Modeling ion sensing in molecular electronics Caroline J. Chen, Manuel Smeu, and Mark A. Ratner Citation: The Journal of Chemical Physics 140, 054709 (2014); doi: 10.1063/1.4863860 View online: http://dx.doi.org/10.1063/1.4863860 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Theoretical investigation on the chemical sensing of metalloporphyrin-based molecular junction J. Chem. Phys. 132, 244702 (2010); 10.1063/1.3456542 Spin filter effect of manganese phthalocyanine contacted with single-walled carbon nanotube electrodes J. Chem. Phys. 132, 054703 (2010); 10.1063/1.3302258 Benchmarking the performance of density functional theory based Green’s function formalism utilizing different self-energy models in calculating electronic transmission through molecular systems J. Chem. Phys. 125, 204717 (2006); 10.1063/1.2397676 Analysis on the contribution of molecular orbitals to the conductance of molecular electronic devices J. Chem. Phys. 125, 194113 (2006); 10.1063/1.2388272 Intermolecular effect in molecular electronics J. Chem. Phys. 122, 044703 (2005); 10.1063/1.1825377
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THE JOURNAL OF CHEMICAL PHYSICS 140, 054709 (2014)
Modeling ion sensing in molecular electronics Caroline J. Chen,a) Manuel Smeu,b) and Mark A. Ratnerc) Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
(Received 12 September 2013; accepted 17 January 2014; published online 6 February 2014) We examine the ability of molecules to sense ions by measuring the change in molecular conductance in the presence of such charged species. The detection of protons (H+ ), alkali metal cations (M+ ), calcium ions (Ca2+ ), and hydronium ions (H3 O+ ) is considered. Density functional theory (DFT) is used within the Keldysh non-equilibrium Green’s function framework (NEGF) to model electron transport properties of quinolinedithiol (QDT, C9 H7 NS2 ), bridging Al electrodes. The geometry of the transport region is relaxed with DFT. The transport properties of the device are modeled with NEGF-DFT to determine if this device can distinguish among the M+ + QDT species containing monovalent cations, where M+ = H+ , Li+ , Na+ , or K+ . Because of the asymmetry of QDT in between the two electrodes, both positive and negative biases are considered. The electron transmission function and conductance properties are simulated for electrode biases in the range from −0.5 V to 0.5 V at increments of 0.1 V. Scattering state analysis is used to determine the molecular orbitals that are the main contributors to the peaks in the transmission function near the Fermi level of the electrodes, and current-voltage relationships are obtained. The results show that QDT can be used as a proton detector by measuring transport through it and can conceivably act as a pH sensor in solutions. In addition, QDT may be able to distinguish among different monovalent species. This work suggests an approach to design modern molecular electronic conductance sensors with high sensitivity and specificity using well-established quantum chemistry. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4863860] I. INTRODUCTION
With the continuing advancement of silicon-based electronic devices and recent progress in nano-technology, device components are rapidly approaching the molecular scale.1–5 In terms of theoretical modeling, the methodology and framework to simulate and predict the properties of molecular electronic devices have been developed and extended to include sophisticated transport mechanisms and to capture complex phenomena,6–15 although complications persist.16, 17 The systems considered mostly consist of a single or few molecules providing the pathways for electrons to move between two metal electrodes. Chemical modification of the molecules in molecular devices may alter the current passing through them. It is natural to utilize this change in current by chemical modification for the purpose of detection. These putative molecular sensors could be used for certain entities without false positives, possessing essential chemical specificity, and yielding a detectable change in current after chemical recognition. The single-molecule molecular electronic sensor brings together two advances in modern technology: cutting-edge electronics and nano-engineering. Nanotechnology permits measuring specific chemical interactions at the singlemolecule level. The electric signal caused by chemical modia) Work done while attending New Trier Township High School, 385
Winnetka Avenue, Winnetka, Illinois 60093, USA. Current address: Columbia College, Columbia University, 1130 Amsterdam Avenue, New York, New York 10027, USA. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] c) Electronic mail: [email protected]
0021-9606/2014/140(5)/054709/7/$30.00
fications/interactions can be detected and measured quantitatively with modern electronics, as routinely seen in scanning tunneling microscopy studies. Therefore, the single molecule sensor/detector can be used as a specific and sophisticated chemical measuring device. Progress has been made in the area of sensors composed of single-molecule junctions. An example includes experimental work showing that the conductance of single peptide molecules, upon binding with transition-metal ions such as Cu2+ and Ni2+ , can change depending on the sequence and length of the peptides.18 Theoretical work has also shown that the presence of the side groups of oxygen and bipyridine on molecules of 2.5 nm length, consisting of fluorine units, can lead to Fano resonance,19 which can result in changes in electron transport.20 More recently, a bis(2-pyridylmethyl)amine (BPA) model sensor has been studied to detect Zn, Fe, Ni, and Cu ions by measuring changes in conductance when coupled to a gold two-probe junction; however, in this study, the Au(111)-DTBPA-Au(111) structure was not relaxed.21 That study focused on a molecule with an inherently low conductance due to its lacking an extended π -system and lacking planarity; the gap between the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO gap) is drastically affected by the presence of metal ions. Here, quinolinedithiol (QDT, C9 H7 NS2 ) is chosen as the sensor molecule. This molecule is small enough to be simulated reasonably well by first-principles computational approaches, and it possesses several advantages. QDT has a planar molecular structure with fused rings and π -type molecular
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FIG. 1. Two-probe structure of QDT sandwiched between two Al electrodes (cyan=C, white=H, blue=N, yellow=S). Left and right electrodes are semiinfinite, extending to left and right. The central region contains QDT and some electrode buffer layers (between the vertical solid and dashed lines on either side). The red circle shows the region where the ion is placed. A denotes the four-atom layer and B denotes the five-atom layer (see Fig. 2).
orbitals (see Fig. 1). In general, molecules with π -type orbitals have a smaller HOMO-LUMO gap than molecules having only σ -type molecular orbitals, usually resulting in greater electrical conductance through them. In addition, QDT has thiol groups at the two ends, which interact strongly with noble metal electrodes. The molecule has a nitrogen atom within the conjugated network that can bind positively charged ions to its lone pair. Here we investigate whether the QDT molecule can be used to differentiate between different monovalent cations. The insights gained can then be used to design molecules capable of efficient detection of relevant ions. The computational technique has been well-developed and is welldocumented.7, 8, 22–27 Here, however, we apply the methodology to detection. The same approach might be used to design molecular sensors for detecting a wide range of agents, including multivalent ions, chemical groups, and possibly even larger species such as protein fragments, viruses, or bacteria.
II. THEORETICAL METHODS
The entire model sensor system consists of three parts: left electrode, right electrode, and the central/scattering region (see Fig. 1). The left and right electrodes are identical and composed of aluminum atoms that extend to infinity in both the left and right directions. Other metals, such as gold, could be used due to the ability of sulfur to bind with noble metals relatively strongly. However, for the convenience of modeling, aluminum is used here since the main purpose of this work is to investigate the sensing property of the organic molecule. In this study, the electrodes are quasi-onedimensional aluminum wires having a 3 × 3 cross section, composed of periodic units repeating along the face-centeredcubic (001) direction. The repeating sub-unit consists of four layers that alternate between containing four and five aluminum atoms. In Fig. 1, the four-atom layer is labeled as A, and the five-atom layer as B. Figure 2 depicts the view down the wire, with just the S and the nearest two Al layers. Binding occurs at the hollow site from computational minimization, which is centered above the four-atom layer, where the sulfur atom in the molecule is coordinated to the four aluminum atoms. In the computation, the coordinates of the atoms in the electrodes are fixed by the aluminum lattice structure, with a lattice constant of 4.05 Å.
