Electron rectification through donor-acceptor ... - De Gruyter

DOI: 10.2478/s11532-007-0022-z Research article CEJC 5(3) 2007 793–812

Electron rectification through donor-acceptor-heterocyclics connected to cumulenic bridge: a computational study J. Laxmikanth Rao∗ Inorganic Chemistry Division, Indian Institute of Chemical Technology, Hyderabad-500007, India

Received 22 January 2007; accepted 27 March 2007 Abstract: Density Functional Theory (DFT) calculations and Frontier Molecular Orbital (FMO) analysis have been carried out at B3LYP/6-31G(d,p) level of theory on some Donor-Bridge-Acceptor (D-B-A) molecules for their electrical rectification behavior. The donor-acceptor-heterocyclics (D/Aheterocyclics) (namely thiophene, furan and pyrrole rings) are attached as donor and acceptors to the two ends of cumulenic bridge. FMO analysis indicates that the molecules having even number of double bonds in the bridge, possess a complete localization of the MOs i.e., the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are localized on the donor and the acceptor side of the molecules respectively, and LUMO+1 is localized on the donor side, where as in case of odd number of double bonds in the bridge, both the HOMO and LUMOs are delocalized all over the molecule. The Potential Drop (PD) in the former case decreases as the number of double bonds increases in the bridge and due to the presence of the mutually orthogonal and noninteracting π-clouds, they can act as molecular rectifiers. For the molecules with the odd number of double bonds due to the low-lying LUMO delocalized all over the molecule, may find application as molecular wires in molecular electronics circuits. c Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved. Keywords: Heterocyclic substituted cumulenes, molecular electronics, rectifier, potential drop

1

Introduction

The field of molecular electronics is gaining importance in recent times experimentally as well as theoretically [1–18]. The era of molecular electronics began with the pioneering theoretical prediction of single D-σ-A molecular rectifier by Aviram and Ratner [19], which mimics the junction diode in nature. In this D-σ-A molecule, the HOMO and ∗

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J. Laxmikanth Rao / Central European Journal of Chemistry 5(3) 2007 793–812

LUMO are localized on the donor and acceptor parts of the molecule and at the same time the intervening σ-bond acts as a barrier and obstructs the charge transfer from the donor part to acceptor part, there by preventing the spreading of the molecular orbitals from one part of the molecule to the other part. When such a D-σ-A molecule is subjected to the suitable bias voltage in the positive (forward) direction, there will be an inelastic tunneling of electrons from the acceptor side to the donor side, provided the acceptor is connected to the cathode and the donor to the anode. This inelastic tunneling results in asymmetric I-V characteristic similar to that of the junction diode. In case of negative (reverse) applied bias voltage, rectification occurs at higher applied voltage when compared to the positive voltage, which is not feasible. Based on this approach of break in conjugation between the donor and acceptor a lot of theoretical as well as experimental reports have been published till to date [20–26]. Different types of mechanisms can be found in the literature [2, 27–31] for this rectification property associated with the single molecular systems. The common feature in all these proposed mechanisms is the tunneling of electrons from acceptor to donor in a D-σ-A system in a suitable applied bias voltage, but differs in the tunneling mechanisms. As per the mechanism proposed by Ellenbogen and Love [30], the resonant transport of electron occurs from the LUMO (as soon as it is loaded from the cathode) to the next unoccupied level LUMO+K (K = 0, 1, 2), which is localized on the donor part of the molecule. In case of the junction diode, the pnjunction part controls the flow of electrons, where as in the D-B-A molecular rectifier, the bridging unit controls the electron flow. Thus choice of the bridge, which is in between the donor and acceptor is very crucial and plays an important role in controlling the flow of electron. Based on our previous study with cumulenes [32], and the synthetic and structure feasibility associated with the cumulenes, we have considered cumulenic bridge for our present study. Despite the growing interest in the field of molecular electronics, detailed studies on the structure-property relationships containing five-membered heterocyclic rings are few [33–36]. However, it is very interesting to see how the electron transfer and rectification property will vary by replacing the D/A-aryl rings which are attached to the cumulenic bridge [32] with the D/A-five membered heterocyclics. Simple five-membered heterocyclics such as thiophene, pyrrole and furan possess lower delocalization energy relative to benzene and therefore are expected to be more effective than benzene in promoting charge transfer. For this study, D/A-five membered heterocyclics i.e., thiophene, pyrrole and furan, substituted with donor (NH2 ) and acceptor (NO2 ) groups were chosen as donor and acceptor respectively and were attached to the two ends of the cumulenic bridge (varying in double bonds) as shown in Figure 1. The main aim of the present study was to explore the possibility and suggest these molecules to serve as molecular rectifiers/conductors in the molecular electronics circuits using FMO analysis.


