In Search of Flexible Molecular Wires with Near Conformer

Article pubs.acs.org/JPCC

In Search of Flexible Molecular Wires with Near ConformerIndependent Conjugation and Conductance: A Computational Study Rikard Emanuelsson,† Henrik Löfås,‡ Jun Zhu,†,§ Rajeev Ahuja,‡,⊥ Anton Grigoriev,*,‡ and Henrik Ottosson*,† †

Department of Chemistry − BMC, Uppsala University, Box 576, 751 23 Uppsala, Sweden Department of Physics and Astronomy, Uppsala University, Box 516, 751 20, Uppsala, Sweden § State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China ⊥ Materials Physics, Department of Materials and Engineering, Royal Institute of Technology (KTH), SE-10044, Stockholm, Sweden ‡

S Supporting Information *

ABSTRACT: Oligomers of 1,4-disila/germa/stannacyclohexa-2,5-dienes as well as allcarbon 1,4-cyclohexadienes connected via EE single bonds (E = C, Si, Ge, or Sn) were studied through quantum chemical calculations in an effort to identify conformationally flexible molecular wires that act as molecular “electrical cords” having conformerindependent conjugative and conductive properties. Our oligomers display neutral hyperconjugative interactions (σ/π-conjugation) between adjacent σ(EE) and π(CC) bond orbitals, and these interactions do not change with conformation. The energies and spatial distributions of the highest occupied molecular orbitals of methyl-, silyl-, and trimethylsilyl (TMS)-substituted 1,4-disilacyclohexa-2,5-diene dimers, and stable conformers of trimers and tetramers, remain rather constant upon Si−Si bond rotation. Yet, steric congestion may be a concern in some of the oligomer types. The calculated conductances for the Si-containing tetramers are similar to that of a σ-conjugated linear allanti oligosilane (a hexadecasilane) with equally many bonds in the conjugated paths. Moreover, the Me-substituted 1,4-disilacyclohexadiene tetramer has modest conductance fluctuations with Si−Si bond rotations when the electrode−electrode distance is locked (variation by factor ∼30), while the fluctuations under similar conditions are larger for the analogous TMS-substituted tetramer. When the electrode−electrode distance is changed several oligomers display small conductance variations within certain distance intervals, e.g., the mean conductance of TMS-substituted 1,4-disilacyclohexa2,5-diene tetramer is almost unchanged over 9 Å of electrode−electrode distances.

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INTRODUCTION

each other. Still, a simplified molecular version of a cord should be a suitable design target. Recently, we reported on a compound class, the 1,4disilacyclohexa-2,5-dienes (Figure 1), in which σ- and π-bonded segments interact leading to a strong neutral cyclic crosshyperconjugation when substituted with σ-electron donor groups at the two silicon atoms.5 This cross-hyperconjugative effect is orbital-analogous to the cross-π-conjugation in pxylylene and it results in large substituent variations in the lowest UV absorption energies, the first electron binding energies, and the first oxidation potentials. Cross-hyperconjugation arises from the combination of a properly aligned local π(ER2) orbital (E = C or Si) on the saturated segments with properly symmetry adapted combination of π-orbitals of two CC multiple bonds, and we first observed this effect in acyclic bis(phenylethynyl)silanes,6 and also explored charge transfer through these systems.7 Now, can 1,4-disilacyclohexa-

Despite that an enormous number of differently conjugated molecules and polymers have been synthesized and investigated there is so far no conformationally flexible conjugated molecule with a conjugation that is invariant with conformation.1−3 If molecules of such type would be designed and synthesized they could act as single-molecule “electrical cords” displaying (nearly) the same conductance whichever conformation they adopt. Using density functional theory (DFT) calculations we have earlier examined the ability of organometallic multidecker wires, composed of bis(benzene)chromium sandwich complexes as repeat units, to display essential molecular cord features.4 We now use quantum chemical calculations to design and probe organosilicon, -germanium, and -tin based molecular wires as well as the all-carbon analogues in this context. At this point it should be noted that there is, however, not a one-toone correspondence between macroscopic electrical cords and our molecular electrical cords since a macroscopic cord, besides a high structural flexibility and a high “conformer-independent” conductance, is composed of two parallel wires insulated from © 2014 American Chemical Society

Received: October 1, 2013 Revised: February 17, 2014 Published: February 20, 2014 5637

dx.doi.org/10.1021/jp409767r | J. Phys. Chem. C 2014, 118, 5637−5649

The Journal of Physical Chemistry C

Article

connecting 1,4-disilacyclohexa-2,5-diene units via the Si atoms (or other E atoms). This connectivity should lead to conformationally flexible oligomers with large primary hyperconjugative overlap between adjacent σ(EE) and π(CC) bond orbitals, but small secondary orbital overlap between nonadjacent bond orbitals on different monomer units (Figure 2). Whereas the secondary orbital interaction varies with

Figure 2. Illustration of the large conformer-independent primary orbital overlap between adjacent σ(EE) and π(CC) bond orbitals (E = C, Si, Ge, or Sn), and the small conformer-dependent secondary orbital overlap between two nonadjacent π(CC) bond orbitals in a 1,4-disila/germa/stannacyclohexa-2,5-diene or cyclohexa-1,4-diene dimer. The R−E−E−R dihedral angle ω, which is varied in the calculations, is also displayed.

