classical kinetic approaches with only a fraction of the number of separate
experiments” [11].
Like what Table 1 shows, the RPKA methodology provides a sort of a catalog of
several types of catalytic cycles that represent the overall reaction mechanisms and
the corresponding RPKA signature or fingerprint (left column, two representations
of the same data set) that should be observed by carrying out a few experiments and
some graphical manipulation of concentration over time data [12]. For example, by
using the RPKA methodology, the different kinetic profiles displayed in entry
(a) prompt us which is the catalyst resting state in each case for the catalytic
A + B ¼ C reaction shown. The plots of entry (b) suggest that there are off-cycle
equilibria, the plots of entry (c) that there is a product acceleration effect, and so
other cases not shown here.
Note that in all cases the reaction mechanism corresponds to the same overall
chemical reaction A + B ¼ C. Thus, valuable hints toward identifying the underlying
mechanisms can be obtained by carrying out an RPKA study at the outset of a
reaction modeling task. As shown with a variety of examples in Ref. [11], a simple
protocol encompassing just four experiments provides a comprehensive, if in some
cases preliminary, kinetic analysis of any new reaction.
3 Calculation of DFT Energies: Theoretical Tools
In a DFT-based microkinetic model (Fig. 1), all reaction steps are elementary
reactions. For a single transition-state reaction like
A þ B Ð
k 1
k À1
C
the rate of change of [A] is
À
d A
½
dt
¼ k 1 A
½ B
½ À k À1 C
½
where k 1 , k À1 are the forward and reverse rate constants, respectively. Following the
transition-state theory (TST) [13], each rate constant is given by the Eyring equation
k ¼
k B T
h
e
ÀΔG
o,{ =RT
¼
k B T
h
e
ÀΔH
o,{ =RT e
ΔS
o,{ =R
dH
0Ã , dS
0Ã are the enthalpy and entropy differences between the transition state and
the reactants (k 1 ) or products (k À1 ) of this elementary reaction step. The G
0 values,
calculated with a QM software at standard conditions of 1.0 atm, are transformed to
use concentrations in units of mol/L instead of pressure in atm according to
86
M. Jaraíz
experiments” [11].
Like what Table 1 shows, the RPKA methodology provides a sort of a catalog of
several types of catalytic cycles that represent the overall reaction mechanisms and
the corresponding RPKA signature or fingerprint (left column, two representations
of the same data set) that should be observed by carrying out a few experiments and
some graphical manipulation of concentration over time data [12]. For example, by
using the RPKA methodology, the different kinetic profiles displayed in entry
(a) prompt us which is the catalyst resting state in each case for the catalytic
A + B ¼ C reaction shown. The plots of entry (b) suggest that there are off-cycle
equilibria, the plots of entry (c) that there is a product acceleration effect, and so
other cases not shown here.
Note that in all cases the reaction mechanism corresponds to the same overall
chemical reaction A + B ¼ C. Thus, valuable hints toward identifying the underlying
mechanisms can be obtained by carrying out an RPKA study at the outset of a
reaction modeling task. As shown with a variety of examples in Ref. [11], a simple
protocol encompassing just four experiments provides a comprehensive, if in some
cases preliminary, kinetic analysis of any new reaction.
3 Calculation of DFT Energies: Theoretical Tools
In a DFT-based microkinetic model (Fig. 1), all reaction steps are elementary
reactions. For a single transition-state reaction like
A þ B Ð
k 1
k À1
C
the rate of change of [A] is
À
d A
½
dt
¼ k 1 A
½ B
½ À k À1 C
½
where k 1 , k À1 are the forward and reverse rate constants, respectively. Following the
transition-state theory (TST) [13], each rate constant is given by the Eyring equation
k ¼
k B T
h
e
ÀΔG
o,{ =RT
¼
k B T
h
e
ÀΔH
o,{ =RT e
ΔS
o,{ =R
dH
0Ã , dS
0Ã are the enthalpy and entropy differences between the transition state and
the reactants (k 1 ) or products (k À1 ) of this elementary reaction step. The G
0 values,
calculated with a QM software at standard conditions of 1.0 atm, are transformed to
use concentrations in units of mol/L instead of pressure in atm according to
86
M. Jaraíz