The “central region,” which is modeled with density functional theory (DFT) within the Keldysh non-equilibrium Green’s function (NEGF) framework, includes a few layers of each electrode. Because the left and right electrodes are identical, it is necessary for there to be an asymmetry in the number of buffer layers on the left and right sides of the central region (see Fig. 1). In this way, both the sulfur atoms on the two sides of the molecule can bind to the hollow site above the four-atom layer labeled A in Fig. 1. These buffer regions allow for a smooth transition between the electronic density and potential in the periodic electrodes to those of the extended molecule. The aluminum crystal lattice constant is used so that the buffer layers act as a continuation of the electrodes. The central region consists of the organic molecule sensing candidate (QDT) bound to the buffer layers, following the “extended molecule” scheme.28 In this region, a proton or an alkali metal cation, shown as a red spot in Fig. 1, was initially placed close to the nitrogen atom, and then relaxed (for simplicity, no solvent is included). The relaxation (energy minimization) of the entire system was carried out with the GAMESS29 package at the B3LYP/6-31G(d)30, 31 level of theory to obtain the optimal structure. The geometry optimizations were carried out on the Al4 QDT-Al4 subunit of the molecular sensing region. An initial specific distance for Al electrode-electrode separation was
FIG. 2. View down the wire. The orange atoms are a part of the four-atom layer labeled A in Fig. 1 which is nearest to the S atom, and the green atoms, the five-atom layer labeled B in Fig. 1. The white center atom is sulfur.
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chosen. At this separation, the molecule is allowed to relax while the Al atoms are fixed at their crystal lattice positions. Relaxations at various Al electrode-electrode separations are carried out to find the value that yields the minimum total energy, where the Al electrode-electrode separation is defined as the distance between the two closest Al buffer layers on each side of the molecule. The energy minimum is found for the Al electrode-electrode separation of 12.10 Å. At this geometry, the closest Al-S distance is 2.68 Å. For the systems containing cations, an ion was initially placed near the nitrogen atom in the minimized Al4 -QDT-Al4 subsystem; the entire subsystem is then relaxed again at the fixed Al electrode-electrode separation. These relaxations allow for QDT to adopt the appropriate geometry in the presence of each ionic species. Any changes in conductance properties can then be attributed to the presence of a given ion. The Nanodcal package7, 8 was used to obtain the quantum transport properties. Nanodcal – a nano-electronic device calculator – is a computational package to calculate non-equilibrium quantum transport properties of two-probe systems (see Fig. 1). It uses pseudopotentials to describe the core electrons, and fully treats the valence electrons, calculating the transport properties using real space DFT analysis using the local density approximation within the Keldysh nonequilibrium Green’s function framework. We should point out that, since Nanodcal uses the local density approximation, it only takes into consideration the electronic density at each point in space. More advanced (hybrid) functionals are not yet implemented into our NEGF-DFT code due to their complexity and computational cost. With this in mind, the work aims to study the ion sensing abilities of the organic molecule as a simple, semi-quantitative model. In Nanodcal, the electronic quantum states are determined from the system Hamiltonian, using DFT. The density matrix is constructed by populating the states with appropriate statistics. Fermi-Dirac statistics are used for the equilibrium situation, while NEGF is used to determine the non-equilibrium quantum statistics of the transport system. Specifically, the transmission function, which represents the probability for an electron to successfully move from one electrode to the other, is calculated by9 T (E) = Tr(1 G2 G† ) ,
(1)
where is the broadening matrix at each electrode, related to the imaginary part of the self-energy matrix by = i( − † ) .
Landauer-Büttiker equation32 2e μ2 I (V ) = T (E)dE , h μ1
(4)
where e is the electron charge, h is Planck’s constant, and μ1 and μ2 denote the chemical potentials of the two electrodes. In summary, the systems studied are relaxed with GAMESS (energy-minimized to obtain the optimal structure), and then the transport properties are calculated by Nanodcal. III. RESULTS AND DISCUSSION
The properties of the organic QDT molecule are first studied. For QDT, the HOMO energy level is calculated to be at −5.39 eV and the LUMO energy at −2.86 eV, relative to the vacuum level, giving a HOMO-LUMO gap of 2.53 eV. Figure 3 shows a visual representation of the frontier KohnSham orbitals of QDT. The π bonds are clear because there is a node in the molecular plane. The HOMO and LUMO levels of QDT are made up of π orbitals that extend along the entire molecule. The transmission calculations are first performed for the control system (QDT alone). Figure 4 shows the transmission as a function of energy for the control system. The transmission spectra are calculated for different bias voltages applied to the right electrode with the left electrode remaining electrically grounded. These different biases are from −0.5 V to 0.5 V at increments of 0.1 V.33 For a given bias, the transmission curve has one main peak in the [−1.0, 1.0] eV energy window. The transmission spectra for the systems with the various ions behave similarly. To investigate which molecular orbitals mainly contribute to the transmission peaks, the scattering states are examined. Scattering states7 are analogous to Kohn-Sham eigenstates, but they apply to open-boundary systems such as the twoprobe geometries considered in this work. These represent the pathway of an electron with a given energy passing from one electrode, through the molecule, and into the other electrode. There can be multiple scattering states for each energy point in the transmission spectrum. It is instructive to plot these to identify which have amplitude on both the left and right electrodes, since these will contribute to transmission peaks. Once this is determined, the scattering states can be compared to
(2)
The self-energy is due to the surroundings from the left and right electrodes and accounts for both the broadening of molecular eigenstates and their shift in energy. The broadening and shift are represented by the imaginary and real part of the self-energy, respectively. The Green’s function, G, in the transmission formula is defined by G = [ES − H − 1 − 2 ]−1 ,
(3)
where S is the overlap matrix and H is the Hamiltonian of the extended molecule (“central region” in Fig. 1). Using the transmission function, the current is calculated by the
FIG. 3. Examples of Kohn-Sham orbitals for isolated QDT. (a) The highest occupied molecular orbital and (b) the lowest unoccupied molecular orbital.
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Transmission
1.5 Control H+ Li+ Na+ K+
1
0.5
0 −1
−0.5
0 E − E (eV)
0.5
1
F
FIG. 4. Transmission for different bias voltages, varied from −0.5 V to 0.5 V at 0.1 V increments on the control system (QDT molecule without any ions). The transmission curves for positive, zero, and negative biases are plotted in blue, black, and red, respectively. The leftmost peak corresponds to an applied bias of 0.5 V, and the second rightmost peak to an applied bias of −0.5 V.
the Kohn-Sham orbitals of the isolated molecules in the central region. The molecular orbital is said to be the main contributor to the transmission peak at that energy if its orbital structure matches that of the scattering state. Figure 5 shows an example of this procedure. Scattering state analysis is performed for the control system at 0.29 eV, relative to the EF of the electrodes, the energy value of the transmission peak near EF . Eight scattering states are found at this energy. Of these eight, three have amplitude on both electrodes, one of which is shown in Fig. 5(a). After the comparison of the scattering state to the Kohn-Sham orbital of the isolated molecule, it can be seen that the scattering state matches with the LUMO of the isolated molecule, and it can be said that electron transport primarily occurs through this MO at that energy. Similarly, the analysis shows that the main transmission peaks of the systems with one H+ , Li+ , Na+ , or K+ ion present near the Fermi level correspond to the LUMO of the QDT molecule. However, for the Na+ + QDT system, there is also a contribution from the LUMO+4 of the QDT molecule to the transmission peak. This results in a transmission greater than one within a certain range for the Na+ + QDT system due to nearly degenerate energy levels (see Fig. 6).
