Section 4.2 - 1

4.2 Molecular Conductors What are the necessary requirements for constructing a molecule-based conductor ? 1. 2. 3. Molecular Conductors – 3 types

Radical Ion Conductor

Neutral Radical Conductor Closed Shell Conductor

• Composed of donor (D) and acceptor (A) molecules

• Composed of a single type of uncharged radical molecule

• Composed of a single type of (uncharged) closed shell molecule, but part of the molecule acts as a donor (D) and part as an acceptor (A)

• Intermolecular charge

transfer is required • Charge transfer is not

required • Intramolecular charge

transfer is required

• Any level of band filling is possible

• Only ½-filled bands are possible (for simple 1D stacks)

• Any level of band filling is possible

e.g., [TTF+][TCNQ-] e.g., PLY e.g., Ni(tmdt)2

S

S

S

S

CN

CN

NC

NC

TTF(tetrathiafulvalene)

TCNQ(tetracyanoquinodimethane)

PLY(phenylenyl)

S

S

S

S

SNi

S

S

S

S

S

S

S

Ni(tmdt)2(tmdt = trimethylenetetrathiafulvalenedithiolate)

Section 4.2 - 2

Radical Ion Conductors • 2 molecular components: Donor (D) and Acceptor (A) • Electron transfer must occur: D+• and A-• • This redox process relies on the compatibility of the frontier molecular orbitals. Q. What does this imply? Charge Transfer (CT) Salt...e.g., TTF-TCNQ

Section 4.2 - 3

Bechgaard Salts

N.B. not 1:1 • A well-known example of a RIC. • TMTSF is the donor • PF6 is the acceptor

How do you design a RIC or CT salt ? Q. What do Bechgaard salts have in common with TTF-TCNQ?

1. The donor molecules have similar molecular structures

2. The crystal structures both involve π-stacking such that a column of donors is formed.

3. The heteroatoms (S and Se) have very diffuse p-orbitals and π-stacking overlap is

expected to be significant.

S

S

S

S

TTF

HOMO

3 b1u

Se

Se

Se

Se

TMTSF

HOMO

Section 4.2 - 4

Some RIC and CT design principles • The radical ions must have an extended π-system such that the SOMO is not strongly

localized.

i.e., prevent formation of Mott insulator

• The radical ions must STACK in the solid state such that there is overlap between the π-systems of neighboring molecules. → BAND FORMATION!

Q. What happens if the stacking is –D-A-D-A- ? Q. How do you design a RIC or CT salt that stacks: -A-A-A-A- -D-D-D-D- ? HOMO and LUMO of TTF and TCNQ

These are orthogonal orbitals. Therefore, no bonding-type overlap is possible.

S

S

S

S

TTF

HOMO

3 b1u

CN

CN

NC

NC

TCNQ

LUMO

3 b2g

D2h

Section 4.2 - 5

Partial Charge Transfer: [TTF][TCNQ] & [TTF][Br]x

[TTF][TCNQ]

[TTF][Br] [TTF][Br]0.7

σ = 104 Scm-1 @ 58 K

σ = 10-11 Scm-1 σ = 102 Scm-1

Q. Why is the conductivity so high?

Complete charge transfer gives exactly one unpaired electron and one (+)ve charge per TTF molecule

Complete charge transfer give exactly 0.7 unpaired electrons and 0.7 (+)ve charges per TTF molecule

A.

Why does partial charge transfer matter? [TTF][TCNQ] – a semi-metal • Much of the older literature dealing with [TTF][TCNQ] states that organic CT salts

with very high conductivities are organic metals. • This is not strictly true since none of these materials possess a single partially filled

energy band. CT salts are either semiconductors (or insulators) or semi-metals.

Source: J. B. Torrance, Ann.N.Y.Acad.Sci., 1978, 210.

"HOMO"band of

TTF

"LUMO"band of TCNQ

before CT

"HOMO"band of

TTF

"LUMO"band of TCNQ

after CT

Section 4.2 - 6

Some well-known donors and acceptors that generate radical cations and radical anions for RICs and CT salts:

X

X

X

X R

R

R

R X R1. S H TTF2. Se H TSF3. S Me TMTTF4. Se Me TMTSF5. Te H TTeF

X

X

X

X

6. X = S HMTTF7. X = Se HMTSF

X

X

X

X

Y

YY

Y

X Y8. S S BEDT-TTF9. S O BEDO-TTF10. Se Se BEDS-TSF11. S Se BEDS-TTF

S

S

Se

SeS

S12. DMET

S

S

S

S

13. MDT-TTF

DONORS

ACCEPTORS

CN

CN

NC

NCR

R

14. R = H TCNQ15. R = Me 2,5-DMTCNQ

SS

S

SNi

S

S

S

S

SS

16. Ni(dmit)2

NN

R

RNC

CN

17. R = H DCNQI18. R = Me 2,5-DMDCNQI

Historical Perspective Year Discovery 1954 Perylene-bromide salt; first conducting molecular compound; σRT = 1 Scm-1

1962 Semiconducting salts of TCNQ reported 1973 TTF-TCNQ prepared; first organic metal; σRT = 500 Scm-1; TM-I = 53 K 1974 TSF-TCNQ prepared; σRT = 700-800 Scm-1; TM-I = 40 K 1975 HMTSF-TCNQ; TM-I < 1 K ... increased dimensionality (Se...N contacts) 1978 HMTSF-2,5-DMTCNQ; TM-I suppressed under pressure; σ1K,10kbar = 105 Scm-1 1979 TMTTF-tetrahalo-p-benzoquinones; no TCNQ! 1980 (TMTSF)2 X salts; organic superconductivity @ 0.9 K; 12 kbar for X = PF6

