Orbital Determining Spintronic Properties of a Ï-Conjugated System

Article pubs.acs.org/JPCC

Orbital Determining Spintronic Properties of a π‑Conjugated System Yuta Tsuji,† Aleksandar Staykov,‡ and Kazunari Yoshizawa*,†,‡ †

Institute for Materials Chemistry and Engineering and International Research Center for Molecular Systems, and ‡International Institute for Carbon-Neutral Energy Research, Kyushu University, Fukuoka 819-0395, Japan S Supporting Information *

ABSTRACT: Spintronic properties of cyclobutadiene (CBD) systems are investigated based on a qualitative frontier orbital analysis. CBD undergoes a Jahn−Teller distortion from the square triplet state to the rectangular singlet state. According to the qualitative Hückel molecular orbital analysis, the electron transport through the square triplet state is symmetry allowed, whereas that through the rectangular singlet state is symmetry forbidden. The magnetic triplet state is a possible coexisting system of conductivity and magnetism. Sophisticated first-principles quantum chemical calculations are performed by using a realistic molecular junction model. Obtained results are in good agreement with the prediction based on the qualitative orbital analysis. Interesting spin filtering properties are found in the square-shaped CBD system. The high- and low-spin states of the square-shaped CBD system produce the spin-α and spinβ polarized conductance, respectively. The qualitative orbital analysis is useful as a guiding principle for designing molecular spintronics. spin−orbit coupling20,23 and paramagnetic ring current,19,24 which make the magnetic properties of CBD systems of great interest, are widely investigated in the literatures. The Jahn− Teller distortion can be viewed as a molecular analogue of the Peierls distortion.25 The Peierls theorem states that a onedimensional system with an incompletely filled band distorts in such a way as to open up a gap at the Fermi level, and as a consequence its conductivity goes down.26 Since the Jahn− Teller distortion process in CBD systems is accompanied with the spin inversion from the triplet state to the singlet state, the distortion can be also viewed as a molecular analogue of the spin-Peierls transition,2 where the dimerization of neighboring electron spins produces an energy gap between the singlet nonmagnetic ground state and the triplet magnetic excited state. Thus, the conductivity and magnetism are intimately entangled in the Jahn−Teller phenomena in CBD systems. In this work, we perform a qualitative orbital analysis on CBD systems to discuss the effect of the Jahn−Teller phenomena accompanied with spin transition on the electron transport.

1. INTRODUCTION The research field for the interplay between magnetism and conductivity is called as spintronics.1 The design and fabrication of a coexisting system of conductivity and magnetism is essential for the development of spintronic devices. The influence of magnetic field upon the conductance of solidstate materials such as transition metal oxides, ion-radical salts, organic radical crystals, and charge-transfer complexes has been extensively investigated.1−3 To meet the requirements for the miniaturization of conventional silicon-based electronic devices, molecule-based spintronics has attracted a lot of attention in recent years. Sugawara and co-workers have experimentally investigated a pyrrole-based spin-polarized wire molecule that connects gold nanoparticles.1,4 In the past several years some theoretical studies of the spin-dependent electron transport through a single molecule such as metal-bound peptide,5 carbon nanotube,6 graphene,7,8 organometallic nanowire,9 organic radical,10,11 porphyrin,12 metal atom chain,13−15 and metal-complexed DNA16 have been published. To realize a spintronic device based on organic compounds, we consider cyclobutadiene (CBD), the simplest cyclic unsaturated compound with antiaromatic electronic structure. The automerization interconverting two equivalent rectangular D2h structures via a square D4h structure of CBD has been observed experimentally.17,18 The rectangular D2h structure represents the singlet ground state, whereas the square D4h structure is associated with the first excited state with a triplet multiplicity.19,20 Wirz et al. have experimentally generated and observed the triplet state of a CBD derivative using flashspectroscopic sensitization.21 The geometrical distortion from the square D4h structure to the rectangular D2h structure is known as a second-order Jahn−Teller distortion.19,22 The © 2012 American Chemical Society

