Electronic communication through molecular bridges Supporting Information
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1 Electronic communication through molecular bridges Supporting Information Carmen Herrmann and Jan Elmisz Institute of Inorganic and Applied Chemistry, University of Hamburg, Martin-Luther-King-Platz 6, Hamburg, Germany Date: August, 2013 Status: resubmitted to Chem. Commun. for the Molecular Spintronics web themed issue 1
2 1 Computational Methodology 1.1 Molecular structures and energies Molecular structures were optimized using Kohn Sham density functional theory [1] with the BP86 exchange correlation functional [2,3] in combination with the resolution-of-the-identity ( RI ) density fitting technique as implemented in Turbomole 6.0 [4 6], until the norm of the gradient was below 10 4 a.u. The convergence criterion in the self-consistent-field algorithm was set to 10 7 a.u. for the change in energy. Where explicitly mentioned, the B3LYP functional [7, 8] was employed instead. For the thiophene- and furane-bridged systems, we employed Ahlrichs def-tzvp basis set, and for all other calculations Ahlrichs def2-tzvp basis set [9], which both feature a split-valence triple-zeta basis set with polarization functions on all atoms. Spin-state energy splittings E T E BS were obtained by optimizing the molecular structures for each spin state separately. For the diradical based on the alkyne-linked ethene bridge, we first optimized the structure in the triplet state, and then elongated the outermost C C bond to 1.7 Å and carried out single-point calculations on this structure for both the triplet and the singlet. The artificial elongation was done to prevent open-shell singlet calculations from converging to a closed-shell singlet. For the opt Å calculation, additionally the middle C C bond was elongated by 0.2 Å and triplet and singlet single-point calculations were carried out subsequently (see below for Cartesian coordinates). Initial guess orbitals for the Broken-Symmetry determinants were obtained from a tool implemented in a local version of Turbomole [10]. Equation (1) in the main manuscript is based on spin projection. When arguing that KS determinants need not be pure eigenfunctions of the total spin operator Ŝ 2 [11, 12], so that spin projection is not required, instead J AB = 1 (E 2 T E BS ) would hold. However, accepting one or the other as correct will not change relative values for J AB, so we report trends in E T E BS. For the conductance calculations, dithiol molecules were optimized, the thiol groups hydrogen atoms were stripped off, and the structures were placed between two Au 9 clusters with an sulfur gold distance of 2.48 Å [13]. Au Au distances were set to their value in extended gold crystals (2.88 Å). Fock and overlap matrices as required for the subsequent transport calculation (see below) were then obtained from a single-point electronic structure calculation on the Au 9 molecule Au 9 system using the Gaussian quantum chemistry program package, with the BP86 exchange correlation functional [2, 3] and the LANL2DZ effective core potential (ECP) with matching basis sets of doublezeta quality as implemented in Gaussian [14] MOs were plotted using Molden [15], with isodensity values of 0.02, and postprocessed with a local postprocessing tool by Gemma C. Solomon, University of Copenhagen. For molecular junctions (Au 9 molecule Au 9 structures), central subsystem MOs are plotted, which were calculated by solving the secular equation for the central subsystem only [16]. 1.2 Electron transport calculations Transmission functions were obtained by postprocessing output from electronic structure calculations on these finite-size electrode molecule electrode systems, using routines written in our laboratory [17, 18]. In the Green s function approach, T s is calculated from a trace over matrices describing the coupling of a central region [19] to the left and right electrodes, Γ L/R,s, and the central system 2
![subblock of the retarded and advanced Green s functions of the electrode molecule electrode system G r/a C,s [20, 21], Ts(E) = tr { ΓR,s(E)G r (E)ΓL,s(E)G a (E) ), (1) C,s the advanced Green s](/docs-images/91/105349432/images/3-0.jpg "function being the complex conjugate of the retarded.")
