Orbital Control of the Conductance Photoswitching in Diarylethene

Dec 7, 2009 - Diarylethenes are photosensitive π-conjugated molecules whose application to various molecular devices is expected. The molecular and e...
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J. Phys. Chem. C 2009, 113, 21477–21483

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Orbital Control of the Conductance Photoswitching in Diarylethene Yuta Tsuji, Aleksandar Staykov, and Kazunari Yoshizawa* Institute for Materials Chemistry and Engineering, Kyushu UniVersity, Fukuoka 819-0395, Japan ReceiVed: June 16, 2009; ReVised Manuscript ReceiVed: October 21, 2009

Diarylethenes are photosensitive π-conjugated molecules whose application to various molecular devices is expected. The molecular and electronic structures of diarylethenes are switchable upon photoirradiation with their reversible structural isomerization. Site-specific electron transport phenomena through a diarylethene molecule, 1,2-di(2-methyl-1-naphthyl) perfluorocyclopentene, are studied by using the nonequilibrium Green’s function method combined with the Hu¨ckel molecular orbital method (NEGF-HMO) and density functional theory (NEGF-DFT). On the basis of the orbital symmetry rule, the conductance of the diarylethene is predicted to be efficiently switchable when the C3 and C10 atoms are appropriately connected with electrodes. Transmission spectra, spatial distribution of the MPSH (molecular projected self-consistent Hamiltonian) states, and I-V curves are obtained from DFT calculations. These results obtained from the higher-level DFT calculations are consistent with the prediction based on the qualitative frontier orbital analysis at the HMO level of theory. The computed current for the closed-ring form of the 3-10 connection is about 3 orders of magnitude high compared with those for other connections. The phase, amplitude, and spatial distribution of the frontier orbitals play an essential role in designing the electron transport properties through the photoswitching system. 1. Introduction Diarylethenes are photosensitive π-conjugated molecules whose application to various molecular devices is expected.1 The photosensitive molecules exist in two thermally stable forms, an open-ring form and a closed-ring form, which are separated by a high-energy barrier. Although this barrier cannot be overcome by vibrational excitation, photoexcitation1-3 and redox process4-6 can lead to a reversible switching reaction. The thermal stability of the two forms and the high quantum yield of the photochemical reaction make diarylethene very suitable for a control unit in nanometric-scale devices. The photosensitive properties of diarylethene satisfy the fundamental conditions for optical memories and switches.1,7,8 The switching properties were investigated in solutions,1-5 in crystalline structures,9,10 on metal surfaces,11-14 and as a part of complex organic molecules.7,15 A large variety of diarylethene molecules allow experimentalists to modify their properties by means of molecular design.1,16-18 Among important subclasses are diarylcyclopentenes and diarylperfluorocyclopentenes, in which the unfavorable cis-trans isomerization is avoided, and as a result, the switching quantum yield is significantly improved.1 A series of diarylethene molecules have been successfully applied to a wide variety of photoswitching systems,7 such as fluorescence,19 electrical conductivity,20 and magnetism21 switches. The change of electrical conductance through diarylethene is one of the most important properties because, in this way, this molecule can be directly applied to nanometric-scale devices.1,7,8 The conductance switch was experimentally investigated by using the mechanically controllable brake junction (MCBJ) and scanning tunneling microscopy (STM) techniques.12,13,22 Sulfur-terminated molecules were used for the experiments because the sulfur atom has good affinity with a gold surface; therefore, it is usually employed as electrodes. The current measured with the MCBJ * To whom correspondence should be addressed. E-mail: kazunari@ ms.ifoc.kyushu-u.ac.jp.

