Inelastic electron tunneling spectra and vibronic coupling density analysis of 2,5-dimercapto-1,3,4-thiadiazole and tetrathiafulvalene dithiol

Abstract

We calculate inelastic electron tunneling (IET) spectra for 2,5-dimercapto-1,3,4-thiadiazole (DMcT) and tetrathiafulvalene dithiol (TTF-DT) sandwiched between two gold electrodes using non-equilibrium Green's function (NEGF) theory. The calculated peak positions are in reasonable agreement with the experimental data. We also calculate IET spectrum for thiophene dithiol (Th-DT) sandwiched between two gold electrodes and compare it with that for the Au/DMcT/Au junction. Th-DT and DMcT can be distinguished using the IET spectroscopy by the peak of the C–C stretching mode. The peak intensity in the IET spectra is analyzed using vibronic coupling density (VCD) analysis. For the Au/DMcT/Au junction, large distribution of electron-density difference Δρ_HOMO on the C–N bond is responsible for the intense peak of the C–N stretching mode; on the other hand, for Au/TTF-DT/Au junction, large distribution of Δρ_HOMO on the central C=C bond is responsible for the intense peak of the C=C stretching modes.

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Introduction

Inelastic electron tunneling (IET) spectra for metal–molecule–metal junctions have been studied extensively in recent years.^1–6 Peak positions of an IET spectrum correspond to vibrational energies of a molecule that interacts with a carrier, and peak heights reflect relative strength of electron–molecule vibration interaction, or vibronic coupling.⁷ Thus, IET spectra contain information about vibronic coupling between the carrier and the molecular vibrations. IET spectra are characteristic for molecules and IET spectroscopy can be an identification method for molecular species adsorbed on an electrode. IET spectra are also useful for choosing a molecule when we construct a molecular wire junction, and therefore, a fundamental understanding of IET spectra is needed for development of future nanoelectronics.

Selection rules for IET spectra are as yet controversial. For oligo (phenylene ethynylene) (OPE), the ring mode and C≡C stretching mode show intense peaks; for oligo (vinylene ethynylene) (OPV), the ring mode and C=C stretching mode show intense peaks.⁴ This result shows that the carrier is scattered by IR and Raman active modes. In contrast, the systematic experimental observation of the IET spectra for semifluorinated alkanethiol junctions has made it clear that the relative intensity of the spectra is not necessarily proportional to the calculated IR nor Raman intensities of the isolated semifluorinated alkanethiols.⁵ Using a scanning tunneling microscope (STM), Okabayashi et al. have measured high-resolution STM IET spectra of alkanethiol self-assembled monolayers (SAMs)^8,9 and reported that inelastic intermolecular scattering is important in electron tunneling in the SAMs. Troisi et al. have estimated peak intensities in IET spectra by calculating the first derivative of the Green's function with respect to the normal mode coordinates, and concluded that only the totally symmetric modes show peak when a single tunneling channel is available.¹⁰

Our purpose is to provide an understanding of relative intensities in IET spectra based on vibronic coupling density (VCD) analysis.^11–14 The VCD analysis tells us the reason for relative order of strength of vibronic coupling, and hence, gives a new insight into the shape of an IET spectrum. We have applied the VCD analysis to various molecules, revealed a local picture of vibronic coupling in molecules, and shown that we can tune vibronic couplings by controlling electron-density difference Δρ.^11–19 This guiding principle provides an effective way to design functional materials such as molecular wires, as well as to interpret IET spectra.

In this study, using the VCD analysis, we investigate vibronic coupling in 2,5-dimercapto-1,3,4-thiadiazole (DMcT) and tetrathiafulvalene dithiol (TTF-DT) sandwiched between two gold electrodes. We calculate IET spectra for the Au/DMcT/Au and Au/TTF-DT/Au junctions employing the non-equilibrium Green's function (NEGF) formalism²⁰ and compare the spectra with the experimental results obtained using nanofabricated mechanically-controllable break junctions (MCBJs).^6,21 Tetrathiafulvalene (TTF) and its derivatives have been studied as electron donors for molecular conductors and superconductors;^22–24 DMcT has been known as a cathode-active material for lithium rechargeable batteries²⁵ and an understanding of charge transfer between DMcT and metal electrodes is quite important. These molecules are promising building blocks for molecular wires and their conducting properties when sandwiched between gold electrodes have been investigated intensively.^21,26,27

We also calculate an IET spectrum for an Au/thiophene dithiol (Th-DT)/Au junction and compare it with that for the Au/DMcT/Au junction. The VCD analysis reveals the reason for the difference between the spectra of the two junctions. This analysis provides a new insight for IET spectra and guiding principle of design for molecular wire junctions.