- @ 1.4 K; ambient P for X = ClO4

-

1982 (BEDT-TTF)2 ClO4 (1,1,2-trichloroethane)0.5; metallic @ T = 298 – 1.4 K 1983 (BEDT-TTF)2 ReO4; superconductor Tc = 1.4 K @ 4 kbar 1984 β-(BEDT-TTF)2 I3; superconductor Tc = 1.4 K @ ambient pressure 1986 [TTF][Ni(dmit)2]2; superconductor Tc = 1.6 K @ 7 kbar 1987 Cu(2,5-DMDCNQI)2; metallic σ3.5K = 5 x 105 Scm-1 1988 κ-(BEDT-TTF)2Cu(SCN)2; ambient pressure superconductor @ 10.4 K … ... you get the picture!

Section 4.2 - 7

The Big Picture

Neutral Radical Conductors – NRCs • By their nature, RICs and CT salts are either semi-metals or semi-conductors • NRCs, in principle, are capable of exhibiting truly metallic conductivity • To date, there are no molecular NRCs that display metallic conducting properties.

This is mainly due to the problems associated with ½-filled bands.

PLY

N

N

SS

NNS

S O

Nhex

O

NB

hex

σRT = 0.2 Scm-1 @ 5 GPa

NMBDTAspiro-PLY

σRT = 5 x 10-2 Scm-1 @ ambient pressure RECALL: WHAT ARE THE PROBLEMS WITH ½-FILLED BANDS?

Section 4.2 - 8

Closed Shell Single Molecule Conductors • do not rely on intermolecular charge transfer (i.e., only one type of molecule required

in the solid). • are not neutral radicals • essentially, designed as charge transfer species wherein the D and A components are

both on the same molecule

σRT = 4 x 102 Scm-1

• Displays metallic conductivity down to 0.6 K as a single component crystal • Correct classification is a semi-metal Source: Tanaka et al., Science, 2001, 291, 285. (SN)x - a lesson in 3-dimensionality • (SN)x has metallic conductivity

σRT ≈ 103 Scm-1 • Becomes superconductive at low temperature • Unfortunately, the starting material S4N4 and intermediate

S2N2 are highly explosive and polymerization takes several weeks

Q. Why doesn’t (SN)x succumb to Peierls type distortions?

S

S

S

S

SNi

S

S

S

S

S

S

S

Ni(tmdt)2(tmdt = trimethylenetetrathiafulvalenedithiolate)

HOMO

LUMOΔE

ΔE ~ 0.1 eV

Section 4.2 - 9

… but (SN)x isn’t a 1D system!

S N

S N

π

π*

FMO manifoldof -S=N-

radical fragment

band structureof 1D (SN)x

Section 4.2 - 10

Fermi Surfaces and the concept of Nesting • The Fermi surface is the constant-energy plot, in k-space, of the highest occupied

energy levels at absolute zero (T = 0). • It represents the junction between filled and empty levels at T = 0. • For systems with filled bands, there is no Fermi surface at all, so the concept only

applies to metals.

• The Fermi surface is simply a constant-energy surface at E = EF. • For a 2D lattice (shown above), there will be two values of β in the two directions. • If βb = 0, then clearly the result is a series of uncoupled one-dimensional chains with

no dispersion along the X → M direction. • If βa = βb, then a square lattice results. • The area (volume in three-dimensions) of the first Brillouin zone enclosed by the

Fermi surface is proportional to the band filling.

Section 4.2 - 11

• In a one dimensional system, the Fermi surface is actually just a set of point. For the half-filled band, it is given by the two point ±2kF (see 3.12 below)

• In three dimensions, drawing the Fermi surface can be rather difficult.

Section 4.2 - 12

• The concept of the Fermi surface is most useful as a tool for understanding distortions

in solids. To understand this, the concept of “nesting” of the Fermi surface is needed. • When a section of the Fermi surface can be moved by a vector q such that it is exactly

superimposed on another section of the surface, then the Fermi surface is nested by this vector q.

• The Fermi surface shown in Figure 13.6(a) is nested by an infinite set of vectors, two

of which are shown below.

• A more complex example is shown in Figure 3.19. The dispersion behaviour of two

bands of a two dimensional structure are shown, along with the Fermi surface. The inner two pieces of the Fermi surface come from the lower energy band and the outer pieces from the higher energy band.

• Although there are two distinct pieces of the Fermi surface that are nested, the nesting

vector is identical for each.

Section 4.2 - 13

• The utility of these descriptions lies in the insights provided into electronically driven

geometrical instabilities. • The potential associated with the distortion may be written as

V = Vq exp(i q · r) + V-q exp(-i q · r) where q is a reciprocal lattice vector • The nature of q defines the way the structure changes. • E.g., for a simple one-dimensional case, if q = π/a , then a distortion that leads to a

doubling of the unit cell in this direction is indicated (i.e., dimerization.) MEANING If there is a single vector q that nests the Fermi surface, then there is a single distortion that can lower the energy of the system. TAKE HOME MESSAGE In a 1D system, it is easy to find single vector q that nests the Fermi surface, since the Fermi surface is simply a set of points. Adding multiple dimensions (2D or 3D) can reduce the possibility of finding a vector q that nests the Fermi surface… ...see, for example, the dispersion curves for two interacting chains... …in other words, a distortion that might be favoured (i.e., lower the energy) in one direction might give rise to unfavourable interactions (i.e., raise the energy) in another.