Effect of length on the transport and magnetic properties of diradical substituted molecular wires

Abstract

Extended π-conjugated molecules are known to have interesting applications as conducting nanowires, memory devices, and diodes. In the present work, we investigate the effect of the length of unsaturated organic molecular wires and radical substituted wires on the conduction properties of hybrid devices. At the same time, we also study the effect of the length of unsaturated radical substituted organic molecular wires on the magnetic properties. It was found that the value of magnetic exchange coupling constant (J) depends on the distance between spin centers. In order to measure the transmission characteristics of these conjugated molecular wires, we have designed a molecular bridge structure where the phenyl based molecular system containing conjugated multiple bonds of varying length is used as a bridging fragment between two semi-infinitely widened Au₉ fcc clusters along the Au(111) direction. A state of the art non-equilibrium Green's function (NEGF) method coupled with density functional theory (DFT) based approach has been applied on this two-probe molecular bridge system to understand its electrical transport characteristics. It was observed that the molecular wires with smaller length show higher transmission. The transmission spectra of the ferromagnetically coupled diradical based molecular wires show similar behavior to those of the wires without any substitution. Hence, there is no effect of radical substitution on transport properties for ferromagnetically coupled diradical based molecular wires, whereas for antiferromagnetically coupled systems, the scenario is different.

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Introduction

The term molecular wire is usually employed in molecular electronics to signify molecular scale objects that conduct electrical current with a highly preferential axis for conduction. The electrical conduction properties of molecular wires have been the focus of many studies in recent years.^1–4 Individual molecular wires are divided into two categories.¹ The first category is based on n-alkane chains [CH₃–(CH₂)_n−1], which have a large (∼6 eV or greater) band gap separating their highest occupied molecular orbital (HOMO) and their lowest unoccupied molecular orbital (LUMO) and are relatively insulating.^5,6 The second category is based on conjugated molecules that have a small (2–4 eV) HOMO–LUMO gap and behave like ordinary semiconductors.^7–9 This second category of molecules are rigid and possess delocalized π-electrons. Jalili et al. investigated the effect of the length of the molecular wire on the conduction spectra of organic nanowires,³ where the I–V curve for thiophenthiol based systems is non-ohmic in nature. Recently, a hybrid device was designed where gold nano particles are connected by saturated organic molecules of different lengths (alkanedithiol chains)² and it was observed that the conductivity increases with the length of the molecule. Electron tunneling through a molecular wire has also been studied as a function of the length and chemical structure of the molecule by Magoga et al.⁴ They found that the tunneling phenomenon through a molecular wire relies on the damping factor and the contact conductance. The effect of bond length alternation on transport behavior has also been experimentally and theoretically demonstrated.¹⁰ A study of charge and spin transport through para-phenylene oligomers reveals that the oligomeric para-phenylene bridge can act as a molecular wire for the charge recombination reaction. The rate of charge transport through such molecules decreases exponentially when the super-exchange mechanism dominates.¹¹ The decay constants (β) of diradical substituted conjugated molecular wires have been studied by Nishizawa et al. and they found that β is well correlated with the electronic transmission.¹²

In this work we investigate the transport property of two molecular wires of different lengths (Fig. 1) to show the effect of the length of the wire on the electrical transport properties. In this context, we designed six diradicals (Fig. 2) by substituting a methylene radical at different positions in molecular wire 1 to generate series 1 and similarly ten diradicals based on molecular wire 2 to generate the systems of series 2 (Fig. 3) to study the effect of spin polarization on the transport properties and the dependence of magnetic coupling on the distance between the radical centers. The wires we have studied here are addition polymers, and such polymers are important for application in the electronic industry.¹³ The effects of entropy, the amount of molecules and their root-mean-square end-to-end distance on the physical properties of polymers are very important issues and these points were properly discussed by Lu et al.^14,15

Fig. 1 Two molecular wires (1 and 2) on which transport calculations have been carried out.

Fig. 2 Designed diradical based molecular wire 1.

Fig. 3 Designed diradical based molecular wire 2.

Theoretical and computational methodology

In order to determine the transport properties of the system, we need to describe the finite left electrode–molecular region–right electrode part of the infinite system. For this purpose, the gold-cluster–dithiolate–gold-cluster system has been divided into three sub systems: left gold cluster, central dithiolate, and right gold cluster, as illustrated in Fig. 4. Wires with radical substitutions are also treated in a similar manner. The magnetic properties of the diradicals are calculated on the structures without –SH and gold cluster.¹⁶

Fig. 4 (a) and (b) are the Au–molecule–Au two probe structures designed primarily for the transport calculation. The gray, white, yellow and green colors represent carbon, hydrogen, gold and sulfur atoms, respectively (L stands for lead and M stands for molecule).