Theory

Vibronic coupling constant and vibronic coupling density

A molecular Hamiltonian can be written as

[script letter H](r,R) = [script letter H]_e(r,R) + [scr T, script letter T]_n(R) (1)

where r and R denote sets of electronic and nuclear coordinates, respectively, and [script letter H]_e(r,R) and [scr T, script letter T]_n(R) are an electronic Hamiltonian and the nuclear kinetic energy, respectively. We assume that the molecular wire is in a neutral state at first, and vibronic coupling occurs when the molecule is ionized by a carrier.

Once an equilibrium nuclear configuration R₀ and vibrational frequencies of the molecule are obtained, we can calculate vibronic coupling constant (VCC) V^α_ij for the αth mode:

where Ψ⁺_i(r, R₀) is an electronic wave function of the cation state in which an electron is removed from the ith molecular orbital and {Q_α} is a set of mass-weighted normal coordinates.

For i = j, V^α_i (≡ V^α_ii) can be expressed as the space integration of the VCD η^α_i:^11–14

V^α_i = ∫η^α_i(x)dx (3)

where x is a position in the three-dimensional space and η^α_i is defined by

η^α_i = Δρ_i(x) × v_α(x) (4)

where Δρ_i is an electron-density difference and v_α is the one-electron operator of the derivative of nuclear–electronic potential with respect to Q_α. Δρ_i and v_α are defined by

Δρ_i(x) = ρ⁺_i(x) − ρ₀(x) (5)

where ρ⁺_i is the electron density of the cation state in which an electron is removed from the ith molecular orbital; ρ₀ is the electron density of the neutral state. M_A and R_A are the mass and the nuclear coordinate of the nucleus A, respectively. e_A^(α) is the Ath component of a vibrational vector in mass-weighted coordinates e^(α).

The contribution to η^α_i from the Ath atom is given by

η^α_i,A(x) = Δρ(x) × v_α,A(x) (7)

The space integration of η^α_i,A gives the contribution to V^α_i from the Ath atom:

V^α_i,A = ∫η^α_i,A(x)dx (8)

where V^α_i,A is called the atomic VCC (AVCC) and

Inelastic electron tunneling spectrum

Within the framework of the Holstein–Peierls model, we can write the molecular Hamiltonian [script letter H] in the second quantization form aswhere c_i^† and c_i are electron creation and annihilation operators in the ith molecular orbital, respectively, and b^†_α and b_α denote phonon creation and annihilation operators of the mode α, respectively. ε_i is the orbital energy of the ith molecular orbital. λ^α_ij and ω_α are electron–phonon coupling constant and frequency of the mode α, respectively. λ^α_ij is related to the VCC V^α_ij:ε_i, ω_α, and V^α_ij are calculated using DFT and CASSCF methods.

A Green's function of the molecular wire junction is given by

G(E) = [EI − H_e − Σ(E)]⁻¹ (12)

where E is an energy of an electron, I is the identity matrix, H_e is a matrix representation of [script letter H]_e, and Σ(E) is a total self-energy,²⁰ which is defined later by eqn (27). H_e is a diagonal matrix and (H_e)_ii = ε_i.

Inscattering and outscattering functions for the left/right electrode is given by

Σ_L/Rⁱⁿ(E) = f_L/R(E)Γ_L/R(E) (13)

Σ_L/R^out(E) = (1 − f_L/R(E))Γ_L/R(E) (14)

where

Γ_L/R(E) = i{Σ_L/R(E) − Σ^†_L/R(E)} (16)

Here, μ_L/R and Σ_L/R are an electrochemical potential and contact self-energy for the left/right electrode, respectively, k_B is the Boltzmann constant, and T is the temperature of the composite system. Σ_L/R incorporates an effect of an interaction between the left/right electrode and the molecule and given by

Σ_L/R(E) = τ_L/R^†g(E)τ_L/R (17)

where τ_L/R is an electronic coupling between the left/right electrode and the molecule and g is a surface Green's function.

