QTAIM and Stress Tensor Characterization of Intramolecular Interactions Along Dynamics Trajectories of a Light-Driven Rotary Molecular Motor

Abstract

A quantum theory of atoms in molecules (QTAIM) and stress tensor analysis was applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor. For selected nonadiabatic molecular dynamics trajectories characterized by markedly different S state lifetimes, the electron densities were obtained using the ensemble density functional theory method. The analysis revealed that torsional motion of the molecular motor blades from the Franck-Condon point to the S energy minimum and the S/S conical intersection is controlled by two factors: greater numbers of intramolecular bonds before the hop-time and unusually strongly coupled bonds between the atoms of the rotor and the stator blades. This results in the effective stalling of the progress along the torsional path for an extended period of time. This finding suggests a possibility of chemical tuning of the speed of photoisomerization of molecular motors and related molecular switches by reshaping their molecular backbones to decrease or increase the degree of coupling and numbers of intramolecular bond critical points as revealed by the QTAIM/stress tensor analysis of the electron density. Additionally, the stress tensor scalar and vector analysis was found to provide new methods to follow the trajectories, and from this, new insight was gained into the behavior of the S state in the vicinity of the conical intersection.

Next‐generation quantum theory of atoms in molecules for the ground and excited states of fulvene

“…The eigenvector‐following path with length H , see Figure B, is shorter for the S 1 compared with the S 0 as this corresponds to lower values of the ellipticity ε , see Figure A, indicating that the torsion θ is easier to perform in the excited state from the form of q i = r i + ε i e 2 , i . This finding is consistent with our earlier work with the value of the ellipticity ε of the torsion BCP being lowered by photoisomerization . The same trend is also true for the fractional lengths H f and H f θ min for the BLA and torsion θ , see Figures C,D and C,D, respectively.…”

“…Previously, it was found that the stress tensor stiffness, S σ produced results that were in line with physical intuition . The stress tensor eigenvalue λ 3σ is associated with the bond path and previously values of λ 3σ < 0 were found to be associated with transition‐type behavior in biphenyl and molecular motors and indicated the BCP was close to rupturing and therefore we described as being unstable .…”

“…Starting point for this exploration will be the ellipticity ε , constructed from the λ 1 and λ 2 eigenvalues of the Hessian of ρ ( r ) associated with the accumulation of the charge distribution in chemical bond. The ellipticity ε , where ε = | λ 1 |/| λ 2 | ‐ 1, has already been found to distinguish between the S 0 and S 1 electronic states . This next‐generation QTAIM interpretation of the chemical bond will be constructed using the ellipticity ε and the associated e 1 and e 2 eigenvectors for all points along the bond path.…”

Next‐generation quantum theory of atoms in molecules for the ground and excited state of the ring‐opening of cyclohexadiene

“…The stress tensor eigenvalue λ 3σ is also associated with the bond‐path and previously values of λ 3σ < 0 were found to be associated with transition‐type behavior in biphenyl and molecular motors and indicated the bond critical point was close to rupturing and therefore we described as being unstable .…”

Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra

“…Theoretically, many studies have been carried out with the aim of understanding the details of the potential energy surface (PES) structures and non-adiabatic coupling (NAC) profiles to determine the rotational degrees of freedom and to simulate fast photoisomerization processes in molecular motors systems [12][13][14][15][16][17][18][19]. In contrast, the thermalization process, * ikeda.tatsushi.37u@kyoto-u.jp † A.G.Dijkstra@leeds.ac.uk ‡ tanimura.yoshitaka.5w@kyoto-u.jp which is known as a rate-limiting step of molecular motors [6][7][8], has not been well explored.…”