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Fig. 1 Molecular structures M1-M15 considered in this study with different heterocyclic moieties (namely M1-M5 with D/A-thiophene, M6-M10 with D/A-pyrrole and M11M15 with D/A-furan).

2

Computational Methods

The rectification behavior predicted for the single organic molecule by DFT method showed good agreement with the experiment [37–39]. In this view, the geometries of all the D/A-heterocyclic substituted cumulenic molecules (Figure 1) are optimized by using DFT/B3LYP method with 6-31G(d,p) basis set implemented in the G03W program [40], in which the inclusion of exchange and correlation function along with the polarization functions on heavier atoms and hydrogens suits correctly to describe the nature of LUMO and other higher unoccupied orbitals. These serve as channels for electron tunneling from acceptor to donor in an applied bias voltage. As the electron transfer process in the molecular system largely depends upon the spatial location as well as spatial orientation

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of the frontier molecular orbitals, a detailed individual molecular orbital analysis will give a clear understanding of the above processes. For the visualization of spatial orientation of the molecular orbitals, the orbital population analysis has been carried out using the B3LYP/6-31G(d,p) optimized geometries. The molecular orbitals can be visualized using Gauss View 3.0 program. From the orbital energy values the Potential Drop (PD) across the molecule is calculated, which gives the idea of the effectiveness of the system to behave as a rectifier, when a suitable bias voltage is applied to the molecule. In a suitable bias voltage the electron is loaded to the acceptor side (LUMO) and then it tunnels to the donor side (LUMO+K). This occurs when the rectifier molecule is in instantaneous negatively charged state. To see the excess charge localization in this instantaneously negatively charged state, single point energy calculation for the anion molecules have been carried out using B3LYP/6-31G(d,p) optimized neutral molecule at same level of theory and methodology.

3

Results and Discussions

3.1 Geometries The molecular structures of all the D-B-A molecules M1-M15, considered for this study are shown in their lowest energy conformation in Figure 1. The molecules namely M1M5, M6-M10 and M11-M15 contain the D/A-thiophene, D/A-pyrrole and D/A-furan heterocyclics respectively, which are connected to the two ends of the cumulenic bridge (varying in double bonds) as shown in Figure 1. The corresponding optimized bond lengths are shown in Table 1. The bond angles and twist angles for each molecule with reference to the central cumulenic bridge are tabulated in Table 2. It is seen from the Table 2, the molecules namely (M1, M3 and M5); (M6, M8 and M10) and (M11, M13 and M15) in which the cumulenic bridge having even number of double bonds, the attached D/A-heterocyclics are mutually perpendicular to each other. In case of the other molecules namely (M2 and M4); (M7 and M9) and (M12 and M14) which have odd number of double bonds in the cumulenic bridge, the attached D/A-heterocyclics are in plane with the cumulenic bridge and show planar characteristics similar to stilbene like system. Thus the positions of these D/A-substituents are in accordance with the rules governing the spatial orientations of the substituents in cumulenic systems [41]. It is also seen that the -NH2 group shows pyramidality in case of the molecules where the D/A-heterocyclics are mutually perpendicular to each other, while in others they remain in the molecular plane. In all these molecules the cumulenic bridge remains almost linear with lesser deviations from the linearity (Table 2). The rigid linear structure of the cumulenic bridge present in these molecules may be attributed to the involvement of the sp-carbon atoms in the bonding, which is one of the essential criteria for device applications.


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Table 1 Optimized bond lengths (in ˚ A) for molecules M1-M15.

