plane at right angles to the axis, a new object is obtained that is indistinguishable
from the original one. In general, a one-fold alternating axis is equivalent to a plane
of symmetry and a two-fold alternative axis is identical with a centre of inversion.
Therefore, the fundamental symmetry condition for optical activity is the absence of
an improper axis. In the case of α-HCH, neither a plane nor a centre nor an
alternating axis of symmetry is encountered, and, as a consequence, α-HCH is chiral,
the only chiral of eight conceivable HCH isomers.
In lectures and monographs of basic organic chemistry (Dalton 2011; Koskinen
2012; Boikess 2015; Tro 2018; Timberlake and Orgill 2019), additional types of
chirality are usually discussed. For completeness, we briefly mention these types
without going into detail, because we do not necessarily need these aspects for the
present monograph. These types of chirality include allene-type chirality (Webster
et al. 2016), in which the central carbon atom is sp-bonded with even numbers of
double bonds, both sides being asymmetrically substituted, helical asymmetry
(represented by hexahelicene) and planar asymmetry (represented by substituted
paracyclophanes) such as described earlier (Zhao et al. 2014). Basically, the same
tests described above (plane or centre or alternating axis of symmetry) can be
applied, in order to find out as to whether or not such molecules are chiral.
1.6.4 Chiral Environmental Pollutants with Two or More
Stereogenic Centres
As described in comprehensive review publication and repeated here (Hühnerfuss
and Shah 2009), when a molecule possesses two asymmetric centres, each centre has
to be attributed its own configuration. The first centre may exhibit R- or S-configuration, and so may the second. Accordingly, a systematic variation of all possibilities
at each stereogenic centre shows that two times two, that is, four stereoisomers can
be formulated. Generalising, the maximum number of stereoisomers existing for a
molecule with n stereogenic centres thus may be 2
n stereoisomers. In order to
distinguish between these different possibilities, the R,S-nomenclature that is based
on the so-called CIP rules is strongly recommended, because these rules can be
universally used also in those cases, where the old D,L-nomenclature is ambiguous. It
would be beyond the scope of the present monograph to develop the exact CIP rules
herein. For descriptions of the system and sets of sequence rules, the reader should
refer to basic organic monographs (Boikess 2015; Tro 2018; Timberlake and Orgill
2019), or to the original publications by Cahn, Ingold and Prelog (¼ CIP) (Cahn
et al. 1956, 1966; Prelog and Helmchen 1982; Helmchen 2016). In the latter case, the
more complicated assignments such as those for (+)-α-1S,2R,3R,4S,5S,6S-HCH will
become accessible, though some time will be required to infer the exact nomenclature for such cyclic compounds.
Although four is the maximum number of isomers when the compound exhibits
two chiral centres, this number may be reduced when the three groups on one
12
1 Introduction
from the original one. In general, a one-fold alternating axis is equivalent to a plane
of symmetry and a two-fold alternative axis is identical with a centre of inversion.
Therefore, the fundamental symmetry condition for optical activity is the absence of
an improper axis. In the case of α-HCH, neither a plane nor a centre nor an
alternating axis of symmetry is encountered, and, as a consequence, α-HCH is chiral,
the only chiral of eight conceivable HCH isomers.
In lectures and monographs of basic organic chemistry (Dalton 2011; Koskinen
2012; Boikess 2015; Tro 2018; Timberlake and Orgill 2019), additional types of
chirality are usually discussed. For completeness, we briefly mention these types
without going into detail, because we do not necessarily need these aspects for the
present monograph. These types of chirality include allene-type chirality (Webster
et al. 2016), in which the central carbon atom is sp-bonded with even numbers of
double bonds, both sides being asymmetrically substituted, helical asymmetry
(represented by hexahelicene) and planar asymmetry (represented by substituted
paracyclophanes) such as described earlier (Zhao et al. 2014). Basically, the same
tests described above (plane or centre or alternating axis of symmetry) can be
applied, in order to find out as to whether or not such molecules are chiral.
1.6.4 Chiral Environmental Pollutants with Two or More
Stereogenic Centres
As described in comprehensive review publication and repeated here (Hühnerfuss
and Shah 2009), when a molecule possesses two asymmetric centres, each centre has
to be attributed its own configuration. The first centre may exhibit R- or S-configuration, and so may the second. Accordingly, a systematic variation of all possibilities
at each stereogenic centre shows that two times two, that is, four stereoisomers can
be formulated. Generalising, the maximum number of stereoisomers existing for a
molecule with n stereogenic centres thus may be 2
n stereoisomers. In order to
distinguish between these different possibilities, the R,S-nomenclature that is based
on the so-called CIP rules is strongly recommended, because these rules can be
universally used also in those cases, where the old D,L-nomenclature is ambiguous. It
would be beyond the scope of the present monograph to develop the exact CIP rules
herein. For descriptions of the system and sets of sequence rules, the reader should
refer to basic organic monographs (Boikess 2015; Tro 2018; Timberlake and Orgill
2019), or to the original publications by Cahn, Ingold and Prelog (¼ CIP) (Cahn
et al. 1956, 1966; Prelog and Helmchen 1982; Helmchen 2016). In the latter case, the
more complicated assignments such as those for (+)-α-1S,2R,3R,4S,5S,6S-HCH will
become accessible, though some time will be required to infer the exact nomenclature for such cyclic compounds.
Although four is the maximum number of isomers when the compound exhibits
two chiral centres, this number may be reduced when the three groups on one
12
1 Introduction