and STM techniques is different in principle. The MCBJ technique measures the current through a molecule trapped in a nanoscale gap between electrodes,12,22 whereas the STM technique measures the current through a molecule in which one end is linked to the surface of one electrode and the other is scanned by an STM tip.13 There are still many open questions in conductance measurements, which require detailed understanding of the nature of molecular electron transport. Theoretical studies on the electron transport in various molecular junctions have been conducted in terms of molecular length, molecular conformation, and applied bias voltage.23-31 Theoretical studies have also shown that molecular orbitals (MO) are of great importance to better understand the electron transport through a single molecule.32-47 Although the electron transport through a single molecule can be described mainly as a physical phenomenon, one of the most important factors that control it has a discrete chemical origin, the phase, amplitude, and spatial distribution of the frontier orbitals of the molecule.32-47 These orbital natures are essential factors that determine the electron transport through a single molecule.32-35 The orbital symmetry rule gives us a powerful tool to predict the conductance through a molecular system weakly interacting with electrodes, and we have shown how to apply it on a system that is strongly perturbed by the junction environment.32 We have studied the importance of frontier orbitals for the electron transport through different molecular species, such as graphene sheets,33-35 DNA,36 conducting polymers,37,38 porphyrin,39 and diarylethenes.40,41 The simple orbital symmetry rule about the significant relationship between molecular conductance and frontier orbitals is very useful for the choice of most favorable atoms that should be connected with electrodes for effective electron transport. In this manuscript, we discuss the electron transport through a diarylethene molecule using the nonequilibrium Green’s function method combined with the Hu¨ckel molecular orbital method (NEGF-HMO) and density functional theory

10.1021/jp905663r  2009 American Chemical Society Published on Web 12/07/2009

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(NEGF-DFT).48 We apply the orbital symmetry rule32 to look at the site-dependent conductance and demonstrate an effective type of connection on the photoswitching system. 2. Orbital Symmetry Rule for Molecular Conductance According to Landauer’s model, which describes the electron transport through a one-dimensional system, the conductance of a molecular junction composed of a molecule and two electrodes, in the limit of zero temperature and zero bias voltage, is written as follows49

g)

2e2 T(EF) h

(1)

where 2e2/h is the quantum conductance, T is the transmission probability, and EF is the Fermi energy. Thus, the conductance is related to the transmission probability at the Fermi energy of electrodes. The transmission probability is derived from the model of Caroli et al.50 and Conbescot.51 This model allocates only one atomic orbital to an electrode and to the molecule in the interaction region. According to this model, the transmission probability is written as follows

T(E) )

2 (2πβC-Au )2 A G (E)GR(E)FR(E)FR′(E) 2

(2)

where βC-Au is the resonance (transfer) integral between the interacting carbon and gold atoms, GA and GR are advanced and retarded Green’s functions, respectively, and F is the local density of states (LDOS), which is obtained from the MOs of a terminating gold atom denoted with R.32-35 The resonance integral βC-Au is considered to be a parameter on qualitative calculations. However, its estimation requires careful attention because the NEGF-HMO method is based on a weak-coupling model, which lacks chemical bonding between the molecule and electrodes.32 We adopted the same value as in the previous study32 for βC-Au, that is, βC-Au ) 0.2 βC-C. In eq 2, only advanced and retarded Green’s functions depend on the pattern of connection. Green’s function is regarded as a nearly linear function of the 0th Green’s function G(0)R/A.50,51 Therefore, if the 0th Green’s function takes a large value, the transmission probability is also large. Thus, in the calculations of molecular conductance, the 0th Green’s function plays an essential role in weak coupling systems. The 0th Green’s function is calculated in terms of a molecule itself that does not interact with electrodes.50,51 The 0th Green’s function is written as follows52

G(0)R/A(E) )

∑ k

CrkC/sk E - εk ( iη

(3)

where Crk is the kth MO coefficient at the rth atomic orbital in an orthogonal basis, εk is the kth MO energy, and η is an infinitesimal number determined by a relationship between the LDOS and the imaginary part of Green’s function.34,35 Equation 3 shows the correlation between the MOs and Green’s function and makes it possible to predict the conductance from the MOs. The orbital symmetry rule,32 which is useful to consider effective electron transport in a molecular wire, provides us a necessity condition for large transmission probability. Let us consider the case of E ) EF because eq 1 shows the importance of the transmission probability at the Fermi energy of electrodes. In eq 3, the contributions from the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are written as follows:

/ / CrHOMOCsHOMO CrLUMOCsLUMO + EF - εHOMO ( iη EF - εLUMO ( iη

(4)

