Design Considerations for Oligo(p-phenyleneethynylene) Organic Radicals in Molecular Junctions

TL;DR: Spin polarization in the electron transmission of radicals is important for understanding single-molecule conductance experiments focusing on shot noise, Kondo properties, or magnetoresistance as mentioned in this paper. But spin polarization in electron transmission is not useful for particle physics.

Abstract: Spin polarization in the electron transmission of radicals is important for understanding single-molecule conductance experiments focusing on shot noise, Kondo properties, or magnetoresistance. We ...

Summary

1 Introduction

• Electron transport through molecules is relevant for a variety of scientific fields, such as nanotechnology, biochemistry, catalysis, and materials science [1–3].
• This, along with other observations such as anisotropic magnetoresistance [31,61,62] and electrodeand metal-center-dependent magnetoresistance [63, 64] suggests that spin–orbit coupling, possibly resulting from interactions with the electrodes, may play a role in understanding single-molecule magnetoresistance.
• The authors are evaluating single-molecule conductance assuming coherent tunneling as the dominant transport mechanism (Landauer regime).
• For the other radicals, the inclusion of dispersion corrections does not influence the OPE backbone significantly.

3 An artifical radical–OPE molecule with large spin polar-

• Ization Based on the conclusions drawn above, one can suggest a structure for an organic radical with an OPE backbone which exhibits more strongly spin-dependent transport properties, e.g., an OPE molecule to which a methyl-nitroxide radical attached (see Figure 6).
• Since the methyl residue is small, the N-O radical can be in plane with the OPE backbone, leading to good conjugation of radical and backbone π systems.
• To fully enforce a completely planar structure, the results for this molecule are based on an optimized structure without taking into account dispersion interactions (however, even dispersion interactions do not lead to out-of plane rotation of the radical part here).
• Still, it is interesting to see how strong spin polarization can be for OPE wires with such an “ideal” substituent.
• As the calculated transmission functions for |↑〉 and |↓〉 electrons (see Figure 7) show, this strong conjugation of the methyl nitroxide with the OPE backbone leads to a significant difference between the transmissions for both spin channels over a broad energy range, as well as to a larger spin delocalization onto the backbone than for the tert-butyl-nitroxide–OPE (see Figure 8).

4 A mechanically flexible radical ligand: TEMPO–OPE

• In the “original” OPE radical, which inspired this study, a TEMPO radical is attached to the OPE backbone via an amide linker [11].
• This results in a certain structural flexibility.
• For the cis configuration, rotation of one of the OPE rings induced a significant decrease of the calculated transmission compared to the trans configuration.
• The structural flexibility of the radical substituent might open up additional possibilities of interactions, both with neighboring molecules and with the electrode surfaces, which might be related to the mechanism underlying magnetoresistance.
• A potential energy scan for a set of structures interpolating between the two, twisted stepwise around the amide bond with that bond dihedral fixed and all other degrees of freedom relaxed, followed by an optimization of the transition state, yields a barrier of 84.9 kJ/mol (about 0.880 eV, see Figure 10).

5 Conclusion

• The authors have studied the potential of different radical substituents to induce spin polarization in electron transmission through OPE wires by means of first-principles DFT calculations in the coherent tun- neling regime.
• For OPE-methyl-nitroxide (t-NO), featuring the only substituent with spin density on the atom bonded to the backbone, non-negligible spin polarization at the Fermi energy might be achieved by shifting MO energies and thus transmission to higher energies by half an eV, e.g. via further substituents.
• The main effect is a lowering of the overall transmission minimum, which is, at least for verdazyl, caused by dispersion interactions between the substituents and the backbone, twisting one of the outer phenyl rings.
• This is not unique to the substituent being a radical and could be considered as a general design tool for such compounds (after a careful assessment of conformational dynamics, given the easiness of rotation of the OPE rings [95]).
• This twisting is also pronounced in TEMPO–OPE [11], yet here an additional property comes into play:.

