Pseudoasymmetric centers

A brief history of the varying interpretations of the term pseudoasymmetric has been given (1,3). Prelog and Helmchen (5) have not limited their idea to the pseudoasymmetric center, axis, or plane but have presented the closely related concept of a general pseudoasymmetry... 

The terms stereocenter, chirotopic, and achirotopic will be used in this text in line with the most recent terminology. However, other terms are found in the older literature. C was previously referred to as a chiral or pseudochiral center. The term pseudochiral center is based on the same convention used to classify C as achirotopic instead of chirotopic. The terms asymmetric and pseudoasymmetric center are found in much older literature. 

There is a fundamental difference between a chirality center and a pseudoasymmetric center and that is that reflection and permutation of ligands have the same effect for the chirality center, but not for the pseudoasymmetric center. This is because, on reflection of the latter, the chirality senses of both the center, seen when the bonds are numbered, and each of the enantiomorphic ligands are reversed. Another way of stating the difference is that Re/Si and rejsi descriptors specify absolute and relative configuration, respectively. Pseudoasymmetric is a most unfortunate term, and in order to avoid it, the classical terms chirality center and pseudoasymmetric center would perhaps best be replaced by more neutral terms, such as stereogenic centers of type 1 and type 2, respectively, in order to emphasize the aspect of stereogenicity. 

In analogy to the case of the two-dimensional pseudoasymmetric center (see Section 1.1.2.2.) pseudoasymmetric stereogenic units are encountered when enantiomorphic ligands (F/F) are located in positions of the core (with residual ligands), that are reflection equivalent but not rotationally equivalent, i.e., in enantiotopic positions. Again, lowercase letter descriptors (r/s, pjm) are used in order to express invariance to reflection. The previous criticism concerning the term pseudoasymmetric (see Section 1.1.2.2.) also applies here and will be elaborated in Section 1.1.3.5. 

X(ABCD) and X(FFCD) the centers X are clearly chirotopic and achirotopic, respectively (see Section 1.1.3.5.). However, this possibility is barred, as the permutation characteristics of these units are preserved in chiral models such as X(AFFG), with three chiral ligands. Here we have a pseudoasymmetric center and X is chirotopic. This observation emphasizes again the necessity to separate the concepts of stereogenicity and symmetry relationships. 

Mislow and Siegel11 criticized the CIP system, inter alia, by totally denying symmetry-adaptation of it. The above enumeration, however, should suffice to demonstrate that this disqualification is certainly not appropriate for stereogenic units of tpye 1. Their comments on "pseudoasymmetric centers 11 unfortunately use varying viewpoints and make erroneous assignments of descriptors. The point at issue, which is of fundamental significance, is best explained by the examples 1, 2, and ent-2, also used by these authors. 

The addition criterion may similarly be applied to recognize diastereotopic faces. Methyl a-phenethyl ketone, 58 in Fig. 19 has a chiral center addition clearly gives rise to diastereomers (59a, 59b) the faces of the carbonyl carbon are diastereotopic and the C = 0 group is prochiral. This case is of importance in conjunction with Cram s rule 10). Compounds 60, 62 and 64 also display diastereotopic faces even though the products 61, 63 and 65 are not chiral 60, 62 and 64 have prostereogenic rather than prochiral faces. The C=0 group in 60 is propseudoasymmetric, since C(3) in 61 is a pseudoasymmetric center. a-Phenethyl methyl sulfide (66) displays diastereotopic sides of a molecular plane not due to a double bond 5,24> and may alternatively be considered a case of diastereotopic phantom ligands (unshared pairs on sulfur). This case does involve chirality and the sulfur atom is prochiral. 

Just as chiral centers can be labeled if or S not only in enantiomers but also in many diastereomers, so the designations pro-R and pro-S are not confined to enantiotopic ligands but may also be used for a number of diastereotopic ones (for exceptions, see below). Thus, for example, the labeling in Fig. 13 is such that HA (compounds 30, 32, 34, 36) or Me1 (compound 38) is the pro-R group the reader should verify this proposition. The same is true for compounds 46 and 5(5 in Fig. 18. Compounds 48, 50, 52 and 54 in Fig. 18 cannot be labeled in this manner since replacement of the diastereotopic ligands does not produce chiral products. In 54 (pro-pseudoasymmetric center) the substitution gives rise to a pseudoasymmetric center which, in the compound of the left is s, in the compound on the right r. Hence HA is called pro-r and HB pro-s 6>. 

Supported stereochemical descriptors in computational software are, according to the Cahn-lngold-Prelog, (CIP) system E/Z for double bonds and R/S for asymmetric centers. Pseudoasymmetric centers are also recognized as descriptors r/s (e. g. 2,3,4-trihydroxyglutaric acid, see Fischer projection below) in ChemDraw 6.0. 

The fluorine-19 NMR spectrum of PCFE appears far more complicated. Figure 2 shows the spectra from two PCFE samples, one prepared at 60 °C (a) and one prepared at -80 °C in urea (b). Each backbone carbon is a pseudoasymmetric center in PCFE, compared to every second carbon in PVCF, so that the dispersion of fluorine-19 chemical shift from stereoirregularity is much larger. This dispersion is almost 15 ppm for PCFE, and is similar to the spread observed in the fluorine-19 NMR spectrum of poly(l,2-difluoroethene) (14). 

