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Chapter 10: Prochirality and Pro-RS-Stereogenicity. Stereoisogram Approach Free from the Conventional ``Prochirality´´ and “Prostereogenicity”
“prochirality” to be abandoned (Helmchen 1996, pages 20 and 74). In contrast to this
description, the glossary of a standard textbook (Eliel and Wilen 1994, page 1204) has
adopted the terms “prochirality” and referred to “prostereoisomerism” as a more
general term. The IUPAC Recommendations 1996 does not contain the definition of
the term “prostereogenicity” or “prostereoisomerism” but adopts the ambiguous term
The confusion of these terms (“prochiral”, “prostereogenic”, and “prostereoisomerism”) is so serious that most articles and textbooks other than those of
biochemical fields tend to use “enantiotopic”, “diastereotopic”, and “stereoheterotopic” in place of these terms. However, such replacement conceals problematic situations to be settled, because the confusion reflects misleading situations
concerned with “chiral”, “stereogenic”, and “stereoisomerism”, which are the
cruxes of stereochemistry.
After we clarify that the conventional approach has not been successful in
settling the confusion of these terms, we will demonstrate the stereoisogram
approach as a new terminology for settling the confusion.
Problem Setting — Aims and Scope
To begin with, the present section deals with surveying problematic usages of such
terms as “chiral”, “stereogenic”, “prochiral”, “prostereogenic”, and so on in the
10.2.1 Problems of the Conventional “Chirality”
Since the Cahn-Ingold-Prelog (CIP) system for generating RS-stereodescriptors
was originally proposed under the title “Specification of Molecular Chirality”
(Cahn et al. 1966), such a confused recognition as “Chirality is a basis of the
specification of configurations by the CIP system.” has widely spread over organic
stereochemistry. Although the CIP system has later changed its basis from chirality
to stereogenicity (Prelog and Helmchen 1982; Helmchen 1996), the term “stereogenicity” itself has not been directly defined as found in a rulebook (IUPAC
Chemical Nomenclature and Structure Representation Division 2004) and most
textbooks on stereochemistry (Eliel and Wilen 1994; North 1998; Eliel et al. 2001),
so that discrimination between chirality and stereogenicity has not been fully
demonstrated. As a result, a related misleading remark such as “Each pair of
RS-stereodescriptors is given to discriminate between a pair of enantiomers.” is
used even now, as found in the section title “P91.1 Enantiomers: the CIP priority
system” of the IUPAC 2004 Provisional Recommendations (IUPAC Chemical
Nomenclature and Structure Representation Division 2004), which presumes a
direct linkage between the term enantiomers and the CIP system.
Prochirality and Pro-RS-Stereogenicity. . .
In particular, the term “chirality center” (Prelog and Helmchen 1982) has caused
serious confusions, as found in a misleading or rather erroneous statement,
“Stereogenic centers thus may be or may not be chiral (i.e., centers of chirality).
Conversely, however, all chiral centers are stereogenic.” (Eliel et al. 2001, page 33).
For example, let us examine a molecule (1) with two achiral ligands (a) and (b) and two
chiral ligands of the same kind (p), where the ligand a (or b) can be superposed on its
mirror image in isolation and the ligand p cannot be superposed its mirror image in
isolation. If the term chiral of “chiral center” indicates a geometric meaning, the carbon
center (C) of the molecule (1) is chiral, because a reflection operated on 1 generates the
carbon center of its enantiomer (1), where the ligand p represents the mirror image of
p in isolation. Note that the carbon center (C) of the molecule (1) is enantiomeric
(a mirror image) to that of 1. Because the two mirror-image carbons are not superposable, the carbon center of 1 (as well as that of 1) is chiral, but “not stereogenic”. Hence,
the statement cited above (Eliel et al. 2001, page 33) is erroneous, so long as the term
chiral of “chiral center” indicates a geometric meaning. From the viewpoint of
the conventional stereochemistry coupled with the CIP system, on the other hand, the
carbon center of 1 (as well as that of 1) is “not chiral” and “not stereogenic”. Thus,
the statement (Eliel et al. 2001, page 33) would be justified only if the term chiral of
a geometric meaning has suffered semantic transmutation (which has once been
discussed in a review (Mislow 2002)) to give the term “chiral” of the CIP system.
