Theoretical Approach to Evaluate the Gas-Sensing Performance of Graphene Nanoribbon/Oligothiophene Composites.

Composite formation with graphene is an effective approach to increase the sensitivity of polythiophene (nPT) gas sensors. The interaction mechanism between gaseous analytes and graphene/nPT composite systems is still not clear, and density functional theory calculations are used to explore the interaction mechanism between graphene/nPT nanoribbon composites (with n = 3-9 thiophene units) and gaseous analytes CO, NH3, SO2, and NO2. For the studied analytes, the interaction energy ranges from -44.28 kcal/mol for (C54H30-3PT)-NO2 to -2.37 kcal/mol for (C54H30-3PT)-CO at the counterpoise-corrected ωB97M-V/def2-TZVPD level of theory. The sensing mechanism is further evaluated by geometric analysis, ultraviolet-visible spectroscopy, density of-states analysis, calculation of global reactivity indices, and both frontier and natural bond orbital analyses. The variation in the highest occupied molecular orbital/lowest unoccupied molecular orbital gap of the composite indicates the change in conductivity upon complexation with the analyte. Energy decomposition analysis reveals that dispersion and charge transfer make the largest contributions to the interaction energy. The graphene/oligothiophene composite is more sensitive toward these analytes than either component taken alone due to larger changes in the orbital gap. The computational framework established in the present work can be used to evaluate and design graphene/nPT nanoribbon composite materials for gas sensors.

Introduction

Electronic devices which consist of sensing materials are generally regarded as chemical sensors. These chemical sensors interact with an analyte and transduce this interaction into an electrical or optical signal. The sensitivity, selectivity, and rapid detection of targeted molecules are the key factors in the design of advanced chemical sensors.[1] Conducting organic polymers, including polyaniline,[2,3] polypyrrole,[4,5,80] polyacetylene, and polythiophene,[6,7] are considered promising materials in the fabrication of smart materials due to their favorable electronic, optical, and magnetic properties and ease of functionalization. Among these materials, polythiophene is considered especially auspicious due to its low cost, better electrical conductivity, high environmental stability, and easy processing for applications in photovoltaics, electronics, electrocatalysis, sensors, and actuators.[8] Conducting polymers interact with various gases through electrochemical or acid–base interactions.[9−11] A polythiophene matrix is introduced with various nanofillers such as metals or metal oxides to enhance the electrical conductivity and thermomechanical properties.[12,13]

The development of polymer composites based on carbon fillers such as carbon nanotubes (CNTs) and graphene (GR) has gained much attention.[14] These polymer composites provide a path to obtaining new sensor materials with better mechanical stability and functional properties than pure components. The high electrical conductivity and large surface area are remarkable features of these carbon allotropes, which are useful for the design of a chemical sensor that responds to electrical or chemical perturbations.[15] Two-dimensional graphene has potential as a gas-sensing material owing to the high surface area to volume ratio.[16] The electronic properties of graphene are altered on gas adsorption, which enables graphene to detect gases such as NH3,[17−19] SO2,[20] H2,[9] and NO2[21] with high precision. Graphene-based gas sensors have been extensively used due to their high carrier mobility, mechanical strength, and astounding optical and electronic properties. Graphene with one atom-thick layer has a significant role in sensing several gases such as NH3, NO2, H2O, and CO with a detection limit of 1 ppb.[22] Hybrid materials of graphene can be used to design and regulate the sensing performance. The processes included may be the catalytic reaction with analyte, charge transfer, charge carrier transport, and manipulation of heterojunctions and their combinations.[23]

The theoretical studies indicate that the adsorption of different gases on graphene introduces inconsistent doping states.[24,25] The blending of pure graphene with other functional materials increases the sensitivity of graphene toward gas molecules due to the symbiotic effects of various components. Carbon–polymer composite-based chemiresistors possess great stability, improved lifetime, tunable selectivity, reversibility, and reproducibility.[26] Semiconductors,[27] carbon materials,[28] and organic/inorganic composites[29,30] are all used as sensing materials, but they function based on different mechanisms and principles. The conductive carbon particles in these systems allow the passage of current through continuous pathways between the parallel electrodes of the transducer. The polymer film swells up upon sorption of chemical vapor and some of the continuous pathways are interrupted, which increases the resistance of the composite. Therefore, solvation parameters are considered key to designing polymer-based sensors that are selective to various classes of volatile organic components.[31]

In situ chemical polymerization[32] and plasma methods[14] are used to synthesize graphene/polythiophene composites. The functionalized polythiophene/graphene nanostructures are synthesized to study the variation in their optoelectronic properties.[33] Poly(methyl methacrylate) chemically blended with graphene enhances carrier scattering properties and serves as an adsorbent layer to concentrate gas molecules on the surface of graphene.[34] The synthesis of polythiophene/graphene oxide (PT/GrO) composites by interfacial polymerization is achieved to evaluate their electrical and electrochemical properties.[8] The graphene/polythiophene composites with different mass proportions are synthesized for their use as supercapacitor electrodes.[35] The theoretical insights of graphene/polythiophene composites with various sheet and ribbon models of graphene and different proportions of oligothiophene (nPT) in these composites are obtained to study the variation in the optical band gap.[36] The molecular-level dispersion of graphene is related to the efficiency of GR-conducting polymer composites that protects the intrinsic electronic properties of graphene and permits the homogeneous distribution of nanofillers by an appropriate selection of the polymer matrix through π–π stacking or van der Waals interactions.[1] Stacking interactions play an important role in controlling the structure and molecular recognition. Therefore, dispersion forces are important for their interaction with aromatic, polycyclic, and planar ligands. The interaction of molecules with other molecules or particle changes the electronic structure as well as the charge distribution.[37] The other type of interactions is CH···π and lone-pair···π interactions that play a significant role in structural manifestation. The lone-pair···π interactions are mostly repulsive, that is, between non-bonding electrons and π electrons. The binding energies for these interactions lie in the range of ∼1–2 kcal/mol.[38] The oxidative or reductive gas molecules adsorbed on the surface of the graphene–polymer composite persuades the doping or de-doping of the polymer component, which results in the change in conductance of the composite.