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15

R12

R23

R34

R45

1.449 1.423 1.436 1.209 1.430 1.446 1.418 1.430 1.415 1.424 1.440 1.415 1.427 1.415 1.435

1.316 1.344 1.329 1.345 1.336 1.319 1.348 1.333 1.349 1.340 1.316 1.344 1.330 1.344 1.333

1.317 1.255 1.277 1.258 1.270 1.318 1.256 1.277 1.257 1.269 1.316 1.253 1.276 1.257 1.270

1.457 1.343 1.278 1.307 1.287 1.457 1.345 1.280 1.309 1.290 1.449 1.343 1.277 1.307 1.286

R56

R67

R78

R89

1.436 1.327 1.259 1.286

1.446 1.343 1.271

1.434 1.334

1.442

1.435 1.329 1.259 1.285

1.446 1.343 1.273

1.435 1.333

1.441

1.428 1.329 1.258 1.288

1.439 1.342 1.269

1.427 1.336

1.422

Table 2 Optimized bond angles (in deg) and dihedral angles (in deg) for molecules M1 - M15. A234 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15

179.2 179.3 179.0 178.8 178.7 179.3 178.4 179.5 179.0 179.2 178.9 178.1 178.8 178.3 178.8

A345

A456

A567

179.6 179.8 179.9 179.7

179.2 179.7 179.9

179.6 179.8

179.8 179.8 179.8 179.9

179.4 179.8 179.8

178.9 179.9

179.8 179.8 179.9 179.8

179.2 179.7 179.9

179.1 179.9

A678

Dihedral Angle (D12XY)

90.5

(D1245) 180.0 (D1256) 89.9 (D1267) 180.0 (D1278) 89.7 (D1289) (D1245) 180.0(D1256) 89.7 (D1267) 180.0 (D1278) 89.3 (D1289) (D1245) 180.0 (D1256) 89.6 (D1267) 179.9 (D1278) 89.6 (D1289)

178.9 90.3

179.4 90.2

179.0

3.2 Molecular Orbital Energy Levels To understand the structure-property relationship of these molecules M1-M15, populations analyses were carried out using the B3LYP/6-31G(d,p) optimized geometries on the individual D/A-heterocyclics (i.e., Thiophene-NH2 (Th-NH2 ), Thiophene-NO2 (ThNO2 ), Pyrrole-NH2 (Py-NH2 ), Pyrrole-NO2 (Py-NO2 ), Furan-NH2 (Fu-NH2) and FuranNO2 (Fu-NO2)),and all were optimized using the same methodology. Table 3 shows orbital energies of HOMO, LUMO, LUMO+1 and HOMO-LUMO gap (HLG) for M1-

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M15, alongwith their unsubstituted counter part molecules and the individual donor and acceptor heterocyclics. The HLG can be calculated using the following equation 1. HOMO − LUMOgap (HLG) = |EHOM O − ELU M O |

(1)

where EHOM O and ELU M O are the energies of HOMO and LUMO respectively. Figure 2, shows the orbital energy level diagram for molecules M1-M5 having ThNH2 as donor and Th-NO2 as acceptor attached to the two ends of the cumulenic bridge along with the individual D/A-thiophenes, considering the ten highest occupied and ten lowest occupied orbitals. Similarly Figures 3 and 4, shows the orbital energy diagram for molecules M6-M10 and M11-M15 having the D/A-pyrrole and D/A-furan moieties respectively along with the individual D/A-heterocyclics. Table 3 Orbital Energies of HOMO, LUMO, LUMO+1 and HLG (in eV), for molecules M1-M15 with their unsubstituted counter parts molecules, along with their individual heterocyclic donor and acceptor molecules. The Potential Drop (PD)s (in eV), for molecules showing the molecular rectification are also shown. molecules

HOMO

LUMO

M1 M2 M3 M4 M5 T h − N H2 T h − N O2 M6 M7 M8 M9 M10 P y − N H2 P y − N O2 M11 M12 M13 M14 M15 F u − N H2 F u − N O2

−5.331 −5.025 −5.258 −4.973 −5.201 −6.167 −6.954 −5.057 −4.625 −4.968 −4.619 −4.926 −5.545 −6.461 −5.115 −4.889 −5.083 −4.939 −5.054 −6.036 −6.953

−2.555 −2.681 −2.713 −2.919 −2.904 0.050 −2.017 −2.168 −2.215 −2.348 −2.536 −2.583 0.176 −2.068 −2.348 −2.463 −2.500 −2.806 −2.717 −0.546 −2.594

Substituted LUMO+1 −1.106 −1.518 −1.882 −1.760 −2.385 −0.613 −1.120 −1.596 −1.441 −2.155 −0.710 −1.398 −1.666 −1.677 −2.228

HLG$

PD#

2.776 2.344 2.545 2.054 2.297 6.217 4.937 2.889 2.410 2.620 2.083 2.343 5.721 4.393 2.767 2.426 2.583 2.133 2.337 5.490 4.359

