Sensitivity analysis
is a powerful tool in interpreting the results of computational simulations. Sensitivity
analysis is used to determine quantitatively the dependence of a solution on certain
parameters that appear in a model’s definition. The "raw" first-order
sensitivity coefficient matrices 
report the partial derivatives of the dependent variable vector
(for example, temperature, mass fractions, surface composition) with respect to a
parameter vector 
(for example, reaction rate constants). Since there is much mathematical literature
on sensitivity analysis and various methods to compute the sensitivity coefficients from the
solution, we do not discuss the computation of 
here.
However, given the sensitivity matrix it is possible to manipulate it further to obtain the sensitivities of species production rates with respect to the dependent variables:
 | (4–34) |
where the components of 
are the mass
fractions, site
fractions, and activities for
gas-phase, surface,
and bulk
species, respectively. The term 
converts from concentration units to the units of 
:
 | (4–35) |
We have included two subroutines in the Surface
Kinetics
Subroutine Library to facilitate calculation of these
terms. The first gives the partial derivative of the production rate of species
with respect to the pre-exponential
constant of the Arrhenius expression for
surface reaction
:
 | (4–36) |
Note: Note that subroutine SKDRDA
calculates the derivative with respect to the Arrhenius pre-exponential if the reaction was originally stated in standard Arrhenius form, or with respect to the
sticking
coefficient pre-exponential if a sticking coefficient was used.
The production rate of species 
due to reaction 
is
 | (4–37) |
Therefore, the dependence of 
upon the concentration of some species 
is
 | (4–38) |
The terms inside the curled braces will only be present if species 
modifies the rate of reaction 
through coverage parameters, as in Equation 4–7
. The partial of the production
rate of species 
due to all reactions with respect to the concentration of species
is then
 | (4–39) |
These terms can all be combined to calculate the desired 
in the executable.