We calculate inscattering and outscattering functions for the vibronic coupling within the first Born approximation:²⁸

where

(λ^α)_ij = λ_ij^α (20)

Here, N_α is an occupation number of phonons with energy ℏω_α. Gⁿ and G^p are electron and hole correlation functions that are given by

Gⁿ(E) = G(E)Σⁱⁿ(E)G^†(E) (22)

G^p(E) = G(E)Σ^out(E)G^†(E) (23)

where

Σⁱⁿ(E) = Σ_Lⁱⁿ(E) + Σ_Rⁱⁿ(E) + Σ_Sⁱⁿ(E) (24)

Σ^out(E) = Σ_L^out(E) + Σ_R^out(E) + Σ_S^out(E) (25)

A self-energy for vibronic coupling Σ_S is a function of the energy E of the incoming electron and is related to Σ_Sⁱⁿ and Σ_S^out through the following equation:

i{Σ_S(E) − Σ_S^†(E)} = Σ_Sⁱⁿ(E) + Σ_S^out(E) (26)

Σ(E) is a sum of the self-energies:

Σ(E) = Σ_L(E) + Σ_R(E) + Σ_S(E) (27)

G ⁿ and G^p are calculated self-consistently using eqn (12), (18), (19), and (22)–(27).

The electric current through the molecular wire junction is given by

where e is the elementary charge. The first and second derivative of I with respect to bias voltage V_b yield the conductance (dI/dV_b) and IET spectrum (d²I/dV_b²vs.V_b), respectively.

Method of calculation

All the DFT calculations were done using Gaussian 03 software.²⁹ For carbon, hydrogen, nitrogen, and sulfur atoms the 6-311+G* basis set was used; for gold atoms, LANL2DZ basis set was used. We considered intramolecular vibronic coupling in the molecules containing gold atoms: terminal hydrogen atoms of DMcT, TTF-DT, and Th-DT are replaced by gold atoms. We denote them as Au₂DMcT, Au₂TTF-DT, and Au₂Th-DT, respectively.

Geometry optimization and vibrational analysis of neutral Au₂DMcT, Au₂TTF-DT, and Au₂Th-DT were done using the B3LYP method. We assumed C_2v symmetry for Au₂DMcT, C_i symmetry for Au₂TTF-DT, and C₂ symmetry for Au₂Th-DT. We calculated wavefunctions of the cationic states in which the electron is removed from the HOMO (denoted as |Ψ⁺_HOMO〉) using the UB3LYP method and that in which the electron is removed from the next HOMO (denoted as |Ψ⁺_HOMO–1〉) using the CASSCF method. The active space of our CASSCF calculation includes three electrons and three molecular orbitals (LUMO, HOMO, and next HOMO).

We calculated conductances and IET spectra for Au₂DMcT, Au₂TTF-DT, and Au₂Th-DT sandwiched between two gold electrodes (denoted as Au/DMcT/Au, Au/TTF-DT/Au, and Au/Th-DT/Au, respectively). We adopt the Green's function for a semi-infinite one-dimensional gold chain as g.²⁰ The coupling between a molecule and electrode τ_L/R depends on device geometry and molecular orientation. However, since the junction geometry is unclear, we consider τ_L/R as a parameter.

We adopt the opposite sign of the work function of a gold surface (5.53 eV)³⁰ as the Fermi energy of the electrode surface E_F. The electrochemical potential μ_L/R at an applied bias voltage V_b is set to be μ_L/R = E_F ± eV_b/2.

