Figure 2 shows illustrative carbon skeletons for reactants and products. Table I summarizes the pertinent quantities. The
carbon numbers (n1, n2), initial isotopic compositions (δ1, δ2), fractions of reactants remaining unconsumed (f1, f2), and summed isotope effects (Σε1, Σε2) were chosen to be representative of a typical synthetic scheme. All isotope effects were assumed to be kinetic. Values of
δP* (i.e., the isotopic compositions that would be observed if isotopic fractionations were absent) were calculated using Equation 4
with ΔA = ΔB = 0; that is, the simple mass balance Equations 1–2. Values of δP, the isotopic compositions that would actually be observed for the successive products, were calculated using exact forms
of integrated rate equations (14).
Table I: Properties of a four-step synthetic sequence.*
This example illustrates the interplay of the four factors that control the isotopic compositions of manufactured products,
namely the stoichiometries and isotopic compositions of the starting materials, isotope effects associated with the synthetic
reactions, and the degree to which conversions of precursors to products are quantitative. The isotopic compositions of all
products are dominated by the initial isotopic abundance of the precursor materials and are modulated (viz., depleted) by the degree of completion (f) and the magnitude of any isotopic effects (ε, see Figure 3a). Figure 3b shows a plot that summarizes the difference between
the isotopic compositions that are predicted and those that would be observed in the absence of isotope effects (δP* – δP). The last two columns of Table I shows these values. In the first synthetic step, isotope effects on reactant B are rather
large, but that reactant is consumed almost completely. The resulting isotopic fractionation is less than 1‰ (the larger value
shown in Figure 3b pertains to the product and reflects fractions affecting both reactants).
In the second step, a large isotope effect and poor conversion of reactant C lead to a large isotopic fractionation at the
reaction site. Fractionation is diluted, however, now that the product contains 14 carbon atoms. As shown in Figure 3b, the
overall difference between real and hypothetical unfractionated products is barely doubled. In the remaining steps, when isotope
effects are moderate and the consumption of reactants is relatively efficient, isotopic fractionation declines.
Applications in the pharmaceutical industry
Measuring and tracking isotopic fractionations in synthetic pathways used to prepare pharmaceutical products has potential
uses in process analytical chemistry and for the protection of process patents. In process analytical chemistry, the matrix
of information obtainable provides a complete isotopic description of pharmaceutical materials from starting materials through
synthetic intermediates to final products. Starting materials reacted under consistent conditions with isotopically controlled
reagents should always produce products of known isotopic composition. Divergences from the predicted isotopic pathways suggest
uncontrolled variables in pharmaceutical manufacture and provide insight into process consistency. When the goal of process
analytical chemistry is understanding manufacturing processes, the complete stable-isotopic record of synthesis summarizes
many key process variables: reaction rate as affected by the synthetic pathway, reaction rates, temperature, pressure, compound
concentration, and so forth.
Observations such as those summarized in Figure 2 can be used to monitor synthetic processes. Once the sequence of isotopic
compositions characteristic of a process is known, any variations must be traceable to (1) utilization of reactants from some
new source (δ), or (2) variations in the extent to which reactants are converted to products (f), or (3) changes in the reactions used (ε). In this way, very simple and inexpensive analyses integrate information (n, δ,
f, ε) of considerable value for understanding the synthetic pathway employed and for process control.