1.449 0.831 0.519

1.555 0.752 0.428

1.638 0.834 0.489

Unsubstituted HOMO LUMO HLG$ −5.760 −5.090 −5.542 −5.024 −5.400

−1.031 −2.157 −1.770 −2.563 −2.281

4.729 2.933 3.772 2.462 3.119

−5.239 −4.577 −5.117 −4.582 −5.035

−0.333 −1.633 −1.369 −2.157 −1.968

4.906 2.944 3.747 2.425 3.068

−5.560 −4.927 −5.384 −4.892 −5.271

−0.602 −1.927 −1.537 −2.401 −2.119

4.958 3.000 3.847 2.490 3.152

Th=Thiophene, Py=pyrrole; Fu=Furan $ HLG= |E # PD=ΔE HOM O -ELU M O |; Lumo = ELumo+1 - ELumo

From Table 3 and Figures 2, 3 and 4, it can be seen that in the case of acceptor substituted heterocyclics (i.e., Th-NO2 , Py-NO2 and Fu-NO2) both HOMO and LUMO are stabilized as compared to donor substituted heterocyclics (i.e., Th-NH2 , Py-NH2 and


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Fig. 2 Molecular Orbital Energy level diagram for Molecules M1-M5 along with Thiophene-NH2 and Thiophene-NO2 , using the B3LYP/6-31G(d,p) optimized geometries.

Fig. 3 Molecular Orbital Energy level diagram for Molecules M6-M10 along with Pyrrole-NH2 and Pyrrole-NO2 using B3LYP/6-31G(d,p) optimized geometries. Fu-NH2 ), wherein their HLG differs by more than 1eV. Also it can be seen from these results that the acceptor substituted heterocyclics are more susceptible to reduction since the LUMO of these are stabilized as compared to the LUMO of the donor substituted heterocyclics.Hence electron injection to the LUMO will be a lower energy process. On the other hand donor substituted heterocyclics are amenable to oxidation as HOMO of

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Fig. 4 Molecular Orbital Energy level diagram for Molecules M11-M15 along with Furan-NH2 and Furan-NO2 using the B3LYP/6-31G(d,p) optimized geometries. these are less stabilized as compared to HOMO of the acceptor substituted heterocyclics. Therefore removal of one electron from HOMO will be a less energetic process. If this redox couple is connected through a suitable barrier (here a cumulenic bridge), then the whole system could act as a rectifier/conductor (depending on the number double bonds present in the cumulenic bridge), involving electron transfer that would be taking place from one end to the other end of the molecule in the presence of the external applied bias voltage. Thus nitro group substituted heterocyclics are chosen as acceptors and amine group substituted heterocyclics are chosen as donors and are attached to the two ends of the cumulenic bridge as shown in Figure 1. It can be seen that from Table 3, the HOMO and LUMOs of all the substituted molecules M1-M15 are stabilized and possess lower HLGs as compared to the HOMO, LUMO and HLGs of the unsubstituted ones. This is because of chemical perturbation arising from donor-acceptor substitution. From Table 3 and Figures 2, 3 and 4, it also can be observed that the HOMOs of all the M1-M15 molecules are slightly destabilized as compared to the individual HOMOs of the D/A substituted ones. The LUMOs of M1M15 are more stabilized compared to the LUMOs of the individual D/A-heterocyclics. This type of stabilization and destabilization of molecular orbitals may be attributed to the different π-charge delocalization associated heterocyclic rings, resulting in the drastic decrease in the HLGs of M1-M15 as compared to the HLGs of individual D/Aheterocyclics. From Table 3 and Figure 2, it can be seen that the HLG gap is very high for both the individual D/A-thiophene i.e., Th-NH2 and Th-NO2 with the values 6.217 and 4.937 eV


