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.