Figure 1. The orbital analogy between cross-hyperconjugated 1,4disilacyclohexa-2,5-dienes and the cross-π-conjugated p-xylylene, where the π(CC) orbitals of the ring interact with the properly symmetry-adapted combinations of 2 × π(SiR2) and 2 × π(CC), respectively.

rotation about the EE bond, the primary interaction will be conformer-independent even though it to some extent will vary with the compression or stretching of the molecule. If the primary orbital interaction is strong it leads to linearly hyperconjugated paths which stretch from one end of the molecule to the other. Dimers, trimers, and tetramers of 1,4-disilacyclohexa-2,5dienes (nSiR, n = 2−4, Figure 3), having different substituents

2,5-dienes, as well as analogous compounds with other Group 14 elements in the 1- and 4-positions, be used as building blocks for oligomers and polymers with the basic features of conformer-independent conjugation and conductance? Our study reported herein focuses on the Si-based oligomers as we recently reported experimental results for the corresponding monomers with ER2 = SiR2 (R = Me, TMS or Cl). Yet, we also briefly expanded the present investigation to oligomers with E = C, Ge, or Sn. It has been shown that the conductance in π-conjugated biphenyls scales with the orbital overlap (and conjugation strength) between the two phenyl groups because it varies as cos2 θ, with θ being the angle between the planes of two phenyl rings. Accordingly, the highest conductance is displayed by biphenyls with θ = 0°.8−10 Conformational effects on electronic and optical properties have also been illustrated in σ-conjugated systems, and extensive studies by Tamao, Michl, and coworkers have shown that gauche and cis Si−Si−Si−Si kinks in an oligosilane chain block conjugation while anti and transoid conformers extend it (anti (a±) ≈ 180° and transoid (t±) ≈ ± 165°, respectively).11−16 By computations of the transport properties of different oligosilane conformers it has been shown that the conductance through oligosilanes follows the same trends as the conjugation because a 3 orders of magnitude difference was found between the most and the least conducting conformations of a 1,6-diaminohexasilane, respectively, these being the anti and syn conformations.17 The results indicate conductance dependence due to shifts in the HOMO energies. The conductance of permethylated oligosilane chains has also been investigated experimentally, and these measurements revealed a much lower decay of conductance with length as compared to the analogous carbon chains.18 Macroscopic electrical cords are highly conducting and they conduct equally well at every “conformation” they adopt. For a molecule to have these basic features the transport should be (nearly) ballistic and there should only be a minute change in the frontier orbitals (both in energies and spatial distributions) as one rotates about the single bonds or as one stretches or compresses the molecule. Although the criterion on ballistic transport is difficult to realize we now argue that the conformational variations in the orbitals can be reduced by

Figure 3. The investigated oligomers of 1,4-disila/germa/stanna/ cyclohexa-2,5-dienes and cyclohexa-1,4-dienes with methyl (nEMe), silyl (nESiH3), or TMS (nETMS) groups or hydrogens (nEH) as the substituents R at the 1- and 4-positions of the monomers.

R at the 1- and 4-positions of the monomers (R = Me (nSiMe), SiH3 (nSiSiH3), and TMS (nSiTMS)), as well as a few oligomers with E = C, Ge, or Sn (nCR, nGeR, and nSnR) were investigated by computational means. We first analyze dimers of substituted 1,4-disilacyclohexa-2,5-dienes and their geometries and ground state potential energy surfaces (PES), as well as the variations in frontier orbital energies, electronic excitation energies, and oscillator strengths. For the trimers and tetramers we did not investigate the complete conformational space for EE bond rotations but focused on symmetric conformers which represent a wide variation in the R−E−E−R dihedral angles. For oligo(1,4-disilacyclo-2,5-hexadiene)s steric congestion at some conformers influences the rotational flexibility and for that reason we also explored a few oligomers with 1,4-digerma- and 1,4-distannacyclohexadiene repeat units. Moreover, we examined the all-carbon oligomers as one may expect these to display the lowest hyperconjugation, yet, having the shortest EC bonds the overlap between a local σ(EE) orbital and the four surrounding π(CC) orbitals should be 5638



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calculations, with the exception that the supercell in the transport direction only consisted of three gold layers. The junction was evolved under 60 fs (with time steps of 1 fs) at room temperature (300 K) before the Hamiltonian (H)- and overlap (O)-matrices were saved. In the case of the static junction, the calculation is then run like this for the desired amount of steps, in this case a total of 6 ps, saving the H- and O-matrices every 60 fs. In the case of compressing or stretching the junction, the junction is compressed/stretched by 0.1 Å every 60 fs and the coordinates are scaled appropriately. This gives a compression/stretching speed of ∼167 m/s (0.1 Å/60 fs), many orders faster compared to real experiments but lower compared to the thermal motions of the atoms in the junction at 300 K (∼194 m/s for Au atoms). Benchmarks with different speeds have been made and seen not to influence the results. The stored H- and O-matrices from the MD-simulation are then used for conductance calculations by the method proposed and described by Paulsson et al.,34 using the Inelastica code.35

the largest, potentially leading to strong hyperconjugation. Finally, we examined the conductance properties of selected oligomers at their various conformers and performed molecular dynamics simulations to simulate the stretching process in a mechanically controllable break junction.

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COMPUTATIONAL METHODS Isolated Molecule Calculations. All computations were performed with the Gaussian 09 program package, revision A.1.19 The structures of the isolated molecules were optimized at the PBE0/6-311G(d) hybrid density functional theory level20,21 at C2 symmetry. For 2SiTMS, 3SiTMS, and 4SiTMS the geometry optimizations were also performed at the same level by using M06-2X,22,23 a dispersion-corrected hybrid meta DFT method, to properly account for the steric congestion in the TMS-substituted oligomers. The germaniumand tin-containing compounds were calculated by using PBE0/ LANL2DZdp.24,25 Frequency calculations were performed at all optimized geometries to verify that they correspond to minima on the potential energy surface. For the dimers the potential energy surfaces were constructed by rotation about the central E−E bond with 10° increments with the R−E−E−R dihedral angle fixed while all other geometry parameters were optimized. The stationary points for the trimers and tetramers were found by scanning the PES using different starting geometries. A small imaginary frequency was found for a±a± conformer of 3SiSiH3 (i11.59 cm−1). The potential energy surface of 2SiTMS was also examined at the PBEPBE level as this functional was used in the molecular dynamics simulations of the charge transport through gradually more stretched or compressed molecules. Time-dependent density functional theory (TD-DFT) calculations26 were performed by using TD-PBE0/6-311+G(2d,p) at the optimized PBE0/6-311G(d) geometries. The ten lowest vertical excitations to singlet states were calculated.27,28 We also analyzed the Kohn−Sham orbitals and orbital energies (eigenvalues to the Kohn−Sham equations) obtained at PBE0/6-311+G(2d,p)//PBE0/6-311G(d) level. Conductance and Molecular Dynamics Calculations. Transport calculations were carried out from first principles with a method based on nonequilibrium Green’s functions (NEGF) combined with DFT as implemented in the TranSIESTA package.29 The relaxed molecular structures were inserted between two Au(111) surfaces and relaxed once more to optimize the Au−Si bonding. The device consists of three parts: left electrode, molecule, and right electrode. The electrodes are modeled through six layers of gold atoms where the three outer layers are relaxed while the others are kept at the experimental bulky positions. In the lateral dimension a 6 × 6 supercell (17.5 Å × 17.5 Å) was used, large enough to remove interactions between periodic images. All relaxations are performed at the DFT level with the SIESTA package,30,31 and core electrons are modeled by using Troullier−Martins32 soft norm-conserving pseudopotentials. The valence electrons are expanded in a basis set of local orbitals by using a double-ζ plus polarization orbital (DZP) set for electrons in the molecule and a single-ζ plus polarization orbital (SZP) for electrons in the gold electrodes. The GGA of Perdew, Burke, and Ernzerhof was used for the exchange-correlation (XC) functional.33 The molecular dynamics (MD) results presented were obtained by using first-principles DFT-MD in the Born− Oppenheimer approximation as implemented in the SIESTA package with the same setup as described for the transport