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respectively. In contrast, when these two are connected through the cumulenic bridge as shown in Figure 1 resulting in M1-M5, there is a drastic decrease in the HLG varying from 2.054 to 2.776 eV. This decrease in the HLG plays a crucial role when these molecules are connected to the two electrodes, since it is believed that the Fermi level of the contact lies in between the HLG of the molecule. Thus this decrease in the HLG can lead to a more favorable path for the electron injection process in the system when a suitable bias voltage is applied. A similar trend is observed with the other molecules i.e., for M6-M10 with the HLG varying from 2.083 to 2.889 eV, as opposed to the individual Py-NH2 and Py-NO2 which have the values 5.271 and 4.393 eV respectively (Table 3 and Figure 3). For molecules M11-M15 the HLG varies from 2.133 to 2.767 eV, as compared to the individual Fu-NH2 and Fu-NO2 which have the values 5.490 and 4.359 eV respectively (Table 3 and Figure 4). In general it can be seen from Table 3, that the molecules associated with the same D/A-heterocyclics, both the HOMO and LUMOs of the molecules that have odd number of double bonds in the cumulenic bridge are stabilized as compared to molecules having the even number of double bonds. This results in an decrease in the HLG value of the former as compared to the latter. This may be due to the molecular planarity present in the former molecules which increases the π-conjugation as compared to the latter in which the attached D/A-heterocyclics are mutually perpendicular to each other. This reduces the conjugation between the heterocyclic ring and the cumulenic bridge (Table 2). It is also seen from the Table 3, that as the number of sp-carbons (from 1 to 5) in the cumulenic bridge increases, a general trend of descending saw tooth type of characteristic in HLG is observed with a low discrepancy, irrespective of the D/A-heterocyclics attached to the cumulenic bridge. It is observed in M1-M5 molecules having D/A-thiophene attached to the cumulenic bridge, that as we go from M1 to M3 to M5 (having even number of double bonds in the cumulenic bridge), the HLG decreases from 2.776 (M1) to 2.545 (M3) to 2.297 eV (M5) as the number of the sp-carbon atoms increases (vide supra), which reflects as a decrease in the PD (Table 3). In M2 and M4 molecules (having odd number of double bonds in the cumulenic bridge) the HLG still decreases from 2.344 (M2) to 2.054 eV (M4) which results in an increase in the molecular conduction (vide supra). A similar trend is observed in M6-M10 and M11-M15 molecules having the D/Apyrrole and D/A-furan respectively attached to the cumulenic bridge. In the case of M6, M8 and M10 (having even double bonds), the HLG decreases from 2.889 (M6) to 2.620 (M8) to 2.343 eV (M10) whereas in case of M7 and M9 (having odd number of doubles bonds), it decreases from 2.410 (M7) to 2.083 eV (M9). Similarly, in molecules M11, M13 and M15 (having even number of double bonds), the HLG decreases from 2.767 (M11), 2.583 (M13) and 2.337 eV (M15) whereas in case of M12 and M14 (having odd double bonds) it decreases from 2.426 (M12) to 2.133 eV (M14). The varied nature of HLG among these molecules (M1-M15) may be attributed to the varying electron densities associated with the heteroatoms and π-charge delocalization associated with the thiophene, pyrrole and furan moieties.

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3.3 Electron Transport Analysis In general when the D-B-A molecule is connected through the electrodes i.e., donor is connected to the anode and acceptor is connected to cathode and a suitable bias voltage is applied one electron will be injected to the molecule from the cathode. The incoming electron inside the system will be loaded to the LUMO of the molecule localized on the acceptor side. Then this electron tunnels inelastically through the cumulenic bridge to the donor side and finally escapes to the anode through the unoccupied molecular orbital situated on donor side of the molecule. This tunneling process in a rectifying molecular system is largely controlled by the unoccupied orbitals (unoccupied orbitals are the channels for the electrical conduction inside the molecule) and is based on the energy mismatch between the two conducting unoccupied levels localized on different parts of the molecule [30]. In view of the above described mechanism, electron transfer in both the forward and reverse bias condition for the molecules considered in this study can be described as follows: In the forward bias condition, the necessary condition for the electron flow is that the applied voltage bias must be sufficient enough to raise the Fermi energy of the electron in the occupied level of gold contact on the acceptor side, approximately as high as the energy of the LUMO, which is localized on the acceptor part of the molecule. The injected electron from the gold contact to the acceptor part of the molecule can tunnel through the central cumulenic bridge to the unoccupied molecular orbital present in the donor half of the molecule and finally escape into the gold contact lying in the donor part. Similar to the forward bias condition, in a reverse bias condition for the electron transfer from the donor to the acceptor part of the molecule through the central cumulenic bridge, the applied voltage bias must be sufficiently high to raise the Fermi energy of the gold contact on the donor side of the molecule, so that it would match with the energy of the LUMO+1 localized on the donor part of the molecule. However, in the reverse bias case, the amount of voltage that must be applied is considerably greater than in the forward bias case. To achieve current flow across these molecules, in an applied bias condition, the LUMO and LUMO+1 levels must align with each other [30]. To understand the electron transport through the molecule and as a consequence the rectifying properties of the molecular systems, population analyses were carried out. The spatial orientation of the molecular orbitals plays an important role in accounting for the electron transport in the molecule. The PD across the molecule, which gives the idea of the effectiveness of the system to behave as a rectifier when a suitable bias voltage is applied to the molecule is calculated from the molecular orbital energy values using the following equation 2 [30]. P otentialDrop(P D) = ΔELU M O = ELU M O+K − ELU M O ;

