Copyright © 2002–2016 by A. Miyoshi
GPOP reference manual - basic introduction
GPOP reference manual -
This chapter introduces the basics of the research fields for which
the GPOP software is used.
This introduction was prepared for the researchers and students who are
not familiar with these fields, but are willing to start studies
or to see what they deal with.
Gas-Phase Chemical Kinetics
Gas-phase "chemical kinetics" deals with the chemical
reactions occurring in gas-phase, such as gas-phase combustion,
atmospheric processes of anthropogenic hydrocarbons, or gas-phase
reactions in petroleum and semiconductor industries.
The purpose of the research in the chemical kinetics is to reveal
the basic physical and chemical processes governing the phenomena.
In many cases, the system consists of a number —
e.g., a few tens to tens of thousands — of
elementary reactions which are inseparable smallest units
of chemical reactions at the level of molecular and atomic collisions.
For example, the combustion of hydrogen is usually represented
as 2H2 + O2 → 2H2O, but actually
consists of 20 elementary reactions, namely,
H + O2 ↔ OH + O (1),
O + H2 ↔ OH + H (2),
OH + H2 ↔ H2O + H (3),
H + O2 + M ↔ HO2 + M (4),
2OH ↔ O + H2O (5),
OH + HO2 ↔ H2O + O2 (6),
H + HO2 ↔ H2 + O2 (7),
2HO2 ↔ H2O2 + O2 (8),
etc. To know the true elementary steps is not only to
satisfy the intellectual curiosity — it is of practical importance.
The rate of combustion (oxidation) is not at all proportional
to [H2]2[O2] or
[H2][O2]1/2, but is a complex
function of [H2], [O2], pressure and temperature.
The phenomena can only be expressed by the solutions to the system
of differential equations including 20 elementary reactions and energy
conservation, transport phenomena, etc.
This type of modeling is called as "kinetic simulation" or
"detailed chemical kinetic modeling".
The chemical kinetics deals with (1) resolution of a phenomenon
into elementary reactions, (2) how the rate of elementary reaction depends
on the temperature and pressure, (3) what are the products of the
elementary reaction, and (4) physical and chemical interpretation of the
Thanks to the recent development of quantum chemical methods and
improvement of the speed of computation, the quantum chemical calculation
is becoming a powerful tool for the chemical kinetics.
GPOP program suite has been developed for the theoretical
interpretation and prediction of the rate constants of elementary
reactions from the outputs of the quantum chemical calculation packages.
Thermodynamic data are also important information for the
kinetic simulation. They are inevitable for the simulation
with energy conservation, for example for the simulation involving the
change of temperature, since the heats of reactions and the heat
capacities are required.
Thermodynamics is still conceptually important for understanding the
nature of reactions, such that the highly endothermic reaction is
impossible at around room temperature, even when they are not required for
the simulations, for example for the atmospheric reactions in which the
heat of reactions of largely diluted chemical species does not affects the
Another importance of thermodynamic data is that the rates of forward
and reverse elementary reactions are strictly connected by the equilibrium
constants determined by the thermodynamics (or the Gibbs energy change)
according to the detailed balancing principle.
For these reasons, in many of the kinetic simulation packages such as
"CHEMKIN", the thermodynamic data are mandatory input.
The rate of heat release as well as the rate of reverse reactions
is calculated by using the thermodynamic data.
The thermodynamics of chemical species, atoms and molecules, can
be also predicted by the quantities calculated by the quantum chemical
calculations, that is, the structure and vibrational frequencies of the
In a sense of statistical theory of reactions, the rates of chemical
reactions can be calculated from the thermodynamic data of the transition
states and reactants.
In other words, GPOP program suite can be used to predict the
thermodynamics of transition states as well as the chemical species.
Statistical Theory for Thermodynamics and Reactions
From the statistical theory, in a thermal equilibrium at temperature
T, the each of the energy level (or "state", here it is
designated by subscript i) of a chemical species can be
populated according to the Boltzmann distribution function,
Pi = gi
exp(−εi / kBT ).
So, if we know the degeneracy (gi) and energy
(εi) of all the states of a molecule (or an atom),
it is possible to predict the thermodynamic function of the species.
Since the "internal" energy (in the thermodynamic definition)
is distributed into the translational, rotational, and vibrational motion
of the molecule, the information needed to calculate the thermodynamics includes
molecular mass (for translational motion), rotational constants (determined from
the structure of the molecule), and vibrational frequencies.
In many cases, the structure of the molecule can be assumed to be
independent of vibrational states (rigid rotor [RR] assumption).
If we can assume the harmonic vibrational motion (harmonic oscillator [HO]
assumption), a simple formulation called RRHO (rigid-rotor harmonic oscillator)
assumption can be used to calculate the thermodynamics.
The RRHO formulation is used by GPOP when no extra information is
provided (i.e., the default).
However, this is not always a good assumption.