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RESULTS AND DISCUSSION We present and discuss the results in the following order: computed geometries and relative conformer energies, orbital energies, and single-molecule conductance. These properties are analyzed in terms of what is required for an oligomer to function as a molecular electrical cord as described in the Introduction. Calculated electronic excitation energies and oscillator strengths of the isolated molecules are presented and discussed in the Supporting Information. Ground-State Potential Energy Surfaces and Geometries. The permethylated linear tetrasilane, n-Si4Me10, displays minima at dihedral angles ωSi−Si−Si−Si of ±55°, ± 90°, and ±165°, corresponding to gauche (g±), ortho (o±), and transoid (t±) conformers, respectively.36 However, the PESs for twisting around the central R−Si−Si−R bond of the 1,4disilacyclohexa-2,5-diene dimers reveal that among the dimers 2SiMe, 2SiSiH3, and 2SiTMS only 2SiTMS displays three separate minima types (ωR−Si−Si−R = ±60°, ±92°, and ±176°, Figure 4) corresponding to g±, o±, and a± conformers. Dimers 2SiMe and 2SiSiH3 only display two different types of minima. The methylated 2SiMe has the minima at ωR−Si−Si−R ≈ ±60° and ±180°, corresponding to g± and a, while the silylsubstituted dimer 2SiSiH3 has minima at dihedral angles of ±58° and ±158°, corresponding to g± and t±, respectively. With regard to the Si−Si bond rotational barriers, 2SiTMS has very high barriers separating the ortho and anti conformers as well as the g+ and g− conformers whereas the corresponding barriers in 2SiMe and 2SiSiH3 are considerably lower. Here, it can be noted that the M06-2X calculations of 2SiTMS reproduce the results of the PBE0 calculations with minima at g± (±54°), o± (±98°), and t± (±169°), however, with somewhat different rotational barriers (for the full PES plot see the Supporting Information). Moreover, a change from the PBE0 hybrid functional to the PBEPBE GGA functional, which is used in the molecular dynamics simulations (vide infra), gives essentially the same PES as the PBE0 hybrid functional for 2SiTMS (see the Supporting Information). The large rotational barriers of 2SiTMS and its high energy of the minima at a± clearly stem from the steric congestion between the two internal and two external TMS groups (Figure 5). Replacing the TMS groups with smaller silyl groups, as in 2SiSiH3, or with methyls, as in 2SiMe, transforms the anti conformer to the global minimum (Figure 4A). This is in line 5639



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Figure 5. Dimer 2SiTMS in the syn and anti conformations calculated at PBE0/6-311G(d) level. The structures show the central Si−Si bond lengths as well as the closest nonbonded H···H interaction between the two internal and between the two external TMS groups for the syn conformation and between the internal TMS groups for the anti conformer.

R dihedral angles. The large steric bulk of the TMS groups results in minima of the trimer 3SiTMS at the g±g± and at two different o±o± conformations, however, no additional minimum was found, neither with PBE0 nor M06-2X. This could be a drawback of the nSiTMS oligomers in a molecular cord context. The conformers differ in relative energies by less than 1.0 kcal/mol with PBE0 and by 2.4 kcal/mol with M06-2X, in line with the dimer calculations where larger energy differences were found with M06-2X (see the Supporting Information). In our earlier study the 1,4-disilacyclo-2,5-hexadiene monomer with R = SiMe3 displayed the most interesting electronic and optical properties.5 However, the rotation about the Si−Si bond connecting two repeat units in the oligomers is hampered by the steric congestion at the syn and deviant (ω = 140°) conformations, and this may negatively affect the ability of nSiTMS oligomers to function as molecular cords as these must change conformation smoothly upon stretching or compression. Steric congestion at crowded conformations should therefore be lowered, and two approaches can be taken for this purpose. First, the size of the R group can be reduced, and the nSiMe oligomers represent that approach. Second, a change from 1,4-disilacyclohexa-2,5-diene monomers to 1,4-digerma- or 1,4-distannacyclohexa-2,5-dienes leads to longer interunit E−E distances. To explore what effect the latter approach has on the shapes of the potential energy surfaces and orbital energies we computed dimers 2GeTMS and 2SnTMS at the PBE0/LANL2DZdp level. The results displayed in Figure 4B show the effect of the gradually longer E−E bonds because 2GeTMS has a similar PES as 2SiTMS but

Figure 4. Potential energies as a function of R−E−E−R dihedral angles [deg] in the different dimers. (A) The dimers 2SiMe, 2SiSiH3, and 2SiTMS and the permethylated linear tetrasilane, n-Si4Me10, calculated at PBE0/6-311G(d) level. (B) The dimers 2SiTMS, 2GeTMS, and 2SnTMS calculated at PBE0/LANL2DZdp level. (C) The 1,4-disilacyclohexa-2,5-diene dimer 2SiMe and the all-carbon cyclohexa-1,4-diene dimers 2CH and 2CMe calculated at PBE0/6311G(d) level.