3 subblock of the retarded and advanced Green s functions of the electrode molecule electrode system G r/a C,s [20, 21], Ts(E) = tr { ΓR,s(E)G r (E)ΓL,s(E)G a (E) ), (1) C,s the advanced Green s function being the complex conjugate of the retarded. Γ X,s and G r C,s are calculated from the overlap and Fock matrices of a finite-cluster electrode molecule electrode system, Γ X,s = 2Im[(ES X C H X C,s ) g X,s (ES X C H X C,s )] (2) GC,s r = (ES C H C,s + i 2 Γ R,s + i 2 Γ L,s ). (3) The Fock and overlap matrices of the electrode molecule electrode system are divided into central, left-electrode, and right-electrode regions. S X C and H X C,s denote the coupling block of electrode X and molecule in the overlap and Fock matrix, respectively, while the molecule (or central region ) subblocks of these matrices are indicated by the subscript C. The central region consisted of the molecule only (i.e., no gold atoms were included) as we are interested in qualitative trends only. The Green s function matrices of the isolated electrodes X (X {L, R}) were calculated in the wide-band-limit (WBL) approximation, C,s (g X ) ij = i π LDOS const δ ij, (4) i.e., the local density of states (LDOS) was assumed to be independent of the energy, and furthermore, the same LDOS value of ev 1, obtained from the s-band LDOS for bulk gold from DFT calculations [22] was assigned to all basis functions. Although this is a rather crude approximation, it typically works very well for electrode metals such as gold, which feature a comparatively flat LDOS distribution around the Fermi energy (when plotted as a function of energy), and whose conduction properties are dominated by the broad s band [23]. Energies were not shifted by the system s Fermi energy. 2 Total energies and Cartesian Coordinates All coordinates are given in Å; all energies in hartree. 2.1 Alkyne-linked ethene bridge Figure 1: Structure of diradical formed from alkyne-linked ethene bridge. Optimized with KS- DFT(BP86)/def2-TZVP in the triplet state, then both outermost C C bonds set to 1.7 Å and middle C C bond elongated by 0.2 Å. 3
4 Diradical: BP86/def2-TZVP optimized in the triplet, both outermost C C bonds set to 1.7 Å C C C C C C C C H H H H H H Total energy triplet BP86/def2-TZVP: Total energy singlet BP86/def2-TZVP: Diradical: as above, additionally middle C C bond elongated by 0.2 Å C C C C C C C C H H H H H H Total energy triplet BP86/def2-TZVP: Total energy singlet BP86/def2-TZVP: Junction from optimized dithiol C C C
5 C H H C C S S Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction from optimized dithiol, middle C C bond elongated by 0.2 Å C C C S C C C S H H Au Au Au Au Au Au Au Au
6 Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Furane- and thiophene-bridged systems with fused rings Increasing*quinoidal*character* 1" 2" 3" 4" 5" Figure 2: Lewis structures X o = f O fu " rane- (X=O) and thiophene- (X=S X ) = b S ri " dged diradicals. In the junctions, the NNO radical groups are replaced by S Au 9 units (with the structures constructed as described in the methodology section). Diradical X=O, ring 1 Singlet BP86/def-TZVP optimized: C C C O C C C C C C C N F N ig L 96 e 7 wi - s 0ṡ3 t 4 r 3 u 1 c 5 t 0 ure 4 s.2 ( 5 to 08 p 4 ) 6 and trends in different communication measures (middle) for furane and th 6 iophene bridges;, and magnetic MO (bottom) for furane system 1. DE = E T kj/mol. KS-DFT(BP86). E BS. Energies in Fig tra top 3 4
7 C C O O C C C C H H H H H H H H H H H H N N C C C C C C O O H H H H H H H H H H H H C C H H Total energy singlet BP86/def-TZVP:
8 Triplet BP86/def-TZVP optimized: C C C O C C C C C C C N N C C O O C C C C H H H H H H H H H H H H N N C C C C C C O O H