FIG. 6. The effect of ions (H+ , Li+ , Na+ , and K+ ) on the transmission through QDT at zero bias. The transmission of the Na+ is greater than one within a certain range due to nearly degenerate energy levels.
A comparison for the transmission spectra at zero bias for all the systems (control, H+ , Li+ , Na+ , and K+ ) from the energy range of [−1.0, 1.0] eV is shown in Fig. 6. The transmission curves for all the systems show one or more peaks. An analysis of scattering state calculations at the energy points of the transmission coefficient peaks is used to find which molecular orbitals contribute most significantly to the peaks near EF at zero bias as described above. The Li+ and K+ systems have an additional peak to the right of their main peaks, both correspond to the LUMO+4 of the QDT molecule. It can also be seen that Na+ causes the biggest transmission peak, while H+ produces the smallest one. The main peaks for H+ , Li+ , Na+ , and K+ are centered around 0.0 eV, while the main peak for the control system is centered at 0.29 eV. This shift is attributed to the electrostatic influence of the ion upon the orbital energetics of the molecule. When a charged species interacts with the N lone pair, which is in the plane of the molecule, it does not destroy the π -system. The effect is similar to that of an electron withdrawing group (in the case of positive ions), resulting in a lowering of the energy levels.27, 34 Ions with the same charge will have a similar effect, with small differences due to the respective size, electronegativity and hardness, which determine the interaction of the ion with the lone pair, and with QDT as a whole. From the transmission, the current can be evaluated (Eq. (4)). The calculated I–V relationship for biases from
FIG. 5. (a) The scattering state with amplitude at both ends for the control system at 0.29 eV. ((b)–(e)) Frontier molecular orbitals for the isolated molecule. The overall structure of the LUMO matches best with all the scattering states.
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J. Chem. Phys. 140, 054709 (2014) TABLE II. Conductance at various biases for different systems. Conductance (μS)
FIG. 7. The I-V relationships for the control, H+ , Li+ , Na+ , and K+ systems. Note that the Li+ data lie directly underneath the Na+ data.
−0.5 V to 0.5 V with increments of 0.1 V is presented in Fig. 7. The current for QDT starts from −2.85 μA at −0.5 V and increases almost linearly to 2.99 μA at 0.5 V. For the H+ , Li+ , Na+ , and K+ , the I-V relationships are less linear. In addition, they show a weak rectification because of the stronger asymmetry of the ion + QDT system, compared to bare QDT. Rectification has also been observed in the work of Xiao et al.,18 for example, which is attributed to the asymmetry of the junction. This was verified by the authors who also studied a symmetric molecular junction containing octanedithiol where rectification was not observed. The (weak) rectification is similarly achieved in this theoretical work, particularly when the ion binds to QDT. Table I summarizes the currents of all systems considered at ±0.5 V biases to show the weak rectification effect. Table I suggests that the goal of ion detection is achieved because the current is nearly three times larger at 0.5 V when an ion is present. However, the I-V relationships for the H+ , Li+ , Na+ , and K+ systems are essentially identical at positive bias, and only with the application of negative bias can they be differentiated. QDT is capable of distinguishing protons from monovalent cations, because the current through H+ + QDT system at negative biases is detectably smaller than those of alkali ion + QDT systems. This is clear from comparing the positions of the transmission peaks relative to EF . The Li+ , Na+ , and K+ systems all have their peaks centered slightly to the right of EF while the peak for the H+ system is centered very slightly to the left of EF . Consequently, the Li+ , Na+ , and K+ systems have a higher conductance at negative bias than at positive bias, while the I/V curve is nearly symmetric for the H+ system. Therefore, while the Li+ , Na+ , and K+ are hard to differentiate, the H+ system can clearly be distinguished from its I-V characteristics. It seems that the QDT molecule TABLE I. Current at ±0.5 V for different systems. Current (μA) Bias (V)
Control
H+
Li+
Na+
K+
0.5 − 0.5
3.0 − 2.9
8.5 − 5.9
8.7 − 11.3
8.3 − 11.3
8.3 − 10.5
Bias (V)
Control
H+
0.5 0.4 0.3 0.2 0.1 0.0 − 0.1 − 0.2 − 0.3 − 0.4 − 0.5
6.0 6.4 6.6 6.7 6.7 6.7 6.6 6.5 6.3 6.1 5.7
16.9 19.8 24.6 32.1 44.5 53.0 35.2 22.3 17.0 13.9 11.9
Li+
Na+
K+
17.3 20.8 25.7 33.2 47.9 64.1 55.8 42.5 33.6 27.3 22.6
16.5 19.9 24.2 30.6 41.5 60.1 55.3 42.5 33.6 27.3 22.6
16.6 20.0 24.4 31.0 42.1 53.8 51.2 38.7 31.1 25.5 21.0
interacts with H+ (lacking any core electrons) differently than with alkali metal ions (with core electrons) of various sizes. The QDT molecule can possibly be used as a pH sensor, but it cannot distinguish among alkali metal cations. The binding of different metal ions to different peptides was also investigated in the experimental work of Xiao et al.18 The measured difference in conductance due to the binding of Cu2+ versus Ni2+ ions shows that this approach can be used to distinguish different metal ions with similar binding configuration to a host peptide molecule. In the present work, it is possible that QDT could differentiate between H+ and the other M+ ions. The conductance at different biases is summarized in Table II. This is obtained by dividing the current by the voltage at that particular data point.35 In the table, the conductance of the control system (QDT) remains nearly constant, while all other systems show sub-linear I-V behavior because of the current saturation at large bias; once the entire transmission peak is inside the integration windows of Eq. (4), larger bias does not increase the current substantially.36 In Xiao’s work,18 the conductance ratio for the peptide with and without the ion varied from 1 to over 300, depending on the peptide and the ion. Here, the ratio (at zero bias) is about 10, as shown in Table II. Of course, a direct comparison cannot be made since the molecules and ions considered are quite different, but the important result of ion sensing is consistent between the experiment and this theoretical work. It should be pointed out that these simulations very approximately address the conditions of an experiment on such systems. Under experimental conditions, the molecular junction and ions would be present in a solution, which would also contain counter ions. While the effect of the counter ions and solvent, which are not included in this work, will influence the conductance result, we believe the major conclusion of ion sensing is valid for the following reasons. Regarding the effect of counter ions, these will have negative charge and will have a repulsive interaction with the lone pair in QDT. Therefore, any effect of negative counter ions on the molecular junction will be minor. In terms of the solvent effect, this will influence the electronic properties of the QDT molecule and screen the charge on the ion.37, 38 However, we believe that the ions will still be detectable, as described in the work of Xiao et al.,18 who showed that molecular junctions
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composed of peptides could detect single ions in solution. In any case, for the situation where we compare similar species (H+ , Li+ , Na+ , and K+ ), the solvent and counter ion effects, to a first approximation, are the same for all those cations, so direct comparisons between them can be made.