As found in the preceding discussions, it is safe to say that the term “chirality”
for explaining the CIP system (Cahn et al. 1966; Prelog and Helmchen 1982) no
longer has the same meaning as the term chirality of an original geometric meaning.
Note that the original term chirality is essential to discuss enantiomeric relationships in organic stereochemistry. It follows that the term “chirality” different from
the original term chirality should be abandoned, after a theoretical framework is
developed to rationalize the abandonment of the transmuted term “chirality”.
Moreover, the theoretical framework to be developed should explain the difference
between chirality and stereogenicity.
10.2.2 Problems of the Conventional “Prochirality”
The pro-R/pro-S system (Hanson 1966) (or the Re/Si system (Prelog and
Helmchen 1972)) for specifying intramolecular environments has been widely
adopted in organic stereochemistry. The term “prochirality” for supporting the
pro-R/pro-S system (Hanson 1966) has originally coined to aim at indicating
a geometric property, because the prefix pro designates a precursory stage of
chirality. The original aim of the coinage has been a failure. For example, the
central carbon atom of 1 is “prochiral” because the ligands (two p’s) can be named
by the pro-R/pro-S system. However, the carbon atom at issue is already chiral
geometrically, as discussed in the preceding subsection.
Fig. 10.1 Geometrically
chiral but not stereogenic
centers. The ligand p
represents the mirror image of
p in isolation and the ligand a
(or b) is achiral when
Thereby, the same carbon of 1 is concluded (1) to be “prochiral” from the
viewpoint of the pro-R/pro-S system, (2) not to be “chiral” from the viewpoint of
the CIP system, and (3) to be chiral geometrically. Note that Item 1 can be deduced
from Item 2 because not to be “chiral” is a prerequisite for being “prochiral”. This
means that the problem of the term “chiral” in the CIP system is immediately linked
to the problem of the term “prochiral” of the pro-R/pro-S system. As a result, it
is strange that Helmchen (1996, page 12) maintains the usage of the term “chirality
center” in spite of the proposal of the term stereogenic units of type 1 (for chirality
units) and type 2 (for pseudoasymmetric units) as being more appropriate. Moreover,
it seems to be inconsistent to the usage of the term “chirality center” that he has stated
(Helmchen 1996, page 20): “Terms containing prochiral, such as prochiral unit or
element, prochiral molecules or prochirality, must be abandoned.” The abandonment
of “prochirality” for the pro-R/pro-S system should inevitably reach the abandonment
of “chirality” for the CIP system because of the situation shown in Fig. 10.1.
In a parallel with the revision of the CIP system (Prelog and Helmchen 1982),
the basis of the pro-R/pro-S system has been changed from “prochirality” into
“prostereoisomerism” or “prostereogenicity” (Hirschmann and Hanson 1971b).
Mislow and Siegel have recommended that the usage of “prochirality” with reference to prostereoisomerism should be altogether abandoned (Mislow and
Siegel 1984) after their convincing discussions on geometric features of molecules.
In spite of these situations, the term “prochiral” connected with the pro-R/pro-S
system is still used in place of the term “prostereoisomerism” or “prostereogenicity” (IUPAC Organic Chemistry Division 1996). Moreover, discrimination
between “prochirality” and prostereogenicity (or prostereoisomerism) has not been
fully demonstrated, as symbolized by the title “Prostereoisomerism (Prochirality)”
of a review (Eliel 1982). Although the review has expressed, “Correspondingly, the
concept of prochirality must be generalized to one of prostereoisomerism”
(Eliel 1982, page 4), is this a promising way to be followed?
