Copyright © 2002–2016 by A. Miyoshi
GPOP reference manual - basic introduction

GPOP reference manual - basic introduction

  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.

Basic Introduction

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 elementary reactions.   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 temperature.
  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 molecules.   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.