Results and discussion

Vibronic coupling density analysis

Fig. 1 shows the optimized geometries of neutral Au₂DMcT and Au₂TTF-DT with atomic numbering schemes. The optimized geometry of Au₂DMcT is planar. The optimized bond angles and lengths of Au₂DMcT are in good agreement with the experimental values of 2-amino-5-phenyl-1,3,4-thiadiazole;³¹ the optimized bond angles and lengths of Au₂TTF-DT are in agreement with the experimental data for TTF obtained by Cooper et al.³² The dihedral angles S1–C1–C1′–S2′, S2–C1–C1′–S1, C1′–C1–S1–C2, and C1′–C1–S2–C3 are 0.5°,179.5°, 179.4°, and 178.7°, respectively, suggesting that the central TTF moiety is almost planar. Au₂DMcT and Au₂TTF-DT have eight and 21 totally symmetric modes, respectively, that couple to the electronic state.

Fig. 1 Optimized geometries with atomic numbering schemes: (a) Au₂DMcT; (b) Au₂TTF-DT. Bond lengths are in Å and bond angles in degrees.

Calculated VCCs and peak positions in IET spectra for Au₂DMcT and Au₂TTF-DT together with the experimental data^6,21 are listed in Tables 1 and 2, respectively. a(α) denotes the αth totally symmetric mode. V^α_{HOMO/HOMO–1} is the VCC for the cation state in which the electron is removed from the HOMO/next HOMO:

Table 1 Vibrational modes and vibronic coupling constants (10⁻⁴ a.u.) for Au₂DMcT cation together with the experimental peak positions of the IET spectrum.⁶

Mode		Peak position			V ^α HOMO	V ^α HOMO–1
		Calc.		Exp.
		cm^−1	mV	mV
a(1)	C–S–Au bending	26.91	3		−0.02	−0.07
a(2)	S–Au stretching	131.17	16		−0.08	−0.17
a(3)	S–Au stretching	351.23	44		−0.13	−1.05
a(4)	S–Au stretching	361.13	45	26	−1.01	−0.52
a(5)	C–S–C bending	615.64	76	80	−0.77	−1.44
a(6)	S–C–N stretching	977.45	121		−0.12	−1.42
a(7)	N–N stretching	1026.19	127	128	−1.63	−0.18
a(8)	C=N stretching	1373.01	170	168	−5.34	−4.74

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Table 2 Vibrational modes and vibronic coupling constants (10⁻⁴ a.u.) for Au₂TTF-DT cation together with the experimental peak positions of the IET spectrum.²¹

Mode		Peak position			V ^α HOMO
		Calc.		Exp.
		cm^−1	mV	mV
a(10)	C–S stretching	452.55	56	82	−1.09
a(13)	C–S stretching	609.31	76		−0.31
a(15)	C–S stretching	790.62	98	105	−0.37
a(18)	in-plane C–C–H bending	1181.96	147	142	−0.17
a(19)	C=C stretching	1458.59	181		−2.70
a(20)	C=C stretching	1521.81	189	165	−3.16

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A scaling factor of 0.963³³ was used for theoretical frequencies.

Fig. 2 shows vibrational modes with the three largest V^α_HOMO: the a(4), a(7), and a(8) modes of Au₂DMcT; the a(10), a(19), and a(20) modes of Au₂TTF-DT. The direction of the vibrational modes is chosen such that V^α_HOMO is negative.

Fig. 2 Vibrational modes with the large V^α_HOMO: (a1) a(4), (a2) a(7), and (a3) a(8) modes of Au₂DMcT; (b1) a(10), (b2) a(19), and (b3) a(20) modes of Au₂TTF-DT.

First, we discuss V^α_HOMO using the vibronic coupling density analysis. For Au₂DMcT, the C=N stretching mode (the a(8) mode) has quite a large VCC. The N–N stretching (the a(7) mode) and S–Au stretching modes (the a(4) mode) have relatively large VCCs. The C–S–C bending and N–N stretching modes (the a(5) and a(6) modes) have small VCCs.

For Au₂TTF-DT, the C=C stretching modes (the a(19) and a(20) modes) have large VCCs, and the C–S stretching mode (the a(10) mode) has a relatively large VCC. For the a(19) mode, the phase of the stretching vibration of the central C=C double bond is the same as that of terminal C=C double bonds, that is, the three C=C double bonds lengthen/shorten simultaneously; for the a(20) mode, the phases are opposite, that is, when the central double bond lengthens/shortens, the terminal double bonds shorten/lengthen.