All these eye-catching properties of polymeric-GR based materials make them perfect candidates for replacing the ordinary heavy sensing equipment with high-tech highly sensitive next-generation gas sensor materials.[39,40] Polythiophene thin films, derivatives, microstructures, and nanofibers have been explored experimentally as sensors for gases and oxidizing vapors including H2S, NH3,[6,41] CH3OH, C2H5OH,[6,42] NO2, Cl2, SO2,[43,44] and volatile organic compounds.[45] The hybridization of polythiophene with graphene provides many advantages in the gas-sensing performance. There are few reports about the use of hybrids of graphene, polythiophene, or its derivatives for gas detection. The hybrid of reduced graphene oxide and poly(3,4-ethylenedioxythiophene) is used for the sensing of NO2 at room temperature.[46,47] Self-assembled functionalized polythiophene and graphene are used for the sensing of toxic ions, nitroaromatics, and surfactants.[33]

Herein, we examine a graphene–polythiophene nanoribbon model (C54H30-nPT) as a potential sensing material for gaseous analytes such as CO, NH3, SO2, and NO2. The presence of these gases in ambient environments is hazardous, even at ppm and ppb concentrations. Therefore, their detection is important but as of yet there is no theoretical insight in the literature regarding the adsorption of gases on graphene–polythiophene composite surfaces. The present study aims to explain the sensing mechanism of gases over composite surfaces by examining the geometrical structures of C54H30-nPT before and after interaction with the aforementioned gas molecules. Estimation of interaction energies, frontier molecular orbital analysis, energy decomposition analysis, natural bond orbital (NBO) analysis of charge transfer, noncovalent interaction (NCI) analysis, and UV–vis spectroscopic analysis are performed to check the selectivity and sensitivity of sensors.

Results and Discussion

Geometrical Parameters

Geometry optimization is important to ascertain the most stable structure. The geometries of different graphene sheets (C30H14, C46H18, and C59H20) and ribbons (C38H22, C46H26, and C54H30), in composites with nPTs (n = 1–13) are examined in vertical, tilted, and π-stacking orientations. Stable composites are obtained in the π-stacked configuration as the size of the graphene model increases, see Figure for an example. The ribbon models of graphene/nPT composites gave large interaction energies and stable complexes.[36] As such, we selected a C54H30-nPT graphene ribbon/nPT model for sensing gaseous analytes. Geometries of graphene–polythiophene nanoribbon composites, C54H30-nPT (n = 3, 5, 7, 9), were optimized both in isolation, and in complexes with CO, NH3, SO2, and NO2 analytes. In the composite complexes, the analyte-to-composite distance, interlayer distance (between the nPT and the graphene ribbon), bond angle, and dihedral angle are important parameters that characterize the interaction between the composite and analyte. The analyte-to-composite distance characterizes the interaction of the graphene-nPT composite with the analyte, while the bond and dihedral angles indicate whether the composite is planar upon complexation.

Figure 1

Reference geometry for the numbering scheme: C54H30···3PT···X (X = CO, NH3, SO2, NO2).

The length of the nPT varies in these composites while the size of graphene ribbon remains the same. Analytes are oriented on the surface of the composite from the nPT side, in order to study the change in the geometry and interaction behavior. The geometries of nanoribbon composites (C54H30-nPT) with analytes (CO, NH3, SO2 and NO2) are optimized. The optimized geometrical parameters are given in Table . The numbering scheme for the C54H30-3PT-X is shown in Figure for X = CO.

Table 1

Optimized Geometric Parameters of C54H30···nPT···X Composite–Analyte Complexes, for n = 3, 5, 7, and 9 Thiophene Units and for Analytes X = CO, NH3, SO2, and NO2a

system	d(S11-X108a) Å	∠C14S11Xa (degrees)	∠S11C9C1S5 (degrees)
C54H30···3PT			163
C54H30···3PT···CO	3.57	63	165
C54H30···3PT···NH3	3.60	71	165
C54H30···3PT···SO2	3.55	84	166
C54H30···3PT···NO2	3.53	68	170
C54H30···5PT			165
C54H30···5PT···CO	3.47	71	163
C54H30···5PT···NH3	3.63	80	163
C54H30···5PT···SO2	3.55	83	166
C54H30···5PT···NO2	3.53	69	170
C54H30···7PT			169
C54H30···7PT···CO	3.55	64	168
C54H30···7PT···NH3	3.62	70	168
C54H30···7PT···SO2	3.56	88	170
C54H30···7PT···NO2	3.42	62	173
C54H30···9PT			172
C54H30···9PT···CO	3.54	66	170
C54H30···9PT···NH3	3.62	71	171
C54H30···9PT···SO2	3.56	89	170
C54H30···9PT···NO2	3.52	69	173

Computed at the M06-2X/6-31G** level of theory.

C54H30-nPT-CO

Geometry of isolated composites changes after interactions with carbon monoxide. Different orientations of CO molecules are considered on the composite surface in recognition of the fact that CO may adopt either a carbene-like (:C=Ö) or a dipolar (−C≡O+) resonance structure. The stable geometry is found to consist of a parallel orientation of CO on the composite surface, where both oxygen and carbon interact with nPT. The optimized geometry of C54H30-3PT-CO is depicted in Figure and other less stable geometries are given in Figures S2 and S3.

Figure 2

Optimized geometries of (a) C54H30···3PT···CO, (b) C54H30···3PT···NH3, (c) C54H30···3PT···SO2, and (d) C54H30···3PT···NO2 composite–analyte complexes.

The intermolecular bond distance dS11-C108 in C54H30-3PT-CO is 3.57 Å and dS11-O109 is 3.48 Å, whereas the interlayer distance between nPT and graphene ribbon is 3.63 Å. The interlayer distance in the larger nPT composite C54H30-5PT-CO increases to 3.96 Å as the graphene ribbon bends at the center. The bond distance dS11-C108 decreases to 3.47 Å and dS11-O109 increases to 3.58 Å. This decrease in the dS11-C108 bond distance indicates a favorable interaction between S and C than S and O as the dS11-O109 bond distance increases. In the C54H30-7PT-CO complex, the dS11-C108 bond distance increases to 3.55 Å, whereas the interlayer and dS11-O109 distances decrease to 3.86 and 3.52 Å, respectively. This decrease in the interlayer distance results as nPT (7PT) becomes parallel to the graphene ribbon, but the increase in the dS11-C108 distance indicates a decrease in the interaction between CO and higher nPT composites. The interlayer distance in C54H30-9PT-CO is slightly smaller still, at 3.83 Å, due to the bending of the nPT with the graphene ribbon at the center. The dS11-C108 intermolecular distance slightly decreases to 3.54 Å, whereas the dS11-O109 bond distance remains the same at 3.52 Å. These changes indicate the variation in the interaction strength among graphene-nPT composites and CO. The variations in the interlayer distance between the C54H30 ribbon and nPT indicate the strength of π-stacking interactions.

