Supplementary Information. Exploiting the Extended π-system of Perylene Bisimide for Label-free Single-Molecule Sensing
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1 Electronic Supplementary Material (ESI) for Journal of Materials Chemistry C. This journal is The Royal Society of Chemistry 205 Supplementary Information. Exploiting the Extended π-system of Perylene Bisimide for Label-free Single-Molecule Sensing Qusiy Al-Galiby, Iain Grace, Hatef Sadeghi and Colin Lambert* Physics Department, Lancaster University, LA 4YB UK Py-PBI HOMO LUMO
2 apy-pbi HOMO LUMO
3 S-PBI HOMO LUMO
4 P-PBI HOMO LUMO
5 Cl-PBI HOMO LUMO Figure S. Frontier molecular orbitals of the all perylene bisimide derivatives obtained using the DFT code SIESTA. Red corresponds to positive and blue to negative regions of the wave functions. (a) (b) (c) (d) (e) Figure S2. Optimized configurations of the single molecules (a) apy-pbi, (b) Py-PBI, (c) P- PBI, (d) Cl-PBI, and (e) S-PBI attached to two metallic leads.
![Side group with eigenvalue ε It can be shown [33] that the transmission coefficient for such a combination is given by E ε 4ΓΓ * E ε 2 2 (Γ Γ 2 2) (S) A plot of](/docs-images/94/119867805/images/6-1.jpg "this expression is shown in figure S5. 0.8 TBM 0.6 0.4 0.2 Destructive Interfer. = -.5, =0.5 = 0.24 = 0.4 = 0.04 0-3 -2.5-2 -.5 - -0.5 0 0.5.5 2 2.")
6 The origin of Fano resonaces To illustrate the origin of Fano resonances, consider the sketch showing a bound state (blue) of energy ε, coupled to an extended backbone state (brown) of energy ε by a coupling matrix element. Side group with eigenvalue ε It can be shown [33] that the transmission coefficient for such a combination is given by E ε 4ΓΓ * E ε 2 2 (Γ Γ 2 2) (S) A plot of this expression is shown in figure S TBM Destructive Interfer. = -.5, =0.5 = 0.24 = 0.4 = Energy (ev) Figure S3. A plot of equation S for values of the level broadening due to the contacts of Γ = 0., Γ 2 = 0..
7 E-5 apy-pbi Py-PBI S-PBI P-PBI Cl-PBI I/I0 6E-5 4E-5 2E Voltage (V) Figure S4. DFT calculations for the corresponding results for the room-temperature current as a function of the voltage for the five perylene bisimides in case.
8 Figure S5. DFT calculations of the transmission coefficients as a function of energy for Py- PBI with different configurations of the single-molecules absorbates (a) TCNE, (b) TNT, and (c) BEDT-TTF, and (the pink line) is case.. The fourth figure (d) shows the average of current as a function of voltage at T=300K which pass across Py-PBI with three analytes molecules (TCNE, TNT, and BEDT-TTF), where the error bars in figure S5d shows the standard deviation in the means of the currents.
9 Figure S6. DFT calculations of the transmission coefficients as a function of energy for P- PBI with different configurations of the single-molecules absorbates (a) TCNE, (b) TNT, and (c) BEDT-TTF, and (the pink line) is case.. The fourth figure (d) shows the average of current as a function of voltage at T=300K which pass across P-PBI with three analytes molecules (TCNE, TNT, and BEDT-TTF), where the error bars in figure S6d shows the standard deviation in the means of the currents.
10 Figure S7. DFT calculations of the transmission coefficients as a function of energy for apy-pbi with different configurations of the single-molecules absorbates (a) TCNE, (b) TNT, and (c) BEDT-TTF, and (the pink line) is case.. The fourth figure (d) shows the average of current as a function of voltage at T=300K which pass across apy-pbi with three analytes molecules (TCNE, TNT, and BEDT-TTF), where the error bars in figure S7d shows the standard deviation in the means of the currents.
11 Figure S8. DFT calculations of the transmission coefficients as a function of energy for Cl- PBI with different configurations of the single-molecules absorbates (a) TCNE, (b) TNT, and (c) BEDT-TTF, and (the pink line) is case.. The fourth figure (d) shows the average of current as a function of voltage at T=300K which pass across Cl-PBI with three analytes molecules (TCNE, TNT, and BEDT-TTF), where the error bars in figure S8d shows the standard deviation in the means of the currents.
12 (a ) (b ) (c ) (d ) Figure S9. DFT calculations of the transmission coefficients as a function of energy for S- PBI with different configurations of the single-molecules absorbates (a) TCNE, (b) TNT, and (c) BEDT-TTF, and (the pink line) is case. The fourth figure (d) shows the average of current as a function of voltage at T=300K which pass across S-PBI with three analytes molecules (TCNE, TNT, and BEDT-TTF), where the error bars in figure S9d shows the standard deviation in the means of the currents.