Fig. 3(a) shows Δρ_HOMO for Au₂DMcT. Δρ_HOMO is large on the C1–N1 bond, while it is small on the S1 and Au1 atoms. Δρ_HOMO has also a large value on the S2 atom bonded to the terminal Au atom. On the N1–N1′ bond, Δρ_HOMO is large only near the N atoms, and is not distributed in the middle of the bond. Positive regions have a σ-character and originate from the occupied molecular orbitals other than the HOMO. The positive regions weaken the repulsion between negative regions.

Fig. 3 Electron-density difference Δρ_HOMO: (a) Au₂DMcT at an isosurface value of 0.005 a.u.; (b) Au₂TTF-DT at an isosurface value of 0.004 a.u. White regions are positive; blue regions are negative.

Fig. 3(b) shows Δρ_HOMO for Au₂TTF-DT. Δρ_HOMO is more spread out for Au₂TTF-DT than for Au₂DMcT, because Au₂TTF-DT is a larger π-conjugated system than is Au₂DMcT. Δρ_HOMO is distributed mainly on the S1 and S2 atoms and C1–C1′ bond. Positive regions around the C1 and C1′ atoms relax repulsion between the negative regions above and below the C1–C1′ bond. Δρ_HOMO is small around the C2, C3, H1, S3, and Au1 atoms.

Fig. 4(a1–3) shows derivative of the nuclear–electronic potential v_α for the a(4), a(7), and a(8) modes of Au₂DMcT. A head and tail of an arrow in Fig. 2 correspond to blue and white regions in Fig. 4. Numbers in Fig. 4 are AVCCs in 10⁻⁴ a.u.

Fig. 4 Derivative of nuclear–electronic potential v_α: (a1) a(4), (a2) a(7), and (a3) a(8) modes of Au₂DMcT at an isosurface value of 0.02 a.u.; (b1) a(10), (b2) a(19), and (b3) a(20) modes of Au₂TTF-DT at an isosurface value of 0.01 a.u. White regions are positive; blue regions are negative. Numbers are atomic vibronic coupling constants V^α_HOMO,A (10⁻⁴ a.u.).

The a(8) mode is the C=N stretching mode and v₈ is large on the C1–N1 bond (Fig. 4(a3)). Since Δρ_HOMO is also large on the C1–N1 bond (Fig. 3(a)), v₈ and Δρ_HOMO overlap significantly on the bond. Hence, η₈ has a large value on the C=N double bonds, and the C and N atoms have large AVCCs (−1.522 and −1.108 × 10⁻⁴ a.u., respectively).

The a(7) mode is the N–N stretching mode and v₇ is largely distributed on the N1–N1′ bond (Fig. 4(a2)). However, since Δρ_HOMO is small in the middle of the N1–N1′ bond, the region in which η₇ is large is limited around the N atoms. Hence, only the N atoms have large AVCCs (–1.384 × 10⁻⁴ a.u.), and V⁷_HOMO is smaller than V⁸_HOMO.

The a(4) mode is the S–Au stretching mode, and v₄ is large around the S2 atom (Fig. 4(a1)). v₄ and Δρ_HOMO overlap on the S2 atom, however, since the extent of the overlap is small, the AVCC of the S2 atom (–0.539 × 10⁻⁴ a.u.) is smaller than that of the N1 atom for the a(7) mode (–1.384 × 10⁻⁴ a.u.). Hence, V⁴_HOMO is smaller than V⁷_HOMO. Thus, we can understand the reason for the relative order of the VCCs by analyzing the VCD distributions.

Fig. 4(b1–3) shows v_α for the a(10), a(19), and a(20) modes of Au₂TTF-DT. The a(19) and a(20) modes are C=C stretching modes, and hence, v₁₉ and v₂₀ are large on the C=C double bonds. Since v₁₉ and v₂₀ overlap significantly with Δρ_HOMO on the C1–C1′ bond, η₁₉ and η₂₀ are large on the bond, which leads to the large AVCCs of the C1 and C1′ atoms: −0.962 × 10⁻⁴ a.u. for the a(19) mode; −1.768 × 10⁻⁴ a.u. for the a(20) mode.