10.2.3 Problems of the Conventional Dichotomy Between
Enantiomers and “Diastereomers”
The conventional stereochemistry has heavily relied on the dichotomy between
enantiomers and diastereomers, as found in reviews (Jonas 1988; Mislow 2002),
textbooks on stereochemistry (Morris 2001; Mislow 1965; Eliel and Wilen 1994;
North 1998; Eliel et al. 2001), glossaries (IUPAC Organic Chemistry Division 1996;
Prochirality and Pro-RS-Stereogenicity. . .
Fig. 10.2 Two achiral
stereoisomers of meso-type
where the ligand p represents
the mirror image of p in
IUPAC Chemical Nomenclature and Structure Representation Division 2004),
and several reports on a flow-chart approach (Jonas 1988; Black 1990; Mislow 1977;
Vollhardt and Schore 2003). The dichotomy is typically expressed as: “Diastereomers
(or diastereoisomers) are stereoisomers not related as mirror images.” (Eliel and
Wilen 1994, page 1196), “Any pair of stereoisomers which are not enantiomers of
one another are called diastereomers.” (North 1998, page 17), or other almost
Strictly speaking, these expressions involve enantiomeric relationships (based
on reflection operations) and stereoisomeric relationships (based on projection
operations for giving respective common graphs) as definitely specified categories.
They do not directly define diastereomeric relationships, because stereoisomeric
relationships minus enantiomeric relationships are generically called diastereomeric relationships. Note that a set of diastereomers does not provide a definite
assembly, although a pair of enantiomers (or a set of stereoisomers) provides a
definite assembly (an orbit, group-theoretically speaking).
Let us consider two achiral stereoisomers (2 and 3) shown in Fig. 10.2. They are
also stereoisomeric to 1 and 1 shown in Fig. 10.1. By the above definitions, the
relationship between 1 and 2 (or 3) is concluded to be diastereomeric, because the
enantiomer 1 is different to the achiral 2. On the other hand, the relationship between
the achiral 2 and 3 is also concluded to be diastereomeric, because their mirror images
(2 and 3 themselves) are different to each other. It should be noted, however, that the
diastereomeric relationship between 1 and 2 is different from the diastereomeric
relationship between 2 and 3 in whether there exist enantiomeric relationships or not.
From another point of view, an isomerization from 1 (chiral) to 2 (achiral) is
different from an isomerization from 2 (achiral) to 3 (achiral), where both of the
isomerizations correspond to the above-mentioned diastereomeric relationships of
different types. Hence, we should say that there exist at least two diastereomeric
relationships of different types. The conventional stereochemistry is silent about such
diastereomeric relationships of different types. In other words, the dichotomy between
enantiomers and diastereomers in the conventional stereochemistry is oversimplified.
10.2.4 Problems of the Conventional Dichotomy Between
Enantiotopic Relationships and “Diastereotopic” Ones
The terms enantiotopic and “diastereotopic” have been first coined for describing
geometric features (Mislow and Raban 1967). Note that a set (pair) of enantiotopic
e.g., C -1 of ethanol
e.g., C-3 of a butan-2-ol
(X2 : “diastereotopic”)
e.g., C-3 of a pentane-2,4-diol
(X2 : “diastereotopic”)
Fig. 10.3 “Prostereogenic centers” due to “stereoheterotopic” relationships of different types in
the conventional terminology of stereochemistry, where the ligands a, b, and X represents achiral
ligands in isolation and the ligand p represents a chiral ligand that is the mirror image of a chiral
ligand p in isolation
ligands produces a definite assembly (i.e., an equivalence class), while a set (pair)
of “diastereotopic” ligands is incapable of producing a definite assembly. Thus,
the two terms for describing geometric features belong to different categories
of concept. Later, the term “stereoheterotopic” has been defined as a combined
concept of the conceptually different terms (enantiotopic and “diastereotopic”)
(Hirschmann and Hanson 1971a) in a parallel way to the dichotomy between
enantiomers and “diastereomers” for classifying stereoisomers (stereoisomeric
relationships). The term “stereoheterotopic” has been a key to test “prostereogenicity centers” (substituted for “prochiral centers”), where an atom of a molecule which becomes a “stereogenic center” (or “chiral center”) by replacing one
of the two “stereoheterotopic” ligands attached to it by a different ligand is said to
be a “prostereogenicity center” (or a “prochirality center”), e.g., C-1 of ethanol
(an enantiotopic case), C-3 of butan-2-ol (a diastereotopic case) (IUPAC Organic
Chemistry Division 1996).
