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 .