The impact of the intermolecular angle ∠C14S11X (X = C108, O109) on the overall complex formation has also been examined. The ∠C14S11C108 and ∠C14S11O109 bond angles in C54H30-3PT-CO are 63 and 78°, respectively. These ∠C14S11C108 and ∠C14S11O109 angles increase to 71 and 87° in C54H30-5PT-CO, respectively. The bond angle increases to minimize repulsion between bonding electrons. In C54H30-7PT-CO, the ∠C14S11C108 and ∠C14S11O109 angles decrease to 64 and 78°, respectively. The nPT becomes parallel over the graphene ribbon in all other complexes, so a decrease in bond angles is observed as the bond distance also increases in this complex. The ∠C14S11C108 and ∠C14S11O109 angles in the C54H30-9PT-CO complex are 66 and 80°, respectively. This increase in the angle is again due to changes in the geometry of the composite as both nPT and graphene ribbon bend at the center, and this change is in accordance with the bond distance. Another geometrical parameter is the dihedral angle that is influential in the planarity of the composites after complexation (i.e., conductivity change). The dihedral angle between two planes is the measure of coplanarity, and the ∠S11C9C1S5 dihedral angle varies after interaction with the analyte. It is 163° in the C54H30-3PT composite and increases to 165° after complexation with CO. The increase in the dihedral angle signifies a decrease in coplanarity. In C54H30-5PT, the dihedral angle is 165° and decreases to 163° in C54H30-5PT-CO. Similarly, the dihedral angle in C54H30-7PT is 169° and slightly decreases to 168° in C54H30-7PT-CO. The dihedral angle of C54H30-9PT composite decreases from 172 to 170° after complexation with CO in the C54H30-9PT-CO complex. This decrease in the dihedral angle increases the coplanarity. The overall variation in geometrical parameters is due to changes in the geometry of composites when nPT becomes bent and parallel over the graphene ribbon.

C54H30-nPT-NH3

The optimized geometrical parameters of C54H30-nPT composite change upon complexation with NH3 (Table ). The optimized geometry of C54H30-3PT-NH3 is given in Figure and other less stable structures are given in Figures S2 and S3. The analyte-to-composite distance (dS11-N108) in the C54H30-3PT–NH3 complex is 3.60 Å and the interlayer distance is 3.63 Å. The dS11-N108 intermolecular distance increases to 3.64 Å in C54H30-5PT-NH3 and the interlayer distance increases to 3.96 Å due to the bending of the graphene ribbon at the center. The increase in the intermolecular distance indicates a decrease in interaction strength between NH3 and the composite. The dS11-N108 distance in the larger C54H30-7PT-NH3 complex slightly decreases to 3.62 Å and remains the same in the C54H30-9PT-NH3 complex. The interlayer distance decreases to 3.86 Å in C54H30-7PT-NH3 as nPT becomes parallel to the graphene surface. This distance further decreases to 3.83 Å in the C54H30-9PT-NH3 complex due to the bending of nPT and graphene ribbon at the center. The ∠C14S11N108 bond angle in the C54H30-3PT-NH3 complex is 71° and increases to 80° in the C54H30-5PT-NH3 complex. The graphene ribbon is bent at the center and the central thiophene ring of the 5PT becomes slightly flat over the graphene ribbon and the interacting angle varies. In the C54H30-7PT–NH3 complex, the angle decreases to 70° and then slightly increases to 71° in the C54H30-9PT–NH3 complex. This variation is due to changes in the geometry of the composite, which is parallel in C54H30-7PT-NH3 and then bent slightly at the center in the C54H30-9PT-NH3 complex. The bond angle varies as the bond distance changes. The ∠S11C9C1S5 dihedral angle of the C54H30-3PT composite is 163° and increases to 165° after complexation with NH3 in C54H30-3PT-NH3. The increase in the dihedral angle decreases the coplanarity. In C54H30-5PT, the dihedral angle is 165° and decreases to 163° in C54H30-5PT- NH3. The dihedral angle in C54H30-7PT is 169° and slightly decreases to 168° after complexation with NH3 in C54H30-7PT- NH3. The decrease in the dihedral angle (∠S11C9C1S5) increase the coplanarity. The dihedral angle of the C54H30-9PT composite is 172° and in the C54H30-9PT-NH3 complex, it decreases to 171°.

C54H30-nPT-SO2

The optimized geometry of C54H30-3PT-SO2 is depicted in Figure , whereas other less stable geometries are shown in Figures S2 and S3. The impact of geometrical parameters for these composite–analyte systems is also elucidated and listed in Table . The analyte-to-composite distance (dS11-S108) in the C54H30-3PT-SO2 complex is 3.55 Å and remains the same in the C54H30-5PT-SO2 complex. The interlayer distances in C54H30-3PT-SO2 and C54H30-5PT-SO2 complexes are 3.63 Å and 3.96 Å, respectively. The intermolecular distance (dS11-S108) slightly increases to 3.56 Å in C54H30-7PT-SO2 and does not change in the C54H30-9PT-SO2 complex. SO2 is oriented on the composite surface in a bent or V shape and its distance does not change much as the size of nPT increases in the composite. The interlayer distance decreases to 3.86 Å in C54H30-7PT-SO2 and 3.83 Å in C54H30-9PT-SO2 complexes in which 7PT is parallel over the graphene ribbon and 9PT becomes slightly bent at the center, respectively. The change in intermolecular angle ∠C14S11S108 in all C54H30-nPT-SO2 complexes is comparatively greater than all other composite/analyte complexes. The SO2 is V-shaped and the sulfur atom of SO2 is slightly displaced away from the interacting sulfur of the nPT. The intermolecular angle (∠C14S11S108) in the C54H30-3PT-SO2 complex is 84°, and it slightly decreases to 83° in the C54H30-5PT-SO2 complex. This is a negligible variation in the intermolecular angle as the bond distances in C54H30-3PT-SO2 and C54H30-5PT-SO2 remain the same. Then, a slight increase of 88° is observed in C54H30-7PT-SO2, which further increases to 89° in the C54H30-9PT-SO2 complex. This increase is due to a change in the position of nPT in these composites. This change in intermolecular angle results in a decrease in the interaction between SO2 and higher graphene-nPT composites. The variation in the dihedral angle (∠S11C9C1S5) also shows the same trend as the intermolecular angle. The ∠S11C9C1S5 dihedral angle of the C54H30-3PT composite is 163°, and it increases to 166° after interaction with SO2 in C54H30-3PT-SO2. In C54H30-5PT, the dihedral angle is 165° and increases to 166° in C54H30-5PT-SO2. This increase in the dihedral angle decreases the coplanarity. The C54H30-5PT-SO2 complex shows an increase in the dihedral angle than C54H30-5PT-CO and C54H30-5PT-NH3, which is due to the V-shape geometry of SO2 and the strength of interaction. The dihedral angle in C54H30-7PT is 169° and slightly increases to 170° in C54H30-7PT-SO2. This slight increase is due to the planarity of nPT (7PT) over the graphene ribbon. ∠S11C9 C1 S5 increases the coplanarity. The dihedral angle (∠S11C9 C1 S5) of the C54H30-9PT composite is 172° and in the C54H30-9PT-SO2 complex, it decreases to 170° and coplanarity increases slightly which increases conjugation.