When the Fermi energy is reasonably assumed to be located at the midgap of the HOMO and LUMO,32,33 the contributions of these frontier orbitals are significant in the 0th Green’s function, for which the denominators of eq 4 are the smallest of all the terms of eq 3. To obtain large transmission probability, the value of eq 4 must be large. In eq 4, the signs of the denominators are different; the sign of EF - εHOMO is positive, and the sign of EF - εLUMO is negative. Therefore, in order for the contributions from the HOMO and LUMO to be enhanced, the / sign of the CrHOMOCsHOMO term must be different from the sign / of the CrLUMOCsLUMO term. On the other hand, when the sign / of the CrHOMOCsHOMO term is the same as the sign of the / CrLUMOCsLUMO term, the contributions from the HOMO and LUMO are reduced. In order for this enhancement and reduction to be complete precisely, the electron-hole symmetry (the pairing theorem)53 should hold true in an investigated system. The electron-hole symmetry is exactly applicable to alternant hydrocarbons within the framework of the Hu¨ckel method. When we assume that the Fermi energy lies just at the midgap of the HOMO and LUMO, the corresponding bonding and antibonding MOs of alternant hydrocarbons can make a pair up and down of the Fermi energy. Another condition for large transmission probability is that the amplitudes of the HOMO and LUMO have to be large at connecting sites to electrodes.32,33 The larger the magnitudes of the coefficients of the HOMO and LUMO, / / CrHOMOCsHOMO and CrLUMOCsLUMO , the more the contributions from the HOMO and LUMO are enhanced. The orbital symmetry rule for electron transport properties can be summarized as follows: for effective electron transport in a molecular wire, (a) two atoms, r and s, where the sign of / / CrHOMOCsHOMO is different from the sign of CrLUMOCsLUMO , should be connected and (b) two atoms, where the amplitudes of the HOMO and LUMO are large, should be connected. This rule clearly shows the approximate relationship between frontier orbitals and molecular conductance. Because the phase and amplitude of frontier orbitals thus play an essential role in molecular conductance, one can qualitatively predict the conductance of a molecule using the orbital symmetry rule. To design molecular conductance photoswitching, we applied this rule to a diarylethene molecule, 1,2-di(2-methyl-1-naphthyl) perfluorocyclopentene, shown in Figure 1. The thermal stability of this molecule and its photochemical properties were experimentally investigated.1,54 The closed-ring form remains stable for more than 500 h at 70 °C, the relative stability of its closedring form being attributed to the involved styryl structures. In this study, we have investigated the site-dependent electron transport through the diarylethene molecule. Here, let us consider two sets of atoms connected to electrodes. One set is the 3-10 connection, and the other set is the 3-11 connection.

Figure 1. Photoisomerization of 1,2-di(2-methyl-1-naphthyl)perfluorocyclopentene.

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3. Computational Methods On the basis of the formalism given in eqs 1-4 as described in the literature,32,33 we obtained the transmission spectra at the NEGF-HMO level of theory. These calculations give us qualitative, but essential, insights into the electron transport through the diarylethene molecule. We can predict and explain the photoswitching properties of the molecule and easily determine which connection is desirable for effective electron transport on the basis of the frontier orbitals calculated with the Hu¨ckel method. The qualitative and descriptive characters of Hu¨ckel calculations combined with the computational simplicity make the NEGF-HMO method a useful tool in the study of the electron transport through aromatic hydrocarbons. The HMO theory is characterized with π-electron approximation and neglect of the overlap integrals, which is applicable only to planar aromatic hydrocarbons. To incorporate the steric features of the open-ring form into the Hu¨ckel method, we modified the resonance integrals of the bonds that have large dihedral angles. The angular dependence of the resonance integral, β(θ), can be written as follows:55

β(θ) ) βC-C cos θ

(5)

The dihedral angles of the investigated diarylethene with respect to the two naphthalene parts fall in 70-90° in general, and therefore, we assumed here the dihedral angles to be 80°. The relationship between GR/A and G(0)R/A is written as follows:50,51

GR/A )

G(0)R/A DR/A

(6)

