ReceiveddynamicsIn restricted chemical reactions,activation energyEa is the difference between the average molar energy of the activation collision and the average molar energy of all collisions;The energy barrier E isActivated complexAndreactantThe difference of zero point energy of.
Chinese name
Energy barrier
Foreign name
energy barrier
Features
Difference of zero point energy between activated complex and reactant
If the energy barrier is large, it is not easy to form activated intermediates and the reaction is difficult to proceed.The energy barrier E is the difference between the zero point energy of the activated complex and the reactant, which is different from the activation energy.General chemical reactions are carried out under constant temperature and pressure. Spontaneous and non spontaneous reactions are based on delta G, that is, Gibbs free energy change.Either way, the reason to break through the energy barrier, that is, the activation energy, is that it needs to go through a transitional state (transient, or say, transition state).Spontaneity and non spontaneity refer to thermodynamics, and activation energy refers to kinetics.
The minimum energy contained in activated molecules that can participate in chemical reactions is called the energy barrier of chemical reactions, orEnergy thresholdPossible barriers.
Preliminary study on the relationship between hydrocarbon molecular size and diffusion barrier
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Molecular mechanics, molecular dynamicsQuantum mechanical methodThe lowest energy conformation of hydrocarbon molecule was calculated, and the three-dimensional size of the molecule was obtained, which was compared with the dynamic diameter. The relationship between the hydrocarbon molecular size and the diffusion energy barrier in MFI and FAU molecular sieves was preliminarily studied.The results show that it is more reasonable to describe the size of hydrocarbon molecule with three-dimensional size than with dynamic diameter in the study of molecular sieve catalysis.Compared with cycloalkanes and aromatics, the molecular structure of long-chain alkanes is more flexible. The molecular size of long-chain alkanes should not only consider the size of their lowest energy conformation, but also consider the dynamic change of molecular conformation.In the same molecular sieve, the diffusion energy barrier increases with the increase of the minimum cross section size of hydrocarbon molecules;The diffusion energy barrier of the same molecule in MFI molecular sieve is greater than that in FAU molecular sieve.The research results have certain theoretical value for exploring the shape selective catalytic mechanism of molecular sieves.[1]
Calculation method of diffusion barrier
The Solids Diffusion module in Insight II software provides a tool to study the diffusion behavior of molecules in the lattice or on the surface.This method proposes that the diffusion of molecules along a certain path in the pore channel of molecular sieve is controlled by the thermodynamic energy barrier existing in the path.This thermodynamic energy barrier is called diffusion energy barrier, which represents the energy that molecules need to overcome when passing through the pores.The diffusion rate of molecules in molecular sieve channels is mainly determined by the diffusion energy barrier. Therefore, the diffusion energy barrier can give the difficulty of molecular diffusion in molecular sieve channels from the perspective of energy, and then obtain the relative speed of molecular diffusion.
The main steps of calculating the diffusion energy barrier of molecules in the pore channel of molecular sieve are as follows: the diffusion path is defined in advance with several pseudo atoms in the main structure of molecular sieve, and the guest molecules move along the path according to the defined step size (the calculation is set as 0.05 nm);At each continuous position, optimize the energy of the system composed of molecular sieves and diffusion molecules, and record the lowest energy obtained from the optimization, so as to obtain a diffusion energy curve varying along the trajectory coordinates.The difference between the peak value (Emax) and the valley value (Emin) of the diffusion energy curve is the diffusion energy barrier (ED).CVFF force field is used in diffusion barrier calculation.In the calculation, the skeleton atoms of the molecular sieve are fixed at the crystallographic coordinates.[1]
Relationship between hydrocarbon molecular size and diffusion energy barrier