C54H30-nPT-NO2

The optimized geometry of C54H30-3PT-NO2 is shown in Figure and other less stable geometries are given in Figures S2 and S3. The results of computed geometrical parameters of these composite–analyte systems are listed in Table . The analyte-to-composite distance (dS11-N110) in the C54H30-3PT-NO2 complex is 3.53 Å and remains invariable in the C54H30-5PT-NO2 complex. The nPT become planar over the graphene ribbon (Figures and S2). The interlayer distance in C54H30-3PT-NO2 is 3.81 Å, and it slightly increases to 3.82 Å in C54H30-5PT-NO2, which is due to the sliding of nPT over the graphene ribbon. The intermolecular distance (dS11-N110) decreases to 3.42 Å in C54H30-7PT-NO2 as NO2 becomes parallel and slightly moves ahead to interfacing sulfur of nPT than the orientation of NO2 in other composites (Figure S3). The nPT also becomes parallel to the graphene ribbon in this composite system and the interlayer distance decreases to 3.73 Å. The (dS11-N110) intermolecular distance then increases to 3.52 Å, which indicates the decrease in interactions between NO2 and C54H30-9PT composite. The interlayer distance is 3.73 Å. The intermolecular angle (∠C14S11N110) in C54H30-3PT-NO2 is 68° and slightly increases to 69° in the C54H30-5PT-NO2 complex. The intermolecular angle decreases to 62° in C54H30-7PT-NO2 and then increases to 69° in the C54H30-9PT-NO2 complex. This change in the intermolecular angle causes either an increase or decrease in the interaction between the NO2 and the composites. The ∠S11C9C1S5 dihedral angle of the C54H30-3PT composite is 163° and it increases to 170° after complexation with NO2 in C54H30-3PT- NO2. In C54H30-5PT, the dihedral angle is 165° and increases to 170° in C54H30-5PT- NO2. The dihedral angle in C54H30-7PT is 169° and further increases to 173° after complexation with NO2 in C54H30-7PT-NO2. In C54H30-nPT-NO2 complexes, the continuous increase is observed in the dihedral angle than all other complexes, which decreases the coplanarity. The anomalous behavior of NO2 with the composite is due to its difference in polarity relative to the other analytes. The dihedral angle of the C54H30-9PT composite is 172° and in the C54H30-9PT-NO2 complex, it increases to 173°.

Based on geometric parameters (intermolecular distances and angles) of all these complexes, it is clear that NO2 shows the maximum change, indicating that it has the strongest interaction with the composites among the analytes considered here.

Interaction Energies

The strength of the interaction between the composites C54H30-nPT (n = 3, 5, 7, and 9) and selected analytes (CO, NH3, SO2, and NO2) is studied at the ωB97M-V/def2-TZVPD level of theory. Interaction energies are provided in Table . The interaction energies of noncovalent complexes are generally overestimated because of the basis set superposition error (BSSE), which can be mitigated by counterpoise (CP) correction,[48] and results both with and without the CP correction are reported in Table .

Table 2

Interaction Energies of C54H30···nPT···X Composite–Analyte Complexes (for X = CO, NH3, SO2, and NO2)a

	Eint (kcal/mol)
system	no CP	with CP
C54H30···3PT···CO	–2.8	–2.4
C54H30···3PT···NH3	–3.3	–2.6
C54H30···3PT···SO2	–16.7	–15.7
C54H30···3PT···NO2	–45.0	–44.3
C54H30···5PT···CO	–2.3	–2.2
C54H30···5PT···NH3	–3.0	–2.4
C54H30···5PT···SO2	–5.5	–4.4
C54H30···5PT···NO2	–33.1	–32.8
C54H30···7PT···CO	–2.3	–1.8
C54H30···7PT···NH3	–2.9	–2.1
C54H30···7PT···SO2	–5.1	–3.8
C54H30···7PT···NO2	–14.8	–14.1
C54H30···9PT···CO	–2.2	–1.8
C54H30···9PT···NH3	–2.7	–2.2
C54H30···9PT···SO2	–2.1	–1.1
C54H30···9PT···NO2	–3.9	–3.4

Computed at the ωB97M-V/def2-TZVPD level of theory.

At the ωB97M-V/def2-TZVPD level of theory, the CP corrections are quite modest, no more than 1.3 kcal/mol but usually much less, and in the discussion that follows we will quote the CP-corrected results. In contrast, interaction energies computed at the M06-2X-D3/6-31G(d,p) level of theory (not shown) exhibit considerable variation when the CP correction is applied and are therefore not considered further in the present work.

The interaction energy of C54H30-3PT-CO at the ωB97M-V/def2-TZVPD level is −2.8 kcal/mol (or −2.4 kcal/mol upon CP correction) and decreases to −2.3 kcal/mol (−2.2 kcal/mol with CP correction) in the C54H30-5PT-CO complex. The NCIs between a π system and a polar molecule leads to polar-π interactions,[49,50] and the strength of these interactions decreases upon increasing the length of the nPT constituent as the delocalization of π the electrons reduces the charge density available to CO for polar-π interaction. CO is a polar molecule and oriented over the composite so as to interact with the π electrons of the composite. The interaction energy of the C54H30-7PT-CO complex is −2.3 kcal/mol (−1.8 kcal/mol with CP) and it decreases to −2.2 kcal/mol (−1.8 kcal/mol with CP) in C54H30-9PT-CO. The interaction energies decrease as conjugation in the π system and the length of nPT chain increase, for the reasons described above.

Ammonia is a trigonal pyramidal asymmetric polar molecule. The noncovalent polar-π interaction energies of the C54H30-nPT-NH3 complexes are listed in Table . The interaction energy of the C54H30-3PT-NH3 complex is −3.3 kcal/mol (−2.6 kcal/mol with CP). This energy is greater than the C54H30-3PT-CO complex (−2.8 kcal/mol) because NH3 is more polar than CO. The interaction energies decrease to −3.0 kcal/mol (−2.4 kcal/mol with CP) and −2.9 kcal/mol (−2.1 kcal/mol with CP) in the C54H30-5PT-NH3 and C54H30-7PT-NH3 complexes, respectively. The interaction energy further decreases to −2.7 kcal/mol (−2.2 kcal/mol with CP) in the C54H30-9PT-NH3 complex. The strength of the polar-π NCI decreases with increasing delocalization of the π electrons because less charge is available to NH3 in complexes with larger oligomers.