Transmission
1
IV. EXTENSION TO DIFFERENT SPECIES
To understand more about the sensing abilities of QDT, the effects of an alkaline earth metal cation, a hydronium ion, and a water molecule on the transmission and current-voltage relationships were also examined. The ability to sense the hydronium ion is of interest because this is a more realistic representation of H+ in water. It is also desirable to know how an H2 O molecule affects the conductance of QDT, since these sensors would likely be immersed in solvent. Calculations on the transmission of the systems sensing H2 O, H3 O+ , and Ca2+ were performed. These systems were relaxed in the same manner as with the H+ , Li+ , Na+ , and K+ systems. For the H2 O and H3 O+ systems, an H is directed towards the lone pair of the N atom in QDT, in a typical Hbonding geometry. Figure 8 shows the transmission spectra of the control, H+ , H3 O+ , and H2 O systems. The control and H2 O containing systems have similar spectra, with the only difference being a slight shift to the left when the H2 O molecule is present. This is reasonable since the H atom in water can be thought of as having a partial positive charge, thereby shifting the transmission peak to the left slightly. The important thing is that the transport properties of QDT are similar when the molecule is in vacuum and when there is a water molecule near the lone pair of the N atom. However, when either H+ or H3 O+ is found near the lone pair of QDT, the transmission peak is shifted to the EF of the electrodes. Scattering state analysis shows that the LUMO of the QDT molecule mainly contributes to the transmission peaks shown in Fig. 8. Because of this drastic change in conductance when H+ or H3 O+ is present, we believe that QDT can conceivably act as a sensitive pH sensor. Figure 9 shows the transmission of Ca2+ system compared to that of the control and K+ systems. The peaks near the Fermi level of the Ca2+ and K+ systems are of comparable size, but there is also a small splitting in the peak of the Ca2+ system. Scattering state analysis for this system revealed that
Transmission
1
Control Ca2+ K+
0.5
0 −1
−0.5
0 E − EF (eV)
0.5
1
FIG. 9. The transmissions for the control, Ca2+ , and K+ systems.
the split transmission peak is due to conductance through the LUMO and LUMO+4 levels of the QDT molecule. V. BINDING ENERGY VALIDATION
Even if the calculated I-V relationship is quite different when the ion to be sensed binds to the lone pair, that interaction has to be reasonably strong for anything to be observed in an experiment. Using the Q-Chem package,39 we calculated the binding energy of various species to QDT in vacuum and in solution by using the Surface and Simulation of Volume Polarization for Electrostatics (SSVPE) implicit continuum solvation model.40 The dielectric constant of water used was 80.1, its value at 20 ◦ C. Table III shows the binding energy of the QDT+X systems, where X is the species being sensed, in vacuum and in solution. The value of H+ is not shown since a proton in aqueous solution is more realistically represented as the hydronium ion, H3 O+ (listed in table). The binding energy is calculated as Ebinding = EQDT+X −EQDT −EX , where EQDT+X is the energy of the QDT+X system, EQDT is the energy of the QDT system, and EX is the energy of the species X. From Table III, it can be seen that all of the binding energy values are negative, showing favorable interaction between QDT and the species in vacuum and in solution. Even more so, the values of the binding energies for the QDT + ion systems are more negative than the binding energy of the QDT + H2 O system. This means that even in the presence of water, QDT will still bind favorably to one of the ions. VI. SUMMARY
Control H+ H3O+
Using NEGF-DFT, we have attempted to test a possible single-molecule electronic sensor, quinolinedithiol, for ions by calculating the change in molecular conductance in the presence of the various charged species. The ions
H2O 0.5
TABLE III. Binding energy (eV) of QDT+X systems.
0 −1
−0.5
0 E − E (eV)
0.5
1
F
FIG. 8. The transmissions for the control, H+ , H3 O+ , and H2 O systems.
X
Li+
Na+
K+
Ca2+
H2 O
H3 O+
Vacuum Water
−2.2 −1.1
−1.6 −0.8
−1.1 −0.6
−4.7 −2.0
−0.4 −0.3
−3.5 −1.6
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considered include protons, alkali metal cations, calcium, and hydronium. The transmission spectra for each of the systems were determined, and scattering state analysis was used to establish which molecular orbitals are the primary contributors to the transmission peaks. Current-voltage relationships were obtained, showing that QDT can distinguish between protons and alkali metal cations, but QDT cannot differentiate among the various metal cations. Finally, the binding energies of all of the systems were calculated in vacuum and in solution to verify whether or not the ions can bind to the N atom, which is necessary if QDT is to act as a sensor in an actual device. While the change in the electrical current depends on many factors, such as the energy levels (including the Fermi energy), orbital hybridization, applied bias, and device geometry, this approach can incorporate these factors to find the maximal change in electric current for detection purposes. Therefore, this approach might be used to design molecular sensors for general purpose detection. ACKNOWLEDGMENTS
The authors thank Mr. Brett Savoie and Mr. Henry Heitzer for helpful discussions. C.J.C. thanks chemistry teacher Mr. Gerald Munley for his encouragement, M.S. thanks the FRQNT, and M.A.R. thanks the National Science Foundation (NSF) (No. CHE-1058896) for financial support. 1 M.
A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science 278, 252 (1997). 2 C. Dekker, Phys. Today 52, 22 (1999). 3 T. Xu, I. R. Peterson, M. V. Lakshmikantham, and R. M. Metzger, Angew. Chem., Int. Ed. 40, 1749 (2001). 4 B. Chen and R. M. Metzger, J. Phys. Chem. B 103, 4447 (1999). 5 C. Kergueris, J.-P. Bourgoin, S. Palacin, D. Esteve, C. Urbina, M. Magoga, and C. Joachim, Phys. Rev. B 59, 12505 (1999). 6 A. Aviram and M. A. Ratner, Chem. Phys. Lett. 29, 277 (1974). 7 J. Taylor, H. Guo, and J. Wang, Phys. Rev. B 63, 245407 (2001). 8 D. Waldron, P. Haney, B. Larade, A. MacDonald, and H. Guo, Phys. Rev. Lett. 96, 166804 (2006). 9 S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, New York, 2005). 10 A. Nitzan and M. A. Ratner, Science 300, 1384 (2003). 11 M. Frei, S. V. Aradhya, M. S. Hybertsen, and L. Venkataraman, J. Am. Chem. Soc. 134, 4003 (2012). 12 P. Darancet, J. R. Widawsky, H. J. Choi, L. Venkataraman, and J. B. Neaton, Nano Lett. 12, 6250 (2012). 13 N. Renaud, Y. A. Berlin, F. D. Lewis, and M. A. Ratner, J. Am. Chem. Soc. 135, 3953 (2013). 14 M. Pavanello, T. Van Voorhis, L. Visscher, and J. Neugebauer, J. Chem. Phys. 138, 054101 (2013). 15 J. Chen, K. S. Thygesen, and K. W. Jacobsen, Phys. Rev. B 85, 155140 (2012).