Figures

Figure 3: Optimized molecular structures of the isolated OPE derivatives functionalized with organic radical substituents (DTDA=1,2,3,5-dithiadiazolyl, t-NO=tert-butyl nitroxide, NNO=nitronyl nitroxide). While for the DTDA and the t-NO radical the OPE backbone remains (nearly) planar, the presence of the NNO and verdazyl radicals leads to twisting of one of the phenyl rings.

Figure 8: Optimized molecular structures and spin densities (isosurface value: 0.001) for the methyl nitroxide and tert-butyl nitroxide radicals. The spin density of the OPE-methyl-nitroxide expands onto the OPE backbone, while for the tert-butyl-nitroxide–OPE molecule, it is mainly localizied on the radical.

Figure 7: Calculated transmission function for the methyl-nitroxide–OPE molecule. The energy is shifted against the estimated EF of -5 eV. A pronounced feature of the SOMO can be observed at about -0.3 eV and |↑〉 and |↓〉 electrons differ significantly over a wide range of energy.

Figure 1: Illustration of a molecular bridge between two gold electrodes, forming a molecular junction. An OPE backbone with a TEMPO radical substituent is shown, as was studied experimentally with respect to its single-molecule magnetoresistance properties [11].

Table 1: Dihedral angles for the optimized structures shown in Figure 3 (in degrees). Upper line of each entry: dihedral angles defining twisting between radical substituent and OPE backbone; lower line: dihedral angles defining twisting between central ring and twisted ring of the OPE backbone.

Figure 6: Lewis structure and optimized molecular structure (B3LYP/def2-TZVP) for the methylnitroxide–OPE molecule. Due to the small methyl residue, the complete structure of the molecule remains planar.

Figure 10: Calculated potential-energy surface (PES)for the transition from trans-TEMPO–OPE to cis-TEMPO–OPE. The energy is plotted against the dihedral angle formed by the nitrogen and carbon atoms of the amide bond and the nearest-neighbor carbon atoms of the OPE-backbone and the TEMPO radical. The blue dots represent the energy calculated from a PES scan, where the dihedral angle was changed successively and kept fixed during the following structure optimization. The green dots represent the optimized structures (cis, trans) and the structure of the transition state (Berny) calculated with the “Berny Algorithm”. The cis and trans structure only differ by about 0.04 eV. However, a rather high rotation barrier of 0.88 eV makes a rotation unlikely under the experimental conditions (T = 4K).

Figure 4: Calculated transmission functions for the OPE-based radicals under investigation. The energy was shifted w.r.t. the estimated Fermi energy (−5 eV).

Figure 2: Lewis structures of the radical wires under study. A DTDA (a), a tert-butyl nitroxide (b), a nitronyl nitroxide (c), and a verdazyl (d) radical were attached to an OPE-backbone with thiolate linkers.

Figure 9: Calculated transmission functions of the TEMPO-OPE molecules (trans- and cis), as already discussed in Ref. [11]. The |↑〉/|↓〉 transmission do not differ close to the estimated EF of -5.0 eV.

Figure 5: Calculated local transmissions for the four OPE-based radicals at EF .

Full text

Design Considerations for Oligo(p-phenyleneethynylene)
Organic Radicals in Molecular Junctions
Martin Sebastian Z¨ollner
∗
, Rukan Nasri
∗
, Haitao Zhang, Carmen Herrmann
∗∗
∗ Shared first authors
∗∗ Corresponding author: carmen.herrmann@chemie.uni-hamburg.de
March 6th 2020
Abstract
Spin polarization in the electron transmission of radicals is important for understanding single-
molecule conductance experiments focusing on shot noise, Kondo properties or magnetoresistance.
We study how stable radical substituents can affect such spin polarization when attached to oligo(p-
phenyleneethynylene) (OPE) backbones. We find that it is not straightforward to translate the spin
density on a stable radical substituent into spin-dependent transmission for the para-connected wires
under study here, owing to increased steric interactions compared with meta-connected wires, and a
resulting twisting of the radical substituent and OPE π systems. The most promising example is a
t-butyl nitroxide substituent, which, despite little pronounced spin delocalization onto the backbone,
yields a spin-dependent transmission feature which one might be able to shift towards the Fermi
energy by additional substituents. We also find that for bulkier substituents, dispersion interactions
with the substituent can lead to twisting of one of the outer OPE rings, reducing the overall conduc-
tance. As a further potential design consideration, attaching radicals via linkers might increase the
possibilities for spin-dependent intermolecular and molecule–electrode interactions.
1