9 H H H H H H H H H H H C C H H Total energy triplet BP86/def-TZVP: Diradical X=O, ring 2 ( = no ring) Singlet BP86/def-TZVP optimized: C C C O C C C C C C C N N C C O O C C C C H H H
10 H H H H H H H H H N N C C C C C C O O H H H H H H H H H H H H H H Total energy singlet BP86/def-TZVP: Triplet BP86/def-TZVP optimized: C C C O C C C C C
11 C C N N C C O O C C C C H H H H H H H H H H H H N N C C C C C C O O H H H H H H H H H H H H H H
12 Total energy triplet BP86/def-TZVP: Diradical X=O, ring 4 Singlet BP86/def-TZVP optimized: C C C O C C C C C C C N N C C O O C C C C H H H H H H H H H H H H N N C C C C C
13 C O O H H H H H H H H H H H H C S C H H Total energy singlet BP86/def-TZVP: Triplet BP86/def-TZVP optimized: C C C O C C C C C C C N N C C O O C C C C H
14 H H H H H H H H H H H N N C C C C C C O O H H H H H H H H H H H H C S C H H Total energy triplet BP86/def-TZVP: Diradical X=O, ring 5 Singlet BP86/def-TZVP optimized: C
15 C C O C C C C C C N N C C O O C C C C H H H H H H H H H H H H N N C C C C C C O O H H H H H H H H
16 H H H H C C H C C H H H C Total energy singlet BP86/def-TZVP: Triplet BP86/def-TZVP optimized: C C C O C C C C C C N N C C O O C C C C H H H H H H H H H
17 H H H N N C C C C C C O O H H H H H H H H H H H H C C H C C H H H C Total energy triplet BP86/def-TZVP: Diradical X=S, ring 1 Singlet BP86/def-TZVP optimized: C C C S C
18 C C C C C C N N C C O O C C C C H H H H H H H H H H H H N N C C C C C C O H H H H H H H H H H H H
19 C C H H O Total energy singlet BP86/def-TZVP: Triplet BP86/def-TZVP optimized: C C C S C C C C C C C N N C C O O C C C C H H H H H H H H H H H H N N C C
20 C C C C O H H H H H H H H H H H H C C H H O Total energy triplet BP86/def-TZVP: Diradical X=S, ring 2 ( = no ring) Singlet BP86/def-TZVP optimized: C C C S C C C C C C C H H N N C C
21 O O C C C C H H H H H H H H H H H H N N C C C C C C O O H H H H H H H H H H H H Total energy singlet BP86/def-TZVP: Triplet BP86/def-TZVP optimized: C C
22 C S C C C C C C C H H N N C C O O C C C C H H H H H H H H H H H H N N C C C C C C O O H H H H H H
23 H H H H H H Total energy triplet BP86/def-TZVP: Diradical X=S, ring 4 Singlet BP86/def-TZVP optimized: C C C S C C C C C C C N N C C O O C C C C H H H H H H H H H H H H
24 N N C C C C C C O O H H H H H H H H H H H H C S C H H Total energy singlet BP86/def-TZVP: Triplet BP86/def-TZVP optimized: C C C S C C C C C C C N N C C
25 O O C C C C H H H H H H H H H H H H N N C C C C C C O O H H H H H H H H H H H H C S C H H Total energy triplet BP86/def-TZVP:
26 Diradical X=S, ring 5 Singlet BP86/def-TZVP optimized: C C C S C C C C C C C N N C C O O C C C C H H H H H H H H H H H H N N C C C C C C O O H
27 H H H H H H H H H H H C C C H C H H H Total energy singlet BP86/def-TZVP: Triplet BP86/def-TZVP optimized: C C C S C C C C C C C N N C C O O C C C C H H
28 H H H H H H H H H H N N C C C C C C O O H H H H H H H H H H H H C C C H C H H H Total energy triplet BP86/def-TZVP: Junction X=O, ring 1 C
29 C C C O C C C C C C H H S S Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=O, ring 2 ( = no ring ) C C C C O C C C C
30 H H S S Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=O, ring 3 C C C C O C C C C C C H O H S S Au Au Au
31 Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=O, ring 4 C C C C O C C C C C C H S H S S Au Au Au Au Au Au Au Au Au Au
32 Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=O, ring 5 C C C C O C C C C C C C H C H H H S S Au Au Au Au Au Au Au Au Au Au Au Au Au Au
33 Au Au Au Au Total energy BP86/LANL2DZ: Junction X=S, ring 1 C C C C S C C C C C C H H S S Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=S, ring 2 ( = no ring ) 33