2. ORBITAL SYMMETRY RULE FOR CBD SYSTEMS Both theoretical and experimental studies on the electron transport in various molecular junctions have shown that molecular orbitals (MOs) are of great importance to a better understanding of the electron transport through a single molecule.27−39 In previous studies we developed an orbital symmetry rule for electron transport properties of π-conjugated systems.30−35 The rule based on the phase of the frontier orbitals agrees with experimental results.36 It is derived from Received: June 4, 2012 Published: July 2, 2012 16325

dx.doi.org/10.1021/jp305448q | J. Phys. Chem. C 2012, 116, 16325−16332

The Journal of Physical Chemistry C

Article

Figure 1. Schematic representations of electrode−molecule−electrode junction (top) and MO energy diagrams (bottom) for the CBD systems with the square D4h structure and the rectangular D2h structure calculated with HMO theory. Two alternative but equivalent representations for the NBMOs, i.e., SOMO1 and SOMO2, and SOMO1′ and SOMO2′, are shown for CBD with the square D4h structure.

the nature of the zeroth Green’s function40 (see the Supporting Information), which describes the propagation of the tunneling electron through a molecule with weak electrode−molecule coupling. The electron transport probability is qualitatively predicted from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) since their contributions are significant in the zeroth Green’s function at the Fermi level (EF) as indicated in eq 1: C R,HOMOC*L,HOMO E F − εHOMO ± iη

+

to the orbital symmetry rule, we expect that the molecular junction of CBD with the rectangular D2h structure is symmetry forbidden, whereas that with the square D4h structure is symmetry allowed. Taking a linear combination of degenerate NBMOs in the D4h structure, we can obtain another pair of NBMOs, i.e., SOMO1′ and SOMO2′. The delocalized pair of NBMOs is better suited for the application of the orbital symmetry rule than the localized one. The application of the rule to the SOMO1′ and SOMO2′ is presented in the Supporting Information and results in the prediction of symmetry allowed. The expectation is consistent with a basic understanding of the electronic properties of a linear πconjugated polymer that a chain with bond alternation is expected to be a semiconductor or insulator, due to the existence of band gap, whereas a regular chain without bond alternation is expected to be a conductor, due to the zero band gap. We show in Figure 2 computed transmission spectra of the CBD systems with the square D4h structure and the rectangular

C R,LUMOC*L,LUMO E F − εLUMO ± iη

(1)

where CR(L),HOMO and CR(L),LUMO are the MO expansion coefficients at an atom connected to the right (left) electrode at the HOMO and LUMO, respectively, εHOMO(LUMO) is the energy of the HOMO (LUMO), and η is an infinitesimal number. To enhance the contributions of the HOMO and LUMO, two atoms in which the sign of CR,HOMOC*L,HOMO is different from the sign of CR,LUMOC*L,LUMO should be connected with electrodes. Note that this condition is based on the reversal of the signs between the denominators in eq 1. A molecular junction that satisfies the rule and indicates high transmission probability is denoted as symmetry allowed, whereas a molecular junction that does not satisfy the rule and indicates low transmission probability is denoted as symmetry forbidden. For the case of systems with two-fold-degenerate nonbonding MOs (NBMOs),35 the HOMO and LUMO in eq 1 are replaced by singly occupied molecular orbital 1 (SOMO1) and SOMO2. Since the denominators in the replaced eq 1 have the same sign, the opposite rule is applicable as follows: two atoms in which the sign of CR,SOMO1C*L,SOMO1 is the same as the sign of CR,SOMO2C*L,SOMO2 should be connected with electrodes. On the basis of the qualitative thinking about the orbital phase, we can easily predict symmetry-allowed and symmetryforbidden connections for transmission probability in CBD systems with the square D4h structure and the rectangular D2h structure. The frontier orbitals of CBD systems calculated with the Hückel molecular orbital (HMO) theory are shown in Figure 1. We consider the molecular junctions, in which the C1 and C3 atoms of CBDs are weakly connected with gold electrodes. The parameters employed for describing the bond alternation in the CBD system with the rectangular D2h structure are βshort = 1.2β and βlong = 0.8β, where β is the resonance (transfer) integral of the C−C bonds in the square D4h structure and βshort and βlong are those of the short and long bonds in the rectangular D2h structure, respectively. According

Figure 2. Computed transmission spectra of the CBD systems with the square D4h structure and the rectangular D2h structure calculated with HMO theory. The Fermi level is located at the origin of the energy (E = 0).