with the well-established existence of several minima in permethylated linear oligosilanes.37,38 The impact of steric congestion on the properties of 2SiTMS is also apparent from the length of the Si−Si bond that links the two 1,4-disilacyclo2,5-hexadiene units. In 2SiTMS this bond is 0.004−0.021 Å longer than in 2SiMe and 2SiSiH3 (see the Supporting Information). The Si−Si bond length elongation is particularly noticeable in the a± conformers of 2SiTMS (Figure 5). For the longer oligomers the number of different conformers will increase rapidly, yet, some potential conformers are nonexistent due to severe steric congestion. We did not examine all different conformers but instead considered those which are symmetric and have significantly different R−Si−Si− 5640



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Figure 6. Drawings of HOMO-1, HOMO, and LUMO of 2SiTMS in its g+, o+, and a+ conformers, and the symmetry labels of the particular orbitals. The orbitals and orbital energies are the Kohn−Sham orbitals and the corresponding eigenvalues obtained through PBE0/6-311G+(2d,p)//PBE0/6311G(d) calculations.

Figure 7. Conformational variation in the energies of the few highest occupied orbitals of the 1,4-disilacyclohexa-2,5-diene dimers 2SiR and permethylated linear tetrasilane, n-Si4Me10. Results from PBE0/6-311G+(2d,p)//PBE0/6-311G(d) calculations performed on the C2 symmetric structures. Red curves correspond to a-symmetric orbitals and blue curves to b-symmetric orbitals. The positions of the stable conformers are marked as vertical lines in the graphs.

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Figure 8. Conformational variation in orbital energies of the few lowest unoccupied orbitals of the 1,4-disilacyclohexa-2,5-diene dimers 2SiR and permethylated linear tetrasilane, n-Si4Me10. Results from PBE0/6-311G+(2d,p)//PBE0/6-311G(d) calculations performed on the C2 symmetric structures. Red curves correspond to a-symmetric orbitals and blue curves to b-symmetric orbitals. The positions of the stable conformers are marked as vertical lines in the graphs.

with lower rotational barriers (6.0 kcal/mol at the syn conformation). The effect is even more pronounced with E = Sn as 4SnTMS displays a shallow PES comparable to that of 2SiMe (Figure 4A). The oligomers of the all-carbon 1,4-cyclohexadienes could also be interesting as they provide the shortest distance between the π(CC) and σ(CC) bond orbitals potentially leading to significant hyperconjugation. However, the calculated PESs reveal that these oligomers may be less able to function as molecular cords which smoothly change their structures because the 1,4-cyclohexadiene dimers 2CH and 2CMe have much larger rotational barriers (Figure 4C) than the dimers with E = Si, Ge, or Sn. Here, the syn conformers are 9.8 and 8.3 kcal/mol above the global minima, respectively. The barriers separating the gauche and anti conformers are also higher compared to the other dimers, and found at 7.5 and 4.3 kcal/mol for 2CMe and 2CH, respectively. This is despite the fact that only small substituents R in the nCR oligomers were considered in anticipation of this problem. Clearly, the short C−C distance between the two repeat units hampers rotation. Orbital and Orbital Energy Variations. One can first note that HOMO-1, HOMO, and LUMO for each of 2SiMe, 2SiSiH3, and 2SiTMS have contributions from σ(SiSi) as well as π(CC) bond orbitals (see Figure 6 for 2SiTMS and the Supporting Information for 2SiMe and 2SiSiH3). The HOMOs have the same orbital symmetry and spatial

distribution at each conformer, and the same applies to HOMO-1. However, for the LUMOs of 2SiSiH3 and 2SiTMS there is a change in character from an a- to a b-symmetric orbital when going from small to large R−Si−Si−R dihedral angles whereas for 2SiMe LUMO keeps the same symmetry for all dihedral angles. The amounts of fluctuations in the frontier orbital energies upon rotation about the central Si−Si bond in the different dimers were investigated in order to reveal if interactions between adjacent monomer units influence the orbital energies more at some conformations than at others. For comparison, the conformers of n-Si4Me10 were calculated to have a 0.30 eV variation in the energy of the HOMO (ΔεHOMO), ranging between −6.60 and −6.30 eV (Figure 7). The 1,4disilacyclohexa-2,5-diene dimers have much smaller ΔεHOMO of 0.10 (2SiMe), 0.09 (2SiSiH3), and 0.11 (2SiTMS) eV, respectively. The HOMOs of 2SiMe and 2SiSiH3 are both centered energetically at −6.50 eV, while the εHOMO of 2SiTMS is found at higher values, centered at −5.70 eV. Thus, it is noteworthy that 2SiTMS has a small ΔεHOMO despite the very strained s± and d± conformations. The M06-2X and PBEPBE calculations of 2SiTMS reveal similar pictures with ΔεHOMO of 0.15 and 0.09 eV, respectively, yet, with somewhat shifted lowest energies (see the Supporting Information). These calculations confirm that the trends are the same at the three DFT levels, and in order to compare the different dimers, the 5642