The a(10) mode includes C1–S1 and C1–S2 stretching vibrations and v₁₀ is large around the S1 and S2 atoms. v₁₀ and Δρ_HOMO are distributed around the S1 and S2 atoms. However, the overlap between them is small compared with those for the a(19) and a(20) modes. Hence, the AVCCs of S1 and S2 atoms for the a(10) mode are smaller than that of the C1 atom for the a(19) and a(20) modes. This is the reason why V¹⁰_HOMO (= −1.09 × 10⁻⁴ a.u.) is smaller than those of V¹⁹_HOMO (= −2.70 × 10⁻⁴ a.u.) and V²⁰_HOMO (= −3.16 × 10⁻⁴ a.u.).

For the a(19) and a(20) modes, the AVCCs of the atoms other than the carbon atoms are quite small. The sums of the AVCCs of the carbon atoms for the a(19) and a(20) modes are −2.684 × 10⁻⁴ and −3.146 × 10⁻⁴ a.u., respectively, which correspond to 99.4% of V¹⁹_HOMO and 99.6% of V²⁰_HOMO, suggesting that vibronic coupling occurs mainly on the carbon atoms. V²⁰_HOMO is larger than V¹⁹_HOMO, because for the a(20) mode, the AVCC of the C1 atom is much larger than that for the a(19) mode, which originates from the fact that v²⁰_HOMO is larger than v¹⁹_HOMO on the C1–C1′ bond.

Second, we discuss the relative V^α_HOMO–1 ordering for Au₂DMcT. The a(8) mode has quite a large V^α_HOMO–1 and the a(3), a(5), and a(6) modes have relatively large V^α_HOMO–1 values (Table 1). The difference between the order of V^α_HOMO–1 and V^α_HOMO reflects the difference between the distribution pattern of Δρ_HOMO–1 and Δρ_HOMO.

Fig. 5(a) shows Δρ_HOMO–1 for Au₂DMcT. In contrast to Δρ_HOMO (Fig. 3(a)), Δρ_HOMO–1 is largely distributed on the S1 and Au1 atoms and is not largely distributed on the middle of the C1–N1 bond. Moreover, Δρ_HOMO–1 is larger on the C1 atom than on the N1 atom. Hence, vibronic coupling in the sate |Ψ⁺_HOMO–1〉 is strong around the S1, C1, and Au1 atoms compared with that in the sate |Ψ⁺_HOMO〉.

Fig. 5 (a) Electron-density difference Δρ_HOMO–1 for Au₂DMcT at an isosurface value of 0.01 a.u.; (b) v₃, (c) v₅, and (d) v₆ of Au₂DMcT at an isosurface value of 0.02 a.u. Numbers in (b–d) are atomic vibronic coupling constants V^α_HOMO–1,A (10⁻⁴ a.u.).

Fig. 5(b–d) shows v₃ (S–Au stretching), v₅ (C–S–C bending), and v₆ (S–C–N bending) for Au₂DMcT. v₃ overlaps with Δρ_HOMO–1 on the S1 and S2 atoms, which leads to the large AVCCs of the S1 and S2 atoms; v₅ overlaps with Δρ_HOMO–1 on the S1 and N1 atoms, which leads to the large AVCCs of the S1 and N1 atoms; v₆ overlaps with Δρ_HOMO–1 on the C1 atom, which leads to the large AVCC of the C1 atom. The large V^α_HOMO–1 of the a(8) mode is due to the significant overlap between Δρ_HOMO–1 and v₈ on the C1 and N1 atoms.

Inelastic electron tunneling spectra

The energy levels of HOMO of Au₂DMcT and Au₂TTF-DT are −6.08 and −5.16 eV, respectively, and the HOMO is the closest to the Fermi level of the electrode (–5.53 eV). An energy gap between the Fermi level of the electrode and the HOMO is small for the Au/TTF-DT/Au junction, suggesting that a carrier transport occurs more efficiently through the Au/TTF-DT/Au junction than through the Au/DMcT/Au junction.