13 <G/G0> e 06 Py-PBI with TCNE with TNT with BEDT-TTF <G/G0> e 06 apy-pbi with TCNE with TNT with BEDT-TTF e 08 e 08 <G/G0> e 06 e E F -E S-PBI with TCNE with TNT with BEDT-TTF <G/G0> e 06 e E F -E P-PBI with TCNE with TNT with BEDT-TTF <G/G0> e E F -E Cl-PBI with TCNE with TNT with BEDT-TTF E F -E e E F -E Figure S0. The room-temperature, configurationally-averaged as a function of Fermi energy for three analyte molecules (TCNE, TNT, and BEDT-TTF) absorbed on five PBI molecules.
14 Locating the optimal value of E F The optimal value of E F was chosen by minimising the quantity Y 2 (E F ) = 5 i = (Log(G theo ) Log(G exp i i )) 2 (S2) G theo Where i is the theoretical conductance for a given E F and i is the experimental conductance reported in ref [2], where i labels the PBIs. This mean-square deviation between theory and experiment is plotted in figure S8 and shows a minimum at E F = 0.08eV, which is the values chosen throughout this paper. G exp 0 Y E F (ev) Figure S. The mean square deviation of theory from the experiment as a function of Fermi energy.
15 Evaluating of error in the currents for a distribution of geometries The error value of the 24 current curves is given by σ m = σ/ 24 (S3) σ = (I i I ) 2 i = (S4) where σ m is standard deviation in the mean of current I.
16 Classification of the amount of charge-transfer complex In particular we used the customised basis set definitions to investigate the effects on the Mulliken population count in SIESTA when using the generalized gradient approximation (GGA-PBE) for the exchange and correlation (GGA) [], but we also made these calculations with the local density approximation (LDA-CA) [2] and van der waals interactions. The Hamiltonian and overlap matrices are calculated on a real-space grid defined by a plane-wave cutoff of 50 Ry. Each PBI molecule with three analytes which are (TCNE, BEDT-TTF, and TNT) are relaxed into the optimum geometry until the forces on the atoms are smaller than 0.02 ev/å. Tolerance of Density Matrix is 0-4, and in case of the isolated molecules a sufficiently-large unit cell was used. For steric and electrostatic reasons. Table S. shows DFT calculation of charge- transfer complex and binding energy of TCNE which is analyzed around the backbone of five PBI molecules where all configurations were found in optimum position among 24 configurations for each PBI molecule. Py+TCNE apy+tcne S+TCNE P+TCNE Cl+TCNE GGA Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV) LDA Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV) Vdw Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV)
17 Table S2. shows DFT calculation of charge- transfer complex and binding energy of BEDT- TTF which is analyzed around the backbone of five PBI molecules where all configurations were found in optimum position among 24 configurations for each PBI molecule. Py+BEDT-TTF apy+ BEDT-TTF S+ BEDT-TTF P+ BEDT-TTF Cl+ BEDT-TTF GGA Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV) LDA Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV) VdW Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV)
18 Table S3. shows DFT calculation of charge- transfer complex and binding energy of TNT which is analyzed around the backbone of five PBI molecules where all configurations were found in optimum position among 24 configurations for each PBI molecule. Py+TNT apy+tnt S+TNT P+TNT Cl+TNT GGA Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV) LDA Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV) Vdw Q E(eV) Q E(eV) Q E(eV) Q E(eV) Q E(eV)
19 (a) (d) (b) (e) (c) Figure S2. Optimized configurations of a single TCNE adsorbed on (a) Py-PBI, (b) apy- PBI, (c) S-PBI, (d) P-PBI, and (e) Cl-PBI attached to two metallic leads. (a) (d) (b) (e) (c) Figure S3. Optimized configurations of a single TNT adsorbed on (a) Py-PBI, (b) apy-pbi, (c) S-PBI, (d) P-PBI, and (e) Cl-PBI attached to two metallic leads.
20 (a) (d) (b) (e) (c) Figure S4. Optimized configurations of a single BEDT-TTF adsorbed on (a) Py-PBI, (b) apy-pbi, (c) S-PBI, (d) P-PBI, and (e) Cl-PBI attached to two metallic leads.
21 (a) with TCNE 0.0 (b) with TNT e e 06 e E-E E-E (c) with BEDT-TTF I/I (d) with TCNE with TNT with BEDT-TTF e e E-E Voltage (V) Figure S5. DFT calculations using LDA approximation of the transmission coefficients as a function of energy at T=0K for optimum configuration of Py-PBI with (a) TCNE, (b) TNT, and (c) BEDT-TTF. The fourth figure (d) shows the current as a function of voltage at T=300K for the Py-PBI and in the presence of the three analyte molecules (TCNE, TNT, and BEDT-TTF).