If the coupling between the molecule and electrodes is weak, the denominator DR/A could be approximated by 1. Therefore, we can view GR/A to be a linear function of G(0)R/A in weak coupling systems and obtain important information from G(0)R/A about effective electron transport. The models used for the NEGF-HMO method are slightly different from those used for the NEGF-DFT method. The former model is characterized with weak coupling between the molecule and electrodes, whereas the latter model is characterized with relatively strong coupling between the molecule and electrodes through the Au-S chemical bonds. To compare the qualitative results obtained from the NEGF-HMO method with more quantitative results obtained from calculations closer to more realistic systems, we performed a NEGF-DFT study. Prior to the electron transport calculations, geometry optimizations were performed with the Gaussian 03 program56 at the B3LYP level of theory56-59 with the 6-31G* basis set.60 Because dithiolate derivatives are commonly used in experimental studies because of the strong affinity of sulfur to gold atoms, geometry optimizations were done for the open- and closed-ring forms of diarylethene dithiolate derivatives at sites C3 and C10 and at C3 and C11. Electron transport calculations were performed for the zero bias optimized geometries because studies in the literature61,62 have shown that the applied electric field between electrodes does not significantly alter the molecular geometry. The electron transport calculations were done by using the ATK 2008.07 program.63 The method includes the full self-consistentfield (SCF) treatment of molecular device. The effect of the external electric field on the electronic properties of molecules is taken into account.63 The electron transport calculations with the NEGF-DFT method provide us more quantitative information about the transmission spectra, I-V curves, and spatial distribution of the orbitals of the diarylethene molecule interacting with electrodes

Figure 2. Model for electron transport calculations with the NEGF-DFT method. Several layers from the Au(111) electrodes are included in the central region.

compared with those obtained with the NEGF-HMO method. As schematically represented in Figure 2, the model used in our electron transport calculations consists of the left bulk electrode, central region, and right bulk electrode. The central region includes an optimized dithiolate derivative of the diarylethene and several layers of Au(111) electrodes. The gold atoms included in the central region are perturbed by the diarylethene molecule and are considered as a part of the extended molecule,48 whereas the gold atoms included in the bulk electrodes are calculated under the periodic boundary conditions as separated semi-infinite bulk systems. The semiinfinite left and right electrodes were modeled by two Au(111)(3 × 3) surfaces (i.e., each layer includes 9 gold atoms) in connection 3-10 and by two Au(111)-(4 × 4) surfaces (i.e., each layer includes 16 gold atoms) in connection 3-11 because the molecule is inclined with respect to the axis of the electrode, and therefore, a larger area of contact surface is required. The two probe models we used for the central region includes 99 gold atoms in the case of connection 3-10 and 176 gold atoms in the case of connection 3-11; five layers and six layers were used for the left and right electrodes, respectively. There are three possible orientations of the sulfur atoms on the Au(111) surface in the adsorption sites of the dithiolate derivatives. The on-top site has an interaction with a single gold atom, the bridge site has interactions with two gold atoms, and the hollow site has interactions with three gold atoms. However, because the conductance ratio is not significantly affected by the interaction between the sulfur atoms and the electrodes,64 the adsorption sites were not considered in detail. To save computational efforts, the single-ζ basis set (SZ) was used for the gold atoms and the double-ζ basis set with polarization (DZP) was used for all other atoms.65 The exchange-correlation potential described by the Perdew-Zunger local density approximation (LDA-PZ) was employed.66 4. Results and Discussion The HOMO and LUMO of the diarylethene molecule for the open- and closed-ring forms calculated at the HMO level of theory are shown in Figure 3. For connection 3-10 of the closedring form, the product of the MO coefficients on atoms 3 and 10 in the HOMO is different in sign from that in the LUMO and the orbital amplitudes of the HOMO and LUMO on those atoms are sufficiently large. Therefore, enhancement occurs between the HOMO and LUMO in the sense of eq 4. We expect that the 3-10 connection for the closed-ring form should have high conductance. As mentioned earlier, we introduced angular dependence in the open-ring form between the cyclopentene part, which is not taken into account in the Hu¨ckel calculations, and the naphthalene parts by modifying two resonance integrals based on eq 5. We assumed a value of 80° for the dihedral angles, which results in 0.17βC-C for the resonance integral. The closed-ring form that is characterized with a planar structure was calculated by the conventional HMO method. The four orbitals in the

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Figure 3. HOMO and LUMO of the open- and closed-ring forms of a diarylethene. The MO energies are given in parentheses.