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PBE0 results are used in the further discussion. Another potentially beneficial property for conformer-independent conductance is the rather small variations in the differences between the εHOMO and εHOMO‑1 energies of the three 2SiR dimers along their PESs (Figure 7), i.e., the variation Δ(Δ(εHOMO − εHOMO‑1)), which are 0.14 (2SiMe), 0.22 (2SiSiH3), and 0.22 (2SiTMS) eV, respectively, while for nSi4Me10 it is as large as 0.84 eV. The situation for the lowest unoccupied molecular orbitals (LUMOs) among the various oligomers is different from that of the HOMOs. The tetrasilane n-Si4Me10 has the LUMO at an average energy of −0.20 eV with only minor variation (ΔεLUMO = −0.17 to −0.21 eV) across the PES (Figure 8). The methylated 2SiMe, with an average εLUMO at −0.90 eV, has a ΔεLUMO of 0.21 eV, however, similar values across nearly the complete PES and a raise in energy first when approaching s± conformations. For 2SiSiH3, a b-symmetric orbital is LUMO for R−Si−Si−R dihedral angles which are smaller than 95° (energies between −1.32 and −1.52 eV) while an a-symmetric orbital is LUMO at larger dihedral angles (energies between −1.22 and −1.47 eV). Similarly, LUMO of 2SiTMS also switches between two orbitals across the PES (b-symmetric: −0.73 to −0.90 eV at dihedral angles up to 80°; a-symmetric: −0.61 to −0.82 eV at dihedral angles in the range 80−160°, while at large dihedral angles (above 160°) three orbitals are nearly isoenergetic). Yet, the ΔεLUMO of 2SiTMS is 0.17 eV. Taken together, the HOMOs of 2SiMe, 2SiSiH3, and 2SiTMS display smaller variations in energy than the HOMO of n-Si4Me10, whereas the LUMOs display larger variations. Moreover, the variations in the energy differences between the HOMO and HOMO-1 orbitals are much smaller for 2SiMe, 2SiSiH3, and 2SiTMS than for n-Si4Me10. These results should be promising because charge transport at low bias voltages can be expected to be dominated by HOMO when gold electrodes are used. The conformational conductance variations will not be completely diminished, but they should be reduced substantially when compared to the permethylated linear oligosilanes for which a 3 orders of magnitude variation was calculated earlier.17 To ensure as good molecular cord features as possible the spatial distributions of the frontier orbitals should also remain similar between the different conformers. Ideally, the HOMO and LUMO should be delocalized over the complete molecule (or conducting path) at each of the conformers adopted, and this is the situation for the present oligomers (for 2SiTMS, see Figure 6). For a further discussion on the orbital energies and orbital energy variations of the HOMO-1, HOMO-2, LUMO +1, and LUMO+2, see the Supporting Information. When regarding longer oligomers the small variation in orbital energies is again evident because ΔεHOMO between the different conformers of the various trimers (3SiR) and tetramers (4SiR) are at most 0.05 eV (Table 1). A small ΔεLUMO and ΔεHOMO‑1 (maximum 0.10 eV) is also evident for all oligomers except for 3SiMe, which changes between two orbitals that both display ΔεLUMO in the range of 0.3−0.4 eV. The elongation of the oligomers to the trimers and tetramers causes the εHOMO of 3SiMe and 4SiMe to rise from −6.50 eV in 2SiMe to −6.20 eV in 3SiMe, and to −6.14 eV in 4SiMe, i.e., changes in εHOMO of 0.30 and 0.36 eV, respectively (Figure 9 and Table 1). The εHOMO of the silyl-substituted oligomers 3SiSiH3 and 4SiSiH3 is raised slightly less than for the methylated oligomers when expanding from the dimer to the trimer (0.17 eV) and tetramer (0.23 eV), respectively. Finally,

Figure 9. Variations in εHOMO for the gradually longer 1,4disilacyclohexa-2,5-diene oligomers (nSiR). Values for the (g+)n conformers are plotted for the longer oligomers except for 4SiTMS for which the value of the g+o+g+ conformer is plotted since the allgauche conformation does not correspond to a minimum. Results from PBE0/6-311+G(2d,p)//PBE0/6-311G(d) calculations.

Table 1. Orbital Energies, ε (eV), and Orbital Symmetries of Oligomers of Various Lengths and Conformers, Calculated at PBE0/6-311+G(2d,p)//PBE0/6-311G(d) Level εHOMO (sym) εHOMO‑1 (sym) εLUMO (sym)

oligomer 3SiMe g±g± 55.3° a±a± 178.3°

−6.24 (b) −6.20 (b)

−6.86 (a) −6.91 (a)

−1.01 (a) −1.08 (b)

g±g±g± 54.5°/62.3° a±g±a± 179.6°/55.8° a±a±a± 180.0°/180.0°

−6.14 (a) −6.12 (a) −6.09 (a)

−6.53 (b) −6.52 (b) −6.58 (b)

−1.06 (b) −1.09 (b) −1.15 (b)

−6.38 (b) −6.33 (b)

−6.83 (a) −6.80 (a)

−1.49 (a) −1.46 (a)

−6.31 (a) −6.28 (a) −6.27 (a)

−6.63 (b) −6.58 (b) −6.59 (b)

−1.52 (b) −1.44 (b) −1.45 (b)

−5.59 (b) −5.58 (b) −5.59 (b)

−5.95 (a) −5.94 (a) −5.94 (a)

−0.86 (a) −0.85 (a) −0.86 (a)

−5.56 −5.55 −5.56 −5.53

−5.83 −5.79 −5.79 −5.77

−0.92 −0.88 −0.86 −0.97

4SiMe

3SiSiH3 g±g± 57.7° t±t± 161.3° 4SiSiH3 g±g±g± 59.7°/57.5° t±g±t± 155.2°/56.2° t±t±t± 156.0°/164.5° 3SiTMS g±g± 58.7° o±o± 96.5° o±o± 99.1° 4SiTMS g±o±g± 57.5°/100.4° o±o±o± 96.8°/101.0° o±e±o± 94.7°/132.8° a±o±a 178.5/97.0 4CH g±g±g± 65.9°/65.7° a±g±a± 180.0°/66.9° a±a±a± 180.0°/180.0° 4SnTMSa e±e±e± 120.5°/132.4° t±o±t± 174.8°/101.8° a±a±a± 178.7°/179.8°

(a) (a) (a) (a)

(b) (b) (b) (b)

(b) (b) (b) (b)

−6.34 (a) −6.36 (a) −6.35 (a)

−6.58 (b) −6.57 (b) −6. 63 (b)

−0.01 (a) −0.08 (a) −0.03 (a)

−5.51 (a) −5.50 (a) −5.47 (a)

−5.74 (b) −5.74 (b) −5.73 (b)

−0.91 (b) −0.93 (b) −0.99 (b)

a

Orbital energies from PBE0/LANL2DZdp//PBE0/LANL2DZ calculations.

the εHOMO of 3SiTMS and 4SiTMS, similar to 3SiSiH3 and 4SiSiH3, increases by approximately 0.2 eV when compared to the dimer. We also analyzed the frontier orbital energy variations for 2ER oligomers with E = C, Ge, and Sn (see the Supporting 5643