The diffusion energy barriers of different isomeric alkanes in the channels of MFI molecular sieves are obviously different;With the increase of isomerization degree, the minimum cross section size of alkanes increases, and the diffusion energy barrier increases significantly.This is due to the small pore size of MFI molecular sieve. With the increase of the minimum cross section size of the molecule, the interaction between the molecule and the atoms on the pore wall increases, and diffusion becomes difficult.However, their diffusion energy barriers in the pore channels of FAU molecular sieves have not changed significantly. This is because the effective pore size of FAU molecular sieves is 0.73nm, which is much larger than the minimum cross section size of these alkane molecules. The pore channels of molecular sieves have no obvious restriction on molecular diffusion, and molecular diffusion is more free.The diffusion energy barrier of naphthenic hydrocarbon and aromatic hydrocarbon molecules in the pore channel of MFI molecular sieve increases significantly with the increase of the minimum cross section size of the molecule, and the variation law of the diffusion energy barrier in FAU molecular sieve is the same as that in MFI molecular sieve.The diffusion energy barrier of the same molecule in MFI molecular sieve is larger than that in FAU molecular sieve. This is because the effective pore size of MFI molecular sieve is smaller than that of FAU molecular sieve, and the molecule in MFI molecular sieve is subject to greater diffusion restrictions and more difficult diffusion.[1]
Accurate calculation of extracting reaction energy barrier and rate constant
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The hydrogen extraction reaction of ethane and hydrogen peroxide radical was selected as the reference reaction, and other reactions were taken as the target reaction(d）The horizontal approximate energy barrier and the reaction rate constant were corrected.To verify the reliability of the method, select CfiveFor the following alkane molecular systems, the calibration results of the equal bond reaction method were compared with the results of the high-precision CCSD (T)/CBS direct calculation, and the maximum absolute error was 5.58kJ ∙ mol-1. Therefore, the use of the equal bond reaction method can reproduce the high-precision CCSD (T)/CBS calculation results only by using the low-level HF ab initio method,Thus, the accurate calculation of the energy barrier of the macromolecular system in this kind of reaction is solved.The hydrogen extraction reaction between alkanes and hydrogen peroxide radicals, which is important in the simulation of low temperature combustion of hydrocarbons, provides accurate kinetic parameters.[2]
The expression of the rate constant of this reaction is:k=κ(kBT/h)(Q≠/QXQY)exp(－ΔV≠/RT）Among them,κIs the tunneling factor,kByesBoltzmann constant，hIs Planck's constant,TIs the temperature,RyesIdeal gas constant，Q≠Is the partition function of the transition state,QX、QYIs the partition function of reactant X and reactant Y respectively,ΔV≠Is the energy barrier of reaction.The above partition function only includes the contributions of vibration, rotation and translation, and is only related to the optimized vibration frequency and geometric structure, and has nothing to do with the single point energy. Therefore, the calculation level of the single point energy only affects the energy barrier of the reaction.
set upPAs a reference reaction, T is the target reaction, and the target reaction potential energy is as follows according to method 18 of equal bond reaction:
ΔVT≠ʹ= ΔVT≠+ ΔΔVP≠
ΔΔVP≠= ΔVP≠ʹ－ ΔVP≠
Wherein, ≠ is the symbol representing the transition state,ΔVP≠ʹandΔVP≠The reaction energy barrier of the reference reaction calculated by the high-level ab initio theoretical method and the low-level ab initio theoretical method respectively,ΔΔVP≠Corrected value for reference reaction energy barrier.ΔVT≠It is the reaction energy barrier of the target reaction calculated by the low level ab initio theoretical method,ΔVT≠ʹIt is the reaction energy barrier of high-precision target reaction obtained by the reaction energy barrier correction.Exact rate constant of target reactionkʹRate constant that can pass the target reactionkThe energy barrier correction term of the reference reaction yields:
kʹ =kexp[(－ΔΔVP≠)/RT][2]
Reaction energy barrier
The approximate energy barrier of the target reaction at HF/6-31+G (d) level was corrected by using the equal bond reaction method.In order to verify the reliability of the method, the molecular system below C5 is selected, and the high-precision CCSD (T)/CBS method is used for accurate calculation and extrapolation of dataE∞HFandE∞corr(See Supporting Information). Compared with the reaction energy barrier calculated directly by HF method and corrected by equal bond reaction method, it can be seen that the reaction energy barrier calculated by HF method and CCSD (T)/CBS methodMean absolute errorUp to 90.19kJ ∙ mol－1, which is much larger than the average absolute error of 2.96kJ ∙ mol calculated by the equal bond reaction method and CCSD (T)/CBS method－1。Calculation of reaction energy barrier by HF method and CCSD (T)/CBS methodMaximum absolute error92.81 kJ ∙ mol－1, which is still far greater than the maximum absolute error 5.58kJ ∙ mol of reaction energy barrier calculated by equal bond reaction method and CCSD (T)/CBS method－1。The results corrected by the equal bond reaction method have been within the accuracy of chemical reaction, indicating that the reliable reaction energy barrier can be obtained by calculating the hydrogen extraction reaction of alkanes with hydrogen peroxide radical using HF method and correcting by the equal bond reaction method.The energy barriers of 23 target reactions were corrected by the method of equal bond reaction.[2]