D2h structure calculated with the nonequilibrium Green’s function method at the HMO level of theory (NEGF-HMO), where the parameters employed for gold atoms are βAu−Au = 0.6βC−C and βC−Au = 0.2βC−C.31 The NEGF method is a powerful technique to compute electron transport properties of single molecules. Details of the method are described in the 16326



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diphenyl-2,4-bis(trimethylsilyl)cyclobutadiene (HS− Ph2(Me3Si)2C4−SH; denoted as PMSC−SH in the following) as a model system. This CBD derivative has yet to be synthesized, but the dilithium salt of PMSC has been actually synthesized.41,42 Geometry optimizations were performed on PMSC−SH for the singlet and triplet spin states by using the Gaussian 09 program 43 with the hybrid density functional B3LYP method43−46 combined with the 6-31G(d) basis set.47 The electron transport calculations were performed for the optimized structures of PMSC−SH in the singlet and triplet states by using the fully self-consistent NEGF-DFT method implemented in the ATK 11.8.1 program.48,49 The generalized gradient approximation (GGA) in the Perdew−Burke− Ernzerhof (PBE) form50 was employed for the exchangecorrelation functional. Numerical basis sets of single-ζ (SZ) on the gold atoms and the double-ζ + polarization (DZP) on all other atoms were used. We performed spin-restricted calculations for the singlet-optimized structure and spinunrestricted calculations for the triplet-optimized structure. The initial spin density for the spin-unrestricted calculations was polarized to both high-spin (triplet) state and low-spin (open-shell singlet) state. The semi-infinite left and right electrodes were modeled by two Au(111)-(4 × 4) surfaces (i.e., each layer includes 16 Au atoms). Three layers from each electrode (in total 96 Au atoms) were included in the central region. The adsorption site of the sulfur atoms in PMSC−S, in which the thiol hydrogen atoms are removed, is set to be the face-centered cubic (fcc) threefold hollow site, whose

Supporting Information. The transmission probability at the Fermi level is important to evaluate the conductance through a single molecule. Figure 2 shows that the D4h structure has high transmission probability at the Fermi level (E = 0), whereas the D2h structure has low transmission probability. These computational results are fully consistent with the qualitative predictions based on the orbital symmetry rule. Small geometrical distortions due to the Jahn−Teller effect can cause significant changes in molecular conductance.

3. COMPUTATIONAL METHODS To verify the efficacy of the qualitative calculations with the HMO theory, we performed more quantitative calculations with the NEGF method combined with spin-polarized density functional theory (NEGF-DFT) using more realistic molecular junction models. Nonsubstituted CBD is so instable that it can easily undergo dimerization and other intermolecular reactions.19 One of the most appropriate synthetic strategies is the introduction of bulky substituent groups that spatially block the dimerization. Silyl and phenyl groups were proposed as protective substituents by Sekiguchi and co-workers.41,42 As shown in Scheme 1, we consider a dithiol derivative of 1,3Scheme 1

Figure 3. Optimized structures of PMSC−SH (top) and MO energy diagrams near the Fermi level (bottom) for (a) the singlet state and (b) the triplet state calculated at the B3LYP level of theory. Interatomic distances are presented in angstroms. 16327



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Figure 4. Molecular projected self-consistent Hamiltonian (MPSH) states of the molecular junction between PMSC−S and gold electrodes for (a) the singlet state, (b) the triplet state, and (c) the open-shell singlet state. Isovalue surfaces of the spin density are shown for the triplet and the openshell singlet states. The yellow and purple surfaces represent α and β spin densities, respectively.