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Information for the full conformational variations of εHOMO and εLUMO). For these it is found that both 2GeTMS and 2SnTMS have small variations upon E−E bond rotation, similar to 2SiTMS, with ΔεHOMO of 0.10 eV for both compounds. Among the two all-carbon dimers, 2CMe has a ΔεHOMO of 0.26 eV while 2CH has a ΔεHOMO of merely 0.08 eV. Notable is that both dimers have εHOMO at approximately the same energies as 2SiMe and 2SiSiH3. These small variations persist for the stable conformers of tetramers 4CH which, despite having high-energy minima at the g±g±g± and a±g±a± conformers, only have minute εHOMO differences (variation within −6.34 to −6.36 eV). Tetramer 4SnTMS has similarly small εHOMO differences, but unlike its silicon analogue it has a stable a±a±a± conformer. Conductance Variations. To investigate the variations in the currents running through the different conformers of the nER oligomers we performed theoretical calculations of the conductance based on a DFT-NEGF method. Here we have studied the two 1,4-disilacyclo-2,5-hexadiene tetramers 4SiMe and 4SiTMS, the less sterically congested 1,4-distannacyclohexa-2,5-diene tetramer 4SnTMS, as well as the cyclohexa-1,4diene tetramer 4CH. The relaxed structures of the conformers were used in the conductance calculations, and in addition, dynamic structures obtained under MD simulations were also used for some of the compounds. To anchor the tetramers to the gold electrodes we used two silyl (SiH3) groups on each side of the tetramer. The silyl group has previously been shown to bind in a 3-fold manner to the Au(111) surface under ultrahigh vacuum conditions (Figure 10).39−43 We choose silyl

Figure 11. Transmission spectra (V = 0) of (A) three conformers of 4SiMe(SiH3), (B) two conformers of 4SiTMS(SiH3) and three conformers of 4SnTMS(SiH3), and (C) three conformers of 4CH(SiH3). Figure 10. Optimized structure of the binding of two Si atoms at a terminal 1,4-disilacyclo-2,5-hexadiene to the Au(111) electrode surface and with the bond lengths [Å] displayed.

difference in conductance between the conformers should result from weakened conjugation in the gauche conformers. With regard to the zero-bias conductance of 4SiTMS(SiH3) (Figure 11B) it differs less between the two conformers a±a±a± and a±o±a± than between the a±a±a± and a±g±a± conformers of 4SiMe(SiH3). For 4SiTMS(SiH3) there is again a difference in electrode−electrode distance between its various conformers, but similar as in the case of 4SiMe(SiH3) the current paths of the conformers are nearly equal in length. Here it is noteworthy that the two tetramers 4SiMe(SiH3) and 4SiTMS(SiH3) have very similar conductances (Table 2) despite that the HOMO of 4SiTMS(SiH3) is closer to EF. This last feature can be seen in the transmission spectra where 4SiTMS(SiH3) has a sharp peak (at the position of the HOMO) about 0.7 eV below EF. It seems that by enhancing the hyperconjugation along the chain by the TMS substituents in 4SiTMS(SiH3), a large part of the orbital density of HOMO is pushed toward the TMS groups and this apparently lowers the electronic coupling through the chain.

anchors so as to match the σ-conjugation of the tetramers as this has been shown earlier to be important for good conductance.44 Experimentally, trimethylsilylethynyl groups have previously been used in conductance measurements, and this silyl group gives comparable values to the more commonly used thiol (−SH) or amine (−NH2) anchoring groups.45 The oligomers with SiH3 anchors are labeled as nER(SiH3). The calculated zero-bias conductance of 4SiMe(SiH3) (Figure 11A) shows a small variation between the three conformers (a factor of 32 in contrast to a factor of more than 1000 found for an amino-terminated linear hexasilane17), where the a±a±a± conformer has the highest conductance. The a±g±a± and the g±g±g± conformers are respectively factors 4 and 20 less conducting than the all-anti-conformer. Even though the gold electrode−electrode distance (Table 2) is shorter for the two conformers with gauche kinks, the actual lengths of the current paths in the chains are similar in all three conformers. Thus, the 5644



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dynamic cord. The distance between the two electrodes can either be kept fixed or the junction can be compressed/ stretched. Since we are interested in the behavior of the oligomers, the atoms in the gold electrodes as well as the four anchoring Si-atoms are kept fixed during the simulations so as to remove the effects of changes in the Au−Si interaction. In Figure 12 the calculated zero-bias conductance traces for

