. Electronic spectroscopy suggests a significant interaction and © 2012 American Chemical Society
Received: February 9, 2012 Revised: May 18, 2012 Published: June 4, 2012 12725
dx.doi.org/10.1021/jp301321e | J. Phys. Chem. C 2012, 116, 12725−12737
The Journal of Physical Chemistry C
Article
tetrathiafulvalene (TTF).5 In this work, we report our theoretical design of R1−(SiR2SiR3)n−R4 (n = 1−4) molecular systems and the corresponding polymer (polysilylene), where R1, R2, R3, and R4 vary as the hydrogen or oVER moiety depending on the systems. The monoradical center o-VER has been used to generate magnetic characteristics. First we investigate monomer units for n = 1 to n = 4 by quantum chemical methods. We show that properly designed monomers (polyradicals) show good intramolecular ferromagnetic (FM) exchange with coupling constant varying up to 184 cm−1. Next, we consider three one-dimensional chains, one of ferromagnetically coupled monomers and the other two of antiferromagnetically coupled monomers. The coupling constants for these polysilenes are estimated from the n → ∞ limits of the corresponding monomers. Crystal density functional (DF) calculations reveal the first (ferromagnetic) polymer to be a possible semiconductor with a band gap of 1.27 eV that lies between Si (∼1.1 eV) and GaAs (∼1.4 eV) band gap values.6 The second (antiferromagnetic) is a possible conductor with Fermi level at about −3.75 eV, within the overlapping valence and conduction bands, and the third (antiferromagnetic) is a semiconductor with a really small band gap of 0.57 eV. Thus, we predict the first (substituted) silicon chain to be a possible material for spintronics.
These polymers are shown in Figure 4. Of course, the exact parallel stacks are less stable than the distorted parallel stacks, and in all probability, chemical synthesis would yield the distorted stacks. The reason for investigating the second and third polymers is to show that these and their distorted counterparts can have conducting properties.
III. METHODOLOGY Theory. The interaction between two localized spins S1 and S2 in a diradical is normally described by the Heisenberg effective spin Hamiltonian Hex = −2JS1·S2 (1) The quantity J is known as the magnetic exchange coupling constant. The J value can be calculated with the help of spinpolarized solutions for the triplet (T, S = 1) and singlet (S, S = 0) states J=
1 [E(S = 0) − E(S = 1)] 2
(2)
The positive and negative values of J correspond to FM and AFM characters of the spin coupling, respectively. The unrestricted Hartree−Fock method with a comparatively small basis set can easily generate a good molecular geometry and also gives good spin-polarized states.7 Nevertheless, it fails to give an accurate magnetic exchange coupling constant because the singlet spin state of a diradical cannot be correctly represented by a single determinant wave function. The Configuration Interaction (CI) method is a good option to solve this problem, but it requires a tremendously large computational effort as the size of the diradical increases. This dilemma was solved by Noodleman8 who proposed a density functional (DF) based approach in the unrestricted framework. It requires the calculation of the energy of a broken symmetry (BS) solution. The BS state is not a pure spin state but a mixture of higher and lower spin states. Ideally, the BS solution should correspond to = 1, but the calculated BS state generally turns out to be spin contaminated. Taking the effects of spin contamination into account, Noodleman derived the relation
II. SYSTEMS The structure of o-VER is shown in Figure 1. The molecule is a monoradical, and it contains two methyl groups bonded to two
Figure 1. Oxo-Verdazyl radical: (a) with hydrogen atoms in place of methyl groups and (b) the original radical.
JN =
nitrogen atoms. Binding with other species may take place via the nitrogen atoms that have no substituent or the carbon atom of the ring that is bonded to a hydrogen atom. The C-terminal is chosen in this work. Two species are considered: the o-VER radical itself and a variant that has hydrogen atoms in place of the two methyl groups. Monomers. The initial stage of this work involves calculations on 39 polyradicals of silicon with o-VER groups as substituents. Monomers 1−20 have the monoradical center o-VER with hydrogen in place of methyl groups. In the later part of this work, we will see that these can be classified as planar antiferromagnetic (AFM) radicals, planar ferromagnetic (FM) radicals, distorted parallel stacks, and exact parallel stacks (see Figure 2). Monomers 21−39 have the monoradical center o-VER with methyl substituents and are shown in Figure 3. These belong to the same four classes. Polysilenes. Three polymers are investigated here for the solid state properties. These are of species 4 (planar FM system) and the exact parallel stacks of modified o-VER and original o-VER. We will see in the subsequent sections that the last two polysilenes have antiferromagnetically coupled spins.
(E BS − E T ′) 1 + Sab 2
(3)
where ET′ is the energy of the triplet wave function built from the BS orbitals, and Sab is the overlap between the magnetically active orbitals a and b. As the spin contamination in the triplet is normally small, ET′ can be replaced by the calculated energy of triplet ET. However, eq 3 is applicable to systems which have very weak overlap between the two magnetic orbitals. If the overlap Sab increases, the result obtained from this equation becomes unreliable. To tackle this problem, Yamaguchi et al.9 developed a modified form for the magnetic exchange coupling constant JY =
(DFTE LS −
DFT
2
E HS)
2
⟨S ⟩HS − ⟨S ⟩LS
(4)
where LS stands for the lower spin state and HS stands for the higher spin state. Equation 4 is also applicable to polyradicals, for which the Hamiltonian is given by Hex = −2J ∑ Si ·Sj i