conjugation of π-electrons between the benzene and CBD rings, which leads to the formation of a weak-coupling junction. A calculated triplet−singlet energy gap, ΔE = ET − ES, is 5.8 kcal/mol, which is quite close to the value for nonsubstituted CBD.20 The frontier orbitals of PMSC−SH mainly stem from those of the nonsubstituted CBD molecule. In the triplet state, the localized orbital representation is adopted (see the Supporting Information). The shapes of the α and β orbitals are almost identical, but the α orbitals are more stabilized relative to the β orbitals because of exchange interactions working only between electrons of the same spin. In the pair of α HOMO − 1 and β LUMO, the silicon atoms of the trimethylsilyl groups have little effect on the energy level of the NBMO of the CBD molecule, due to the orbital energy difference between the 2p orbitals of carbon and the 3p orbitals of silicon. In the pair of α HOMO and β LUMO + 1, the

adsorption structure was determined by reference to the literature.51 The electron transport calculations include the full self-consistent field treatment of molecular devices, in which the effect of the external electric field on the electronic properties of the molecules is taken into account.

4. RESULTS AND DISCUSSION Figure 3 shows optimized structures and MO energy diagrams of the singlet and triplet states of PMSC−SH calculated at the DFT-B3LYP level of theory. The CBD part in the singlet state exhibits a rectangular structure with bond alternation, whereas that in the triplet state is nearly square planar. The bond lengths are in reasonable agreement with those reported for other CBD molecules.20,52 The dihedral angles between benzene and CBD rings are 43° for the singlet state and 37° for the triplet state. The dihedral angles can weaken the 16328



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The triplet−singlet energy gap between the square D4h structure and the rectangular D2h structure is reduced to 3.7 kcal/mol in the junction environment. The energy level alignments and orbital distributions of the MPSH states of the closed-shell singlet and triplet states are almost all consistent with those of the isolated molecules shown in Figure 3. In Figure 4c, the open-shell character of the singlet state with the square CBD part comes from two half-occupied NBMOs. The pair of α HOMO and β LUMO and the pair of α LUMO and β HOMO are almost identical, respectively, and they correspond to a broken-symmetry wave function of antiferromagnetically coupled spins. The triplet state corresponds to the ferromagnetic arrangements of the same spin pair, i.e., these orbitals become occupied in the α space and unoccupied in the β space (see α HOMO, α HOMO − 1 vs β LUMO, β LUMO + 1 shown in Figure 4b). The small triplet−singlet energy gap corresponds to the flipping between the antiferromagnetic and the ferromagnetic orientation of this pair of electrons. For spin-polarized systems the conductance in the zerotemperature limit is written as follows:6,14

NBMO of the CBD molecule undergoes a weak antibonding interaction with the phenyl groups and is a little destabilized compared to that in α HOMO − 1 and β LUMO. We show in Figure 4 molecular projected self-consistent Hamiltonian (MPSH) states,53 which are the eigenstates of the molecule placed between two electrodes, and spin densities of the high- and low-spin states with the triplet-optimized structure. The Fermi level is located at the origin of the energy (E = 0), which was determined from DFT calculations of the bulk gold electrodes. Relative energies calculated in the junction environment are listed in Table 1. The open-shell Table 1. Relative Energies in the Two-Probe Systems, Transmission Probabilities at the Fermi Level, and SpinFiltering Efficiency (SFE) transmission probability at the Fermi levelb state closed-shell singlet open-shell singlet triplet

relative energy (kcal/mol)a

α

β

total

SFE (%)c

0.0

0.0014

0.0014

0.0028

0

2.1

0.0518

0.4581

0.5099

80

3.7

0.6929

0.1212

0.8141

70

g=

a

Relative to the total energy of the closed-shell singlet state in the twoprobe system. bCalculated from NEGF-DFT at zero bias. cCalculated from eq 3.

e2 h

∑ Tσ(EF) σ

(2)

where e is the electron charge, h is Planck’s constant, and Tσ (σ = α, β) is the spin-dependent transmission probability. Parts a and b of Figure 5 show zero-bias total transmission spectra (Tα + Tβ) and spin-dependent transmission spectra calculated with the NEGF-DFT method, respectively. The intensity of the total transmission spectra is normalized to 2 in accordance with eq 2.

singlet state is more stable than the triplet state, but the energy difference is small (1.6 kcal/mol). The lowering of the energy of the open-shell singlet state below the triplet state can be attributed to higher order effects such as electron correlation.54

