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

Tools for overcoming reliance on energy-based measures in chemistry: a tutorial review

The vast majority of literature in the chemical sciences describes fundamental chemical and physical phenomena using scalar measures, such as the energy, even though many phenomena are beyond the scope of scalar-based considerations. This problem exists no matter how accurately the associated energies are calculated. The solution that is explained in this work is to remove the reliance on scalar quantum chemical measures and instead utilize the vector-based and full symmetry-breaking nature of next generation quantum theory of atoms in molecules (NG-QTAIM). The connection with experiment on neutral chiral molecules is explained. A selection of non-energy-based explanations are provided: the functioning of molecular devices, why the cis-effect is the exception rather than the rule, stereochemical phenomena including chiral discrimination, quantifying chiral character of formally achiral molecules, mixed S and R stereoisomer character and the effect of an applied electric field. Current and future developments along with suggestions for future avenues of investigation are discussed. This tutorial review provides the practical details required to implement NG-QTAIM for a range of phenomena that are not accessible with energy-based measures. Step-by-step worked examples are included with data sets and instructions for use of commercial and open-source software along with examples of how to interpret the results.

The Cis-Effect Explained Using Next-Generation QTAIM

We used next-generation QTAIM (NG-QTAIM) to explain the cis-effect for two families of molecules: C₂X₂ (X = H, F, Cl) and N₂X₂ (X = H, F, Cl). We explained why the cis-effect is the exception rather than the rule. This was undertaken by tracking the motion of the bond critical point (BCP) of the stress tensor trajectories T_σ(s) used to sample the U_σ-space cis- and trans-characteristics. The T_σ(s) were constructed by subjecting the C1-C2 BCP and N1-N2 BCP to torsions ± θ and summing all possible T_σ(s) from the bonding environment. During this process, care was taken to fully account for multi-reference effects. We associated bond-bending and bond-twisting components of the T_σ(s) with cis- and trans-characteristics, respectively, based on the relative ease of motion of the electronic charge density ρ(r_b). Qualitative agreement is found with existing experimental data and predictions are made where experimental data is not available.

Chirality without Stereoisomers: Insight from the Helical Response of Bond Electrons

The association between molecular chirality and helical characteristics known as the chirality-helicity equivalence is determined for the first time by quantifying a chirality-helicity measure consistent with photoexcitation circular dichroism experiments. This is demonstrated using a formally achiral S_N 2 reaction and a chiral S_N 2 reaction. Both the achiral and chiral S_N 2 reactions possess significant values of the chirality-helicity measure and display a Walden inversion, i. e. an inversion of the chirality between the reactant and product. We also track the chirality-helicity measure along the reaction path and discover the presence of chirality at the transition state and two intermediate structures for both reactions. We demonstrate the need for the chirality-helicity measure to differentiate between steric effects due to eclipsed conformations and chiral behaviors in formally achiral species. We explain the significance of this work for asymmetric synthetic reactions including the intermediate structures where the Cahn-Ingold-Prelog (CIP) rules cannot be used.

Interatomic exchange-correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding-integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)-and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.

3-D bond-paths of QTAIM and the stress tensor in neutral lithium clusters, Lim (m = 2-5), presented on the Ehrenfest force molecular graph

In this investigation we set out to understand the origins of non-nuclear attractors (NNAs) found for neutral lithium clusters Lim (m = 2-5) on the QTAIM molecular graph but not on the Ehrenfest force F(r) molecular graph. Therefore, we pursued the stress tensor σ(r) without using the dependency on the QTAIM partitioning, since previously σ(r) was only calculated within the QTAIM partitioning, to see if any indication of NNA character can be determined. Because the stress tensor σ(r) lacks an associated scalar- or vector-field as is the case for QTAIM and the Ehrenfest F(r) partitioning schemes respectively, a stress tensor σ(r) partitioning scheme cannot be constructed. Therefore, to overcome this difficulty we use next generation QTAIM, constructed from the most preferred directions of electronic charge density accumulation, to calculate the stress tensor σ(r) 3-D bond-paths on the Ehrenfest force F(r) molecular graph. Using next generation 3-D bond-paths within the Ehrenfest force F(r) partitioning, we can classify the degree of NNA character in the absence of NNAs. A much higher degree of NNA character is found to be present for the stress tensor σ(r) 3-D bond-paths than for the corresponding QTAIM or Ehrenfest force F(r) 3-D bond-paths. The stabilizing effect of the NNA is demonstrated by undertaking Li2 bond-path compression and stretching distortions sufficient to cause the annihilation of the NNA. The compression and stretching distortions also lead to a large increase in the 3-D bond-path asymmetry and persistent bond-path torsion respectively.

Intramolecular mode coupling of the isotopomers of water: a non-scalar charge density-derived perspective

Left: The BCP trajectories T(s) for H₂O for the bending (Q1) mode, the axes labels of the trajectory T(s). The green spheres correspond to the bond critical point (BCPs). Right: The corresponding T(s) for H₂O for the symmetric-stretch (Q2) mode.

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.