transient localisation · molecular crystals

One phonon bath, three observables

The same soft intermolecular phonons set the shear stiffness, modulate the transfer integrals as dynamic disorder, and carry the lattice heat. Choose a crystal, then drive C₄₄, T and J.

mechanistic chain · MT-pyrene

●

C₄₄ — shear elastic modulus

mechanical face · input

–GPa

↓

ℏω_sh = 2ℏv_T/a, v_T = √(C₄₄/ρ)

zone-boundary shear · a = plane spacing

–meV

↳

κ_L/κ_L,0 = (C₄₄/C₄₄_,0)^3/2·300 K/T

thermal face · 0: default C₄₄, 300 K

–

↓

⟨u²⟩ = k_BT/(Mω_sh²), M = ρV

displacement per molecule

–Å²

↓

σ_J = g·δu, δu² = ⁴⁄₃⟨u²⟩

g from DFT · largest bond

–meV

↓

Δ = σ_J/J

localisation parameter

–

↓

L_τ — TLT spread at t = τ

transient localisation length

–nm

↓

μ = eL_τ²/(2k_BTτ)

electronic face · τ = 1/ω_sh

–cm²V⁻¹s⁻¹

Model.

side view1 nm

top view1 nm

mobility μ(T)

Deepak Venkateshvaran — June 2026, revised October 2026

Temperature T = 300 K

50 K400 K

Shear modulus C₄₄ = 2.674 GPa

0.290 GPa · softstiff · 5 GPa

Largest transfer integral J = 114 meV

60 meV150 meV

95	The page computes the chain it states	Every number matches an independent Python version to 0.1 %; the transport tables match direct calculations to 3–4 % (worst 9 %).
60	C₄₄ → ℏω_sh: one shear mode sets the lattice timescale	Coupling fluctuations come from a band of low-frequency modes, librations included. Simulations (Giannini et al. 2023) give ℏ/τ ≈ 9 meV for DNTT and 16 meV for C8-DNTT-C8; the chain gives 2.7 meV for C8-DNTT-C8.
80	⟨u²⟩ from C₄₄	Classical harmonic lattice. For MT-pyrene the CIF displacement parameters (100–300 K) give a slide within about 13 % of the chain’s.
70	σ_J = g·δu	g is computed (DFT gradients of every bond, weighted by the measured motion), not fitted. C8-DNTT-C8 gets σ_J = J/5.4; molecular dynamics give J/4–5. Assumes all rigid-body motion softens with C₄₄.
85	Transient localisation → L_τ, μ	Established theory, solved on each crystal’s own network of transfer integrals. The weak-disorder correction is an interpolation, so the stiffest settings are the least secure.
80	Trends: stiffer is faster; μ ∝ T⁻ⁿ	μ rises with C₄₄ at every setting. C8-DNTT-C8 gives n ≈ 1.1 at 300 K; experiment gives 1.0 ± 0.1 (Giannini et al., Nat. Mater. 2023).
45	Absolute mobility	Intrinsic values (no traps) run above measured ones: C8-DNTT-C8 15 against 4.8, MT-pyrene 47 against 30 cm²V⁻¹s⁻¹. DNTT uses a placeholder C₄₄.
45	κ_L/κ_L,0	A scaling estimate (κ ∝ sound velocity cubed): right in direction, not in size.
90	Drawing	The CIF molecules in their crystal orientations; slide from the chain, sideways motion and rocking in the measured proportions. DNTT moves too much because of its placeholder C₄₄.
75	Overall	A faithful, internally consistent picture of the hypothesis and of how stiffness controls mobility; trends more reliable than absolute numbers.