Figure 5. (a) Zero-bias total transmission spectra (Tα + Tβ) of the molecular junction between PMSC−S and gold electrodes and (b) spindependent transmission spectra for the triplet and open-shell singlet states calculated with the NEGF-DFT method. 16329



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Figure 6. (a) Computed total current−voltage (I−V) curves, (b) spin-dependent I−V curves for the triplet and open-shell singlet states, and (c) SFE vs bias voltage curves calculated with the NEGF-DFT method. Similar to eq 3, the SFE at the finite bias voltage is defined as follows: SFE(V) = | Iα(V) − Iβ(V)|/|Iα(V) + Iβ(V)|.

transmission probability of the open-shell singlet state is slightly lower than that of the triplet state. The origin of the transmission peaks is rationalized by looking at the frontier MOs of the MPSH shown in Figure 4. MOs delocalized parallel to the transmission direction such as the pair of α HOMO and β LUMO of the triplet state and the pair of α LUMO and β HOMO of the open-shell singlet state can provide transmission channels. On the other hand, MOs delocalized perpendicular to the transmission direction such as α HOMO − 1 of the triplet state and the pair of α HOMO and β LUMO of the open-shell singlet state cannot provide transmission channels. In the triplet state α HOMO is the transmission channel closest to the Fermi level, whereas in the open-shell singlet state β HOMO is the transmission channel closest to the Fermi level. Thus, the zero-bias conductance of the triplet state is dominated almost by the α spin channel, whereas that of the open-shell singlet state is dominated almost by the β spin channel. The spin-flip transition between the triplet and the open-shell singlet states leads to the switching between the spin-α and spin-β transmissions. A theoretical study performed by Shigeta et al. reported that an external magnetic field applied perpendicular to the molecular plane of a four-membered ring molecule with D4h symmetry induces spin level crossing and spin-flop transition from the open-shell singlet state to the triplet state.55 We can control the spinpolarized electron transport properties of the CBD molecule with the square D4h structure by changing the spin state by applying an external magnetic field. The spin-dependent current Iσ (σ = α, β) is obtained after integration of a finite part of the transmission spectra called bias window as follows:10,11

The Fermi level is located at the origin of the energy (E = 0). Both the triplet and open-shell singlet states with the square CBD part have higher transmission probability at the Fermi level than the closed-shell singlet state with the rectangular CBD part. The transmission probabilities at the Fermi level are listed in Table 1. The single-molecule conductance of the triplet state is 2 orders of magnitude larger than that of the closed-shell singlet state. This result is in good agreement with the qualitative expectations based on the frontier orbital analysis on the nonsubstituted CBD molecule and the computed transmission spectra calculated with the HMO theory. The conductance change between the square D4h structure and the rectangular D2h structure allows the CBD systems to function as a molecular switch using the Jahn−Teller distortion. The electron transport through the open-shell singlet and triplet states shows the spin asymmetry. To estimate the spin polarization of the transmission probability, the spin-filtering efficiency (SFE) is defined as follows:8−10 SFE =

Tα(E F) − Tβ(E F) Tα(E F) + Tβ(E F)

(3)

where Tα(EF) and Tβ(EF) are the transmission probabilities of the spin-α and spin-β states at the Fermi level, respectively. Systems with higher SFE values can perform as a spin filter, through which only electrons of a certain spin orientation are preferentially allowed to pass. The transmission probabilities of the spin-α and spin-β states at the Fermi level and the SFE values are listed in Table 1. The SFE values for the open-shell singlet and triplet states are calculated to be 80% and 70%, respectively. The CBD systems are applicable to not only a molecular switch but also a spin-filtering device. The spinfiltering functionality results from the transmission peak splitting near the Fermi level between the spin-α and spin-β states and the proximity of the Fermi level to the transmission peak of a certain spin state rather than the opposite spin state, as shown in Figure 5b. The peak splitting between the spin-α and spin-β states of the open-shell singlet state is slightly larger than that of the triplet state, which accounts for a slightly large SFE value of the open-shell singlet state. However, a large transmission peak splitting between the spin-α and spin-β states can cause a small overlap between α and β transmission at the Fermi level, leading to low conductance. Thus, the total