34 C C C C S C C C C H H S S Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=S, ring 3 C C C C S C C C
35 C C C H O H S S Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=S, ring 4 C C C C S C C C C C C H S H S
36 S Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction X=S, ring 5 C C C C S C C C C C C C H C H H H S S Au Au Au
37 Au Au Au Au Au Au Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Cross-conjugated systems N H H H H H H E T,E BS (((=(((,17.0(kJ/mol( (,6.0(kJ/mol( (12.5(kJ/mol( Figure 3: Lewis structures of cross-conjugated diradicals. In the junctions, the CH 2 radical groups are ε 1,εreplaced 2 (((((=((((((9.2(kJ/mol( by S Au 9 units (with the structures 44.5(kJ/mol(( constructed as described in the (70.0(kJ/mol( methodology section). ε 1,ε D2i ( r ( a j d u ic n al c = & C o H n) s ( i ( d = e (( g 6 rȯ 0 up 7(eV( 6.48(eV( 6.92(eV( 2 H H H Singlet BP86/def2-TZVP optimized: C C C C C C F C H T(E )((((=(((((0.10( 0.11( 0.22( 37
38 H C H H H H Total energy singlet BP86/def2-TZVP: Triplet BP86/def2-TZVP optimized: C C C C C C C H H C H H H H Total energy triplet BP86/def2-TZVP: Singlet B3LYP/def2-TZVP optimized: C C C C C C C H H C H H H H
39 Total energy singlet B3LYP/def2-TZVP: Triplet B3LYP/def2-TZVP optimized: C C C C C C C H H C H H H H Total energy triplet B3LYP/def2-TZVP: Diradical =NH side group Singlet BP86/def2-TZVP optimized: C N C C C C C H H C H H H Total energy singlet BP86/def2-TZVP:
40 Triplet BP86/def2-TZVP optimized: C N C C C C C H H C H H H Total energy triplet BP86/def2-TZVP: Singlet B3LYP/def2-TZVP optimized: C N C C C C C H H C H H H Total energy singlet B3LYP/def2-TZVP: Triplet B3LYP/def2-TZVP optimized: C N C C C C
41 C H H C H H H Total energy triplet B3LYP/def2-TZVP: Diradical =O side group Singlet BP86/def2-TZVP optimized: C O C C C C C H H C H H Total energy singlet BP86/def2-TZVP: Triplet BP86/def2-TZVP optimized: C O C C C C C H H C H H
42 Total energy triplet BP86/def2-TZVP: Singlet B3LYP/def2-TZVP optimized: C O C C C C C H H C H H Total energy singlet B3LYP/def2-TZVP: Triplet B3LYP/def2-TZVP optimized: C O C C C C C H H C H H Total energy triplet B3LYP/def2-TZVP: Junction =CH 2 side group C H C
43 C C C H C S S Au Au Au Au Au Au Au Au Au AU AU AU AU AU AU AU AU AU Total energy BP86/LANL2DZ: Junction =NH side group C N C C C C H S S Au Au Au Au Au Au Au Au Au
44 Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ: Junction =O side group C O C C C S C S AU AU AU AU AU AU AU AU AU Au Au Au Au Au Au Au Au Au Total energy BP86/LANL2DZ:
45 3 Molecular orbitals bonding magne4c MO ε 2 = ev LUMO ev an4bonding ε 1 = ev HOMO ev Figure 4: MO isosurface plots and energies calculated for the conjugated bridge with the middle C C distance (carbon atoms 4 and 5) at the triplet optimized value. KS-DFT(BP86). 45
46 MO 2 magne8c MO MO 1 ε 2 = ev LUMO ev ε 1 = ev HOMO ev Figure 5: MO isosurface plots and energies calculated for the cross-conjugated bridge with a methylene side group. KS-DFT(BP86). 46
47 magne8c MO an8bonding bonding ε 2 = ev LUMO ev ε 1 = ev HOMO ev Figure 6: MO isosurface plots and energies calculated for the cross-conjugated bridge with a NH side group. KS-DFT(BP86). 47
48 magne8c MO an8bonding bonding ε 2 = ev LUMO ev ε 1 = ev HOMO ev Figure 7: MO isosurface plots and energies calculated for the cross-conjugated bridge with an O side group. KS-DFT(BP86). 48
49 magne7c MO structure 1, X=O MO 2 MO 1 ε 2 = ev LUMO ev ε 1 = ev HOMO ev Figure 8: MO isosurface plots and energies calculated for a furane-bridge with annelated ring 1. KS-DFT(BP86). 49
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