SO2 exhibits a larger interaction energy with C54H30-nPT composites as compared to CO or NH3. SO2 is a bent V-shaped molecule and therefore polar, with oxygen withdrawing electron density from sulfur and polarizing the S–O bond. Polar-π interactions are generated between the electropositive sulfur and the conjugated π system. The interaction energies of C54H30-nPT-SO2 complexes are given in Table . The interaction energy of C54H30-3PT-SO2 is −16.7 kcal/mol (−15.7 kcal/mol with CP). The interaction energy decreases to −5.5 kcal/mol (−4.4 kcal/mol with CP) and −5.1 kcal/mol (−3.8 kcal/mol with CP) in the C54H30-5PT-SO2 and C54H30-7PT-SO2 complexes, respectively. This sharp decrease in the interaction energy from −16.7 kcal/mol (C54H30-3PT-SO2) to −5.1 kcal/mol (C54H30-7PT-SO2) is due to the decreasing strength of polar-π interactions and an increase in π–π interactions with an increase in size of nPT. As compared to larger composites, in C54H30-3PT-SO2 there is not much delocalization of π electrons within the conjugated system because of the smaller size of nPT. As a result, the π electrons are easily available to the electropositive sulfur in C54H30-3PT-SO2 and the interaction energy is much larger. In C54H30-9PT-SO2, the interaction energy further decreases to −2.1 kcal/mol (−1.1 kcal/mol with CP).

The interaction energy of C54H30-3PT-NO2 is −45.0 kcal/mol (−44.3 kcal/mol with CP). This value is much greater that the corresponding values for another analytes (CO, NH3, or SO2). In NO2, nitrogen is surrounded by two electronegative oxygens and it is also smaller in size than oxygen. The withdrawing effect of electronegative oxygen creates more positive charge density on the nitrogen atom leading to favorable interactions with the π electrons, resulting in a strong polar-π interaction. The interaction energy decreases to −33.1 kcal/mol (−32.8 kcal/mol with CP) in the C54H30-5PT–NO2 complex and further decreases to −14.8 kcal/mol (−14.1 kcal/mol with CP) and −3.9 kcal/mol (−3.4 kcal/mol with CP) in C54H30-7PT-NO2 and C54H30-9PT-NO2, respectively. As with other systems considered above, increasing delocalization of the π electrons with increasing polymer length reduces the strength of the analyte–composite polar-π interaction. In combination with the survey of the optimized geometrical parameters, these interaction energies make clear that NO2 exhibits the strongest interaction with the composite.

Natural Bond Orbital Analysis

Charge transfer may play a significant role in electronic properties and changes in molecular charge upon complexation may help to account for the sensing ability of the composite substrate toward analytes. Here, the amount of charge transfer between the graphene-nPT composite and the analyte is investigated using the natural atomic charges that come from NBO analysis, as listed in Table .

Table 3

Natural Population Analysis of Composite–Analyte Complexes C54H30···nPT···X (n = 3, 5, 7, and 9; X = CO, NH3, SO2, and NO2)

	amount of charge transfer
system	nPT	graphene	analyte
C54H30···3PT	+0.027	–0.027
C54H30···3PT···CO	+0.030	–0.025	–0.005
C54H30···3PT···NH3	+0.023	–0.022	–0.001
C54H30···3PT ···SO2	+0.057	–0.018	–0.039
C54H30···3PT···NO2	+0.066	+0.244	–0.310
C54H30···5PT	+0.058	–0.058
C54H30···5PT···CO	+0.060	–0.058	–0.002
C54H30···5PT···NH3	+0.056	–0.055	–0.001
C54H30···5PT···SO2	+0.092	–0.054	–0.038
C54H30···5PT···NO2	+0.083	+0.249	–0.333
C54H30···7PT	+0.071	–0.071
C54H30···7PT···CO	+0.075	–0.070	–0.005
C54H30···7PT···NH3	+0.069	–0.068	–0.001
C54H30···7PT···SO2	+0.086	–0.047	–0.038
C54H30···7PT···NO2	+0.085	+0.241	–0.326
C54H30···9PT	+0.064	–0.064
C54H30···9PT···CO	+0.068	–0.063	–0.005
C54H30···9PT···NH3	+0.316	–0.315	–0.001
C54H30···9PT···SO2	+0.110	–0.070	–0.039
C54H30···9PT···NO2	+0.087	+0.326	–0.324

Overall, we find that complexation transfer a small negative charge to the analyte. The amount of charge transferred is quite small (no more than 0.005e) when the analyte is CO or NH3 and does not change appreciably with the size of the nPT oligomer, in contrast to the interaction energies that do depend on size. The transferred charge is larger in the case of SO2, which develops a charge of −0.039e upon complexation. This increase, relative to CO or NH3, can be ascribed to resonance structures in SO2 that allow it to accommodate more charge. Finally, the amount of charge transferred to the analyte is most significant in the case of NO2, where it exceeds −0.3e. This is consistent with the much stronger interactions of NO2 with the composites, as compared to other analytes.

Frontier Molecular Orbital Analysis

We next analyze the interaction of the composites with the analytes in terms of their effect on the HOMO–LUMO (H–L) gap. These frontier orbital energies are listed in Table , whereas the orbitals themselves are plotted in Figures and S4–S6. The change in HOMO and LUMO energies due to the overlapping of frontier molecular orbitals upon complexation dictates changes in conductivity of the system.[51−53] Changes in the H–L gap of the composite upon complexation with an analyte can be expected due to changes induced in the torsional angles of the composite, leading to increased twisting of the conjugated system and therefore a larger H–L gap in the presence of an analyte.[54,55] The increase in the H–L gap of the composite after sensing increases its resistance which lowers its conductivity.

Table 4

H–L Gaps, λmax, Oscillator Strengths, and Excitation Energies of C54H30···nPT···X Composite–Analyte Complexes (n = 3, 5, 7, and 9; X = CO, NH3, SO2, and NO2)a

system	H–L gap (eV)	λmax (nm)	oscillator strength	excitation energy (eV)	HOMO (eV)	LUMO (eV)
C54H30···3PT	0.63	590	3.61	2.10	–3.85	–3.22
C54H30···3PT ···CO	0.65	603	5.23	2.06	–3.88	–3.23
C54H30···3PT ···NH3	0.65	595	2.88	2.08	–3.92	–3.27
C54H30···3PT ···SO2	0.63	604	5.11	2.05	–3.92	–3.29
C54H30···3PT ···NO2	0.86	808	2.47	1.53	–4.07	–3.21
C54H30···5PT	0.59	652	1.81	1.90	–3.78	–3.19
C54H30···5PT ···CO	0.60	656	1.81	1.89	–3.79	–3.19
C54H30···5PT ···NH3	0.58	651	2.11	1.90	–3.82	–3.24
C54H30···5PT ···SO2	0.59	651	1.93	1.90	–3.82	–3.23
C54H30···5PT ···NO2	0.65	845	1.51	1.47	–4.02	–3.37
C54H30···7PT	0.58	664	1.39	1.87	–3.77	–3.19
C54H30···7PT ···CO	0.59	663	1.50	1.87	–3.78	–3.19
C54H30···7PT ···NH3	0.58	662	2.12	1.87	–3.81	–3.23
C54H30···7PT ···SO2	0.58	665	2.02	1.86	–3.82	–3.24
C54H30···7PT ···NO2	0.84	822	1.80	1.51	–4.03	–3.19
C54H30···9PT	0.58	680	2.06	1.82	–3.76	–3.18
C54H30···9PT ···CO	0.58	680	2.05	1.82	–3.77	–3.19
C54H30···9PT ···NH3	0.58	680	1.96	1.82	–3.80	–3.22
C54H30···9PT ···SO2	0.59	683	1.89	1.82	–3.80	–3.21
C54H30···9PT ···NO2	0.62	820	2.42	1.51	–4.01	–3.39

Computed at the (TD-)B3LYP/6-31G** level of theory.