Figure 4. Computed transmission spectra of (a) the 3-10 connection and (b) the 3-11 connection of a diarylethene at the HMO level of theory.

frontier region of the open-ring form are important for electron transport properties. The energy difference between the HOMO and HOMO-1 is only 0.016βC-C; because of the electron-hole symmetry, the same result is obtained for the LUMO and LUMO+1. The contributions to the conductance from the HOMO and HOMO-1 are nearly same due to the very small energy difference. The same is true for the LUMO and LUMO+1. For connection 3-10 of the open-ring form, the product of the MO coefficients on atoms 3 and 10 in the HOMO has the same sign as that in the LUMO+1. The product of the MO coefficients on atoms 3 and 10 in the HOMO-1 has the same sign as that in the LUMO. Therefore, cancellation can occur between the HOMO and LUMO+1, and the same is true for the HOMO-1 and LUMO. Thus, we can predict the 3-10 connection of the open-ring form to have low conductance. For connection 3-11 of the open-ring form, the product of the MO coefficients on atoms 3 and 11 in the HOMO has the same sign as that in the LUMO. The product of the MO coefficients on atoms 3 and 11 in the HOMO-1 has the same sign as that in the LUMO+1. Therefore, cancellation occurs between the HOMO and LUMO, and the same is true for the HOMO-1 and LUMO+1. We predict that the 3-11 connection for the open-ring form has low conductance. For connection 3-11 in the closed-ring form, the product of the MO coefficients on atoms 3 and 11 in the HOMO has the same sign as that in the LUMO. Therefore, cancellation occurs between the HOMO and LUMO. Thus, we predict the 3-11 connection for the closedring form also to have low conductance. We summarize the qualitative predictions as follows: only the 3-10 connection of the closed-ring form should have high conductance, whereas the other investigated connections should have low conductance. Therefore, we consider using the orbital symmetry rule32 that

the conductance of the diarylethene is efficiently switchable by photoirradiation when the C3 and C10 atoms are appropriately connected with electrodes. Computed transmission spectra for the 3-10 connection and 3-11 connection of the open- and closed-ring forms at the HMO level of theory are shown as a function of electron energy in Figure 4a,b, respectively. The sharp transmission peaks are assigned to the resonance tunneling effect at the location of MO levels. According to eq 1, the transmission probability at the Fermi energy (E ) 0) is very important for the molecular conductance. Figure 4a,b shows that, at the Fermi energy, only the 3-10 connection for the closed-ring form has high transmission probability, whereas the other connections investigated have low transmission probability. These computational results are fully consistent with the qualitative analysis based on the frontier orbitals shown in Figure 3. Thus, the orbital symmetry rule within the framework of the HMO method is very useful for the prediction of effective quantum transport phenomena in the photosensitive diarylethene. We performed more realistic calculations, which are also closer to experimental models, using the NEGF-DFT method implemented in the ATK program. Computed transmission spectra and MPSH (molecular projected self-consistent Hamiltonian)63,67,68 states for the open- and closed-ring forms of the diarylethene dithiolate derivatives for connections 3-10 and 3-11 in zero bias are shown in Figure 5. The MPSH states approximate the orbitals of the two-probe system63 and include the influence of the electrodes on the molecular junction. MPSH analysis helps us to qualitatively understand the origin of the transmission peaks. The Green’s function matrix of the system, G, is obtained after the inversion of the following matrix

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Figure 5. Computed transmission spectra and spatial distribution of the MPSH states for the open- and closed-ring forms of a diarylethene dithiolate for the applied bias of 0.0 V (a) for the 3-10 connection and (b) for the 3-11 connection. The MPSH states energies are given in parentheses.

