Diagramatic expansion

The equations described earlier contain two unknown functions, h(r) and c(r). Therefore, they are not closed without another equation that relates the two functions. Several approximations have been proposed for the closure relations HNC, PY, MSA, etc. [12]. The HNC closure can be obtained from the diagramatic expansion of the pair correlation functions in terms of density by discarding a set of diagrams called bridge diagrams, which have multifold integrals. It should be noted that the terms kept in the HNC closure relation still include those up to the infinite orders of the density. Alternatively, the relation has been derived from the linear response of a free energy functional to the density fluctuation created by a molecule fixed in the space within the Percus trick. The HNC closure relation reads... 

Figure 55 Diagramatic expansion of mycelial mass using grain-to-grain transfer tech-iquc. One petri dish can inoculate 10 spawn jars (G-1) which in turn can be used to oculate 100 more jars (G-2) and eventually l OOOjars of spawn (G-3) provided the cul-tureremainspure.

The important question of the stability of the perturbation expansion to changes in hybridization and the bond polarity parameter is discussed by Jordan et a/.152 The method has been extended to radicals with a well localized odd electron153 and to some excited states.154 A similar ab initio treatment has been developed but can only be applied to small molecules.155 In a paper dealing with calculation of n.m.r. coupling constants, Dennis and Malrieu make some use of INDO terms rather than CNDO.156 A complete derivation of the PCILO equations using diagramatic techniques has been given recently by Kvasnicka.157... 

To summarise, cephalosporins are produced by ring expansion of penicillin N to deacetoxycephalosporin C which is then oxidised to deacetylcephalosporin C. In C. acremonium, this last compound is acet-ylated to cephalosporin C. In 5. clavuligerus deacetylcephalosporin C is transcarbamoylated then converted to the 7a-methoxy derivative cephamycin C, probably via a 7a-hydroxy intermediate. Cephalosporin biosynthesis is shown diagramatically in Fig. 8. 

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