Figure 10.3 summarizes topicity relationships in the conventional terminology
of stereochemistry. The two achiral ligands X’s in 4 (the ligands a and b are also
achiral in isolation) are enantiotopic to each other, while the two achiral ligands X’s
in 5 (a: achiral, p: chiral in isolation) as well as the two achiral ligands X’s in 6
(p and p: enantiomeric in isolation) are “diastereotopic” to each other. The difference between the enantiotopic X’s in 4 and the “diastereotopic” X’s in 5 (or 6) stems
from difference in their substitution products (enantiomers vs. “diastereomers”).
The combination of the two terms (enantiotopic and “diastereotopic”) into a single
term “stereoheterotopic” has aimed at coining such a single term to give a basis to the
pro-R/pro-S system (Hirschmann and Hanson 1971a). After this coinage, all the pairs
of achiral ligands X’s in the respective molecules listed in Fig. 10.3 (3, 4, and 5) can
be apparently referred to as being “stereoheterotopic” so as to be named by the
pro-R/pro-S system. This combination has brought about the dichotomy between
enantiotopic relationships and “diastereotopic” relationships in a molecule (“stereoheterotopic”) in parallel with the dichotomy between enantiomeric relationships and
“diastereomeric” relationships among molecules (“stereoisomeric”) (Mislow 1977).
Prochirality and Pro-RS-Stereogenicity. . .
However, is there a plausible rationalization to combine enantiotopic and
“diastereotopic” into a single term “stereoheterotopic”?
One of such rationalizations belongs to a permutation category (concerned
with permutation groups) such that two ligands X’s of each molecule listed in
Fig. 10.3 are exchangeable by a permutation between them without changing
molecular properties. However, the term enantiotopic belongs to a geometric
category (concerned with point groups), which is different from the permutation
category. The preference of the term enantiotopic for 4 results in the neglect of the
permutational exchangeability, which is common to 4, 5, and 6. Hence, it is
necessary to demonstrate whether the three terms (enantiotopic, “diastereotopic”,
and “stereoheterotopic”) are properly related or not.
The discussion described in the preceding paragraph brings us back to an
additional question on the dichotomy between enantiomeric relationships and
“diastereomeric” relationships among molecules: Is there a plausible rationalization
to combine enantiomeric (geometric category) and “diastereomeric” (permutation
category) into a single term “stereoisomeric”?
10.2.5 Problems of the Transmuted Term “Enantiotopic”
The original term enantiotopic defined by Mislow and Raban (1967) has a geometric meaning. By applying this geometric definition strictly, the ligands p and p in 2
(or 3 in Fig. 10.2 or 6 in Fig. 10.3) are concluded to be in an enantiotopic relationship. According to the conventional terminology described in Sect. 10.2.4, such
enantiotopic ligands as p and p should be named by the pro-R/pro-S system,
although they do not require the differentiation by the pro-R/pro-S system. This
inconsistency means that there is an enantiotopic pair beyond the scope of the
pro-R/pro-S system, so that the criteria for rationalizing the pro-R/pro-S system,
i.e., enantiotopic, “diastereotopic”, and “stereoheterotopic”, are proven to be futile.
