Probing chirality fluctuations in molecules by nonlinear optical spectroscopy

Abstract

Symmetry breaking caused by geometric fluctuations can enable processes that are otherwise forbidden. An example is a perylene bisimide dyad whose dipole moments are perpendicular to each other. Förster-type energy transfer is thus forbidden at the equilibrium geometry since the dipolar coupling vanishes. Yet, fluctuations of the geometric arrangement have been shown to induce finite energy transfer that depends on the dipole variance, rather than the mean. We demonstrate an analogous effect associated with chirality symmetry breaking. In its equilibrium geometry, this dimer is non-chiral. The linear chiral response which depends on the average geometry thus vanishes. However, we show that certain 2D chiral optical signals are finite due to geometric fluctuations. Furthermore, the correlation time of these fluctuations can be experimentally revealed by the waiting time dependence of the 2D signal.

FIG. 1.

Sketch of the chemical structure of an orthogonally arranged perylene bisimide donor acceptor pair (PBDA) together with the transition dipole moments.

FIG. 2.

Left: Sketch of the arrangement of the two transition dipole moments μ₁ and μ₂ and the connecting vector R of the PBDA pair. Right: Illustration of the angle θ and ϕ when μ₂ does not point along the x-axis.

FIG. 3.

Real (upper row) and the imaginary (lower row) part of the chiral linear spectrum versus frequency ω and angle ϕ with fixed θ = π/4 for J = 85 cm⁻¹, Γ = 50 cm⁻¹, σ = 0.24 and δε = 2500 cm⁻¹ (left column), δε = 85 cm⁻¹ (middle column), and 25 cm⁻¹ (right column).

FIG. 4.

Real (left) and imaginary part of ${\mathcal{R}}_c({\omega }_3,t_2,{\omega }_1)$ for very short waiting times Dt₂ = 10⁻⁵ for the PBDA pair with J = 85 cm⁻¹, δε = 2500 cm⁻¹, and σ_ϕ = 2π and σ_θ = 0.24.

FIG. 5.

Maximal amplitude of the real part $R\left(t_2\right)={\max }_{{\omega }_1,{\omega }_3}{\mathcal{R}}_c({\omega }_3,t_2,{\omega }_1)$ scaled to R₀ = R(t₂ = 10⁻⁵D⁻¹) versus waiting times Dt₂ for J = 85 cm⁻¹, δε = 2500 cm⁻¹, and σ_ϕ = 2π and σ_θ = 0.24.