The less sterically congested tetramer of 4SnTMS(SiH3) with E = Sn shows a similar conductance behavior to that of 4SiTMS(SiH3) (Figure 11B, Table 2) with the conductances of the a±a±a± and a±o±a± conformers being very similar despite that they have a difference in electrode−electrode distance of 4 Å. For 4SnTMS(SiH 3 ) we also calculated the o ± o ± o ± conformer and it has roughly a factor of 4 lower conductance than the two other conformers, despite that the electrode− electrode distance for this conformer is intermediate between those of the other two. Thus, it once again becomes clear that the length and conformation of the current path instead of the electrode−electrode distance dictates the conductance. Finally, when comparing 4SnTMS(SiH3) with 4SiTMS(SiH3) it is noteworthy that the conductance of the a±a±a± conformer of 4SnTMS(SiH3) is about a factor of 8 lower than that of the same conformer of 4SiTMS(SiH3). At this point a comparison with the conductance of the established σ-conjugated oligomer with the same number of bonds as in the hyperconjugated paths of 4ETMS(SiH3) is useful. Clearly, the conductance in neither of the oligomers examined thus far is ballistic, yet, how do they compare with the all-anti linear oligosilane? And how does it compare with the corresponding linear alkane, which should be a very poorly conducting oligomer? To answer these questions we calculated the conductances of the 1,16-disilyl-substituted linear hexadecasilane and hexadecane. These computations show that the tetramers 4SiMe(SiH3), 4SiTMS(SiH3), and 4SnTMS(SiH3) have zero-bias conductances which are 45−400 times higher than that of the 1,16-disilylhexadecane (G = 0.0038 × 10−4 G0). Thus, nER oligomers are far from insulators. Moreover, their conductances at zero bias are 1−10 times higher than that of the 1,16-disilylhexadecasilane (G = 0.15 × 10−4 G0), i.e., a strongly σ-conjugated oligomer. Similar as found by George, Ratner, and Lambert,17 the linear oligosilane, however, has a strongly conformer dependent conductance because the allgauche conformer of 1,16-disilylhexadecasilane has a conductance (G = 1.3 × 10−10 G0) that is merely 1/100 000 that of its all-anti conformer. The 4ER tetramers display significantly less varied conductance with change in conformation. Yet, it is not necessary for reasonable conductance to have E as a heavy Group 14 element because the zero-bias conductance of the a±a±a± conformer of 4CH(SiH3) is essentially the same as for 4SiMe(SiH3), 4SiTMS(SiH3), and 4SnTMS(SiH3). Clearly, the σ(EE) bond orbital as a result of the shorter EC bonds for E = C than for E = Si can interact more strongly with the four flanking CC double bonds leading to a significant hyperconjugation. Here, a valid concern is the shorter electrode−electrode distance of the 4CH(SiH3) when compared to 4SiTMS(SiH3) and 4SnTMS(SiH3), thus they have a shorter tunneling path through the molecule. Still, elongation to the 5CH(SiH3) oligomers which is approximately as long as 4SiMe leads to a surprisingly high conductance (G = 0.02 × 10−4 G0). So far we have only considered transport through the relaxed geometries at fixed conformers; however, to probe if the oligomers are suitable as cords, the dynamical behavior during stretching or compression is also important. We exclusively examined the 4SiR(SiH3) oligomers as these are the most closely related to monomeric compounds which earlier have been synthesized and studied experimentally.46 To investigate how the oligomers would act under thermal fluctuations around the ground state we used a method based on DFT-MD which we combine with NEGF to compute the conductance for the

Figure 12. Calculated zero-bias conductance from molecular dynamics simulations. Top panels display results for static electrode−electrode distances during 6-ps simulations, the green dashed line shows mean value, and the indigo dashed lines show ± standard deviation. Bottom panels show results when the junctions are compressed (brown lines) or stretched (black lines), green and indigo dashed lines show mean and max/min values obtained from calculations with static electrode− electrode distance.

4SiMe(SiH3) and 4SiTMS(SiH3), both for static electrode− electrode situations as well as for the compression/stretching processes, are shown. All the results are also collected in Table 2. First we consider the situations with static electrode− electrode distances and for which the conductance traces obtained during 6 ps at room temperature for 4SiMe(SiH3) and 4SiTMS(SiH3) are shown in the top panels of Figure 12. The conductance is rapidly fluctuating with the conformation of the chain, and for 4SiMe(SiH3) we obtain a mean conductance of 1.44 × 10−4 G0 with a standard deviation (σ) of 1.04 × 10−4 G0, the magnitude difference between the calculated maximum and minimum values is approximately a factor of 30. For 4SiTMS(SiH3), we obtain in the same way a mean conductance of 1.21 × 10−4 G0 with a σ of 1.13 × 10−4 G0. However, here the maximum and minimum conductances differ by a factor of ∼100. The minimum in the conductance trace for 4SiMe(SiH3) corresponds to a d±d±t± conformer while the maximum is very close to an all-anti conformer. For 4SiTMS(SiH3) the maximum corresponds to an e±e±d± conformation (135°, 135°, and 149°), while the minimum is close to an o±o±t± conformation (107°, 107°, and 162°). To evaluate the stability of the suggested cords we start by compressing junctions with 4SiMe(SiH3) and 4SiTMS(SiH3) (brown lines in the bottom panels of Figure 12), and after that, 5645



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Table 2. Results of Conductance Calculations oligomer 4SiMe(SiH3) a±a±a± a±g±a± g±g±g± 4SiTMS(SiH3) a±a±a± a±o±a± 4SnTMS(SiH3) a±a±a± a±o±a± o±o±o± 4CH(SiH3) a±a±a± a±g±a± g±g±g± 5CH(SiH3) a±a±a± 1,16-disilylhexadecasilane all-anti all-gauche 1,16-disilylhexadecane all-anti

Grelaxed [G0 × 10−4]

Au−Au distance (Å)

1.53 0.40 0.068

26.4 24.9 24.9

1.38 0.94

26.4 24.3

0.17 0.20 0.05

29.3 25.4 27.8

0.88 0.31 0.85

21.9 20.4 19.0

0.02

26.4

0.15 1.3 × 10−6

37.4 29.4

0.0038

26.4

Gdynamica [G0 × 10−4]

σb [G0 × 10−4]

max/minc

1.44

1.04

32

1.21

1.13

104

a

Calculated as mean value during 6-ps simulation with static electrode distance. bCalculated standard deviation during 6-ps simulation with static electrode distance. cRatio between maximum and minimum conductance obtained with static electrode distance.

kept fixed, while the conductance of 4SiTMS(SiH3) has somewhat larger fluctuations but instead it is more stable under changes of the electrode distances. It should, however, be noted that for the sterically crowded 4SiTMS(SiH3) utilization of a dispersion-corrected DFT method could generate more accurate geometries and potential energy surfaces with somewhat different profiles. For a further discussion and snapshots of the geometries of 4SiMe(SiH3) obtained during compression or stretching, see the Supporting Information. For the isolated oligomers more pronounced intramolecular steric congestion was found in 4SiTMS(SiH3) than in 4SiMe(SiH3). To study if this congestion causes problems when compressing the cords we use the results from the MD simulations to calculate the necessary force to compress the junction. In Figure 13 the total energy and the force are shown as functions of the Au−Au distance, where the force is calculated from the change in energy (F = ΔE/Δz). Interestingly, the force necessary to compress 4SiMe(SiH3) from the relaxed geometry of the a+a+a+ conformer is minutely higher than for 4SiTMS(SiH3), i.e., opposite to what could be expected based on the PES of the corresponding dimers 2SiMe and 2SiTMS. Except for that, the two force (energy) profiles for compressing or stretching 4SiMe(SiH3) and 4SiTMS(SiH3) are very similar. This suggests that the substituents have only little (or no) influence on how smoothly the cords are compressed or stretched between the conformers that are available for a particular oligomer, and that the dominant factors for the force are geometry changes (bond lengths and bond angles) in the backbone of the oligomer.