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Herrmann, G. C. Solomon, J. E. Subotnik, V. Mujica, and M. A. Ratner, J. Chem. Phys. 132, 024103 (2010). 17 M. G. Reuter and R. J. Harrison, J. Chem. Phys. 139, 114104 (2013). 18 X. Xiao, B. Xu, and N. Tao, Angew. Chem., Int. Ed. 43, 6148 (2004). 19 U. Fano, Phys. Rev. 124, 1866 (1961). 20 T. A. Papadopoulos, I. M. Grace, and C. J. Lambert, Phys. Rev. B 74, 193306 (2006). 21 B. Das, J. Phys. Chem. C 113, 16203 (2009). 22 H. Dalgleish and G. Kirczenow, Nano Lett. 6, 1274 (2006). 23 S. Ke, W. Yang, and H. U. Baranger, Nano Lett. 8, 3257 (2008). 24 S. Ke, H. U. Baranger, and W. Yang, J. Am. Chem. Soc. 126, 15897 (2004). 25 Y. S. Park, J. R. Widawsky, M. Kamenetska, M. L. Steigerwald, M. S. Hybertsen, C. Nuckolls, and L. Venkataraman, J. Am. Chem. Soc. 131, 10820 (2009). 26 M. Paulsson, T. Frederiksen, and M. Brandbyge, Nano Lett. 6, 258 (2006). 27 M. Smeu, R. A. Wolkow, and G. A. DiLabio, J. Chem. Phys. 129, 034707 (2008). 28 Y. Xue, S. Datta, and M. A. Ratner, Chem. Phys. 281, 151 (2002). 29 M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, J. Comput. Chem. 14, 1347 (1993). 30 A. D. Becke, J. Chem. Phys. 98, 5648 (1993). 31 C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988). 32 M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Phys. Rev. B 31, 6207 (1985). 33 The effect of the bias on the molecule is fully taken into account via the NEGF-DFT self-consistent approach. The bias is “applied” to the right electrode, meaning that the energy levels of this electrode are shifted appropriately. In the NEGF-DFT implementation, this is represented by an appropriate change to the self-energy, 2 . As indicated in Eqs. (1)–(4), this value affects the calculated Green’s function, transmission function, and the current. 34 L. Venkataraman, Y. S. Park, A. C. Whalley, C. Nuckolls, M. S. Hybertsen, and M. L. Steigerwald, Nano Lett. 7, 502 (2007). 35 At zero bias, the conductance is obtained from the slope from −0.001 V to 0.001 V in the I-V calculations. 36 The slight increase is due to integrating over the tail of the transmission peak. 37 D. P. Long, J. L. Lazorcik, A. M. Brent, M. H. Moore, M. A. Ratner, A. Troisi, Y. Yao, J. B. Ciszek, J. M. Tour, and R. Shashidar, Nat. Mater. 5, 901 (2006). 38 E. Leary, H. Höbenreich, S. J. Higgins, H. Van Zalinge, W. Haiss, R. J. Nichols, C. M. Finch, I. Grace, C. J. Lambert, R. McGrath, and J. Smerdon, Phys. Rev. Lett. 102, 086801 (2009). 39 Y. Shao, L. F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. T. Brown, A. Gilbert, L. V. Slipchenko, S. V. Levchenko, D. P. O’Neill, R. A. DiStasio, R. C. Lochan, T. Wang, G. Beran, N. A. Besley, J. M. Herbert, C. Yeh Lin, T. Van Voorhis, S. Hung Chien, A. Sodt, R. P. Steele, V. A. Rassolov, P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw, B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C.-P. Hsu, G. Kedziora, R. Z. Khalliulin, P. Klunzinger, A. M. Lee, M. S. Lee, W. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. Min Rhee, J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett, J. E. Subotnik, H. L. Woodcock, W. Zhang, A. T. Bell, A. K. Chakraborty, D. M. Chipman, F. J. Keil, A. Warshel, W. J. Hehre, H. F. Schaefer, J. Kong, A. I. Krylov, P. Gill, and M. Head-Gordon, Phys. Chem. Chem. Phys. 8, 3172 (2006). 40 D. M. Chipman, J. Chem. Phys. 112, 5558 (2000).
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THE JOURNAL OF CHEMICAL PHYSICS 140, 054709 (2014)
Modeling ion sensing in molecular electronics Caroline J. Chen,a) Manuel Smeu,b) and Mark A. Ratnerc) Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
(Received 12 September 2013; accepted 17 January 2014; published online 6 February 2014) We examine the ability of molecules to sense ions by measuring the change in molecular conductance in the presence of such charged species. The detection of protons (H+ ), alkali metal cations (M+ ), calcium ions (Ca2+ ), and hydronium ions (H3 O+ ) is considered. Density functional theory (DFT) is used within the Keldysh non-equilibrium Green’s function framework (NEGF) to model electron transport properties of quinolinedithiol (QDT, C9 H7 NS2 ), bridging Al electrodes. The geometry of the transport region is relaxed with DFT. The transport properties of the device are modeled with NEGF-DFT to determine if this device can distinguish among the M+ + QDT species containing monovalent cations, where M+ = H+ , Li+ , Na+ , or K+ . Because of the asymmetry of QDT in between the two electrodes, both positive and negative biases are considered. The electron transmission function and conductance properties are simulated for electrode biases in the range from −0.5 V to 0.5 V at increments of 0.1 V. Scattering state analysis is used to determine the molecular orbitals that are the main contributors to the peaks in the transmission function near the Fermi level of the electrodes, and current-voltage relationships are obtained. The results show that QDT can be used as a proton detector by measuring transport through it and can conceivably act as a pH sensor in solutions. In addition, QDT may be able to distinguish among different monovalent species. This work suggests an approach to design modern molecular electronic conductance sensors with high sensitivity and specificity using well-established quantum chemistry. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4863860] I. INTRODUCTION
With the continuing advancement of silicon-based electronic devices and recent progress in nano-technology, device components are rapidly approaching the molecular scale.1–5 In terms of theoretical modeling, the methodology and framework to simulate and predict the properties of molecular electronic devices have been developed and extended to include sophisticated transport mechanisms and to capture complex phenomena,6–15 although complications persist.16, 17 The systems considered mostly consist of a single or few molecules providing the pathways for electrons to move between two metal electrodes. Chemical modification of the molecules in molecular devices may alter the current passing through them. It is natural to utilize this change in current by chemical modification for the purpose of detection. These putative molecular sensors could be used for certain entities without false positives, possessing essential chemical specificity, and yielding a detectable change in current after chemical recognition. The single-molecule molecular electronic sensor brings together two advances in modern technology: cutting-edge electronics and nano-engineering. Nanotechnology permits measuring specific chemical interactions at the singlemolecule level. The electric signal caused by chemical modia) Work done while attending New Trier Township High School, 385
Winnetka Avenue, Winnetka, Illinois 60093, USA. Current address: Columbia College, Columbia University, 1130 Amsterdam Avenue, New York, New York 10027, USA. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] c) Electronic mail: [email protected]
0021-9606/2014/140(5)/054709/7/$30.00
fications/interactions can be detected and measured quantitatively with modern electronics, as routinely seen in scanning tunneling microscopy studies. Therefore, the single molecule sensor/detector can be used as a specific and sophisticated chemical measuring device. Progress has been made in the area of sensors composed of single-molecule junctions. An example includes experimental work showing that the conductance of single peptide molecules, upon binding with transition-metal ions such as Cu2+ and Ni2+ , can change depending on the sequence and length of the peptides.18 Theoretical work has also shown that the presence of the side groups of oxygen and bipyridine on molecules of 2.5 nm length, consisting of fluorine units, can lead to Fano resonance,19 which can result in changes in electron transport.20 More recently, a bis(2-pyridylmethyl)amine (BPA) model sensor has been studied to detect Zn, Fe, Ni, and Cu ions by measuring changes in conductance when coupled to a gold two-probe junction; however, in this study, the Au(111)-DTBPA-Au(111) structure was not relaxed.21 That study focused on a molecule with an inherently low conductance due to its lacking an extended π -system and lacking planarity; the gap between the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO gap) is drastically affected by the presence of metal ions. Here, quinolinedithiol (QDT, C9 H7 NS2 ) is chosen as the sensor molecule. This molecule is small enough to be simulated reasonably well by first-principles computational approaches, and it possesses several advantages. QDT has a planar molecular structure with fused rings and π -type molecular
140, 054709-1
© 2014 AIP Publishing LLC
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J. Chem. Phys. 140, 054709 (2014)
FIG. 1. Two-probe structure of QDT sandwiched between two Al electrodes (cyan=C, white=H, blue=N, yellow=S). Left and right electrodes are semiinfinite, extending to left and right. The central region contains QDT and some electrode buffer layers (between the vertical solid and dashed lines on either side). The red circle shows the region where the ion is placed. A denotes the four-atom layer and B denotes the five-atom layer (see Fig. 2).