k = 0, 1, 2

(2)

where ELU M O is the orbital energy localized on the acceptor side and ELU M O+K is the orbital energy of the next unoccupied orbital (here it is LUMO+1), which is localized on the donor side of the molecule. The approximate PD across the proposed molecular rectifiers have been calculated using equation 2 and tabulated in Table 3.


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The spatial location and orientations of frontier molecular orbitals are shown in Figure 5 for molecules M1-M5, in which the two ends of the cumulenic bridge (having 2,3,4,5 and 6 double bonds in the bridge) are substituted with the D/A-thiophene heterocyclics. Similarly, Figures 6 and 7 show the spatial location and orientation of the frontier molecular orbitals of M6-M10 and M11-15, in which the two ends of the cumulenic bridge (having 2,3,4,5 and 6 double bonds in the bridge) are substituted with the D/A-pyrrole and D/A-furan respectively. In all these Figures 5, 6 and 7, the first three molecules represent the suggested molecular rectifiers (namely (M1, M3 and M5); (M6, M8 and M10) and (M11, M13 and M15)) and the others (namely (M2 and M4); (M7 and M9) and (M12 and M14)) represent the suggested molecular conductors respectively. 3.3.1 Cumulenic bridge with even number of double bonds For all the molecules containing even number of double bonds in the cumulenic bridge namely (M1, M3 and M5); (M6, M8 and M10) and (M11, M13 and M15) containing the D/A-thiophene, D/A-pyrrole and D/A-furan respectively, the molecular orbitals namely HOMO, LUMO and LUMO+1 are localized on different parts of the molecule (Figures 5, 6 and 7). This may be due to the asymmetric nature of the electron withdrawing and electron donating groups. It is seen from Figures 5, 6 and 7, that in all these molecules, the HOMOs are localized on the donor side of the molecule and the LUMOs are localized on the acceptor side of the molecule. In both the HOMO and LUMOs of these molecules, the elongation of orbital population onto the cumulenic bridge is observed. This elongation of the orbital population along with the cumulenic bridge can be attributed to be due to the π-electron cloud associated with the cumulenic bridge. In all these molecules the unoccupied orbital LUMO+1, which is the next unoccupied orbital, is localized on the donor side of the molecule. So, the loaded electron in the LUMO from the cathode can tunnel inelastically to the LUMO+1 in a proper applied bias voltage and accordingly an approximate PD has been calculated using Equation 2 (Table 3). Again, it can be seen from the molecular orbitals (Figures 5, 6 and 7) that both LUMO and LUMO+1 orbital populations are spilt over the cumulenic backbone and though orthogonal on the bridge have an extension to the twisted heterocyclic rings on both the sides and will favor electron flow. One more interesting thing that can be observed in all these molecules is the similarity in spatial orientations of LUMO+ 1 with the HOMO. In LUMO+1, it can be seen that an overall decrease in the population density across the molecule along with the orbital contribution coming from different pairs of πbonding atoms in the cumulenic backbone when compare to HOMO. Thus this state, i.e., LUMO+1 can be considered as antibonding orbital of HOMO (Figures 5, 6 and 7).From Table 3, it can be seen that the PD for M1 is 1.449 eV (having 1 sp-carbon atom in the cumulenic bridge), where as in M3 and M5 (having 3 and 5 sp-carbon atoms respectively in the cumulenic bridge), it is 0.831 and 0.519 eV respectively. This decrease in the PD from M1 to M3 to M5 is quite opposite to the trend observed in the D-σ-A systems, in which increase in the -CH2 - units in the D/A-aryl rings results in an increase in the PD[24]. This is the case as opposed to the fact that in both the cases there is a conjuga-