We calculated the transmission property using ARTAIOS code developed by Herrmann et al.^16,17 In this approach the dithiol molecule has been optimized in the unrestricted DFT framework with B3LYP functional and 6-31G(d,p) basis set using the Gaussian 09 quantum chemical package¹⁸ and then the hydrogen atoms are stripped off and the resulting neutral dithiolate is placed between two Au₉ fcc clusters. The bond length between sulfur and the Au(111) surface has been chosen to be 2.48 Å with Au–Au distances of 2.88 Å as in extended gold crystals.¹⁶ Fock and overlap matrices required for the transport calculation are obtained by single point calculation in the Gaussian 09W program package. For the transport calculation, we employed the B3LYP functional and the LANL2DZ basis set to avoid ghost transmission.¹⁴ The transmission function is calculated within the Landauer approximation based on a Green's function approach using the post processing tool ARTAIOS.

Yoshizawa and coworkers developed an orbital rule to predict the right connections between the molecule and the electrodes.^19,20 The rule is: (1) the sign of the product of the orbital coefficients at sites r and s in the HOMO should be different from the sign of the product of the orbital coefficients at sites r and s in the LUMO, and (2) sites r and s should have the large amplitude of HOMO and LUMO. We computed the coefficients of the HOMO and LUMO of the connecting C atoms (Table 1) following Yoshizawa's rule.^19,20 The detailed list of orbital coefficient values of both the wires is given in the ESI (Table S1†).

Table 1 Orbital coefficients of connecting C atoms within molecular wires 1 and 2 (without radical substitution)

Site	Orbital	Molecular wire 1		Molecular wire 2
		HOMO	LUMO	HOMO	LUMO
r1	2pZ	−0.0863	−0.0823	0.0560	0.0464
s1	2pZ	−0.0863	0.0823	0.0572	−0.0465

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The interaction between two magnetic sites 1 and 2 is generally expressed by Heisenberg spin Hamiltonian:

Ĥ = −2JŜ₁ × Ŝ₂ (1)

Where Ŝ₁ and Ŝ₂ are the respective spin angular momentum operators and J is the exchange coupling constant. A positive value of J indicates the ferromagnetic interaction while a negative value indicates the antiferromagnetic interaction between two magnetic sites. For a diradical containing one unpaired electron on each site, J can be represented as:

E_(S=1) − E_(S=0) = −2J. (2)

Many researchers^21–28 have developed different formalisms to evaluate J using an unrestricted spin polarized broken symmetry (BS) solution, depending on the extent of magnetic interaction between two magnetic sites. The equation for evaluating J proposed by Ginsberg,²³ Noodleman²⁴ and Davidson²⁵ is applicable when the interaction between two magnetic orbitals is small. On the other hand, the expression proposed by Bencini^26,27 and co-workers and Ruiz et al.²⁸ is applicable for large interaction. Nevertheless, the well-known expression given by Yamaguchi²⁹ is applicable for both strong and weak overlap limits. Following the well established^30,31 and widely applied method,^30–35 we use the Yamaguchi²⁹ formula for evaluation of J in this work, which is given by:

Where E_BS, E_HS and 〈S²〉_BS, 〈S²〉_HS are the energy and average spin square values for corresponding BS and high spin states, respectively.

Results and discussion

Transport properties of molecular wires 1 and 2

The zero bias transmission spectra of the molecular wires are given in Fig. 5. The horizontal axis corresponds to the electron energy E incident from the electrode. The proper choice of the electrode's Fermi energy is not entirely clear, so for this reason we compared different values (−2.5 eV to −5.5 eV), whereas the Fermi energy of bulk gold is −5.53 eV.³⁶

Fig. 5 Transmission spectra of molecular wire 1 and molecular wire 2 at zero bias.

We can see from Fig. 5 that molecular wire 1 has higher transmission near the Fermi level compared to molecular wire 2, which implies that the smaller wire is more efficient for electrical transport.²

Now from the structures of the two molecular wires one may expect that the conductivity of a system increases with increasing the number of π electrons, but organic molecules are not usually very rigid. The flexing and bending of bonds changes the overlap between different orbitals. If all the benzene rings in the molecule are in the same plane, the p orbitals have the maximum overlap, which leads to the lowest resistance. On the other hand, complete misalignment between the rings leads to the highest resistance. The decrease in transmission with the increase in the length of the wire can also be explained by Pauling's bond order,³⁷ which is proportional to the transmission. According to this concept, with increasing phenyl ring in a molecular wire, Pauling's bond order decreases exponentially and hence the transmission is also decreased.

Molecular orbitals of wire 1 and 2

Molecular orbitals contain all the quantum mechanical information about the electronic structures of a molecule. To understand the transport property through a molecule it is necessary to study the molecular orbitals because they offer spatial conduction channels for electron transport.³⁸ Localization of orbitals can significantly change the transport properties. An external electric field is an appropriate stimulus to tune the MOs of a molecule. It has been shown that the MOs of a molecule with and without electrode atoms at their end have similar characteristics under an external electric field.³⁹ Following this analogy and following one of our recent works,⁴⁰ we applied an electric field (parallel to the molecule) taking the optimized geometry (without thiol groups and lead atoms at their ends) to study the change of molecular orbital under an external electric field.

