1. Introduction
The existence of chirality has important implications[1]–[3] and the origin of chiral asymmetry[4] in molecular biology is one of the great mysteries in the understanding of the origin of life[5]–[12]. In 1848 Louis Pasteur proposed biomolecular homochirality as a possible simple ‘chemical signature of life’[13].
A recent publication by Francl expressed skepticism about using binary measures for chirality and instead proposed considering continuous measures of chirality[14]. In particular the discussion focused around continuous (non-binary) chirality, as developed by Zahrt and Denmark, who argued that chirality is a transmissible property.[15] They used the method of Zabrodsky and Avnir[16] to determine the degree of chirality, based on computing the minimal distance that the vertices of a shape must be moved to attain an achiral system. Zahrt and Denmark argue that the degree of chirality of molecules depends on their ability to transmit that information to another molecule and to differentiate enantiomers. Mislow, Bickart and others presented the idea that a molecule is a vector of measurable properties, such as optical activity, and therefore chirality is not a binary property, but a continuous quantity[14], [16], [17]. A multidisciplinary review by Petitjean on the relationship between the degree of chirality and symmetry involved discussion of concepts such as similarity, disorder and entropy[18]. Jamróz et al. proposed a continuous measure of chirality based on topology, creating the concept of Property Space and similarity between enantiomers for use as a quantitative structure activity relationship (QSAR) measure[19]. Molecular similarity measures[20]–[24] have found frequent use in QSAR investigations, some explicitly including considerations of conventional chirality[25]–[29].
Conventional (scalar) QTAIM is insufficient to distinguish S and R stereoisomers at the energy minimum and can at best quantify the asymmetry of the charge density distribution in the form of the bond critical point ellipticity ε. Next generation QTAIM (NG-QTAIM)[30], a vector-based quantum mechanical theory constructed within the quantum theory of atoms in molecules (QTAIM)[31] using the stress tensor, can differentiate the S and R stereoisomers for all values of the torsion θ, -180.0° ≤θ ≤+180.0°. In this investigation we use Bader’s formulation of the stress tensor[32] and NG-QTAIM on the basis of the superior performance of the stress tensor compared with vector-based QTAIM for distinguishing the S and R stereoisomers of lactic acid[33]. The most (facile) preferred direction of electron charge density accumulation determines the direction of bond motion[34]. Within the electron-preceding perspective a change in the electronic charge density distribution that defines a chemical bond results in a change in atomic positions[35]. Bone and Bader later proposed that the direction of motion of the atoms that results from a slightly perturbed structure coincides with the direction of motion of the electrons[36]; this was subsequently confirmed[37], [38].
In this investigation we will seek to locate the presence of chiral character for electron density and manipulate induced chirality in glycine by varying the direction and magnitude of an applied electric (E) -field to create S and R stereoisomers. The application of an E -field will induce symmetry-breaking changes to the length of the C-H bonds attached to the alpha carbon atom (C1) of formally achiral glycine, as previously studied by Wolk et al . in achiral glycine[39], see Scheme 1 .