How To Design a Molecular Conductor: A Chemist’s Perspective Kathryn E. Preuss Department of Chemistry University of Guelplh Vancouver 2005

Where do we start? Band Theory Model #1: Particle-on-a-Ring V = 0 everywhere on the ring V = ∞ everywhere else  Hamiltonian describes only kinetic energy. Schrödinger Equation: Moving Wave Solutions:

Particle on a Ring of Periodic Potential Model #2: e.g., a string of nuclei V() = V( + 2/n) V = 0 elsewhere on the ring Schrödinger Equation: Moving Wave Solutions: where m = 1, 2, 3, … , n j = 0, 1, 2, … , n-1 BLOCH FUNCTION!

Particle on a Ring of Periodic Potential Free electron Energies Since j is already normalized … Ej =  j *H j d If only nearest neighbor interactions, then only 2 types of integrals:  = umH um d (Coulomb)  = um±1H um d (Resonance) So, working it out and applying Euler’s theorem, we find that Ej =  + 2 cos(2j/n) where j = 0, 1, 2, …, n/2

Particle on a Ring of Periodic Potential E.g., Benzene C6H6 Ej =  + 2 cos(2j/6) for j = (0, ±1, ±2, 3) M.O.s from j = 6-1/2exp(mij2π/6)•um for m = 1, 2, …, 6.

Particle on a Ring of Periodic Potential For this model, the maximum energy dispersion is 4β.

1D Chain of Infinite Length Model #3: A “very large” ring has “very small” curvature … a good model for a 1D chain of infinite length. R = ma Redefine: mij2/n = i(j/a)(2/n)(ma) = ikR Note: k is a vector in reciprocal space. k incorporates j

1D Chain of Infinite Length Free electron wavefunction solutions and energies k = n-1/2 ∑exp(ikma)(r-ma) Ek = k*H k d =  + 2cos(ka) Note: Owing to symmetry, only k = (0 … /a) need be cited.

Dispersion Curves: Mapping E vs. k Map E over the k = (0 … /a) continuum.

Density of States (DOS) Map E over n(E).

Peierls Instability: CDWs Any degree of partial band filling in a 1D system has an associated CDW ... … and is subject to a Peierls distortion.

Peierls Instability: CDWs Redefine lattice constant … … “folding” of dispersion curve.

Peierls Instability: CDWs Energy equation for this distorted system... E = α ± (β12 + β22 + 2β1β2cosk2a)1/2 at k = 0, E = α ± (β1+ β2) at k = π/2a, E = α ± (β1 - β2) Therefore, a band gap is produced.

Peierls Instability: CDWs We can identify the expected distortion for a 1D lattice with ANY level of band filling! Δt = Asin(q*t + ) where: A = amplitude q* = q/2 = N•π/a N = average # charge carriers per site t = l•a l = (1, 2, 3, …)  = phase factor

Peierls Instability: CDWs We can identify the expected distortion for a 1D lattice with ANY level of band filling! * *

Peierls Instability: CDWs So why don’t all 1D systems distort? Driving forces that favour distortion arise from interactions at the highest occupied energy levels. Underlying electronic structure resists this distortion … e.g., σ - bond compression. Hooke’s Law: V = k(a+Δa)2 + k(a-Δa)2 minimum energy at: Δa = 0 * *

Mott Insulators No distortion…but STILL NOT A METAL?! Consider a simple “Hopping” Model. There is a Coulombic barrier (U) to conduction. U ~ ΔHdisp = IP - EA κ = U/4β * *

So…How Do We Design a Molecular Conductor? Extended  - systems Crystal packing...intermolecular  -overlap Planar, aromatic molecules with hetero-atoms (S, Se, …) Avoid very electronegative heteroatoms. Avoid exactly 1 charge carrier per site. Avoid strictly 1D systems. Multiple stable oxidation states Minimize IP - EA * *

Molecular Conductors: 3 Types Radical Ion Conductors Donor + Acceptor Charge Transfer is required Any level of band-filling is possible. E.g., TTF-TCNQ Neutral Radical Conductors Neutral Radicals No Charge Transfer 1/2-filled bands only E.g., PLY Closed Shell Conductors Closed Shell No Charge Transfer Any level of band-filling is possible E.g., Ni(tmdt)2 * *

Radical Ion Conductors and Charge Transfer Salts 2 components: donor (D) + acceptor (A) electron transfer must occur: D+• A-• redox process relies on compatibility of frontier MOs * TTF * TCNQ

Avoiding -D-A-D-A- Stacking Choose D and A of different “shapes”. Choose D and A such that FMOs have different symmetry w.r.t. inversion. HOMO 3b1u * * LUMO 3b2g

Avoiding 1/2-Filled Bands Partial oxidation of the donor or partial reduction of the acceptor [TTF][Br] σ = 10-11 Scm-1 1 unpaired e- 1 (+)ve charge per TTF molecule [TTF][Br]0.7 σ = 102 Scm-1 0.7 unpaired e- 0.7 (+)ve charge per TTF molecule [TTF][TCNQ] σ = 104 Scm-1 0.5 - 0.6 unpaired e- 0.5 - 0.6 (+)ve charge per TTF molecule * *

What’s Available? Donors Acceptors * *

Can We Design New Donors? NOTE: A radical cation oxidation state must be available! * *

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Cyclic Voltammetry E½(0/+) E½(+/++) ΔE 0.41 0.66 0.25 0.61 1.10 0.49 Volts vs SCE in CH3CN E½(0/+) E½(+/++) ΔE 0.41 0.66 0.25 0.61 1.10 0.49 0.80 1.25 0.45 0.81 1.37 0.56 0.93 1.50 0.57 * *

My Ph.D. Thesis Work ... Pressed Pellet: σRT = 10-1 Scm-1 4-probe Crystal: σRT = 10+1 Scm-1 Semiconductor; Band gap = 0.30 eV * * Crystal packing of radical cations. [C4Cl2N2S4][BF4]…anions omitted.

My Ph.D. Thesis Work ... 1:1 salts no π-stacking 2:1 salts Pressed pellet σRT = 10-4 Scm-1 3:2 salts Not able to obtain structure. Ratio confirm by elem. anal. Pressed pellet σRT > 10 Scm-1 * * Crystal packing of radical cation dimers. [C6Cl2N2S4]2[GaCl4]…anions omitted.

My Ph.D. Thesis Work ... 1:1 salts no π-stacking 3:2 salts Pressed Pellet σRT = 10-2 Scm-1 * * [C6H2N2S4]3[ClO4]2 [C6H2N2S4]3[FSO3]2

Other Non-TTF Donors? There are many other examples of [D][TCNQ] salts … … but conductivity is usually dominated by the TCNQ. There are many more variations on the TTF theme. There are few other non-TTF conducting donors. Perylene DTDAF

Take Home Message Many donors and acceptors are known. The redox potentials can be “tuned”. Molecular synthesis is rarely an obstacle. Crystal “engineering” is more difficult.