Next‐generation quantum theory of atoms in molecules for the S₁/S₀ conical intersections in dynamics trajectories of a light‐driven rotary molecular motor

Abstract

Next-generation quantum theory of atoms in molecules was applied to analyze, along an entire bond path, intramolecular interactions known to influence the photoisomerization dynamics of a light-driven rotary molecular motor. The 3D bondpath framework set B 0,1 constructed from the least and most preferred directions of electronic motion, provided new insights into the bonding leading to different S 1 state lifetimes including the first quantification of covalent character of a closed-shell intramolecular bond path. We undertook the first use of the stress tensor trajectory T σ (s) analysis on selected nonadiabatic molecular dynamics trajectories with the electron densities obtained using the ensemble density functional theory method.The stress tensor T σ (s) analysis was found to be well suited to follow the dynamics trajectories that included the S 0 and S 1 electronic states through the conical intersection and also provided to a new measure to assess the degree of purity of the axial bond rotation for the design of rotary molecular motors.light-driven molecular rotary motor, next-generation QTAIM, dynamics trajectories, conical intersection, stress tensor 1 | INTRODUCTION Previously, it was argued that replacing the torsion-pyramidalization conical intersections (CI) by chemical modification of the molecular skeleton would lead to molecular motors that would undergo pure axial rotation of its blades and thus possessing greater quantum efficiency than their overcrowded alkene analogues [1] ; these hypotheses later were confirmed by nonadiabatic molecular dynamics (NAMD) simulations. [2] These modified motors underwent pure axial rotations and the photochemical steps of the rotary motor cycle could access the S 1 /S 0 intersection very rapidly. This provided a purely chemical method for the control of the photoisomerization dynamics because previously this outcome was possible only for thermal relaxation of molecular motors.Previously, a quantum theory of atoms in molecules (QTAIM) [3] and stress tensor analysis were applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor [4] obtained from the ensemble density functional theory method. The definition of the stress tensor is ambiguous due to the nature of the kinetic energy density. [5][6][7][8][9][10] The NAMD simulations of chemically modified molecular motors of the 3-[(2S)-2-fluoro-2-methyl-1-indanylidene]-1-methyl-2-methylindole (F-NAIBP) molecular rotary motor demonstrated the presence of fast (F) and slow (S) categories of dynamics trajectory [2] (Scheme S1 of Supplementary Materials S1). The fast (F) and slow (S)

Beyond energetic and scalar measures: Next generation quantum theory of atoms in molecules

“…The eigenvector‐space trajectory T i ( s ) is constructed without BCP torsions from an ordered sequence of points by tracking a BCP in the U i ‐space; i = { σ , ρ , F }. Examples include: normal mode behaviors, including isotopic effects, 32 prediction of ring‐opening reaction (competitive) inward‐conrotatory or outward‐conrotatory pathways in agreement with experiment 33,34 are determined by the longest T σ ( s ), see Figure 3 (Top), or functioning of rotary motors that follow nonadiabatic dynamics trajectories through a conical intersection (CI), 35 see Figure 3 (Middle and bottom) using the Ehrenfest force F ( r ) 36 …”

“…15,16 NG-QTAIM enables the consideration of deformation anisotropy phenomena 9,10,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] to explain mechanisms of reaction pathways, 9 bond-coupling including the Ehrenfest force F(r), 11 and effects of electric fields 10,31 beyond the capabilities of QTAIM. NG-QTAIM provides understanding of deformation anisotropy of chemical phenomena: normal mode behaviors including isotopic effects, 32 prediction of pathways for ring-opening reactions, that is, inwardconrotatory or outward-conrotatory, 33,34 functioning of rotary motors using nonadiabatic dynamics trajectories, 35,36 see Section 2.1 and also iso-energetic phenomena for example: stereochemistry, 37 chiral discrimination, 7 or following S N 2 reaction pathways, 38 see Section 2.2.…”

“…]propellane 21 and non-nuclear attractors. 29 The symmetrybreaking stress tensor trajectory T σ (s) analysis has been used for iso-energetic phenomena: stereochemistry of achiral and chiral species, reactions, and chiral discrimination, 7,37,38 predict reaction pathways in competitive ring-opening reactions, 33,34 rotors, 35 permutation-inversion isomers, 56 and photochemistry. 9,34,57 Included Python scripts produce tables in text or CSV form and the interactive GUI produces bitmap/vector images or the .x3d 3-D model format.…”

“…The eigenvector-space trajectory T i (s) is constructed without BCP torsions from an ordered sequence of points by tracking a BCP in the U i -space; i = {σ, ρ, F}. Examples include: normal mode behaviors, including isotopic effects, 32 prediction of ring-opening reaction (competitive) inward-conrotatory or outward-conrotatory pathways in agreement with T A B L E 1 The chirality C σ , axiality B σ and the chirality-helicity function C helicity for the torsional C1 C2 BCP of the S N 2 reaction of the attack of Br À on (R)-1-chloro-1-phenylethane (reactant) resulting in (S)-1-bromo-1-phenylethane (product) experiment 33,34 are determined by the longest T σ (s), see Figure 3 (Top), or functioning of rotary motors that follow nonadiabatic dynamics trajectories through a conical intersection (CI), 35 see Figure 3 (Middle and bottom) using the Ehrenfest force F(r). 36 3 | IMPLEMENTION OF NEXT GENERATION QTAIM: QUANTVEC…”

Elucidating the Impact of Molecular Motors on Their Solvation Environment

“…A full rotation is obtained by repeating alternatingly the photo-induced and thermally induced steps . To decipher the operation mechanism in detail, the intramolecular properties governing the unidirectional dynamics have been subject of a number of theoretical − and experimental − investigations. It has been shown that the rotational speed (ranging from nanoseconds to hours) as well as the excitation wavelength (tunable in the range from ultraviolet to visible light) strongly depend on the design of the molecular motor. − …”