orbitals (see Fig. 1). In general, molecules with π -type orbitals have a smaller HOMO-LUMO gap than molecules having only σ -type molecular orbitals, usually resulting in greater electrical conductance through them. In addition, QDT has thiol groups at the two ends, which interact strongly with noble metal electrodes. The molecule has a nitrogen atom within the conjugated network that can bind positively charged ions to its lone pair. Here we investigate whether the QDT molecule can be used to differentiate between different monovalent cations. The insights gained can then be used to design molecules capable of efficient detection of relevant ions. The computational technique has been well-developed and is welldocumented.7, 8, 22–27 Here, however, we apply the methodology to detection. The same approach might be used to design molecular sensors for detecting a wide range of agents, including multivalent ions, chemical groups, and possibly even larger species such as protein fragments, viruses, or bacteria.
II. THEORETICAL METHODS
The entire model sensor system consists of three parts: left electrode, right electrode, and the central/scattering region (see Fig. 1). The left and right electrodes are identical and composed of aluminum atoms that extend to infinity in both the left and right directions. Other metals, such as gold, could be used due to the ability of sulfur to bind with noble metals relatively strongly. However, for the convenience of modeling, aluminum is used here since the main purpose of this work is to investigate the sensing property of the organic molecule. In this study, the electrodes are quasi-onedimensional aluminum wires having a 3 × 3 cross section, composed of periodic units repeating along the face-centeredcubic (001) direction. The repeating sub-unit consists of four layers that alternate between containing four and five aluminum atoms. In Fig. 1, the four-atom layer is labeled as A, and the five-atom layer as B. Figure 2 depicts the view down the wire, with just the S and the nearest two Al layers. Binding occurs at the hollow site from computational minimization, which is centered above the four-atom layer, where the sulfur atom in the molecule is coordinated to the four aluminum atoms. In the computation, the coordinates of the atoms in the electrodes are fixed by the aluminum lattice structure, with a lattice constant of 4.05 Å.
The “central region,” which is modeled with density functional theory (DFT) within the Keldysh non-equilibrium Green’s function (NEGF) framework, includes a few layers of each electrode. Because the left and right electrodes are identical, it is necessary for there to be an asymmetry in the number of buffer layers on the left and right sides of the central region (see Fig. 1). In this way, both the sulfur atoms on the two sides of the molecule can bind to the hollow site above the four-atom layer labeled A in Fig. 1. These buffer regions allow for a smooth transition between the electronic density and potential in the periodic electrodes to those of the extended molecule. The aluminum crystal lattice constant is used so that the buffer layers act as a continuation of the electrodes. The central region consists of the organic molecule sensing candidate (QDT) bound to the buffer layers, following the “extended molecule” scheme.28 In this region, a proton or an alkali metal cation, shown as a red spot in Fig. 1, was initially placed close to the nitrogen atom, and then relaxed (for simplicity, no solvent is included). The relaxation (energy minimization) of the entire system was carried out with the GAMESS29 package at the B3LYP/6-31G(d)30, 31 level of theory to obtain the optimal structure. The geometry optimizations were carried out on the Al4 QDT-Al4 subunit of the molecular sensing region. An initial specific distance for Al electrode-electrode separation was
FIG. 2. View down the wire. The orange atoms are a part of the four-atom layer labeled A in Fig. 1 which is nearest to the S atom, and the green atoms, the five-atom layer labeled B in Fig. 1. The white center atom is sulfur.
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J. Chem. Phys. 140, 054709 (2014)
chosen. At this separation, the molecule is allowed to relax while the Al atoms are fixed at their crystal lattice positions. Relaxations at various Al electrode-electrode separations are carried out to find the value that yields the minimum total energy, where the Al electrode-electrode separation is defined as the distance between the two closest Al buffer layers on each side of the molecule. The energy minimum is found for the Al electrode-electrode separation of 12.10 Å. At this geometry, the closest Al-S distance is 2.68 Å. For the systems containing cations, an ion was initially placed near the nitrogen atom in the minimized Al4 -QDT-Al4 subsystem; the entire subsystem is then relaxed again at the fixed Al electrode-electrode separation. These relaxations allow for QDT to adopt the appropriate geometry in the presence of each ionic species. Any changes in conductance properties can then be attributed to the presence of a given ion. The Nanodcal package7, 8 was used to obtain the quantum transport properties. Nanodcal – a nano-electronic device calculator – is a computational package to calculate non-equilibrium quantum transport properties of two-probe systems (see Fig. 1). It uses pseudopotentials to describe the core electrons, and fully treats the valence electrons, calculating the transport properties using real space DFT analysis using the local density approximation within the Keldysh nonequilibrium Green’s function framework. We should point out that, since Nanodcal uses the local density approximation, it only takes into consideration the electronic density at each point in space. More advanced (hybrid) functionals are not yet implemented into our NEGF-DFT code due to their complexity and computational cost. With this in mind, the work aims to study the ion sensing abilities of the organic molecule as a simple, semi-quantitative model. In Nanodcal, the electronic quantum states are determined from the system Hamiltonian, using DFT. The density matrix is constructed by populating the states with appropriate statistics. Fermi-Dirac statistics are used for the equilibrium situation, while NEGF is used to determine the non-equilibrium quantum statistics of the transport system. Specifically, the transmission function, which represents the probability for an electron to successfully move from one electrode to the other, is calculated by9 T (E) = Tr(1 G2 G† ) ,
(1)
where is the broadening matrix at each electrode, related to the imaginary part of the self-energy matrix by = i( − † ) .
Landauer-Büttiker equation32 2e μ2 I (V ) = T (E)dE , h μ1
(4)
where e is the electron charge, h is Planck’s constant, and μ1 and μ2 denote the chemical potentials of the two electrodes. In summary, the systems studied are relaxed with GAMESS (energy-minimized to obtain the optimal structure), and then the transport properties are calculated by Nanodcal. III. RESULTS AND DISCUSSION
The properties of the organic QDT molecule are first studied. For QDT, the HOMO energy level is calculated to be at −5.39 eV and the LUMO energy at −2.86 eV, relative to the vacuum level, giving a HOMO-LUMO gap of 2.53 eV. Figure 3 shows a visual representation of the frontier KohnSham orbitals of QDT. The π bonds are clear because there is a node in the molecular plane. The HOMO and LUMO levels of QDT are made up of π orbitals that extend along the entire molecule. The transmission calculations are first performed for the control system (QDT alone). Figure 4 shows the transmission as a function of energy for the control system. The transmission spectra are calculated for different bias voltages applied to the right electrode with the left electrode remaining electrically grounded. These different biases are from −0.5 V to 0.5 V at increments of 0.1 V.33 For a given bias, the transmission curve has one main peak in the [−1.0, 1.0] eV energy window. The transmission spectra for the systems with the various ions behave similarly. To investigate which molecular orbitals mainly contribute to the transmission peaks, the scattering states are examined. Scattering states7 are analogous to Kohn-Sham eigenstates, but they apply to open-boundary systems such as the twoprobe geometries considered in this work. These represent the pathway of an electron with a given energy passing from one electrode, through the molecule, and into the other electrode. There can be multiple scattering states for each energy point in the transmission spectrum. It is instructive to plot these to identify which have amplitude on both the left and right electrodes, since these will contribute to transmission peaks. Once this is determined, the scattering states can be compared to
(2)
The self-energy is due to the surroundings from the left and right electrodes and accounts for both the broadening of molecular eigenstates and their shift in energy. The broadening and shift are represented by the imaginary and real part of the self-energy, respectively. The Green’s function, G, in the transmission formula is defined by G = [ES − H − 1 − 2 ]−1 ,
(3)
where S is the overlap matrix and H is the Hamiltonian of the extended molecule (“central region” in Fig. 1). Using the transmission function, the current is calculated by the
FIG. 3. Examples of Kohn-Sham orbitals for isolated QDT. (a) The highest occupied molecular orbital and (b) the lowest unoccupied molecular orbital.
