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a stepwise reaction it is the succession of reaction power set (of a set A) The set of all subsets
coordinates for the successive individual reac- of A (the empty subset included). It is denoted by
A
tion steps. (The reaction coordinate is some- P(A) or 2 . For example, the empty set ∅ has no
times approximated by a quasi-chemical index of element. Its power set P(∅) = {∅} has exactly
reaction progress, such as degree of atom transfer one element. The power set of A ={a, b} is
or bond order of some specified bond.) P(A) ={∅, {a}, {b},A}. In general, if A has n
n
elements, the power set has 2 elements.
potential-energy (reaction) surface A geo-
metric hypersurface on which the potential predator-prey population model A math-
energy of a set of reactants is plotted as a func- ematical model, in terms of a pair of ordinary
tion of the coordinates representing the molecu- differential equations, representing the popula-
lar geometries of the system. tions of two species with prey-predator relation.
For simple systems two such coordinates Such systems are likely to exhibit oscillation or
(characterizing two variables that change during even limit cycles. Generalization to more than
the progress from reactants to products) can be two species is possible and, in fact, is widely
selected, and the potential energy plotted as a used in applications.
contour map.
For simple elementary reactions, e.g., A − prefix An operator written before its
B + C → A + B − C, the surface can show operands. Thus for two operands x and y and
the potential energy for all values of the A,B,C operator f , the syntax is fxy or f (x, y). See
geometry, providing that the ABC angle is fixed. also functor, infix, postfix, and relation.
For more complicated reactions a different
choice of two coordinates is sometimes pre- prey-predator relation Two biological spe-
ferred, e.g., the bond orders of two different cies are in the following relation: the growth
bonds. Such a diagram is often arranged so that rate of the predator increases with increasing
reactants are located at the bottom left corner and prey population, and the growth rate of the prey
products at the top right. If the trace of the rep- decreases with increasing predator population.
resentative point characterizing the route from The popular examples are fish and sharks, and
reactants to products follows two adjacent edges deer and wolves.
of the diagram, the changes represented by the
two coordinates take place in distinct succes- primary sample The collection of one of
sion. If the trace leaves the edges and crosses more increments or units initially taken from a
the interior of the diagram, the two changes are population.
concerted. In many qualitative applications it is The potions may be either combined (com-
convenient (although not strictly equivalent) for posited or bulked sample) or kept separate (gross
the third coordinate to represent the standard sample). Ifcombinedandmixedtohomogeneity,
Gibbs energy rather than potential energy. it is a blended bulk sample. The term “bulk sam-
Using bond orders is, however, an oversim- ple” is commonly used in the sampling literature
plification, since these are not well defined, even as the sample formed by combining increments.
for the transition state. (Some reservations con- The term is ambiguous since it could also mean
cerning the diagrammatic use of Gibbs energies a sample from a bulk lot, and it does not indicate
are noted under Gibbs energy diagram.) whether the increments or units are kept separ-
The energetically easiest route from reactants ate or combined. Such use should be discour-
to products on the potential-energy contour map aged because less ambiguous alternative terms
defines the potential-energy profile. (composite sample, aggregate sample) are avail-
able. “Lot sample” and “batch sample” have also
power series A formal summation of the been used for this concept, but they are self-
∞ n limiting terms. The use of “primary” in this sense
form c (x − a) , where a and c ,c ,... are
1
n
0
n=0 is not meant to imply the necessity for multistage
complex numbers. sampling.

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