Figure 3

HOMOs and LUMOs of (a,e) C54H30···3PT···CO, (b,f) C54H30···3PT···NH3, (c,g) C54H30···3PT···SO2, and (d,h) C54H30···3PT···NO2 composite–analyte complexes.

The H–L gaps in C54H30-nPT are 0.63, 0.59, 0.58, and 0.58 eV for n = 3, 5, 7, and 9, respectively. Upon complexation with CO, these gaps increase slightly, for example, to 0.65 eV for n = 3, although the effect saturates for larger oligomers and for n = 9, the H–L gap of the C54H30-9PT-CO complex is 0.58 eV. These modifications of the gap are expected to manifest as a decrease in conductivity in the presence of the analyte.

The H–L gap of C54H30-nPT also increases upon complexation with NH3, for example, to 0.65 eV in the n = 3 oligomer, although the effect once again saturates quickly as a function of the oligomer size.

In contrast to the case of CO or NH3, the H–L gap of the composite decreases very slightly in the presence of the analyte to 0.63 eV for n = 3, although for larger oligomers there is essentially no change in the gap upon complexation with the analyte.

The C54H30-nPT composites show a considerable variation in the H–L gap after interaction with NO2. In C54H30-3PT, the H–L gap is 0.63 eV and it increases to 0.86 eV upon complexation with NO2, whereas the gap in C54H30-5PT increases from 0.59 to 0.65 eV in the presence of NO2. The H–L gap in this system exhibits a significant variation with respect to the size of the composite, as it is larger once again (at 0.84 eV) for n = 7 and then smaller (0.62 eV) for n = 9.

Electronic Properties and Global Indices

The quantities −EHOMO and −ELUMO are approximations to the ionization potential (IP) and the electron affinity (EA), respectively. IP, EA, and global indices, including chemical potential (μ), chemical hardness (η), softness (s) electrophilicity (ω),[84] values are given in Table S1. The ionization potential decreases as the size of nPT increases in the composite. The IP in C54H30-3PT is 3.86 eV. The IP decreases to 3.78 eV in C54H30-5PT, 3.77 eV in C54H30-7PT, and 3.76 eV in C54H30-9PT composites. The IPs increase in the presence of the analytes, with the largest changes occurring in the case of NO2 and, for example, the IP of C54H30-3PT-NO2 is 4.45 eV. The HOMO energies of C54H30-3PT changes by 0.02, 0.05, 0.06, and 0.60 eV in the presence of CO, NH3, SO2, and NO2, respectively, which is the same order as in the case of the charge-transfer analysis. Similarly, the C54H30-nPT-NO2 complexes have lower EAs than other complexes.

The global reactivity indices are very important to determine the reactivity and stability of complexes. The global hardness is the resistance of a species to deformation under the influence of an electric field. The reactivity of species decreases but the stability of a system increases with increase in hardness.[56] The chemical hardness of the C54H30-3PT composite increases after complexation with CO, NH3, SO2, and NO2 but decreases as the size of nPT increases. The increase in chemical hardness results in decrease in reactivity but increase in stability. Softness is the reciprocal of chemical hardness, and its increases with the length of nPT. The values of the chemical potential also increase after sensing the analytes, which indicates the reactivity of the composite sensor toward analytes. The electrophilicity (ω) also provides data about the stability and reactivity of complexes. The results in the variation of global indices are in accordance with the results of other properties (vide supra).

UV–Vis Absorption Studies

The electronic excitation properties in terms of charge transfer and optical band gaps play a significant role in comprehending the conductivity and sensitivity of the interacting species.[57] Time-dependent density functional theory (TD-DFT) results at the B3LYP/6-31G** level, including λmax, excitation energies and oscillator strength of C54H30-nPT (n = 3, 5, 7, 9) and their complexes (C54H30-nPT-X), are listed in Table . The simulated UV–vis spectra of C54H30-3PT-X are shown in Figure , whereas the spectra of other complexes are given in Figure and S7–S9. These spectra were computed from the lowest 40 singlet excitation energies, using Gaussian broadening with a width parameter of 0.05 eV.

Figure 4

UV–vis spectra of C54H30···3PT, C54H30···3PT···CO, C54H30···3PT···NH3, C54H30···3PT···SO2, and C54H30···3PT···NO2 composite–analyte complexes, computed at the TD-B3LYP/6-31G** level.

The observed λmax of the C54H30-3PT composite is 590 nm, and it is red shifted to 603 nm upon complexation with CO. The absorption maximum of the C54H30-5PT composite appears at 652 nm and increases to 656 nm in the C54H30-5PT-CO complex. The increase in absorption maxima from 603 to 656 nm is due to increased conjugation with increasing chain length of the oligomer, as well as a decrease in the band gap within the complexes. The λmax of C54H30-7PT is 664 nm and remains essentially unchanged after complexation with CO. The non-bonding electrons on the oxygen atom may lead to π-antibonding interactions and therefore a larger shift in absorption spectra. The same is true for C54H30-9PT. Apparently, complexation with CO does not perturb the absorption spectrum of a sufficiently large composite.

The C54H30-nPT-NH3 complexes show a minimal variation in their absorption maxima. The λmax of the C54H30-3PT composite is 590 nm and shows red shift to 595 nm upon the interaction with NH3, whereas λmax shifts from 652 nm in C54H30-5PT to 651 nm in the C54H30-5PT-NH3 complex. Absorption maxima in C54H30-7PT and C54H30-9PT (664 nm and 680 nm, respectively) shift by ≤2 nm upon complexation with NH3. As with the CO complexes, the C54H30-nPT-NH3 complexes show a very small change in their absorption maxima and this is consistent with less charge transfer in these complexes.

The C54H30-nPT-SO2 complexes also exhibit minimal changes in their absorption spectra upon complexation. Although λmax of C54H30-3PT shifts from 590 to 604 nm upon complexation with SO2, in the larger complexes the shift is ≤3 nm.

The red shift in the absorption maximum of C54H30-3PT is very pronounced upon complexation with NO2, shifting from 590 nm to 808 nm, and for larger C54H30-nPT composites, the absorption maximum shifts from 652 nm to 845 nm (n = 5), from 664 nm to 822 nm (n = 7), and from 680 nm to 820 nm (n = 9). In the last two cases, the absorption maximum shifts into the near-IR region. These very pronounced shifts are due to increased conjugation within the composite and unpaired electrons of the nitrogen atom in NO2.

