Conductance Length Dependence in Carbon-Conjugated Nanoscale Systems …
603
and A terms in (31) and (32), thus giving the preliminary result:
G p, p = 2 P p, p // c ,
(33)
with P p, p = 2 p | I
I
p
being the contribution of the frontier Dyson orbitals
to bond order P p, p . In practice we frequently observe that P p, p ≈ P p, p for
long-range bond order P p, p , and one can expect the expression
G
appr
p, p = 2P p, p
c
(34)
to be reasonable for order-of-magnitude estimations of the respective longrange GF elements. This suggestion was verified numerically. In particular, ratio
G p, p
G
appr
p, p is about one for [n]periacene series with large n: 1.41 for n = 2; 1.
21 for n = 3; 1.09 for n = 4; 1.04 for n = 5, etc.; the ratio is equal to 1.22 for
polyquinoids from Fig. 6. At the same time, G p, p
G
appr
p, p is approximately 1.56 for
the para contacts in [n]phenacenes. At least, for all the cases studied in the paper,
(34) has provided sensible estimates of long-range elements of π -electron GF.
References
1. Datta S (2005) Quantum transport: atom to transistor. Cambridge University Press, Cambridge
2. Nitzan A (2001) Electron transmission through molecules and molecular interfaces. Ann Rev
Phys Chem 52:681–720
3. Chen F, Tao NJ (2009) Electron transport in single molecules: from benzene to graphene. Acc
Chem Res 42:573
4. Zimbovskaya NA, Pederson MR (2011) Electron transport through molecular junctions. Phys
Rep 509:1–87
5. Solomon GC, Herrmann C, Ratner MA (2012) Molecular electronic junction transport: some
pathways and some ideas. Top Curr Chem 313:1–38
6. Lambert CJ (2015) Basic concepts of quantum interference and electron transport in singlemolecule electronics. Chem Soc Rev 44:875–888
7. Moth-Poulsen K (ed) (2016) Handbook of single-molecule electronics. Pan Stanford
Publishing, Singapore
8. Xiang D, Wang X, Jia C, Lee T, Guo X (2016) Molecular-scale electronics: from concept to
function. Chem Rev 116:4318–4440
9. Cuevas JC, Scheer E (2017) Molecular electronics: an introduction to theory and experiment,
2nd edn. World Scientific, Singapore
10. Tsuji Y, Estrada E, Movassagh R, Hoffmann R (2018) Quantum Interference, graphs, walks,
and polynomials. Chem Rev 118:4887–4911
11. Stuyver T, Fias S, De Proft F, Geerlings P (2015) The relation between delocalization, long
bond order structure count and transmission: an application to molecular wires. Chem Phys
Lett 630:51–56
12. Stuyver T, Zeng T, Tsuj Y, Geerlings P, De Proft F (2018) Diradical character as a guiding
principle for the insightful design of molecular nanowires with an increasing conductance with
length. Nano Lett 18:7298–7304
603
and A terms in (31) and (32), thus giving the preliminary result:
G p, p = 2 P p, p // c ,
(33)
with P p, p = 2 p | I
I
p
being the contribution of the frontier Dyson orbitals
to bond order P p, p . In practice we frequently observe that P p, p ≈ P p, p for
long-range bond order P p, p , and one can expect the expression
G
appr
p, p = 2P p, p
c
(34)
to be reasonable for order-of-magnitude estimations of the respective longrange GF elements. This suggestion was verified numerically. In particular, ratio
G p, p
G
appr
p, p is about one for [n]periacene series with large n: 1.41 for n = 2; 1.
21 for n = 3; 1.09 for n = 4; 1.04 for n = 5, etc.; the ratio is equal to 1.22 for
polyquinoids from Fig. 6. At the same time, G p, p
G
appr
p, p is approximately 1.56 for
the para contacts in [n]phenacenes. At least, for all the cases studied in the paper,
(34) has provided sensible estimates of long-range elements of π -electron GF.
References
1. Datta S (2005) Quantum transport: atom to transistor. Cambridge University Press, Cambridge
2. Nitzan A (2001) Electron transmission through molecules and molecular interfaces. Ann Rev
Phys Chem 52:681–720
3. Chen F, Tao NJ (2009) Electron transport in single molecules: from benzene to graphene. Acc
Chem Res 42:573
4. Zimbovskaya NA, Pederson MR (2011) Electron transport through molecular junctions. Phys
Rep 509:1–87
5. Solomon GC, Herrmann C, Ratner MA (2012) Molecular electronic junction transport: some
pathways and some ideas. Top Curr Chem 313:1–38
6. Lambert CJ (2015) Basic concepts of quantum interference and electron transport in singlemolecule electronics. Chem Soc Rev 44:875–888
7. Moth-Poulsen K (ed) (2016) Handbook of single-molecule electronics. Pan Stanford
Publishing, Singapore
8. Xiang D, Wang X, Jia C, Lee T, Guo X (2016) Molecular-scale electronics: from concept to
function. Chem Rev 116:4318–4440
9. Cuevas JC, Scheer E (2017) Molecular electronics: an introduction to theory and experiment,
2nd edn. World Scientific, Singapore
10. Tsuji Y, Estrada E, Movassagh R, Hoffmann R (2018) Quantum Interference, graphs, walks,
and polynomials. Chem Rev 118:4887–4911
11. Stuyver T, Fias S, De Proft F, Geerlings P (2015) The relation between delocalization, long
bond order structure count and transmission: an application to molecular wires. Chem Phys
Lett 630:51–56
12. Stuyver T, Zeng T, Tsuj Y, Geerlings P, De Proft F (2018) Diradical character as a guiding
principle for the insightful design of molecular nanowires with an increasing conductance with
length. Nano Lett 18:7298–7304