We can see from Fig. 6 and 7 that at zero external electric field the HOMO and LUMO spread over the entire molecule. After the application of the external electric field, the MOs are squeezed to a few atoms for both the wires. If we closely look at the MOs of wire 1, we can see that the HOMO and the LUMO are always collectively spread over all the molecules (except field 0.02 a.u.). However, for wire 2, the HOMO and LUMO cannot cover the whole molecule even jointly. Thus with the application of an external electric field there is a large separation in the spatial distribution of the HOMO–LUMO for molecular wire 2 as compared to wire 1.

Fig. 6 Molecular orbitals of wire 1 under different electric fields.

Fig. 7 Molecular orbitals of wire 2 under different electric fields.

Magnetic exchange coupling constant of the diradical substituted molecular wire

We substituted the molecular wires with two methylene radicals such that the diradical shows ferromagnetic and antiferromagnetic interaction according to the spin alternation rule⁴¹ and we changed the position of the radicals to vary the distance between the radical centers. We plotted the magnetic exchange coupling constant as a function of the distance between radical centers (Fig. 8). The calculated magnetic exchange coupling constants of the diradical are also given in ESI Tables S2 and S3.† We can see that with increasing the distance between radical centers, the magnetic exchange coupling constant value decreases. The distance-dependent exchange coupling constant of π-conjugated molecular wires has been studied by Nishizawa et al. and they found similar results.¹²

Fig. 8 Plot of magnetic exchange coupling constants as a function of distance between the radical centers.

Spin density distribution between diradical centers

The spin density from the DFT based approach can give us an insight about the spin polarization mechanism in the molecule for magnetic exchange. The spin densities of the high-spin states of the diradical are represented in Fig. 9 and 10. It is clear that with increasing distance between the radical centers, the spin polarization decreases; hence the coupling constant also decreases. Therefore, it is obvious that beyond certain distances between two spin centers, spin polarization is no longer effective although the molecule has a strong π-network. Another important thing is that the magnetic exchange between two spin centers depends only on the environment in between them, not on the outside substitution.

Fig. 9 Spin density distribution of the ferromagnetically coupled diradicals (high spin state) and antiferromagnetically coupled diradicals (BS state) based on molecular wire 1.

Fig. 10 Spin density distribution of the ferromagnetically coupled diradicals (high spin state) and antiferromagnetically coupled diradicals (BS state) based on molecular wire 2.

Transport property of the diradical substituted molecular wires

We studied the transport property of the diradical substituted molecular wires (in Fig. 11 and 12) to see the effect of radical substitution on the transport behavior of the molecular wires. We can see from the figures that the molecular wires belonging to the same series show almost similar transmission, but series 1 exhibits higher transmission than series 2. Again comparing the transmission for the molecular wire without radical substitution (Fig. 5), we observe the same result as that for the ferromagnetically coupled diradicals (Fig. 11 and 12). However, the transmission characteristics are affected by the antiferromagnetically coupled diradicals. Stasiw et al. showed that for donor–bridge–acceptor systems there is a large variation in magnetic exchange coupling and electronic coupling as a function of bridge conformation.⁴² For our designed molecular wires (consisting of several aromatic phenyl rings along with radical substitution on the rings), when transmission occurs through the wire, possibly only local transmission of the aromatic rings appears on the Fermi level of the electrode and the radicals do not participate in the transmission of that region, which may be the reason for the same transmission after radical substitution in the ferromagnetic diradicals, but for antiferromagnetic diradicals, there is a small variation in transmission characteristics between radical substituted molecular wires.

Fig. 11 The transmission spectra of the diradical substituted molecular wire 1 [1(a)–1(c) high spin state; 1(l)–1(n) BS state].

Fig. 12 The transmission spectra of the diradical substituted molecular wire 2 [2(a)–2(e) high spin state; 2(l)–2(p) BS state].

Conclusions

To summarize, we studied the effect of the length of molecular wires on the electrical transport properties. We found that the molecular wires (addition polymer) with smaller length show higher transmission, i.e., higher conduction. Another important point is that the magnetic exchange coupling constant of the radical substituted molecular wire depends only on the distance between the spin centers, not on the outsider substitution. The transmission of the molecular wire without radical substitution shows similar observations as that of the wire with radical substitution for ferromagnetically coupled diradicals; however, the transmission characteristics are slightly affected by the antiferromagnetic diradicals.

Acknowledgements

We are thankful to Prof. Dr Carmen Herrmann for giving us the permission to use her transport code ARTAIOS. AM is thankful to DST, India for financial support. SS is thankful to Sonderforschungsbereich 668, University of Hamburg for a postdoctoral fellowship.

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Footnote

† Electronic supplementary information (ESI) available: Orbital coefficient values of wire 1 and wire 2, optimized XYZ coordinates of the molecular wire, molecular wire with S–H bonds and the actual molecular setup i.e., the Au–molecule–Au junction are available. See DOI: 10.1039/c6ra23147k

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