Calculating the reaction rate constant of elementary reactions is very important and closely related to many practical applications. A diversity of computational approaches have been applied to estimate rate constants for multiple reactions. Common calculation methods include hard-sphere collision theory, trajectory calculation, transition state theory and RRKM theory. Collision theory explains the phenomenon that reaction rate tends to increase with concentration. Trajectory calculation is one of the most accurate and widely-applied method, but it is extremely time-consuming and difficult to realize. RRKM theory is developed based on statistical mechanics and can better elucidate the microscopic characteristics of single molecule reaction dynamics. Transition state theory is proposed on the basis of quantum mechanics and statistical mechanics, and has a wide range of applications in chemical equilibrium.

### Our Calculation Process

The typical steps required to determine rate constants using computational chemistry are:

- Create the initial structure for the ground state using a molecular editor.
- Optimize the geometry of the ground state such that it corresponds to the energy minimum.
- Perform frequency analysis to obtain the partition function and free energy for the ground state
- Create the initial structure for the transition state using a molecular editor.
- Optimize the geometry of the transition state such that it corresponds to the saddle point.
- Perform frequency analysis to obtain the partition function and free energy for the ground state.
- Calculate activation free energy.
- Calculate the rate constant.

### Application of Photocatalytic Reaction

- Collision theory

Collision theory is developed on the basis of the kinetic theory of gas molecules, which holds that the prerequisite for chemical reactions is the collision contact of reactant molecules. Simple collision theory is based on the hard sphere collision model and derives the calculation formula of the rate constant of macroscopic reactions, so it is also called the hard-sphere collision theory.

1. At Alfa Chemistry, we use collision theory to derive the collision frequency and rate constant of bimolecules.

2. Our experts use the collision theory to figure out how frequently hard spheres the size of molecules bump into each other, and calculate the efficiency of a reaction.

3. Moreover, our teams apply it to predict reaction rates of a bimolecular gas phase reaction since collision theory is the extension of the kinetic theory of gases.

- Transition state theory

Transition state theory is the most widely used approach for calculating reaction rate constants. It assumes that the reactants are in thermodynamic equilibrium due to the rapid exchange of energy with the environment, and that the reactants distributed in the transition state (the maximum energy point on the IRC connecting the reactants and the products) will be converted into products. 1. We apply statistical mechanics or chemical thermodynamic approach to calculate the concentration of the activated complex, and the concentration and the reaction rate (the reaction rate at which the activated complex develops into a product) are used to calculate the reaction rate constant.

1. Our scientists fully consider the chemical properties of the reactants and the activated complex, and determine the steric factors or the activation energy to calculate rate constants.

2. At Alfa Chemistry, our teams can perform variational transition state theory (VTST) including canonical variational theory (CVT), improved canonical variational theory (ICVT) and microcanonical variational theory (μVT) to conduct the calculation of reaction rate constant.

3. Tunnel effect on reaction rate constants is taken into consideration. We resolve the tunnel effect by calculating the transmission coefficient and multiplying it by the reaction rate constant obtained by the transition state theory.

4. We apply CVT when the electron energy contribution to the barrier is very small or even zero since the least information about the potential energy surface is needed in this method.

5. An expression for the transition state theory rate constant is provided in terms of the potential of mean force for a general reaction coordinate and the mass-weighted gradient of this reaction coordinate.

- Trajectory calculations

Trajectory calculation is a method that applies ab initio dynamics (such as BOMD and CPMD) to calculate a large number of trajectory, in which many molecules or atoms collide with each other at different kinetic energies and angles. Scientists then analyze whether reactions occur, and average the results according to the Boltzmann distribution to get reaction rate constants.

1. We have abilities in computing reaction probabilities and rate constants using various trajectory calculation methods such as the quasiclassical trajectory method, the reverse quasiclassical trajectory method, and the classical S matrix theory.

2. In addition, we have compared the theoretical rate constant with many experimental data, and the results show that it is in good agreement with experiment and it is found close to other models based on statistical or variational methods.

- Rice-Ramsperger-Kassel-Marcus (RRKM) theory

RRKM theory is a theoretical and computational model about the rate of chemical reaction. According to RRK theory, the energy of high energy molecules is evenly distributed among their internal degrees of freedom. The rate of a particular reaction is entirely determined by the molecular energy, independent of the excitation mode.

1. Alfa Chemistry has designed an accurate RRKM algorithm and our teams apply it to monomolecular reactions such as molecular isomerization.

2. Our variational RRKM theory is also available for a barrierless reaction calculation, supporting the prediction of rate coefficients.

3. Our transition state theory is available for the calculation for the reaction rate constant of different reaction systems and different reaction conditions.

### Advantages of Our Services

- We are capable of calculating reaction rate constants for both monomolecular or bimolecular reactions.
- Our teams have developed various computational modules simulation of gas-phase kinetics using simplified reactor models and for computation of chemical equilibria.

Alfa Chemistry provides reaction rate constant calculation services, We have applied our knowledge of computational chemistry in performing hard-sphere collision theory, trajectory calculation, transition state theory and RRKM theory to study kinetic properties of the reaction and calculate the reaction rate constant accurately. If you have any questions, please feel free to contact us.