stretch the junctions until they break (black lines). The compression starts from the relaxed geometries of the all-anti conformers, which were also used in the static junction calculations. The stretching, on the other hand, starts from a somewhat compressed geometry to show the reproducibility. The figures display the conductance traces in these cases as a function of the distance between the two Au-electrodes; the maximum, minimum, and mean values obtained from the static junction are also shown as dashed lines. From these results different characteristics for the two oligomers arise. The conductance for 4SiTMS(SiH3) is reasonably stable for a wide range of Au−Au distances (∼21 to 30 Å), as it is fluctuating close to the mean value and mostly inside the max− min window (all obtained from the conductance trace of the static junction). In the 21−30 Å region, a ratio of 34 is obtained between the maximum and minimum conductances during stretching/compression. The variation here is smaller compared to the case with the static junction of 4SiTMS(SiH3), which is due to the fact that a smaller conformational space is explored in the stretching/compression process. Thus, larger fluctuations can be expected here as well, but the mean conductance is stable over the whole range considered. For 4SiMe(SiH3), the conductance drops by about a factor of 10 when moving away from the optimal geometry of the a+a+a+ conformer, both when compressing and when stretching. Also, the mean conductance of 4SiMe(SiH3) is stable in a much smaller range of Au−Au distances (∼23 to 27 Å) and the ratio between the maximum and minimum conductances in this window is about 60. Taken together, the two oligomers investigated through MD simulations have important features of molecular cord compounds, although with different characteristics, despite that their conductances are rather low. The conductance of 4SiMe(SiH3) is very stable against thermal fluctuations (rotations within the chain) when the electrode distances are

■

CONCLUSIONS

Substituted oligomers of 1,4-linked 1,4-disila/germa/stannacyclohexa-2,5-dienes, as well as the all-carbon congeners, have been evaluated as potential molecular electrical cords through a series of quantum chemical calculations. Focus was placed on 5646



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A drawback of the compounds investigated herein in the context of “molecular cords” is their rather low conductance. Still, the calculated conductance for the Si-based tetramers are slightly higher than that of 1,16-disilylhexadecasilane in its allanti conformer and much higher than the conductance of 1,16disilylhexadecane. Even though the compounds reported herein are not ideal for molecular electrical cords the results point to a direction for future molecular design, i.e., the frontier orbitals should remain at constant energy levels and have similar spatial distribution throughout the conformational space. Moreover, the PES should be as shallow as possible enabling facile and smooth stretching and compression. The property to improve is clearly the conductance as a molecular cord, in analogy to a macroscopic electrical cord, should provide for essentially ballistic transport.

■

Figure 13. Force (top panel) and change in energy (bottom panel) when stretching/compressing the junctions with 4SiMe(SiH3) and 4SiTMS(SiH3). Here the gold atoms in the electrodes and the silylanchors are fixed so as to probe the effects of the conformational variation of the oligomers. The maximum force is obtained when breaking the Si−Si bond in the center of the oligomer.

ASSOCIATED CONTENT

S Supporting Information *

Results from the M06-2X and PBE calculations, a comparison between the Gaussian and SIESTA results, orbital energy diagrams, orbital pictures, a detailed discussion on the TD-DFT results, discussion of the geometries obtained when compressing and stretching the tetramers, and further transmission spectra as well as Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org.

the Si-containing oligomers as synthetic protocols of suitable monomeric precursors have been published earlier.46 The calculations of the Si-containing oligomers reveal that 1,4-dimethyl-1,4-disilacyclohexa-2,5-diene oligomers (2SiMe to 4SiMe) have the greatest potential to function as such cords, having low barriers of rotation about the Si−Si bonds, good frontier orbital delocalization, and low variation in εHOMO. While the TMS substituent raises the εHOMO compared to methyl substituent, potentially leading to better conductance, the steric bulk of the TMS substituent in nSiTMS hampers the free rotation about the Si−Si bond connecting the monomer units and reduces the number of conformers that exist for the longer oligomers. Conductance calculations on the different conformers of 4SiMe(SiH3) show that the all-anti conformer is approximately a factor of 20 more conducting than the all-gauche conformer, the least conducting conformer. This is in agreement with the molecular dynamics calculations where a factor of 30 was found between the maximal and minimal conductance values. The conductances of the two calculated conformers of 4SiTMS(SiH3), a±a±a± and a±o±a±, differ by less than a factor of 2, but in this case it is not in agreement with the molecular dynamics simulations where we find a difference in the conductance between the lowest and highest value of approximately a factor of 100. On the other hand, the conductance of 4SiTMS(SiH3) is more stable when compared to that of 4SiMe(SiH3) when the electrode−electrode distance is changed. Other group 14 element compounds also display attractive features. The Ge- and Sn-containing oligomers have low barriers of rotation, however, somewhat lower conductance than the corresponding Si-based oligomers. The all-carbon oligomers, rather surprisingly, provide good hyperconjugative orbital overlap and have remarkably stable orbital energies despite the large C−C single bond rotational barriers. The calculated conductances at zero-bias voltage of the all-C oligomers are similar to the analogous Si-based oligomers. Taken together, it seems the silicon-based oligomer compounds provide a good compromise between these features while also tentatively being the most realistic synthetic targets.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: (A.G.) [email protected]. *E-mail: (H.O.) [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS First of all, we are grateful for highly thoughtful referee comments and suggestions, which clearly improved the text. We are also grateful to Uppsala University (U3MEC KoF initiative), the Swedish Research Council (VR), Carl Tryggers Stiftelse fö r Vetenskaplig Forskning, the Wenner-Gren Foundations, the Swedish Energy Agency, and Stiftelsen för Strategisk Forskning (SSF) for financial support. J.Z. is grateful to the National Science Foundation of China (21103142). The computations were performed on resources provided by SNIC through NSC, C3SE, and UPPMAX.

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REFERENCES

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