1 Introduction
Electron transport through molecules is relevant for a variety of scientific fields, such as nanotech-
nology, biochemistry, catalysis, and materials science [1–3]. An important model system for under-
standing such transport processes are single-molecule junctions [4–10], which are often constructed
via mechanical or electromigrated break-junction techniques (see Figure 1).
Figure 1: Illustration of a molecular bridge between two gold electrodes, forming a molecular junction.
An OPE backbone with a TEMPO radical substituent is shown, as was studied experimentally with
respect to its single-molecule magnetoresistance properties [11].
Beyond serving as a means to understand molecular function with certain applications in mind,
single-molecule junctions also provide a highly appealing view into how molecules behave under
unusual conditions, i.e., in nonequilibrium and possibly exposed to additional stimuli such as light,
(static) electrical or magnetic fields, or mechanical control [12–19]. Molecules display particularly
rich behavior when they feature unpaired spins, as present in many transition metal complexes and
in organic radicals [20–30]. In the past few years, such molecules have been more and more in the
focus of single-molecule break junction experiments with nonmagnetic electrodes, and in particular
their response to magnetic fields [11,31], Kondo properties [32–35] and shot noise resulting from spin
correlations [36, 37] have been studied. Radicals adsorbed on graphene were also found to enhance
the conductance and the Seebeck coefficient of graphene nanoconstrictions based on first-principles
simulations [38].
Magnetoresistance in organic molecules has been studied in crystals, thin films and related struc-
tures, and depending on the type of molecule and experimental setup, different mechanisms are dis-
cussed [39]. For single-molecule junctions, it is much less clear which physical mechanisms are respon-
sible for the observed magnetoresistance behavior. Similarly, the link between Kondo signatures and
chemical structures is not fully understood [40], while shot-noise measurements on spin-polarized sys-
2

tems can be related to the difference between majority- and minority-spin transmission [36,37,41,42].
First principles simulations as provided by density functional theory (DFT) have proven valuable for
understanding magneto-structural correlations in magnetic molecules [43, 44], and are a promising
means of gaining insight into structure–property relations for the above-mentioned experiments.
Interestingly, also molecules without any intrinsic magnetic moment but with a helical structure can
display spin-dependent electron transport behavior, a phenomenon which has been named chiral in-
duced spin selectivity [45–60] and which is commonly attributed to Rashba-type spin–orbit coupling.
This, along with other observations such as anisotropic magnetoresistance [31, 61,62] and electrode-
and metal-center-dependent magnetoresistance [63, 64] suggests that spin–orbit coupling, possibly
resulting from interactions with the electrodes, may play a role in understanding single-molecule
magnetoresistance. Given that spin–orbit coupling at metal–molecule interfaces is far from being
understood, in particular from a first-principles perspective, we will focus here on those aspects of
possible relevance for the above-mentioned experiment which can be described well by present-day
first-principles methods, namely molecular structures, spin density distributions, and spin polariza-
tion of electron transmission.
Magnetoresistance has also been observed at room temperature in self-assembled monolayers which,
at least formally, do not feature any unpaired spins [65, 66]. This has been attributed to a (co-
operative) interface effect. Since also in single-molecule conductance measurements, the molecule
bridging between the electrodes is typically surrounded by other molecules of the same type due to
the preparation process, intermolecular interactions and cooperative effects could also play a role in
(formally) single-molecule experiments. Interface-related cooperative effects leading to spin polar-
ization are not well understood yet,which is why we focus in a first step on the relevant properties
of single molecules. We will study how attaching radical substituents to conjugated backbones can
affect overall transmission and spin polarization, and how steric effects, dispersion interactions and
structural flexibility play a role here. We focus on a monosubstituted oligo(p-phenyleneethynylene)
(OPE) backbone, inspired by previous experimental and theoretical work on TEMPO–OPE [11].
3