For the Au/DMcT/Au junction, τ_L/R was scaled to produce the experimental conductance⁶ (0.008G₀ at V_b = 0.2 V) and for the Au/TTF-DT/Au and Au/Th-DT/Au junctions, the same τ_L/R value was used. We calculate the IET spectra for the Au/DMcT/Au junction assuming that an electron tunneling occurs through the HOMO and next HOMO. The two molecular orbitals belong to different irreducible representations: the HOMO and next HOMO are the a₂ and b₁ orbitals, respectively. Therefore the off-diagonal VCCs vanish:

Hence, λ^α is a diagonal matrix.

Fig. 6(a) shows calculated IET spectra for the Au/DMcT/Au junction at T = 4.2, 10, and 20 K. At T = 4.2 K, the a(4), a(5), a(7), and a(8) modes show peaks. At T = 10 and 20 K, the peak due to the a(5) mode is not seen clearly because of the thermal broadening of the peak, that is, the broadening of the Fermi distribution function f_L/R.

Fig. 6 (a) Calculated inelastic electron tunneling spectra for Au/DMcT/Au junction at various temperatures. The solid line shows the spectrum at T = 4.2 K; dashed line shows the spectrum at T = 10 K; dot-dashed line shows the spectrum at T = 20 K. (b) Comparison of calculated and experimental inelastic electron tunneling spectra for Au/DMcT/Au junction at T = 4.2 K. Solid line shows the calculated spectrum; dotted line shows the experimental spectrum.⁶ (c) Calculated inelastic electron tunneling spectra for Au/DMcT/Au junction at T = 4.2 K assuming that the electron tunneling occurs through only the HOMO.

Calculated full-width at half-maximum (FWHM) of the peak of the N–N stretching mode (the a(7) mode) is 8, 11, and 23 mV, respectively, at T = 4.2, 10, and 20 K. These values are small compared with the experimental data (25, 30, 38 mV, respectively).⁶ In our calculation, only the thermal broadening influences the peak widths. The difference between the theoretical and experimental peak widths may originate primarily from instrumental broadening.

Fig. 6(b) shows comparison of the calculated and experimental IET spectra for the Au/DMcT/Au junction at T = 4.2 K. The experimental d²I/dV_b² values are scaled to fit the calculated spectrum at V_b = 127 mV (the peak position of the N–N stretching mode). Peaks corresponding to the a(4), a(5), a(7), and a(8) modes were observed experimentally.⁶ In the experimental spectrum, d²I/dV_b² has a large value near the zero-bias region, which is called the zero-bias anomaly.⁵ The zero-bias anomaly may originate from phonon scattering in the electrodes. For V_b > 0.05 V, the order of the relative intensity of the spectra agrees well. The relative intensity increases in the order: a(5) < a(7) < a(8). By comparing the spectra, the intensity for the a(5) mode (C1–S2 stretching) is underestimated, while that for the a(8) mode (C1–N1 stretching) is overestimated.

Fig. 6(c) shows the calculated IET spectrum for the Au/DMcT/Au junction at T = 4.2 K assuming that the electron tunneling occurs through only the HOMO. Comparing Fig. 6(c) with Fig. 6(b), the two calculated IET spectra are almost identical. This is because the difference between the orbital energy of the next HOMO (–7.07eV) and the Fermi energy of the electrode (–5.53 eV) is large and the vibronic couplings in the state |Ψ⁺_HOMO–1〉 make little contribution to the IET spectrum. This result suggests that an inelastic electron tunneling occurs mainly through the HOMO. For the Au/TTF-DT/Au and Au/Th-DT/Au junctions, we consider the inelastic electron tunneling via only the HOMO.

Fig. 7 shows calculated IET spectrum for the Au/TTF-DT/Au junction at 4.2 K. The a(10), a(19), and a(20) modes show strong peaks. Peaks due to the a(10), a(15), and a(20) modes were observed experimentally for Au/TTF/Au junction.²¹ Although the a(19) mode has the large VCC, since the peak position of the mode is close to that of the a(20) mode, the peak of the a(19) mode would be superimposed with the peak of the a(20) mode and would not be observed in the experimental IET spectrum.