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J. Chem. Phys. 140, 054709 (2014)
Transmission
1.5 Control H+ Li+ Na+ K+
1
0.5
0 −1
−0.5
0 E − E (eV)
0.5
1
F
FIG. 4. Transmission for different bias voltages, varied from −0.5 V to 0.5 V at 0.1 V increments on the control system (QDT molecule without any ions). The transmission curves for positive, zero, and negative biases are plotted in blue, black, and red, respectively. The leftmost peak corresponds to an applied bias of 0.5 V, and the second rightmost peak to an applied bias of −0.5 V.
the Kohn-Sham orbitals of the isolated molecules in the central region. The molecular orbital is said to be the main contributor to the transmission peak at that energy if its orbital structure matches that of the scattering state. Figure 5 shows an example of this procedure. Scattering state analysis is performed for the control system at 0.29 eV, relative to the EF of the electrodes, the energy value of the transmission peak near EF . Eight scattering states are found at this energy. Of these eight, three have amplitude on both electrodes, one of which is shown in Fig. 5(a). After the comparison of the scattering state to the Kohn-Sham orbital of the isolated molecule, it can be seen that the scattering state matches with the LUMO of the isolated molecule, and it can be said that electron transport primarily occurs through this MO at that energy. Similarly, the analysis shows that the main transmission peaks of the systems with one H+ , Li+ , Na+ , or K+ ion present near the Fermi level correspond to the LUMO of the QDT molecule. However, for the Na+ + QDT system, there is also a contribution from the LUMO+4 of the QDT molecule to the transmission peak. This results in a transmission greater than one within a certain range for the Na+ + QDT system due to nearly degenerate energy levels (see Fig. 6).
FIG. 6. The effect of ions (H+ , Li+ , Na+ , and K+ ) on the transmission through QDT at zero bias. The transmission of the Na+ is greater than one within a certain range due to nearly degenerate energy levels.
A comparison for the transmission spectra at zero bias for all the systems (control, H+ , Li+ , Na+ , and K+ ) from the energy range of [−1.0, 1.0] eV is shown in Fig. 6. The transmission curves for all the systems show one or more peaks. An analysis of scattering state calculations at the energy points of the transmission coefficient peaks is used to find which molecular orbitals contribute most significantly to the peaks near EF at zero bias as described above. The Li+ and K+ systems have an additional peak to the right of their main peaks, both correspond to the LUMO+4 of the QDT molecule. It can also be seen that Na+ causes the biggest transmission peak, while H+ produces the smallest one. The main peaks for H+ , Li+ , Na+ , and K+ are centered around 0.0 eV, while the main peak for the control system is centered at 0.29 eV. This shift is attributed to the electrostatic influence of the ion upon the orbital energetics of the molecule. When a charged species interacts with the N lone pair, which is in the plane of the molecule, it does not destroy the π -system. The effect is similar to that of an electron withdrawing group (in the case of positive ions), resulting in a lowering of the energy levels.27, 34 Ions with the same charge will have a similar effect, with small differences due to the respective size, electronegativity and hardness, which determine the interaction of the ion with the lone pair, and with QDT as a whole. From the transmission, the current can be evaluated (Eq. (4)). The calculated I–V relationship for biases from
FIG. 5. (a) The scattering state with amplitude at both ends for the control system at 0.29 eV. ((b)–(e)) Frontier molecular orbitals for the isolated molecule. The overall structure of the LUMO matches best with all the scattering states.
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J. Chem. Phys. 140, 054709 (2014) TABLE II. Conductance at various biases for different systems. Conductance (μS)
FIG. 7. The I-V relationships for the control, H+ , Li+ , Na+ , and K+ systems. Note that the Li+ data lie directly underneath the Na+ data.
−0.5 V to 0.5 V with increments of 0.1 V is presented in Fig. 7. The current for QDT starts from −2.85 μA at −0.5 V and increases almost linearly to 2.99 μA at 0.5 V. For the H+ , Li+ , Na+ , and K+ , the I-V relationships are less linear. In addition, they show a weak rectification because of the stronger asymmetry of the ion + QDT system, compared to bare QDT. Rectification has also been observed in the work of Xiao et al.,18 for example, which is attributed to the asymmetry of the junction. This was verified by the authors who also studied a symmetric molecular junction containing octanedithiol where rectification was not observed. The (weak) rectification is similarly achieved in this theoretical work, particularly when the ion binds to QDT. Table I summarizes the currents of all systems considered at ±0.5 V biases to show the weak rectification effect. Table I suggests that the goal of ion detection is achieved because the current is nearly three times larger at 0.5 V when an ion is present. However, the I-V relationships for the H+ , Li+ , Na+ , and K+ systems are essentially identical at positive bias, and only with the application of negative bias can they be differentiated. QDT is capable of distinguishing protons from monovalent cations, because the current through H+ + QDT system at negative biases is detectably smaller than those of alkali ion + QDT systems. This is clear from comparing the positions of the transmission peaks relative to EF . The Li+ , Na+ , and K+ systems all have their peaks centered slightly to the right of EF while the peak for the H+ system is centered very slightly to the left of EF . Consequently, the Li+ , Na+ , and K+ systems have a higher conductance at negative bias than at positive bias, while the I/V curve is nearly symmetric for the H+ system. Therefore, while the Li+ , Na+ , and K+ are hard to differentiate, the H+ system can clearly be distinguished from its I-V characteristics. It seems that the QDT molecule TABLE I. Current at ±0.5 V for different systems. Current (μA) Bias (V)
Control
H+
Li+
Na+
K+
0.5 − 0.5
3.0 − 2.9
8.5 − 5.9
8.7 − 11.3
8.3 − 11.3
8.3 − 10.5
Bias (V)
Control
H+
0.5 0.4 0.3 0.2 0.1 0.0 − 0.1 − 0.2 − 0.3 − 0.4 − 0.5
6.0 6.4 6.6 6.7 6.7 6.7 6.6 6.5 6.3 6.1 5.7
16.9 19.8 24.6 32.1 44.5 53.0 35.2 22.3 17.0 13.9 11.9
Li+
Na+
K+
17.3 20.8 25.7 33.2 47.9 64.1 55.8 42.5 33.6 27.3 22.6
16.5 19.9 24.2 30.6 41.5 60.1 55.3 42.5 33.6 27.3 22.6
16.6 20.0 24.4 31.0 42.1 53.8 51.2 38.7 31.1 25.5 21.0