22 e 05 (a) with TCNE e E-E (b) with TNT E-5 E-6 E-7 E E-E F DFT (ev) E-5 E-6 (c) with BEDT-TTF E-7 2E E-E F DFT (ev) I/I (d) +TCNE +TNT +BEDT-TTF Voltage (V) Figure S6. DFT calculations using LDA approximation of the transmission coefficients as a function of energy at T=0K for optimum configuration of S-PBI with (a) TCNE, (b) TNT, and (c) BEDT-TTF. The fourth figure (d) shows the current as a function of voltage at T=300K for the S-PBI and in the presence of the three analyte molecules (TCNE, TNT, and BEDT-TTF).
23 e 06 e 08 (a) with TCNE E-E (b) with TNT E-5 E-6 E-7 E-8 E E-E F DFT (ev) (c) with BEDT-TTF I/I e 05 (d) with TCNE with TNT with BEDT-TTF e 06 e E-E Voltage (V) Figure S7. DFT calculations using LDA approximation of the transmission coefficients as a function of energy at T=0K for optimum configuration of P-PBI with (a) TCNE, (b) TNT, and (c) BEDT-TTF. The fourth figure (d) shows the current as a function of voltage at T=300K for the P-PBI and in the presence of the three analyte molecules (TCNE, TNT, and BEDT-TTF).
24 0.0 (a) with TCNE (b) with TNT e 05 e 06 e E-E e E-E 0.0 (c) with BEDT-TTF (d) with TCNE with TNT with BEDT-TTF I/I 0 5e 05 e 06 e E-E Voltage (V) Figure S8. DFT calculations using LDA approximation of the transmission coefficients as a function of energy at T=0K for optimum configuration of Cl-PBI with (a) TCNE, (b) TNT, and (c) BEDT-TTF. The fourth figure (d) shows the current as a function of voltage at T=300K for the Cl-PBI and in the presence of the three analyte molecules (TCNE, TNT, and BEDT-TTF).
25 (a) with TCNE (b) with TNT e 05 e 05 e 0 e E-E E-E 0.0 (c) with BEDT-TTF e 05 (d) e 06 e 08 I/I 0 5e 06 +TCNE) +TNT BEDT-TTF e E-E Voltage (V) Figure S9. DFT calculations using LDA approximation of the transmission coefficients as a function of energy at T=0K for optimum configuration of apy-pbi with (a) TCNE, (b) TNT, and (c) BEDT-TTF. The fourth figure (d) shows the current as a function of voltage at T=300K for the apy-pbi and in the presence of the three analyte molecules (TCNE, TNT, and BEDT-TTF). It is interesting to note that the behaviour of the ensemble average is qualitatively differenet from the ensemble average. Figure S9 shows the transmission coefficient for the molecule apy-pbi, in the absence and presence of the analytes. It is clear that the conductance in the presence of the analytes in their optimal binding configurations is lower than in the case of molecule. In contrast, figure S7 shows that the ensemble-averaged conductance, is higher in the presence of the analytes.
26 Quantifying the sensitivity of the PBIs for discriminating sensing. To quantify the potential of the five PBI derivatives (labeled j=,, 5) for the discriminating sensing of the three analytes TCNE, TNT and BEDT-TTF, (labeled n=,2,3) we calculated the ensemble-averaged, room-temperature currents I jn as a function of voltage V and computed the following correlators of the currents A nm j = V/2 dv(i jn (V) I jm (V)) 2 V/2 (S5) These were then normalized by the squared currents of the backbones to yield the quantities: X nm j = A nm j V/2 dv(i j (V )) 2 V/2 (S6) For n m, table shows the values of X nm j obtained for V=volt. Clearly, as defined, X nm j = 0 when n = m. In practice, a sensing event would involve measurement of a new set of curves (I jm (V) in equation 2) and combining these with a calibration set of curves (I jn (V) in equation 2), in which case X nm j would be small but not zero when n = m. Table. The values of Xnm j J PBIs X 2 j X 3 j X 23 j apy-pbi Cl-PBI P-PBI Py-PBI S-PBI SUM
27 Table and figure 4 shows the value of X nm j when n m. Ideally, to avoid false positives, these numbers should be as large as possible and since they are largest for Py-PBI, we conclude that Py-PBI is the best individual sensor. Nevertheless, for the most accurate discriminating sensing, the fingerprint of an analyte across all five backbones should be used. X TNT 2 TCNE 3 BEDT-TTF Figure 4. Comparison between the normalized correlators X nm j where n labels the three analytes (TNT, TCNE, and BEDT-TTF) and j labels the five PBIs. V=.0 volts. Movies The following movies show the different configurations of the analytes on the PBI backbones, used to compute the transmission curves of figure 8 a-c and the I-V curves of figure 8d. BEDT-TTF-PBI.mpg TCNE-PBI.mpg TNT-PBI.mpg
28 References. Perdew, J.P., K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple. Physical review letters, (8): p Perdew, J.P. and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy. Physical Review B, (23): p
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