(

HL + ΣL VL HC VL† 0

0 VR

VR† HR + ΣR

)

(7)

where HL, HC, and HR are the Hamiltonian matrices in the left region (containing several gold atoms from the left bulk electrode), the central region (containing several gold atoms from both the left and the right electrode), and the right region (containing several gold atoms from the right bulk electrode), respectively, as shown in Figure 2. VL (VR) is the interaction matrix between the left (right) region and the central region, and ΣL (ΣR) is the self-energy of the left (right) bulk semi-infinite system, which takes into account the coupling of the left (right) region to the remaining part of the semi-infinite bulk electrode. In the MPSH analysis, the eigenvectors of the self-consistent Hamiltonian of the central region HC are projected onto the molecule, as shown in Figure 5, where the electrodes and orbitals extended to the electrodes are excluded for simplicity. In the transmission spectra, the Fermi level is located at the origin of the energy (E ) 0),42,49,69-71 which was determined from DFT calculations of the bulk gold electrodes. The calculated transmission probability at the Fermi level for connection 3-10 of the closed-ring form is 0.16; on the other hand, those for connection 3-11 of the open- and closed-ring forms and connection 3-10 of the open-ring form are nearly zero. These

results are in nice agreement with the qualitative expectations based on the frontier orbital analysis discussed earlier in this manuscript. The peaks in the transmission spectra can be ascribed to the MOs, which provide the conduction channels. However, the transmission peaks and the MPSH energies do not always coincide.68 The transmission spectrum of the conductive connection 3-10 of the closed-ring form has broadened peaks, which can result from multiple conduction channels, that is, the HOMO and HOMO-1 and good π-electron delocalization, whereas the transmission spectra of the nonconductive connections have only sharp peaks, which result from the resonance tunneling effect. The π conjugation and the HOMO-LUMO gap are two important factors that determine the conductance of a molecular wire.68 The higher the delocalization is, the easier the electron transfer.61,72 Significant values of amplitude on the terminal sulfur atoms play an essential role in the molecular conductance because the overlap between the molecule and both, left and right, semi-infinite bulk electrodes is important.68 The orbitals of the 3-10 connection of the closed-ring form are welldelocalized and have finite values of amplitude on the sulfur atoms, whereas those of the other investigated systems are localized or have no values of amplitude on the terminal sulfur atoms. In particular, in the open-ring forms, the large dihedral angles reduce the π overlap and prevent orbitals from delocal-

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Figure 6. Computed I-V curves for the open- and closed-ring forms of connections 3-10 and 3-11 for a diarylethene dithiolate with the NEGF-DFT method.

ization, which is unfavorable for high molecular conductance. The HOMO-LUMO gap is related to the molecular conductance. In first approximation, the barrier for the electron transport is proportional to the HOMO-LUMO gap when other factors are kept the same.61,68,72 The smaller the HOMO-LUMO gap is, the higher the molecular conductance is, because the energies of the HOMO and LUMO, which mostly supply the conduction channels, are closer to the Fermi energy in the molecules whose HOMO-LUMO gap is small. As shown in Figure 5, the HOMO-LUMO gap of the closed-ring form of connection 3-10 is the smallest among the investigated systems. In particular, the HOMO-LUMO gaps of the open-ring forms are twice as large as the gap of the closed-ring form of connection 3-10. Computed I-V curves for the open- and closed-ring forms of the diarylethene dithiolate for connections 3-10 and 3-11 are shown in Figure 6. In the NEGF-DFT method, current I through a molecule can be written as follows48

I(V) ) G0

∫-∞+∞ n(E)T(E, V)dE

(8)

where G0 ) 2e2/h and n(E) is the distribution function, which is given by

n(E) ) f(E - µL) - f(E - µR)

(9)

where f is the Fermi function and µL and µR are the electrochemical potentials of the left and right electrodes, respectively. In eq 9, the cancellation between f(E - µL) and f(E - µR) can occur when the energy is far from the Fermi energy. Therefore, only electrons with energy close to the Fermi energy play a significant role in the current. Thus, the range of the bias window can be approximated by [-V/2, +V/2].48,49,67,68 As shown in Figure 6, only the closed-ring form of connection 3-10 has high conductance properties. The ratio of the current for the closedring form of connection 3-10 and the other investigated connections is 3 orders of magnitude. The computed I-V curves clearly show us good agreement between the qualitative predictions based on the phases and amplitudes of the HOMO and LUMO within the HMO method and the more realistic calculations with the DFT method. Finally we propose that conductance photoswitching would be observed between the open- and closed-ring forms of connection 3-10. 5. Summary and Conclusions We applied the orbital symmetry rule32 for the investigation of the site-dependent electron transport properties of a diarylethene molecule, 1,2-di(2-methyl-1-naphthyl)perfluorocyclo-