To remedy this futileness, the geometric definition of the term enantiotopic
has been changed into a transmuted one: “Enantiotopic ligands and faces.
Homomorphic (q.v.) ligands in constitutionally equivalent locations that are
symmetry plane (or center or alternating axis of symmetry) but not a (simple)
symmetry axis.” (Eliel and Wilen 1994, page 1198), where the modifier “homomorphic” has been added. This transmuted term can exclude such cases as a pair
of p and p (in 2, 3, or 6) because p and p are not homomorphic, where the term
“homomorphic ligands” has been defined: “Ligands that are structurally (including configurationally) identical when detached.” (Eliel and Wilen 1994, page
1200). By examining carefully, however, such exclusion by transmuting the
geometrically defined term enantiotopic seems not to be rationalized, causing
latent confusions. Note that p and p (in 2 or 3 or 6) can be differentiated by an
appropriate chiral reagent to generate chiral products (i.e., prochiral geometrically). In other words, this excluded case exhibits the essentially same feature as
the two X’s of the molecule 4. Hence, such exclusion demonstrates the limitation
of the pro-R/pro-S system, even if it is unreasonably justified by the transmuted
Moreover, the remedy by adding the modifier “homomorphic” is incomplete.
Consider a case with p ¼ C(H)(OH)COOH and p ¼ C(OH)(H)COOH in 2 (or 3
or 6). Then, the ligand OH of p and the corresponding ligand OH of p are in an
enantiotopic relationship from a viewpoint of the original geometric term
(Mislow and Raban 1967) as well as from a viewpoint of the transmuted term
(Eliel and Wilen 1994, page 1198), because the ligand OH is homomorphic
according to the definition described above (Eliel and Wilen 1994, page 1200).
In other words, there again emerges an “enantiotopic” (also enantiotopic) case
which indicates such inconsistency that there is an “enantiotopic” pair beyond
the scope of the pro-R/pro-S system. To remedy this inconsistency, a further
transmutation of the transmuted term “enantiotopic” would be necessary. Obviously, such multiple transmutation no longer indicates a proper way to be
10.2.6 Aims and Scope
The problems of various types in the conventional stereochemistry are highly
entangled as the result of the semantic transmutation described in the preceding
subsections. It is impossible to solve the entangled problems if we maintain the
conventional terminology of stereochemistry. Hence, the conventional terminology
should be entirely reconsidered to restructure stereochemistry.
1. The term “prochirality” of the pro-R/pro-S system should be abandoned in the
same way as the transmuted term “chirality” of the CIP system should be
abandoned. In other words, the theoretical framework to be developed should
define a term prochirality by starting from the term chirality of a purely
geometric meaning (Fujita 1991b, 2007c).
2. The term “prostereogenicity” or “prostereoisomerism” of the pro-R/pro-S
system and the term “stereogenicity” for giving RS-stereodescriptors of the
CIP system should be abandoned. Instead, the newly-developed theoretical
framework will define pro-RS-stereogenicity by starting from RS-stereogenicity,
which has recently been developed (Fujita 2004a,c,d, 2005e).
3. The terms “enantiotopic”, “diastereotopic”, and “stereoheterotopic” should be
abandoned to support the pro-R/pro-S system, just as the terms “enantiomeric”,
“diastereomeric”, and “stereogenic” for supporting RS-stereodescriptors of
the CIP system should be abandoned. In particular, the term enantiotopic will
be used only to explain geometric aspects apart from the pro-R/pro-S system,
while the newly-defined term RS-diastereotopic will be used to support the proR/pro-S system. On a similar line, the term enantiomeric will be used only to
Prochirality and Pro-RS-Stereogenicity. . .
explain geometric aspects apart from the CIP system, while the newly-defined
term RS-diastereomeric will be used to support RS-stereodescriptors of the CIP
4. The use of the term “stereoheterotopic” should be entirely ceased to support
the pro-R/pro-S system. Thereby, the dichotomy between enantiotopic and
“diastereotopic” (for the term “stereoheterotopic”) will be abandoned. The
related terms such as “stereoheterotopism” or “stereoheterotopicity” (Hirschmann
and Hanson 1971a; Hirschmann 1983) for supporting the pro-R/pro-S system will
be also abandoned.
