Two-dimensional, phenanthroline-based, extended π-conjugated molecules for single-molecule conduction

The conduction properties of phenanthroline-terminated, polycyclic extended rr -conjugated molecul ar wires are investigated using density fun ctional theory (OFT) in combination with Green 's function techniques and group theory. While these molecules could possibly be thought of as accessible graphene-like fragments, they are calculated to conduct poorly. The decay constant for their exponential decrease of conductance with length is in excess of 0.6 A I for the add ition of internal fused quinoxaline groups and in excess of 0.9 A I for the addition of internal pyrazine-fused pyrene groups. Furthermore, while the bidentate phenanthroline connectors adhere strongly to gold, they are sometimes predicted to be less conductive than related mono dentate connectors. Careful design is thus required for any graphenelike extended rr -system intended for single-molecule conduction applications. The anchoring of organic molecules to metals is an important issue in molecular electronics [1]. Phenanthroline has been suggested as such an 'alligator clip' for attaching molecules with extended rr-conjugation to surfaces [2]. It is particularly appl icable for linking oligoporphyrins, molecules with useful conduction properties [2]. Such systems can be thought of as small synthetically feasible models for graphene-like nanoribbons, materials also of great interest for molecul ar electronics applications [3-6]. Studies of phenanthrolinebased molecules include electrochemical and spectroscopic properties [7] as well as their usefulness for faci litating intramolecular electron transfer processes involving chelated metals [2]. Here, we investigate their single-molecule conduction by means of density functional theory (OFT) in combination with Green's function techniques. We look especially at the length dependence of their conductance as well as the effectiveness of the bridging group in several chemical config urations. 4 AU lhor to whom any correspondence shou ld be addressed. The investigation of these azine-linked, extended rr conjugated molecules is intrinsically linked with the general OFT problem of band line up [8]. Owing to the asy mptotic potential error inherent in most density functionals , the hi ghest-occupied molecular orbital (HOMO) of the organic molecule is poorly represented in relation to the Fermi energy of metals, and this significantly affects hole conductivity. In addition, the large disparity between the OFT band gap (orbital energy difference between the HOMO and the lowest-unoccupied molecular orbital (LUMO» and the correspond ing electrochemical potential difference affects the perceived electron conductivity [8, 9]. In order to overcome these problems, we apply empirical corrections to the OFT calculations in the spirit of Quek et al [1 0] and Mowbray et al [11]. We explore the properties of the phenanthroline-based, extended rr-conjugated molecules shown chemisorbed to gold electrodes in fi gure 1: tetrapyrido[3,2-a;2' ,3'-c;3" ,2"h ;2'" ,3'"-j]phenazine (TPPHZ), dipyrido[3 ' ,2' :5,6;2" ,3":7,8] Table 1. The binding energy, the deduced dominant conduction channels, the most significant molecular orbitals, and the condu c tance both before and after the scissor correction to the orbital energies , for the molecules and gold ligation patterns considered. Au-N bond Binding Molecule Structure length (A) energy (eY) 1,4-benzenediamine Linear 2.5 0.86 1,4-benzenediamine Diagonal 2. 1 0.58 BQPY Bidentate 2.6 2.30 TPPHZ Bidentate 2.3 2. 16 TATPP Bidentate 2.4 2.14 TATPPl -Iinear Monodentate 2.4 1.I 6 TATPPI-diagonal Monodentate 2.4 1.17 TATPP-2 Mixed 2.4 1.69 a Experiment 0.0064 Go [ 17]. Figure 1. (Colour online) Geometries of the Au-BQPY-Au (a), AuTATPP-Au (b), and Au-TPPHZ-Au (c) junctions. The black horizontal lines indicate where the junctions are cut into left and right electrode and extended-molecule. Yellowgold atoms, blue-nitrogen , browncarbon, and grey-hydrogen. quinoxalino[2,3-i ]dipyrido[3,2-a :21,3'_c ]phenazine, commonly known as 9, I I ,20,22-tetraazatetrapyrido[3,2-a:2' ,3'-c:3" , 2"-1 :2 ,3'"-n ]pentacene (TATPP), and dipyrido[3" ,2" :5' ,6' ;2'", 3"':7' ,8' ]quinoxalino[2',3' :9, 1 O]phenanthro[4,5-abc]dipyrido [3,2-h :2' ,3'j]phenazine, often alternatively referred to as bi s-{ dipyrido[3,2-f: 2' ,3'-h]quinoxalol -[2,3-e:2' ,3'-/]pyrene (BQPY). TATPP and BQPY can be considered as the parent molecule TPPHZ extended internally by one repeat unit of a fused quinoxaline group and a pyrazine-fused pyrene (phenanthro[4,5-fgh]quinoxaline) group, respective ly. DFr as implemented in the quantum chemistry package TURBOMOLE v5.7 [12] is used to determine the electronic and nuclear structures of these systems. The basis set is TURBOMOLE's standard Gaussian basis set, which is of split valence polarization quality for all non-hydrogen molecules [13] and the exchange correlation functional is 2 Dominant Dominant Conductance/ Go conduction molecular channels orbitals Raw Corrected A' a' (rr) HOMO 0.086 0.013· A' a' (rr) HOMO 0.027 0 .012" 3 x A bl(rr),(/I(rr) , 1.7 x 108 6.4 X 109 b2 (rr) HOMOs A" bl(rr) LUMO 1.2 x 104 1.0 X 105 A" bl(rr) LUMO 2.3 x 106 6.7 X 107 A" bl(rr) LUMO 6.4 x 105 2 .8 x 107 A" bl(rr) LUMO 2.7 x 105 1.6 X 106 A" bl(rr) LUMO 9.9 x 106 7.0 X 107 BP86 [14, IS), We determine the geometries by placing the molecules symmetrically between two gold atoms and relaxing the structures whilst maintaining their symmetry. This minimalist treatment of the binding of the connecti ng gold atom probably underestimates the AuN bond length, an effect which would be partly cancelled by the overestimation of the bond length through the use of the generalized gradient approximation (GGA) [16]. The gold atoms are replaced after the relaxation process by gold fcc pyramids with a lattice parameter of 4.08 A oriented in the (I II )-direction, where the pyramids consist of four layers, with I , 3, 6, and 10 atoms in the individual layers from the inside to the outside. In the case of BQPY, we relaxed the organic molecule without maintaining the symmetry after placing the pyramids. The resulting optimized geometri es are depicted in figure I and their AuN bond lengths are given in table 1. The nitrogen atoms of the phenanthroline end-groups form bonds with the gold electrodes leading to biligation of the gold tip. The conduction properties of these metalmolecule-metal junctions are ascertained using Green's function techniques and the Landauer formula expressed in a local, non-orthogonal basis, as discussed in detail in [ 1820). The junctions are therefore cut into three parts: the left (L) and right (R) electrode and the extended-molecule (M), which contains the organic molecule and the inner two layers of each pyramid as indicated in figure 1. The transmission channels are obtained, adiabatically tracked , and classified according to their conductance point group [2 I ] as done in our previous work [22]. We also calculate the local density of states (LDOS) of the molecular orbitals (MO), details of which are provided in the supplementary data (available at stacks.iop.org/JPhysCM/201295208). TPPHZ is exem plified here in detail. The analysis o r the other molecules can be found in the supplementary data (available at stacks.iop.org/JPhysCMl201295208). While the geometric point group of TPPHZ is D2h , after connection to the gold electrodes the atomic symmetry reduces to C2h. As the Green 's function formalism inherently removes all atomic symmetry operators that establish end-to-end symmetry in the system [21 ], the conductance point group controlling the symmetry of the conduction c!hannels reduces to Cs , where the mirror plane is the expanse of the organic molecule. Figure 2. (Colour online) Transmission and LDOS versus energy for AuTPPHZ-Au. (a) Total transmiss ion and transmiss ion of the individual channels c lass ified according to their conductance point group Cs . Blacktotal transmiss ion, redchannels of A' symmetry, blue-channels of A" symmetry. T he li nesty le indicates the correspondence of the peaks' positions of that channel compared to the LDOS of TPPHZ's MOs class ified in quas i-C2v symmetry (the geometric point group D2h of TPPHZ reduced by its end-to-end symmetry) . The contributions of the individual MOs to the LDOS are given in different colours in panels (b)(e). The black line in these panels corresponds to the sum of the contributions of MOs of that symmetry. (b) LDOS of MOs of /)1 symmetry. The orbitals with the largest contributions to the LDOS at the numbered peaks are shown in the supplementary data (availab le at stacks.iop.orglJPhysCM/201295208). (c) LDOS of MOs of 0 2 symmetry. (d) LDOS of MOs of 01 symmetry. (e) LDOS of MOs of /)2 symmetry. The Fermi energy is given as the vel1ical, dashed, orange line. Hence, the a -orbitals of TPPHZ can only contribute to channels of A' symmetry, while the IT -orbitals can just take part in channels of A" symmetry. The transmission rigorously decomposed into A' and A" channels is shown in fi gure 2(a). However, as the symmetry-breaking effects of the electrodes on the molecul ar orbitals are quite small , we sort the coupled MOs approx imate ly according to the group C2vthe geometric poinl group D2h of the TPPHZ reduced onl y by its end-lo-end symmetry [21] , complying in fact with the conductance point group of the uncoupled molecule. Thus the MOs can be class ified as being ITor (I orbitals as well as being roughly symmetric or antisymmetric with respect to the plane along the contact axis perpendicul ar to the expanse of the organic molecule. A description of the most significant molecular orbitals, the IT-orbitals of b l symmetry, is provided in supplementary data (avail able at stacks.iop.org/JPhysCMJ201295208). The LDOS of the MOs sorted by their species are plotted in the individual panels (b)(e) in fi gure 2. We also show the sum of the LDOS for the MOs of each species . Comparing these sums with the transmiss ion channcls, we notice that they resemble each other very well. It is thercfore possible to connect the individual transmiss ion channels with a hi gher symmetry than the actual symmetry of conduction of the metalmolecul emctal junction, namely the conductance point group of the uncoupled molecule.