Iσ(V ) =

e h

eV /2

∫−eV /2 dETσ(E , V )

(4)

The bias window includes only energies close to the Fermi level in the interval from −eV/2 to eV/2, which corresponds to the electrochemical potentials of the left and right electrodes. The total current (Iα + Iβ)−voltage (I−V) curves and spindependent I−V curves calculated with the fully self-consistent NEGF-DFT method are shown in Figure 6, parts a and b, respectively. At higher bias (>0.2 V) the calculation of the triplet state has converged to the open-shell singlet state. This is because at the higher bias the tails of the α HOMO and β LUMO levels of the triplet state come into the bias window and 16330



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electron pulling from the α HOMO level and electron pumping into the β LUMO level occur, which leads to the more stable open-shell singlet state. The larger HOMO−LUMO gap in the open-shell singlet state than the triplet state prevents the external electric field from disturbing the electron configuration of the open-shell singlet state. The computed total I−V curves clearly show that both the triplet and open-shell singlet states with the square CBD part have higher current than the closedshell singlet state with the rectangular CBD part. The triplet state shows the largest current, due to the smallest peak splitting between the HOMO and LUMO, as shown in Figure 5. The current of the triplet state is 2 orders of magnitude larger than that of the closed-shell singlet state at 0.2 V. These NEGFDFT results are in good agreement with our qualitative predictions made from the orbital-based arguments and qualitative calculations with HMO theory. The current change between the square D4h structure and the rectangular D2h structure allows us to control the current flow using the Jahn−Teller distortion. The spin-filtering functionality observed in the zero-bias spin-dependent transmission spectra holds true for the spin-dependent I−V characteristics. The total current of the triplet state is dominated by the spin-α current, whereas that of the open-shell singlet state is dominated by the spin-β current. We present the SFE curves as a function of bias voltage in the triplet and open-shell singlet states in Figure 6c. With an increase of bias voltage, the SFE values decrease since the transmission peak splitting between the spin-α and spin-β states is observed only in the vicinity of the Fermi level. Thus, a low-bias condition is appropriate for the effective spin-filtering performance.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS K.Y. thanks Grants-in-Aid for Scientific Research (Nos. 18GS0207 and 22245028) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), the Kyushu University Global COE Project, the Nanotechnology Support Project, the MEXT Project of Integrated Research on Chemical Synthesis, and CREST of the Japan Science and Technology Cooperation. Y.T. thanks JSPS for a graduate fellowship. A.S. thanks World Premier International Research Center Initiative (WPI).

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5. SUMMARY AND CONCLUSIONS We can easily predict symmetry-allowed and symmetryforbidden connections for electron transmission probability in CBD systems with the square D4h structure and the rectangular D2h structure on the basis of the qualitative thinking about the orbital phase. The orbital analysis expects that small geometrical distortions between the square and rectangular structures of CBD can cause large changes in molecular conductance. Computed transmission spectra and I−V curves of a substituent-stabilized CBD molecule at the DFT level of theory provide good agreement with the qualitative predictions based on the orbital analysis. Moreover, significant spin-filtering effects were found in the CBD systems with the D4h structure. The spin selectivity in electron transport varies between the triplet and open-shell singlet states. The CBD systems are applicable to not only a molecular switch but also a spinfiltering device. Although to access the triplet state of CBD is difficult, a technique of flash spectroscopic sensitization has opened the door to the triplet state of an isolable derivative of CBD.21 The qualitative orbital analysis provides a guiding principle for designing molecules for future molecular spintronics since the essential nature of the frontier orbitals’ properties is kept unchanged at the Hückel and spin-polarized DFT levels.

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ASSOCIATED CONTENT

S Supporting Information *

The derivation of the orbital symmetry rule for the electron transport, the application of the rule to the two-fold-degenerate NBMOs, atomic Cartesian coordinates for the optimized geometries of PMSC−SH, and complete ref 43. This material is available free of charge via the Internet at http://pubs.acs.org. 16331



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