Density-of-States Analysis

Density-of-states (DOS) analysis helps in exploring the interaction between the composites and the analytes during sensing, by approximating the number of energy states that might be available to an electron at specific energies. In a DOS spectrum (i.e., the spectrum of Kohn–Sham orbital eigenvalues), relatively small variations in the region of the HOMO and LUMO are expected to bring obvious changes in the corresponding electric conductivity.[56] The LUMO peaks of C54H30-nPT are observed at −3.22 eV (n = 3), −3.19 eV (n = 5 and n = 7), and −3.18 eV (n = 9). The HOMO peaks are located at −3.85, −3.78, −3.77 and −3.76 eV for n = 3, 5, 7, and 9, respectively. Figure shows the DOS spectra of C54H30-3PT and C54H30-3PT-X, with the analogous spectra for larger oligomers shown in Figures S10–S12.

Figure 5

Spectra of Kohn–Sham eigenvalues of (a) C54H30···3PT···CO, (b) C54H30···3PT···NH3, (c) C54H30···3PT ···SO2, and (d) C54H30···3PT···NO2.

The HOMO energy of C54H30-nPT increases as the number of nPT units increases and, after interaction with analytes, new occupied energy states (HOMO) are generated which facilitate the transfer of electrons between the composite and analytes. Moreover, the interaction with analytes varies the peak maxima at different energy levels and this variation in the peak intensity is considered as an optimal condition for the working mechanism of chemical sensors. The new virtual orbitals in C54H30-3PT-X are seen at −3.23, −3.27, −3.29, and −2.56 eV for X = CO, NH3, SO2, and NO2, respectively. The considerable variation in the optical band gap of C54H30-3PT-NO2 is due to the formation of a new orbital at −2.56 eV. The change in the HOMO and LUMO energies with respect to the length of the nPT is small (Table ). The pronounced variation in the position of HOMO and LUMO that is observed for X = SO2 or NO2, as compared to X = CO or NH3, is consistent with the overall low sensitivity of these composites toward the latter two analytes. The variation in the shape and intensity of peaks demonstrates that the transport of electrons can either increase or decrease upon complexation.

NCI Analysis

NCI analysis is used for visualizing NCIs in real space, which is based on quantum mechanical electron density and its derivatives;[58,59] specifically, the reduced density gradient (RDG), which measures deviation from a homogeneous electron distribution:NCI analysis distinguishes color-coded RDG isosurfaces as dispersion interactions, hydrogen bonds, or repulsive steric interactions. The RDG regions are colored as blue (strong) or green (weak) for attractive interactions and red (strong) or yellow (weak) for repulsive interactions. The blue region also represents the hydrogen bonding and green region represents the dispersion interactions. The three eigenvalues (λ1 ≤ λ2 ≤ λ3) of the Laplacian of the density are computed in order to determine the different types of non-bonded interactions. All of these eigenvalues are negative at nuclei where density approaches a local maximum.

For covalent interactions, two of the eigenvalues are negative but the third is positive. Finally, the second eigenvalue is positive for steric interactions and this value is employed to differentiate the regions of the covalent and non-covalent interactions. The covalent and non-covalent interaction regions have negative eigenvalue (λ2 < 0), whereas for steric interactions λ2 > 0. The stronger NCIs have higher density values while weaker interactions have lower density values as the strength of interactions is related to the magnitude of s(r). Figure shows color-mapped isosurfaces of s(r), using an isocontour value of 0.5 a.u., and their respective scatter plots versus sign (λ2) ρ(r), which defines the NCI plot, for C54H30···3PT and C54H30···3PT-X. Analogous plots for other complexes can be found in Figures S13–S15. The color-mapped s(r) isosurface of C54H30···3PT shows dispersion interactions across an isosurface that closely resembles the contours of the atomic van der Waals radii, which is typical of π-stacking interactions.[60,61] In the NCI scatter plot, dispersion interactions appear at low density [sgn(λ2) ρ < −0.01 a.u.] and strongly repulsive interactions at larger densities [sgn(λ2) ρ ∼ 0.02–0.04 a.u.].

Figure 6

Color-mapped RDG isosurfaces (left) and NCI scatter diagrams (right) for C54H30···3PT···X with (a) X = CO, (b) X = NH3, (c) X = SO2, and (d) X = NO2.

Energy Decomposition Analysis

While NCI plots can be used to obtain a qualitative view of NCIs, the (second-generation) absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA)[62−64] approach is used to quantitatively decompose interaction energies into physically meaningful components, as provided in Table for the C54H30···nPT-X complexes. The total interaction energy of these complexes is decomposed into ΔEPREP, ΔEFRZ, ΔEPOL, ΔEDISP, and ΔECT terms. The “preparation energy” ΔEPREP = ΔEHYBRID + ΔEGEOM includes both the energy required to change the hybridization state of the fragments, which is not only relevant in the context of NCIs but also the energy ΔEGEOM that is required to distort the geometry from its isolated-fragment value to the geometry in the supramolecular complex. The latter is significant only in the case of NO2. The “frozen” energy component ΔEFRZ includes both electrostatics (without polarization) and Pauli repulsion, that is , it is the energy associated with bringing the fragments together in the absence of density relaxation. In the present examples, this term is dominated by Pauli repulsion because the analytes are not large enough to experience significant electrostatic attraction. The dispersion term (ΔEDISP) is a key component of the NCIs in these systems and is (unsurprisingly) relatively large, as supported by the NCI analysis. The polarization energy (ΔEPOL) is rather small for each of the analytes except NO2. Finally, the charge-transfer term ΔECT is not insignificant, demonstrating that a relatively small amount of the transferred change can manifest as several kcal/mol in the interaction energy. However, the largest values of ΔECT are observed in the case of SO2 rather than NO2; thus, the ALMO-EDA charge-transfer results do not correlate perfectly with the extent of charge transfer that is predicted by natural population analysis. (There is no particular reason that it should correlate perfectly, as the two procedures for defining charge transfer are different.) Except for the case of NO2, where the polarization energy is quite large, the interactions in these complexes are dominated by the ΔEDISP and ΔECT terms.