DTDA
.
.
Verdazyl
t-NO
.
NNO
.
Figure 2: Lewis structures of the radical wires under study. A DTDA (a), a tert-butyl nitroxide (b),
a nitronyl nitroxide (c), and a verdazyl (d) radical were attached to an OPE-backbone with thiolate
linkers.
The conductance properties of substituted OPE backbones have been studied experimentally and
theoretically before, in particular in the context of negative differential conductance [67, 68] and
modulating destructive quantum interference via controlling resonance structures [69,70]. The effect
of radical substituents on OPE transmission has not been studied in detail yet. We choose four
such substituents, 1,2,3,5-dithiadiazolyl (DTDA), nitronyl nitroxide (NNO), tert-butyl nitroxide (t-
NO) and verdazyl radicals [71] (see Figure 2). They were chosen because they are relatively stable,
leading to considerable potential as components of molecular materials with technologically relevant
properties [72], e.g., DTDA is an important building block for solid-state organic conductors and
magnets [73, 74]. We have studied the t-NO substituent previously with respect to its potential for
increasing exchange interactions between spin centers linked by an organic bridge [75]. Our DFT
data suggested that the effect of t-NO is substantial, being half as large as for (unstable) idealized
radical substituents such as −O·. Given common trends between spin coupling and conductance
through molecular bridges [76, 77, 77–84], this could suggest that t-NO (and the other stable radical
substituents studied here) could have a considerable effect on spin polarization in electron transport
through OPE wires. We again compare with an artificial (unstable) radical substituent, and also
discuss the potential importance of structural flexibility of the “original” TEMPO–OPE system as
an outlook.
4

2 How much spin polarization can we achieve by attaching
stable radical substituents directly to OPE backbones?
We are evaluating single-molecule conductance assuming coherent tunneling as the dominant trans-
port mechanism (Landauer regime). While this assumption can break down for long wires, high
temperatures and in electronic resonance [7, 85], it is reasonable for a (substituted) OPE backbone
with three phenyl units [11, 86]. The zero-bias conductance g can be estimated in this regime from
the transmission T at the Fermi energy E
F
,
g =
2e
h
T (E
F
), (1)
where e is the unit charge and h Planck’s constant. T can be written as a sum over spin-up /
majority-spin transmission and spin-down / minority-spin transmission,
T = T
↑
+ T
↓
. (2)
For spin-polarized systems such as radicals, T
↑
and T
↓
can be different, which is referred to as spin
polarization. We model T
↑
and T
↓
via a Green’s function approach combined with density functional
theory calculations for zero-bias electronic structures in the wide-band limit, as described, e.g., in
Refs. [87–90] and as detailed in the Supporting Information.
Spin flips, which may play a role in tunneling processes [91–94], are neglected here. This appears
justified by the good agreement between shot noise measurements and spin-flip-free theoretical de-
scriptions for spin-polarized systems [41]. It is also supported by validation calculations on simple
radicals, in which a two-component description allowing, in principle, for spin flips, did not lead to
substantial changes of transmission functions for collinear spin arrangements, even when including
spin–orbit coupling (see Supporting Information).
5

Frequently asked questions

Q1. What are the contributions in "Design considerations for oligo(p-phenyleneethynylene) organic radicals in molecular junctions" ?

