Hydrogen Bonding in Infinite Chains

The formalism to incorporate translational symmetry into the usual Hartree-Fock approach, the crystal orbital technique, is not new at all 74,75). Reviews of recent devel-opements and applications of the Hartree-Fock crystal orbital method may be found in refs. 76 79). However, only few investigations on the evaluation of equilibrium geometries and other properties derived from computed potential surfaces of one-dimensional infinite crystals or polymers have been reported. 

Structural data are the most important ones for our purpose here. As discussed in section 4.1 the additive model of intermolecular interactions fails in the case of 

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P2i Z = 2 Dx = 1.458 R = 0.04 for 1,071 intensities. The conformation of the furanose is 2T3 (176.2°), with the dithiane ring and the 4-C-methyl group equatorially attached. The dithiane ring has a chair conformation. The molecules are hydrogen-bonded in infinite chains. 

Some General Features of Hydrogen Bonding in Infinite Chains... 

Li2S04. H2O. This structure provides a good example of the tetrahedral arrangement of four nearest neighbours (2H2O, Li, and 0 of SO4 ) around a water molecule and of water molecules hydrogen-bonded into infinite chains. The orientation of the H-H vector in the unit cell agrees closely with the value derived from p.m.r. measurements. The O-H-0 bonds from water molecules are of two kinds, those to sulphate 0 atoms (2-87 A) and to H2O molecules (2-94 A). 

Carboxylic acids with shorter chains (Ci-Cio) have been examined by Baun (1961). The X-ray data indicate that their structures are related, and the long-spacing values can be described by the relation 2.22 n + 0.86, where n is the number of carbon atoms in the chain. The complete crystal structures have been determined for formic acid (Holzberg et aL, 1953) and acetic acid (Jones and Tempelton, 1958). The molecules are linked by hydrogen bonds forming infinite chains, not dimers which are most common in fatty acids. 

The synthetic work has been extended to di-jU-hydroxo-/ac-triammine derivatives (97) (Table 47 and Scheme 34). The crystals of (97) contain two different centrosymmetric cations, the trans diaqua and trans dihydroxo species, linked alternately in infinite chains by short (2.45 A) hydrogen bonds. The bond distances of the diaqua cation differ slightly from those of the dihydroxo cation.375... 

This result, and others [55,103,1041 from model calculations, gave an early theoretical basis for understanding the predominance of finite and infinite chains of hydrogen bonds in the carbohydrate and cyclodextrin crystal structures in which there is a uniform donor-acceptor direction, as in 4,... 

Fig. 13.9. An example of intramolecular hydrogen bonding in the crystal structure of methyl 1-thio-a-D-ribopyranoside. The infinite 0(2)H 0(4)H 0(3)H 0(2)H chains form a double ribbon linking the molecules. The -S-CH3 group is omitted for clarity [MTRIBP10]...

The -D chair conformation is also stabilized in the crystalline state by the formation of an intramolecular hydrogen bond in both methyl-1,5-dithio-a-ribopyranoside quarterhydrate [MDTRPY20] and methyl-1-thio-a-ribopyranoside [MTRIBP 10]. In the former structure there are two symmetry-independent molecules with different directions for the 0(2)H to 0(4)H bond, as shown in Fig. 13.8. In the methyl-1 -thio-a derivative the direction is 0(2)H 0(4) and the bond forms part of an infinite chain, as shown in Fig. 13.9. In the methyl-1,5-dithio-a-ribopyranoside quarterhydrate, the hydrogen-bond direction is 0(4)H 0(2) in one molecule and 0(2)H 0(4) in the second crystallograph-ically independent molecule in the same crystal structure. As shown in Fig. 13.10, the intramolecular hydrogen bond is part of a cyclic arrangement of eight bonds,... 

The hydrogen bonding in planteose dihydrate is poorly defined. In the crystal structure of planteose dihydrate [PLANTE 10], not all the hydroxyl hydrogen atoms are located and some appear in unlikely positions. The pattern is similar to that of melizitose hydrate, with infinite and finite chains cross-linked by the water molecules and three-center bonds. One of the water molecules, 0(W 1), accepts one strong and one weak bond and donates a strong bond and a weak three-center bond. This includes the interesting chelated configuration shown in Fig. 13.58. 

The hydrogen bonding in the crystal structure of thymidine [THYDIN] consists of two infinite chains (Fig. 17.28), one with both a- and w-cooperativity. An unusual feature is that the C(2)=0 is not included in the hydrogen bonding. A similar scheme is found in 6-azathymidine [AZTYMD] (Fig. 17.29) except that both 0(3 )-H and 0(5 )-H are included in one infinite chain. 

The cooperative, infinite chains and cycles formed by O-H 0 hydrogen bonds in the a-cyclodextrin hydrates are a characteristic structural motif [109]. As with the simpler carbohydrate crystal structures described in Part II, Chapter 13, the hydrogen bonds can be traced from donor to acceptor in the cyclodextrin hydrate crystal structures. Networks of O-H 0-H 0-H interactions are observed in which the distribution of hydrogen bonds follows patterns with two characteristic motifs. One are the "infinite chains which run through the whole crystal lattice, and the others are the loops or cyclically closed patterns (a special case of the "infinite chains). As in the small molecule hydrates, such as a-maltose monohydrate, the chains and cycles are interconnected at the water molecules to form the complex three-dimensional networks illustrated schematically in Fig. 18.5, with some sections shown in more detail in Fig. 18.7 a, b, c. 

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