Homomorphic molecules

The term homomorphic molecules was introduced by Brown et al. [225]. Molecules having the same or closely similar molecular geometry are homomorphs, e.g. ethane is a homomorph of methanol, toluene of phenol, 4-aminobenzenesulfonamide of 4-amlnobenzoic acid, and lV,lV-diethyl-4-nitroaniline of 4-nitroaniline. 

The prochirality concept is useful if it is applied to factored structures within a molecule rather than to the whole, because chiral compounds may also contain centers of prostereoisomerism that would become chiral if their homomorphic ligands were made distinct. The methylene carbons of cholesterol or C(3) of chiral trihydroxyglutaric acid (20b) are appropriate examples. 

There are several different methods of obtaining sets of matrices which are homomorphic with a given point group and in this chapter we discuss these methods in some detail. One way is to consider the effect that a symmetry operation has on the Cartesian coordinates of some point (or, equivalently, on some position vector) in the molecule. Another way is to consider the effect that a symmetry operation has on one or more sets of base vectors (coordinate axes) within the molecule. 

The homomorph of a polar molecule is deLned as a nonpolar molecule having very nearly the same molecular size and shape. Alternatively, the dispersion contributions can be estimated using functional group contribution, and the formula ... 

The ligands must be identical when separated from the rest of the molecule. Such ligands have been called homomorphic (from Greek homos" = same and morphe = form). 3)... 

The term equivalent is overly general and therefore bland and of equivocal meaning. Thus the methylene hydrogen atoms in propionic acid (Fig. 1) are equivalent when detached (i.e. they are homomorphic), but, as already explained, they are not equivalent in the CH3CH2C02H molecules because of their placement — i.e. they are heterotopic. Ligands that are equivalent by the criteria to be described in the sequel are called homotopic from Greek homos = same and topos = place 6>, those that are not are called heterotopic . 

In these definitions, object refers to any rigid array, such as a set of points, or to a geometrical figure, or to a model of a molecule ideally realized (of which more below) properly congruent can be replaced by superposable and homomorphs, which may be either chiral or achiral, are congruent counterparts in Kant s terminology. 

Similarly to other molecules with isoconstitutional chiral substructures, the combination of distinct fullerene addition patterns with enantiomorphic or homomorphic chiral addends can lead to steric arrangements with a certain complexity. However, these can be easily analyzed with the substitution test delineated in Figure 1.1. In the case of the 1,4-addition pattern of Cgo we may consider the following cases (Figure 1.34) If both chiral addend moieties are homomorphic (structure A), the resulting addition pattern is achiral... 

In sum, homomorphic ligands (i.e., those which are identical when detached from the molecule) can be classified as homotopic (equivalent) or heterotopic (nonequivalent). The latter can be further distinguished as diastereotopic or enantiotopic. These divisions are shown in Figure A7-5, and the descriptions presented for the different types of ligands are collected in Table A7-1. 

Molecule homomorphism is a non-ambiguous and effective statement whether two molecule descriptions refer to the same product or not. The importance of, or rather, the necessity for such a statement is obvious. In a certain sense, it is the key statement on which the Automatic Generator is based. Inability to recognize identical structure may cause unnecessary calculations at the best of times but more commonly will lead to infinite loops of calculations. 

The molecule homomorphism is based on a branch and chain algorithm. A branch is a linear portion (including rings), which is connected to the molecule... 

Parameters involved in this equation may be estimated using the concept of the homomorph. The homomorph of a polar molecule is a non-polar molecule with nearly the same size and shape as its polar counterpart. The cohesion energy of the homomorph is assumed to be the measure of the effect of the dispersion forces. The polar contribution to the cohesion energy is the difference between the total cohesion energy and the cohesion energy of the homomorph. 

Hansen firstly determined d for a solvent using the homomorph concept. The energy of vaporisation of a hydrocarbon molecule of the same size and shape as the solvent molecule in question at the same reduced temperature (absolute temperature divided by the critical temperature) is assumed to be that due to dispersion forces existing in the solvent. The difference between the energy of vaporisation of the solvent, AE, and that calculated as the contribution due to dispersion forces, A d, is taken as that due to both polar and hydrogen bonding forces, i.e. ... 

---