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tion break by mutually perpendicular and non-interacting π-bonds in the former case and σ-bonds in the latter case. The reason for this reverse trend may be explained as follows: It can be seen from the energy level plot (Figure 2 and Table 3), that both the HOMO and LUMOs of M1, M3 and M5 lie around the same energy level with nearly equal HLGs, but there is a decrease in the LUMO+1 energy levels, going from M1 (−1.106 eV) to M3 (−1.882 eV) to M5 (−2.385 eV). The lowering of LUMO+1 energy levels may be due to the added extra stability i.e., coming from the additional π-orbital contribution due to the presence of one and two additional sp-carbon atoms in the cumulenic back bone and also the π-charge delocalization associated with the heterocyclic rings and as a consequence of this, a decreasing trend in the PD is observed. In the case of M6, M8 and M10, it is seen from Table 3, that the PD for M6 is 1.555 eV (having 1sp-carbon atom in the cumulenic bridge), where as in M8 and M10 (having 3 and 5 sp-carbon atoms respectively in the cumulenic bridge), it is 0.752 and 0.428 eV respectively. Here also the PD follows the same reverse trend i.e., it decreases as the sp- carbon atoms in the cumulenic bridge increases, which is opposite to the trend observed in conventional D-σ-A molecules (vide supra). The decrease in the PD going from M6 to M8 to M10 may be explained by observing the energy level plot (Figure 3). It can be seen from Figure 3 and Table 3, both the HOMO and LUMOs of M6, M8 and M10 lie around in the same energy level with nearly equal HLGs, but there is a decrease in the LUMO+1 energy levels, going from M6 (−0.613 eV) to M8 (−1.596 eV) to M10 (−2.155 eV) (vide supra). Similarly, in case of M11, M13 and M15, the PD for M11 is 1.638 eV (having 1spcarbon atom in the cumulenic bridge), where as in M13 and M15 (having 3 and 5 sp carbon atoms respectively in the cumulenic bridge), it is 0.834 and 0.489 eV respectively (Table 3). Here also the PD follows the same reverse trend similar to the above-mentioned molecules (vide supra). The decrease in the PD going from M11 to M13 to M15 may be explained by observing the energy level plot (Figure 4). It can be seen from Figure 4 and Table 3, both the HOMO and LUMOs of M11, M13 and M15 lie around the same energy level with nearly equal HLGs, but there is a decrease in the LUMO+1 energy levels, going from M11 (−0.710 eV) to M13 (−1.666 eV) to M15 (−2.228 eV) (vide supra). The trend in PD which gives the idea for the effectiveness of the molecule to behave as a rectifier, among the D/A-heterocyclics connected to the cumulenic bridge is as follows: M11-M15 > M6-M10 > M1-M5. The observed PD trend may be due to the variation in the π-charge delocalization due to their electronegativities of the oxygen, nitrogen and sulfur atoms. If such a type of molecule is connected through the electrical contacts and a suitable bias voltage is applied, the incoming electron is loaded in the LUMO from the cathode and tunnels inelastically to the unoccupied LUMO+1 orbital, which is localized in the donor side and from there to anode. Thus the rectification occurs in one direction only. Therefore it is suggested that these molecules could be treated as molecular rectifiers alternative to the traditional D-σ-A type.


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Fig. 5 Frontier molecular orbital pictures of HOMO, LUMO and LUMO+1 (in the order from upper left to right) for M1-M5 with D/A-thiophene heterocyclic ring.

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Fig. 6 Frontier molecular orbital pictures of HOMO, LUMO and LUMO+1 (in the order from upper left to right) for M6-M10 with D/A-pyrrole heterocyclic ring.


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Fig. 7 Frontier molecular orbital pictures of HOMO, LUMO and LUMO+1 (in the order from upper left to right) for M11-M15 with D/A-furan heterocyclic ring.