pentene. We propose that the conductance of the diarylethene molecule is efficiently switched upon photoirradiation when the C3 and C10 atoms are appropriately connected with electrodes. We compared the qualitative expectations based on the phase and amplitude of the frontier orbitals of the diarylethene with NEGF -DFT calculations for their dithiolate derivatives. The orbital analysis is consistent with the quantitative NEGF-DFT calculations in essential conductance properties, such as transmission spectra, spatial distribution of the MPSH states, and I-V curves. The computed current for the closed-ring form of connection 3-10 is about 3 orders of magnitude higher than those for other investigated connections. The closed-ring form of the diarylethene derivative would lose its conductive properties when it is inappropriately attached to electrodes, that is, connection 3-11. The choice of anchoring site is very important for the control of electron transport, and in case they are appropriate, the conductance switching will be observed. The spatial distribution of the frontier orbitals plays an important role in the molecular conductance. The higher the delocalization is, the higher the molecular conductance is. The closed-ring form for the 3-10 connection is characterized with best delocalization. Finally, we conclude that the qualitative nature of the frontier orbitals’ properties is kept unchanged at the Hu¨ckel theory and DFT, and for that reason, the orbital symmetry analysis is of great use for qualitative predictions for molecular electron transport. The predictions based on Hu¨ckel calculations provide the fundamental information that the site dependence of electron transport through aromatic molecules is a structural property, which depends on the molecular topology and electronic structure based on that topology. This qualitative understanding based on the orbital symmetry rule is useful for designing molecular conductance switches. Acknowledgment. K.Y. acknowledges Grants-in-Aid (Nos. 18066013 and 18GS0207) for Scientific Research from Japan Society for the Promotion of Science (JSPS) and the Ministry of Culture, Sports, Science and Technology of Japan (MEXT), the Nanotechnology Support Project of MEXT, and the Joint Project of Chemical Synthesis Core Research Institutions of MEXT for their support of this work. A.S. acknowledges JSPS. Supporting Information Available: Atomic Cartesian coordinates for the optimized geometries of all investigated structures and complete ref 56. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Irie, M. Chem. ReV. 2000, 100, 1685. (2) Fukaminato, T.; Uemoto, T.; Iwata, Y.; Yokojima, S.; Yoneyama, M.; Nakamura, S.; Irie, M. J. Am. Chem. Soc. 2007, 129, 5932. (3) Nakamura, S.; Kobayashi, T.; Takata, A.; Uchida, K.; Asano, Y.; Murakami, A.; Goldberg, A.; Guillaumont, D.; Yokojima, S.; Kobatake, S.; Irie, M. J. Phys. Org. Chem. 2007, 20, 821. (4) Browne, W. R.; de Jong, J. J. D.; Kudernac, T.; Walko, M.; Lucas, L. N.; Uchida, K.; van Esch, J. H.; Feringa, B. L. Chem.sEur. J. 2005, 11, 6414. (5) Browne, W. R.; de Jong, J. J. D.; Kudernac, T.; Walko, M.; Lucas, L. N.; Uchida, K.; van Esch, J. H.; Feringa, B. L. Chem.sEur. J. 2005, 11, 6430. (6) Matsuda, K.; Yokojima, S.; Moriyama, Y.; Nakamura, S.; Irie, M. Chem. Lett. 2006, 900. (7) Matsuda, K.; Irie, M. J. Photochem. Photobiol., C 2004, 5, 169. (8) Kobatake, S.; Takami, S.; Muto, H.; Ishikawa, T.; Irie, M. Nature 2007, 446, 778. (9) Irie, M.; Fukaminato, T.; Sasaki, T.; Tamai, N.; Kawai, T. Nature 2002, 420, 759. (10) Uchida, K.; Izumi, N.; Sukata, S.; Kojima, Y.; Nakamura, S.; Irie, M. Angew. Chem., Int. Ed. 2006, 45, 6470.

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