Isotactic polymers with identical ends of finite chains turn out to be achiral meso-forms (with a pseudoasymmetric center, if odd-numbered). Similarly, syndiotactic polymers with odd numbers of monomer units and identical chain ends are meso-forms, while even-numbered syndiotactic finite polymer chains are chiral, even with identical chain ends. On the other hand, formal chirality prevails in all types of stereoregular polymers with unequal chain ends (which is actually the case with polymers of x-alkenes). 

The second-order Markov model requires the specification of eight conditional probabilities. This is due to the influence of the last three pseudoasymmetric centers of the growing chain. The details of the second-order Markov model were described by Bovey. For details, the reader is advised to consult the reference. For convenience, the eight conditional probabilities are designated by Greek letters ... 

Vinyl polymers, for which pol5rpropylene serves as a prototype, present some additional issues not encountered in chains with symmetric torsions. The physical properties of these chains depend on the stereochemical composition and stereochemical sequence of the chain, and this dependence must be reflected in Z. Two equivalent methods have been used for description of the stereochemistry of vinyl polymers. One approach uses pseudoasymmetric centers [67]. Although the fragment denoted by -CH2-CHR-CH2- does not contain a chiral center, it can be treated as though it were chiral if one CH2 group is distinguished from the other. This distinction is drawn when the bonds in the... 

Q has the useful property that = E, where E denotes the identity matrix. For a vinyl polymer with a nonarticulated side chain (such as a halogen atom), the -CHR—CH2- bond immediately following a pseudoasymmetric center has a D matrix that is either... 

Proceeding in the same manner, there are four possible statistical weight matrices for the CH2-CHR bond immediately before a pseudoasymmetric center, depending on the stereochemistry at this center and the preceding pseudoasymmetric center. If both pseudoasymmetric centers have the same chirality, the two possibilities, IJdd and U//, can be interconverted using Q. 

The double subscript on o) shows whether the second-order interaction is between two groups in the backbone, o>cc, two side chains, (Urr, or a side chain and a group in the backbone, < >CR. If the two pseudoasymmetric centers have opposite chirality, the two possibilities are given in Eq. (3.20). 

When pseudoasymmetric centers are used for the description of the stereochemical sequence, six distinct statistical weight matrices, Eqs. (3.18)-(3.20), are required. They can be replaced by a total of three statistical weight matrices, denoted by Up,Um, and Ur, if the stereochemical sequence is described instead as a sequence of meso and racemo diads. 

Description of the Stereochemical Sequence. The stereochemical sequence is described using dl pseudoasymmetric centers, as defined on page 175 of Mattice and Suter [4]. The C-C bonds in the chain are indexed sequentially from 1 to . A local Cartesian coordinate system is associated with each bond. Axis x,- lies along bond i, with a positive projection on that bond. Axis yi is in the plane of bonds i — 1 and i, with a positive projection on bond i—l. Axis Zi completes a right-handed Cartesian coordinate system. The chain atom at the junction of bonds i — 1 and / is a if pseudoasymmetric center if it bears a methyl group with a positive coordinate along z, it is an I pseudoasymmetric center if this coordinate is negative. 

The second-order interactions in Ucc x take place between the terminal bold CH group in -CH-CH(CH3)-CH2—CH2-CH- and the two groups in this fragment that are bold in the previous paragraph. Involvement of the methyl group in the second-order interactions demands two forms of V, depending on whether the fragment contains 3l d on I pseudoasymmetric center. 

For long chains in which all of the pseudoasymmetric centers have the same chirality (isotactic chains), Z is dominated by the terms... 

The two simplest stereochemical sequences are those in which pseudoasymmetric centers have the same chirality (either //... 11... 

The consequences for the unperturbed dimensions are brought out in Table 3, which contains results for six distinguishable chains with equal numbers of / and d pseudoasymmetric centers, arranged in different repeating sequences. The first entry, taken from Table 1, is for the shortest such repeating sequence, where there is a strict alternation of / and d along the chain. The next two entries have a strict alternation of a pair of fs and a pair of if s. This sequence can be embedded in the chain in two distinct ways, which differ in whether two bonded carbon atoms with methyl substituents have the same or opposite chirality. The fourth entry has a repeating pattern of three / s followed by three if s. The fifth and sixth entries have a homopair (e.g.. It) followed by the opposite homopair (e.g., dd), and then a heteropair (e.g.. Id), which can be embedded in the chain in two ways. 

The results in Table 3 show that the strictly alternating dl polymer does indeed overestimate the Coo expected for a truly atactic polymer, but the size of the overestimate is small. If one averages over the first three entries in Table 3, the result is 6.77. The average is only slightly smaller (6.73) if one considers all repeating sequences of three -CH2-CH(CH3)-CH(CH3)-CH2-units, assuming equal numbers of d and / pseudoasymmetric centers in each repeat unit, and equal probability that any pseudoasymmetric center is d or /. We infer that the Coo considering all possible sequences with equal numbers of d and / pseudoasymmetric centers cannot be smaller than 6, and... 

Obviously, with the symmetrical substitution the gross chemical structure will be the same whether one or the other of the two bonds to oxygen is being opened in connection with the polymerization. None of the monomers contain an asymmetric center, however, upon ring opening of 2, pseudoasymmetric centers are formed and in principle, tacticity should be possible, although not actually reported. 

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