interacts with H+ (lacking any core electrons) differently than with alkali metal ions (with core electrons) of various sizes. The QDT molecule can possibly be used as a pH sensor, but it cannot distinguish among alkali metal cations. The binding of different metal ions to different peptides was also investigated in the experimental work of Xiao et al.18 The measured difference in conductance due to the binding of Cu2+ versus Ni2+ ions shows that this approach can be used to distinguish different metal ions with similar binding configuration to a host peptide molecule. In the present work, it is possible that QDT could differentiate between H+ and the other M+ ions. The conductance at different biases is summarized in Table II. This is obtained by dividing the current by the voltage at that particular data point.35 In the table, the conductance of the control system (QDT) remains nearly constant, while all other systems show sub-linear I-V behavior because of the current saturation at large bias; once the entire transmission peak is inside the integration windows of Eq. (4), larger bias does not increase the current substantially.36 In Xiao’s work,18 the conductance ratio for the peptide with and without the ion varied from 1 to over 300, depending on the peptide and the ion. Here, the ratio (at zero bias) is about 10, as shown in Table II. Of course, a direct comparison cannot be made since the molecules and ions considered are quite different, but the important result of ion sensing is consistent between the experiment and this theoretical work. It should be pointed out that these simulations very approximately address the conditions of an experiment on such systems. Under experimental conditions, the molecular junction and ions would be present in a solution, which would also contain counter ions. While the effect of the counter ions and solvent, which are not included in this work, will influence the conductance result, we believe the major conclusion of ion sensing is valid for the following reasons. Regarding the effect of counter ions, these will have negative charge and will have a repulsive interaction with the lone pair in QDT. Therefore, any effect of negative counter ions on the molecular junction will be minor. In terms of the solvent effect, this will influence the electronic properties of the QDT molecule and screen the charge on the ion.37, 38 However, we believe that the ions will still be detectable, as described in the work of Xiao et al.,18 who showed that molecular junctions
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J. Chem. Phys. 140, 054709 (2014)
composed of peptides could detect single ions in solution. In any case, for the situation where we compare similar species (H+ , Li+ , Na+ , and K+ ), the solvent and counter ion effects, to a first approximation, are the same for all those cations, so direct comparisons between them can be made.
Transmission
1
IV. EXTENSION TO DIFFERENT SPECIES
To understand more about the sensing abilities of QDT, the effects of an alkaline earth metal cation, a hydronium ion, and a water molecule on the transmission and current-voltage relationships were also examined. The ability to sense the hydronium ion is of interest because this is a more realistic representation of H+ in water. It is also desirable to know how an H2 O molecule affects the conductance of QDT, since these sensors would likely be immersed in solvent. Calculations on the transmission of the systems sensing H2 O, H3 O+ , and Ca2+ were performed. These systems were relaxed in the same manner as with the H+ , Li+ , Na+ , and K+ systems. For the H2 O and H3 O+ systems, an H is directed towards the lone pair of the N atom in QDT, in a typical Hbonding geometry. Figure 8 shows the transmission spectra of the control, H+ , H3 O+ , and H2 O systems. The control and H2 O containing systems have similar spectra, with the only difference being a slight shift to the left when the H2 O molecule is present. This is reasonable since the H atom in water can be thought of as having a partial positive charge, thereby shifting the transmission peak to the left slightly. The important thing is that the transport properties of QDT are similar when the molecule is in vacuum and when there is a water molecule near the lone pair of the N atom. However, when either H+ or H3 O+ is found near the lone pair of QDT, the transmission peak is shifted to the EF of the electrodes. Scattering state analysis shows that the LUMO of the QDT molecule mainly contributes to the transmission peaks shown in Fig. 8. Because of this drastic change in conductance when H+ or H3 O+ is present, we believe that QDT can conceivably act as a sensitive pH sensor. Figure 9 shows the transmission of Ca2+ system compared to that of the control and K+ systems. The peaks near the Fermi level of the Ca2+ and K+ systems are of comparable size, but there is also a small splitting in the peak of the Ca2+ system. Scattering state analysis for this system revealed that
Transmission
1
Control Ca2+ K+
0.5
0 −1
−0.5
0 E − EF (eV)
0.5
1
FIG. 9. The transmissions for the control, Ca2+ , and K+ systems.
the split transmission peak is due to conductance through the LUMO and LUMO+4 levels of the QDT molecule. V. BINDING ENERGY VALIDATION
Even if the calculated I-V relationship is quite different when the ion to be sensed binds to the lone pair, that interaction has to be reasonably strong for anything to be observed in an experiment. Using the Q-Chem package,39 we calculated the binding energy of various species to QDT in vacuum and in solution by using the Surface and Simulation of Volume Polarization for Electrostatics (SSVPE) implicit continuum solvation model.40 The dielectric constant of water used was 80.1, its value at 20 ◦ C. Table III shows the binding energy of the QDT+X systems, where X is the species being sensed, in vacuum and in solution. The value of H+ is not shown since a proton in aqueous solution is more realistically represented as the hydronium ion, H3 O+ (listed in table). The binding energy is calculated as Ebinding = EQDT+X −EQDT −EX , where EQDT+X is the energy of the QDT+X system, EQDT is the energy of the QDT system, and EX is the energy of the species X. From Table III, it can be seen that all of the binding energy values are negative, showing favorable interaction between QDT and the species in vacuum and in solution. Even more so, the values of the binding energies for the QDT + ion systems are more negative than the binding energy of the QDT + H2 O system. This means that even in the presence of water, QDT will still bind favorably to one of the ions. VI. SUMMARY
Control H+ H3O+
Using NEGF-DFT, we have attempted to test a possible single-molecule electronic sensor, quinolinedithiol, for ions by calculating the change in molecular conductance in the presence of the various charged species. The ions
H2O 0.5
TABLE III. Binding energy (eV) of QDT+X systems.
0 −1
−0.5
0 E − E (eV)
0.5
1
F
FIG. 8. The transmissions for the control, H+ , H3 O+ , and H2 O systems.
X
Li+
Na+
K+
Ca2+
H2 O
H3 O+
Vacuum Water
−2.2 −1.1
−1.6 −0.8
−1.1 −0.6
−4.7 −2.0
−0.4 −0.3
−3.5 −1.6
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considered include protons, alkali metal cations, calcium, and hydronium. The transmission spectra for each of the systems were determined, and scattering state analysis was used to establish which molecular orbitals are the primary contributors to the transmission peaks. Current-voltage relationships were obtained, showing that QDT can distinguish between protons and alkali metal cations, but QDT cannot differentiate among the various metal cations. Finally, the binding energies of all of the systems were calculated in vacuum and in solution to verify whether or not the ions can bind to the N atom, which is necessary if QDT is to act as a sensor in an actual device. While the change in the electrical current depends on many factors, such as the energy levels (including the Fermi energy), orbital hybridization, applied bias, and device geometry, this approach can incorporate these factors to find the maximal change in electric current for detection purposes. Therefore, this approach might be used to design molecular sensors for general purpose detection. ACKNOWLEDGMENTS
The authors thank Mr. Brett Savoie and Mr. Henry Heitzer for helpful discussions. C.J.C. thanks chemistry teacher Mr. Gerald Munley for his encouragement, M.S. thanks the FRQNT, and M.A.R. thanks the National Science Foundation (NSF) (No. CHE-1058896) for financial support. 1 M.
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