Table 5

Second-Generation ALMO-EDA Results for C54H30···nPT-X Complexes (X = CO, NH3, SO2, and NO2), in kcal/mol

system	ΔEPREP	ΔEFRZ	ΔEPOL	ΔEDISP	ΔECT	Eint
C54H30···3PT···CO	0.0	3.1	–0.1	–3.9	–2.0	–3.0
C54H30···3PT ···NH3	0.0	1.7	–0.2	–3.8	–2.2	–4.4
C54H30···3PT ···SO2	0.0	8.1	–0.9	–8.0	–6.1	–6.9
C54H30···3PT···NO2	5.8	4.6	–36.0	–6.4	–2.7	–34.6
C54H30···5PT···CO	0.0	2.9	–0.1	–3.8	–1.8	–2.9
C54H30···5PT···NH3	0.0	1.8	–0.2	–3.7	–2.2	–4.2
C54H30···5PT···SO2	0.0	8.1	–0.9	–8.0	–6.0	–6.8
C54H30···5PT···NO2	–15.1	4.6	–14.7	–6.3	–2.7	–34.2
C54H30···7PT···CO	0.0	2.9	–0.1	–3.8	–1.9	–2.8
C54H30···7PT···NH3	0.0	1.9	–0.2	–3.5	–2.2	–4.1
C54H30···7PT···SO2	0.0	8.0	–0.9	–7.8	–5.9	–6.6
C54H30···7PT ···NO2	–15.2	4.7	–14.8	–6.2	–2.7	–34.3
C54H30···9PT ···CO	0.0	2.8	–0.1	–3.7	–1.9	–2.8
C54H30···9PT ···NH3	0.0	1.8	–0.2	–3.5	–2.2	–4.1
C54H30···9PT ···SO2	0.0	7.9	–0.9	–7.8	–5.9	–6.6
C54H30···9PT ···NO2	–15.3	4.7	–14.8	–6.3	–2.7	–34.4

Conclusions

The detection of noxious gases in the environment is very important, and various sensor materials based upon conducting polymers and their composites are under investigation in this regard. Composites consisting of conducting polymers with graphene are of great interest to increase the sensitivity and performance of sensor devices, but the molecular mechanism is unclear. DFT calculations performed herein explore possible gas-sensing mechanisms in graphene/polythiophene composites, with the composite modeled as C54H30···nPT for n = 3–9 thiophene units and exploring analytes CO, NH3, SO2, and NO2. The trend of interaction energies between these analytes and the composite is NO2 > SO2 > NH3 > CO. These differences arise due to variations in the strength of polar−π interactions. The interaction energies themselves range from an estimated value of −44.3 kcal/mol for C54H30···3PT···NO2 to −2.4 kcal/mol for C54H30···3PT···CO.

Analysis of the frontier molecular orbitals may elucidate how the analyte induces conductivity changes in the composite sensor material. The H–L gap of the composite is found to increase upon complexation with each of the aforementioned analytes. UV–vis spectra of the composites red-shifts upon complexation of the analyte, and the predicted absorbance increases with increasing chain polymer length. The NBO analysis helps in identifying the charge donor and acceptor species during the sensing phenomenon and the amount of partial charges on individual atoms in composite/analyte complexes. NCI isosurfaces and scatter plots in terms of RDG reveal the nature of NCI regions in C54H30···nPT···X complexes. The energy decomposition analysis (second-generation ALMO-EDA) provides a quantitative measurement of the NCIs and decompose them into different components that account for the contribution of each component toward the overall interaction energy. The dispersion and charge-transfer components contribute somewhat more than other components to the interaction energy term. Frontier molecular orbital analysis shows variation in the optical band gap of the composite and absorption maxima also red-shifted upon interaction with all analytes. One-electron DOS spectra indicate the observable change upon interaction with NO2 and SO2.

All these results point to the sensitivity of the C54H30···3PT composite among other graphene-nPT chains (5PT, 7PT, 9PT), as several of the aforementioned changes upon complexation with the analyte are present in the 3PT composite but washed out as the length of the polymer increases. Furthermore, this study indicates that these composites are clearly more sensitive toward NO2 as compared to other analytes, and to a lesser extent toward SO2, with only small changes noted upon complexation with either CO or NH3.

Computational Methodology

All calculations are performed using Q-Chem 5.2.[65] The Gauss View[66] and IQmol[67] graphical interfaces are used to visualize results. The graphene/nPT ribbon models exhibit larger interaction energies as compared to graphene/nPT sheet models.[68] Therefore, a C54H30-nPT graphene–polythiophene nanoribbon composite model is selected as a sensor material to check its sensitivity against various gaseous analytes: CO, NH3, SO2, and NO2. Note that the H–L gap converges quickly with the molecular size in linear acenes,[69] justifying our use of the term “nanoribbons” for these materials.

Various possible orientations of each analyte on the composite surface are considered to obtain the lowest energy structure optimized at the M06-2X/6-31G(d,p)[70,71] level of theory. Frequency calculations are performed at the same level of theory to confirm these structures as true minima. Based on our previous work,[36] the M06-2X/6-31G(d,p), M06-2X-D3/6-31G(d,p),[72,73] M06-2X-D3/6-31G(d,p) (CP), and ωB97M-V/def2-TZVPD (CP) level of theories can be used for the reliable estimate of interaction energies, where “CP” indicates the counterpoise correction to reduce BSSE. We will use the ωB97M-V/def2-TZVPD level of theory (with and without CP correction) to estimate interaction energies, as this is one of the best-performing DFT methods for energies,[74,75] although its use requires basis sets of triple-ζ quality.[76] For reasons of cost, structure optimizations are therefore performed at the M06-2X/6-31G(d,p) level. The SG-1 quadrature grid was used for B3LYP, the SG-2 grid for ωB97M-V, and the SG-3 grid for M06-2X.[77]

Interaction energies and their CP-corrected counterparts are calculated aswhere is the electronic energy of the composite–analyte complex, is the electronic energy of the composite, and is the electronic energy of the analyte. The quantity Eint,CP is the CP-corrected interaction energy and EBSSE is the CP correction defined as the monomer energies (composite and analyte) computed in the monomer basis set minus those computed in the supersystem basis set. B3LYP is a reliable method to calculate the electronic properties of materials based on conducting polymers.[3,78−81] Therefore, we have used B3LYP for the frontier molecular orbital (HOMO–LUMO) analysis and other electronic properties. Chemical potential (μ), hardness (η), softness (S), and electrophilicity (ω) are reactivity descriptors. The chemical potential is estimated (using Koopmans’ theorem[82]) aswhere EHOMO is the energy of the highest occupied molecular orbital and ELUMO is the energy of lowest unoccupied molecular orbitals. A similar approach is used for the hardness

Softness and electrophilicity are computed using[83]

NBO analysis is used to study the distribution of atomic partial charges. The TD-DFT approach is used to simulate UV–vis spectra of the isolated and complexed structures, at the B3LYP/6-31G** level within the Tamm-Dancoff approximation. GaussSum software[84] is used to plot the DOS spectra. The Multiwfn 3.7 program[85] is used to make NCI plots,[58] which are color-mapped isosurfaces of the RDG, s(r). The scatter plots are obtained by plotting RDG s(r) versus sign(λ2) ρ, where λ2 is the second largest eigenvalue of the Hessian of electron density.[58] The VMD 1.9.3 program[86] is used to render isosurfaces of s(r), with a contour value of 0.5 a.u. The second-generation ALMO-EDA[62−64,87] is used to further break down the interaction energy into physically meaningful components.