5. The transmuted term “enantiotopic” (Eliel and Wilen 1994, page 1198) should be
abandoned. The term enantiotopic will be used in a purely geometric meaning.
6. In addition, the theoretical framework should explain the difference between
the newly-defined prochirality (geometrically) and pro-RS-stereogenicity, just
as it should explain the difference between chirality (geometrically) and RSstereogenicity.
To prevent such semantic transmutation as described in the preceding subsections, we have developed a diagrammatic approach based on the group theory
(point groups and permutation groups). The diagrammatic approach is here called
stereoisogram approach because it stems from the concept of stereoisograms
(Fujita 2004c,d, 2009b,d,e). The stereoisogram approach is a theoretical framework
common to intermolecular and intramolecular features as well as to geometric and
stereoisomeric features. Although the present discussions will omit the mathematical basis of the stereoisogram approach (Fujita 2004a,b, 2005d,e), it will be
The Stereoisogram Approach
In the stereoisogram approach, reflection operations are differentiated distinctly
from RS-permutations in whether ligand reflections are involved or not. This
section is devoted to demonstrate that such differentiation generates three kinds
of relationships for constructing stereoisograms. The crux of the stereoisogram
approach is that chirality (related to reflections) and RS-stereogenicity (related to
RS-permutations) are independent concepts.
10.3.1 Reflections and RS-Permutations for Promolecules
For the sake of simplicity, the present chapter is restricted to tetrahedral molecules,
which are further simplified into tetrahedral promolecules substituted by a set of
proligands. Promolecules have been defined as abstract molecules in which a set
of proligands are placed on a given skeleton, where such proligands are defined
as abstract ligands having either chirality or achirality (Fujita 1991b,a, 2000a).
This means that each proligand is achiral or chiral in isolation. When chiral, a pair
of enantiomeric proligands in isolation is represents by a pair of an alphabet
and an overlined alphabet, e.g., p and p shown in Fig. 10.1. Differentiation between
reflections and RS-permutations is essential to construct stereoisograms
(Fujita 2004d,a,c). In addition, ligand reflections are created as operations of
another type by operating reflections and RS-permutations successively.
operated on a promolecule generates the
Reflections A reflection
corresponding mirror image. When the original promolecule is not superposable on the mirror image, they are chiral and enantiomeric to each
other. When the original promolecule is superposable on the mirror image,
the promolecule is achiral. During such a reflection, each chiral proligand
in the original promolecule is transformed into its mirror image in isolation
and each achiral proligand is transformed into itself in isolation.
For example, a reflection operated on 1 generates its enantiomer 1. On
the other hand, a reflection operated on 2 (or 3) generates 2 (or 3) itself
because of achirality.
It should be noted that two or more achiral ligands of the same kind can
have local chiralities when they belong to an enantiospheric orbit in a
molecule (Fujita 1991b, Chapter 10).
RS-Permutation An RS-permutation corresponds to a reflection, where the
chirality or achirality of each proligand (in isolation) is not changed.
For example, an RS-permutation on the two proligands p’s of 1 generates 1
itself. On the other hand, an RS-permutation on the proligands p and p of 2
Ligand reflections A ligand reflection () operated on a promolecule
produces a promolecule which have the same skeleton as the original
skeleton (not reflected) where all of the ligands are changed into their
mirror images (in isolation).
10.3.2 Relationships of Three Types and Attributes of Three Types
The three types of operations bring about transformations of promolecules,
where there emerge three types of relationships listed in Table 10.1 (Fujita 2004c).