Fig. 7 Calculated inelastic electron tunneling spectrum for Au/TTF-DT/Au junction at T = 4.2 K.

Comparison of IET spectra for the Au/Th-DT/Au and Au/DMcT/Au junctions

Molecular structure of Th-DT is similar to that of DMcT (nitrogen atoms in DMcT are replaced by –CH– groups in thiophene). Although there is no experimental assignment of IET spectra for the Au/Th-DT/Au junction, it is meaningful to compare the spectra for the Au/Th-DT/Au junction with that for the Au/DMcT/Au junction.

Fig. 8 shows calculated IET spectra for Au/Th-DT/Au junction at T = 4.2 K. The major difference between the IET spectra for the Au/Th-DT/Au and Au/DMcT/Au junctions is the presence of the peak due to the a(13) mode (169 mV, Fig. 9(a)). The a(13) mode contains C2–C2′ stretching and C1–C2–H1 in-plane bending vibrations. For the Au/Th-DT/Au junction, two peaks are observed around 160 mV. In contrast, for the Au/DMcT/Au junction, only one peak is observed. Hence, thiophene and DMcT can be distinguished by the peak of the a(13) mode.

Fig. 8 Calculated inelastic electron tunneling spectrum for Au/Th-DT/Au junction at T = 4.2 K.

Fig. 9 (a) The a(13) mode of Au₂Th-DT; (b) derivative of nuclear–electronic potential v₁₃ (= 0.02 a.u.); (c) electron-density difference Δρ_HOMO (= 0.005 a.u.) of Au₂Th-DT.

The a(13) mode contains displacements of the C1, C2 and H1 atoms, and v₁₃ is large on the C2–C2′ bond and around the C1 and H1 atoms (Fig. 9(b)). Δρ_HOMO is also large around the C1 and C2 atoms (Fig. 9(c)). Hence, Δρ_HOMO overlaps significantly with v₁₃ on the C1 and C2 atoms. This is why the a(13) mode has a large VCC and shows the strong peak in the IET spectrum.

The IET spectrum for Au/Th-DT/Au junction is similar to that for the Au/DMcT/Au junction (Fig. 6(a)). This similarity originates from the similarity in the molecular structures and Δρ_HOMO distributions. Since Δρ_HOMO for Au₂Th-DT is distributed on the C1, C2, and S2 atoms, vibrational modes in which these atoms are displaced show intense peaks; S–Au stretching mode (the a(5) mode, 44 mV), C–C stretching mode (the a(11) mode, 133 mV), and C=C stretching mode (the a(12) mode, 155 mV).

Conclusions

We calculated the VCDs for Au₂DMcT and Au₂TTF-DT cations. The VCD analysis enables us to understand the relative order of the VCCs. For Au₂DMcT, since Δρ_HOMO is large on the C–N bond, the C–N stretching mode couples strongly to the electronic state; for Au₂TTF-DT, since Δρ_HOMO is large on the central C=C bond, the C=C stretching modes couple strongly to the electronic state.

We calculated the IET spectra for Au/DMcT/Au and Au/TTF-DT/Au junctions using the NEGF theory. We calculated the IET spectrum for the Au/Th-DT/Au junction and compared it with that for the Au/DMcT/Au junction. Th-DT and DMcT can be distinguished using the IET spectroscopy by the peak of the C–C stretching mode. The VCD analysis can be an effective way to understand relative intensities in IET spectra.

Acknowledgements

The authors thank Prof. Masateru Taniguchi (The Institute of Scientific and Industrial Research, Osaka University) for helpful discussions and allowing us to present his experimental data. Numerical calculations were performed partly at the Supercomputer Laboratory of Kyoto University and Research Center for Computational Science, Okazaki, Japan. This work was supported by a Grant-in-Aid for Scientific Research (C) (20550163), Priority Areas “Molecular theory for real systems” (20038028) from the Japan Society for the Promotion of Science (JSPS). This work was also supported in part by the Global COE Program “International Center for Integrated Research and Advanced Education in Materials Science” (No. B-09) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, administered by JSPS.

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