The authors study how stable radical substituents can affect such spin polarization when attached to oligo ( pphenyleneethynylene ) ( OPE ) backbones. The authors find that it is not straightforward to translate the spin density on a stable radical substituent into spin-dependent transmission for the para-connected wires under study here, owing to increased steric interactions compared with meta-connected wires, and a resulting twisting of the radical substituent and OPE π systems. The authors also find that for bulkier substituents, dispersion interactions with the substituent can lead to twisting of one of the outer OPE rings, reducing the overall conductance. The most promising example is a t-butyl nitroxide substituent, which, despite little pronounced spin delocalization onto the backbone, yields a spin-dependent transmission feature which one might be able to shift towards the Fermi energy by additional substituents. As a further potential design consideration, attaching radicals via linkers might increase the possibilities for spin-dependent intermolecular and molecule–electrode interactions. 

Q2. What future works have the authors mentioned in the paper "Design considerations for oligo(p-phenyleneethynylene) organic radicals in molecular junctions" ?

The radical substituent is attached via an amide linker to the backbone, which opens up additional possibilities for interactions with other molecules or with the electrodes. Given that TEMPO–OPE shows considerable single-molecule-magnetoresistance, such potential for interactions and flexibility, and how it could be affected by the environment [ 99 ] could be an additional interesting consideration for designing molecules with magnetism-dependent electron transport properties. 

Q3. What fields are relevant to electron transport?

Electron transport through molecules is relevant for a variety of scientific fields, such as nanotechnology, biochemistry, catalysis, and materials science [1–3]. 

Q4. What is the mechanism underlying the magnetoresistance of the molecule?

The structural flexibility of the radical substituent might open up additional possibilities of interactions, both with neighboring molecules and with the electrode surfaces, which might be related to the mechanism underlying magnetoresistance. 

Q5. What is the way to understand the structure of a molecule?

First principles simulations as provided by density functional theory (DFT) have proven valuable for understanding magneto-structural correlations in magnetic molecules [43, 44], and are a promising means of gaining insight into structure–property relations for the above-mentioned experiments. 

Q6. What is the support for spin flips?

It is also supported by validation calculations on simple radicals, in which a two-component description allowing, in principle, for spin flips, did not lead to substantial changes of transmission functions for collinear spin arrangements, even when including spin–orbit coupling (see Supporting Information). 

Q7. What are the conductance properties of substituted OPE backbones?

The conductance properties of substituted OPE backbones have been studied experimentally and theoretically before, in particular in the context of negative differential conductance [67, 68] and modulating destructive quantum interference via controlling resonance structures [69,70]. 

Q8. What is the effect of t-NO on conductance?

Given common trends between spin coupling and conductance through molecular bridges [76,77,77–84], this could suggest that t-NO (and the other stable radical substituents studied here) could have a considerable effect on spin polarization in electron transport through OPE wires. 

Q9. What is the role of the electron transport mechanism in the study of single-molecule junctions?

along with other observations such as anisotropic magnetoresistance [31,61,62] and electrodeand metal-center-dependent magnetoresistance [63, 64] suggests that spin–orbit coupling, possibly resulting from interactions with the electrodes, may play a role in understanding single-molecule magnetoresistance. 

Q10. What is the effect of t-NO on the conductance of a single molecule?

Their DFT data suggested that the effect of t-NO is substantial, being half as large as for (unstable) idealized radical substituents such as −O·. 

Q11. What are the main reasons for the study of single-molecule junctions?

In the past few years, such molecules have been more and more in the focus of single-molecule break junction experiments with nonmagnetic electrodes, and in particular their response to magnetic fields [11,31], Kondo properties [32–35] and shot noise resulting from spin correlations [36, 37] have been studied. 

Q12. What is the difference between the t-NO and the BP86?

In that compound, the t-NO is attached to a a backbone with meta- rather than para-connection, leading to reduced steric interactions and much smaller dihedral angles (9.8◦/12.7◦ 1), and accordingly to a substantial influence on spin-dependent electronic communication [75].