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When one electron is loaded from the cathode to the LUMO level, which is localized on the acceptor side of the molecule, it is assumed that instantaneously it will be negatively charged until the total escape of the electron to the anode from the donor side takes place. To see the excess charge localization in this instantaneously negatively charged state we have done single point calculation for the anions of these rectifier molecules by considering the B3LYP/6-31G(d,p) optimized neutral geometry of these molecules at the same level of theory and the detailed charge accumulation data are shown in Table 4, it is seen from this table that the excess charge is delocalized on the acceptor side. 3.3.2 Cumulenic bridge with odd number of double bonds It is well known that in the electronic circuits, the molecular conductors serve the purpose of molecular wires. Thus the molecules in which the molecular orbitals are fully delocalized all over the molecule (which gives the path for conduction) and the presence of unoccupied orbital levels are responsible for the molecular conduction. It is seen from the Figures 5, 6 and 7, all the molecules containing odd number of double bonds in the cumulenic bridge namely (M2 and M4); (M7 and M9) and (M12 and M14) containing the D/A-thiophene, D/A-pyrrole and D/A-furan respectively, the HOMO and LUMOs are delocalized entirely all over the molecule including the cumulenic bridge (Figures 5, 6 and 7). If such a type of molecule is connected through the electrical contacts and a suitable bias voltage is applied, the loaded electron in the LUMO from the cathode can directly pass to the donor side through the cumulenic bridge and show conductance. Thus the LUMO itself will serve as a conduction channel for electron transport. Thus these molecules could serve as molecular wires in electronic circuits. From Table 3 it is seen that the LUMO of M4 (−2.904 eV) is stabilized compared to the LUMO of M2 (−2.681 eV) and the HLG gap is less for M4 (2.054 eV) than M2 (2.344 eV). According to the assumption that the Fermi level of contact lies in between the HLG, the electron injection process will be easier in the former than that of latter. Hence the molecule M4 can be a more efficient conductor than molecule M2. Similarly in M7 and M9 molecules, the LUMO of M9 (−2.536 eV) is stabilized when compared to the LUMO of M7 (−2.215 eV) and the HLG gap is less for M9 (2.083 eV) than M7 (2.410 eV). In the case of M12 and M14 molecules, the LUMO of M14 (−2.806 eV) is stabilized when compared to the LUMO of M12 (−2.463 eV). The HLG gap is less for M14 (2.133 eV) than M12 (2.426 eV). Hence the molecules M9 and M14 can act as efficient molecular conductors when compared to M7 and M12 (vide supra). It is clear from the Table 3 that the molecules with the 4-sp carbon atoms in the cumulenic bridge namely M4, M9 and M14 can act as efficient molecular conductors as compared to the molecules having the 2-sp carbon atoms namely M2, M7 and M9, respectively. This may be due to the increase in π-conjugation, which involves both the cumulenic bridge and the attached D/A-heterocyclics, thereby facilitating the electron transport through the molecule, which in turn increases the molecular conductance. The molecular conductance trend among the D/A-heterocyclics connected to the cumulenic bridge is as follows Furan>Pyrrole>Thiophene (vide supra).


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Table 4 Mulliken point charge analysis for neutral as well as anions (from single point calculation at B3LYP/6-31G(d,p) optimized neutral geometry) for molecules M1-M15. molecules M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 #1 #2

Excess charge localization on Acceptor part # 1

Excess charge localization on Donor part # 2

−0.675 −0.378 −0.533 −0.377 −0.437 −0.658 −0.422 −0.490 −0.340 −0.391 −0.664 −0.427 −0.322 −0.349 −0.404

−0.148 −0.296 −0.175 −0.280 −0.184 −0.140 −0.290 −0.175 −0.280 −0.188 −0.135 −0.285 −0.166 −0.265 −0.177

(charges on Aanion - charges on Aneutral ); (charges on Aanion - charges on Dneutral )

3.4 Conclusions Using DFT method, systematic studies have been carried out using various D/A- heterocyclics (namely thiophene, pyrrole and furan) connected to the two ends of the cumulenic bridge (having 1 to 5 sp-carbon atoms in the bridge) for their molecular rectification and conductance properties. Population analyses were carried out at the same level of theory to know the exact nature of the orbital population/orientation and also the electron transport properties resulting in the rectifying/conducting behavior of these molecules. From FMO studies, it is observed that the D/A-heterocyclics connected to the cumulenic bridge having even number of double bonds, show molecular rectification and hence can be suggested as molecular rectifiers alternatives to the suggested D-σ-A systems. It is also observed that the D/A-heterocyclics connected to the cumulenic bridge having odd number of doubles bonds, show molecular conductance and are useful as molecular wires in the electronic circuits.

Acknowledgements The author thanks the Director, IICT and the Head, Inorganic Chemistry Division, IICT for their constant encouragement in this work. The author also thanks Dr. K.Bhanuprakash for helpful discussion. (IICT Communication no: 060928)

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