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

2. 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:

3. 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!

4. 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

5. 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.

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

7. 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

8. 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.

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

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

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

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

13. 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.

14. 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

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

16. 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 * *

17. 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 * *

18. 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 * *

19. 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 * *

20. 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

21. 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

22. Avoiding 1/2-Filled Bands
Partial oxidation of the donor
or partial reduction of the acceptor
[TTF][Br]
σ = 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
unpaired e-
(+)ve charge
per TTF molecule * *

23. What’s Available?
Donors
Acceptors * *

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

25. * *

26. 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 * *

27. 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.

28. 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.

29. 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

30. 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

31. 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.