Tianlv Xu

Distinguishing and quantifying the torquoselectivity in competitive ring-opening reactions using the stress tensor and QTAIM

Currently the theories to explain and predict the classification of the electronic reorganization due to the torquoselectivity of a ring‐opening reaction cannot accommodate the directional character of the reaction pathway; the torquoselectivity is a type of stereoselectivity and therefore is dependent on the pathway. Therefore, in this investigation we introduced new measures from quantum theory of atoms in molecules and the stress tensor to clearly distinguish and quantify the transition states of the inward (TSIC) and outward (TSOC) conrotations of competitive ring‐opening reactions of 3‐(trifluoromethyl)cyclobut‐1‐ene and 1‐cyano‐1‐methylcyclobutene. We find the metallicity ξ(rb) of the ring‐opening bond does not occur exactly at the transition state in agreement with transition state theory. The vector‐based stress tensor response βσ was used to distinguish the effect of the CN, CH3, and CF3 groups on the TSIC and TSOC paths that was consistent with the ellipticity ε, the total local energy density H(rb) and the stress tensor stiffness Sσ. We determine the directional properties of the TSIC and TSOC ring‐opening reactions by constructing a stress tensor UσTS space with trajectories TσTS (s) with length l in real space, longer l correlated with the lowest density functional theory‐evaluated total energy barrier and hence will be more thermodynamically favored.

A QTAIM and stress tensor investigation of the torsion path of a light-driven fluorene molecular rotary motor

The utility of the QTAIM/stress tensor analysis method for characterizing the photoisomerization of light driven molecular rotary machines is investigated on the example of the torsion path in fluorene molecular motor. The scalar and vector descriptors of QTAIM/stress tensor reveal additional information on the bonding interactions between the rotating units of the motor, which cannot be obtained from the analysis of the ground and excited state potential energy surfaces. The topological features of the fluorene motor molecular graph display that, upon the photoexcitation a certain increase in the torsional stiffness of the rotating bond can be attributed to the increasing topological stability of the rotor carbon atom attached to the rotation axle. The established variations in the torsional stiffness of the rotating bond may cause transfer of certain fraction of the torsional energy to other internal degrees of freedom, such as the pyramidalization distortion.

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

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 S1 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 S1 energy minimum and the S1/S0 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 S1 state in the vicinity of the conical intersection.

QTAIM and stress tensor interpretation of the (H2O)5 potential energy surface

Using the quantum theory of atoms in molecules a near complete combined directed spanning quantum topology phase diagram (QTPD) was constructed from the nine (H2O)5 reaction‐pathways and five unique Poincaré–Hopf solutions that were found after an extensive search of the MP2 potential energy surface. Two new energy minima that were predicted from earlier work are found and include the first (H2O)5 conformer with a 3‐DQT quantum topology. The stress tensor Poincaré–Hopf relation indicated a preference for 2‐DQT (H2O)5 topologies as well as the presence of coupling between shared‐shell OH BCPs to the hydrogen‐bond BCPs that share an H NCP. The complexity of the near complete combined QTPD was explained in terms of the O…O bonding interactions that were found in six of the nine (H2O)5 reaction‐pathways and for all points of the combined QTPD. The stabilizing role of the O…O bonding interactions from the values of the total local energy density was explored.

A stress tensor and QTAIM perspective on the substituent effects of biphenyl subjected to torsion

The Quantum Theory of Atoms in Molecules (QTAIM) defines quantities in 3D space that can be easily obtained from routine quantum chemical calculations. The present investigation shows that local properties can be related quantitatively to measures traditionally connected to experimental data, such as Hammett constants. We consider the specific case of substituted biphenyl to quantify the effects of a torsion φ, 0.0° ≤ φ ≤ 180.0°, of the C—C bond linking the two phenyl rings for C12H9‐x, where x = N(CH3)2, NH2, CH3, CHO, CN, NO2, on the entire molecule. QTAIM interpreted Hammett constants, aΔH(rb) are introduced and constructed using the difference between the H(rb) value of C12H9‐x and the C12H9‐H, biphenyl which is the reference molecule, with a constant of proportionality a. This investigation unexpectedly yields very good or good agreement for the x groups with the Hammett para‐, meta‐, and ortho‐substituent constants and is checked against para‐substituted benzene. We then proceed to present the interpreted substituent constants of seven new biphenyl substituent groups, where tabulated Hammett substituent constant values are not available; y = SiH3, ZnCl, COOCH3, SO2NH2, SO2OH, COCl, CB3. Consistency is found for the QTAIM interpreted biphenyl substituent constants of the seven new groups y independently using the stress tensor polarizability Pσ. In addition, a selection of future applications is discussed that highlight the usefulness of this approach.

A vector-based representation of the chemical bond for the normal modes of benzene: HUANG et al.

We introduce a vector-based interpretation of the chemical bond within the quantum theory of atoms in molecules (QTAIM), the bond-path framework set

Biphenyl: A stress tensor and vector‐based perspective explored within the quantum theory of atoms in molecules

\mathbb{B} = \{p, q, r\}

The Pt site reactivity of the molecular graphs of Au6Pt isomers

, to follow variations in the 3-D morphology of all bonds for the four infra-red (IR) active normal modes of benzene. The bond-path framework set comprises three unique paths

A stress tensor eigenvector projection space for the (H2O)5 potential energy surface

p

The normal modes of vibration of benzene from the trajectories of stress tensor eigenvector projection space

,