A reflection is related to an enantiomeric or self-enantiomeric relationship,
by which a molecule is categorized to be chiral or achiral. An RS-permutation
is related to an RS-diastereomeric or self-RS-diastereomeric relationship, by which
a molecule is categorized to be RS-stereogenic or RS-astereogenic. A ligand
reflection is related to a holantimeric or self-holantimeric relationship, by which a
molecule is categorized to be scleral or ascleral.
Prochirality and Pro-RS-Stereogenicity. . .
Table 10.1 Three relationships and the corresponding
attributes appearing in stereoisograms (Fujita 2004c)
(Concerned with reflections )
(Concerned with RS-permutations )
(Concerned with lig and reflections )
As summarized in Table 10.1, the newly-defined RS-diastereomeric (or
holantimeric) relationship is a pairwise relationship, just as the enantiomeric
relationship is a pairwise relationship. Thereby, a pair of attributes (properties of
promolecules), i.e., RS-stereogenicity/RS-astereogenicity or sclerality/asclerality,
is introduced in a similar way to a pair of chiralty/achirality.
Because reflections and RS-permutations are distinct operations as described
above, chirality/achirality and RS-stereogenicity/RS-astereogenicity are distinct
and independent concepts, as shown in Table 10.1. On the same line, enantiomeric
relationships are distinct from and independent of RS-diastereomeric relationships,
where the former may be superposed on the latter in special cases. In addition
to the two categories, the existence of sclerality/asclerality provides us with a
further theoretical framework, i.e., RS-stereoisomerism based on RS-stereoisomeric
groups, which integrates chirality/achirality, RS-stereogenicity/RS-astereogenicity,
and sclerality/asclerality (Fujita 2004c, 2005e).
In the conventional approach, on the other hand, the term “stereogenicity” and
the term “stereoisomerism” have been used synonymously, as exemplified by the
definition of “stereogenic unit” (IUPAC Organic Chemistry Division 1996) and by
the phases of “stereogenic elements” (McCasland 1953; Prelog and Helmchen
1982) and “elements of stereoisomerism” (Hirschmann and Hanson 1971b). Such
synonymous usage should be ceased so as to be harmonized with the present
approach which distinguishes between RS-stereogenicity and RS-stereoisomerism,
as discussed later in Sect. 10.3.5.3.
It should be emphasized that “diastereomeric” relationships of the conventional terminology are not pairwise relationships, whereas RS-diastereomeric (or
holantimeric) relationships of the present terminology are pairwise relationships.
This fact is a succinct piece of evidence for stating that the conventional dichotomy
between enantiomers and “diastereomers” are oversimplified.
7 (= 7)
Fig. 10.4 Stereoisogram for characterizing promolecules of Type I, which is characterized
by chiral, RS-stereogenic, ascleral attributes (stereoisogram index: ½À; À; a)
10.3.3 Construction of Stereoisograms
The construction of stereoisograms of Type I–V is illustrated by using representative examples so as to show how three relationships and the corresponding
attributes (Table 10.1) participate in a stereoisogram.
Stereoisograms of Type I
Let us operate the three types of operations on a chiral molecule 7, which have four
achiral ligands (a, b, X, and Y) in isolation (Fig. 10.4).
A reflection operated on 7 is shown in the vertical direction of Fig. 10.4 (C-axis:
chirality-axis), where its enantiomer (7) is generated to be combined to the original
promolecule 7 by means of a vertical two-headed arrow modified by an encircled
solid circle (Table 10.1). The locant of each position is represented by a number
with an overbar, when the position accommodates a ligand with a changed chirality
sense. Note that an achiral ligand (e.g., X on the position 3 of 7) is changed into
itself (e.g., X on the position 3 of 7). This means that the mirror image of X
(in isolation) is identical with the original X, i.e., X ¼ X.
An RS-permutation operated on 7 is shown in the horizontal direction of
Fig. 10.4 (S-axis: RS-stereogenicity-axis), where its RS-diastereomer 7 (¼ 7)