The fundamental models, implemented in Khimera software, allow one to calculate the kinetic parameters of elementary processes in gases, plasma and at gas-solid interface from the data on the molecular structures and properties. The models are available for the following classes and sub-classes of chemical reactions:

Chemistry of Heavy Particles

• Direct bimolecular reactions
• Bimolecular reactions via long-lived intermediate complexes
• Multi-channel unimolecular reactions
• Dissociation of diatomic molecules
• Ion-molecular reactions

Surface Processes

• Gas-surface reactions
• Surface reactions
• Surface diffusion

Electron-Molecular Reaction

• Elastic electron-molecule scattering
• Electronic excitation by electron impact
• Ionization by electron impact
• Electron-ion recombination

Vibrational Energy Transfer

• VT and VV energy exchange
• VRT and VVR energy exchange

Photochemical Reactions and Electronic Energy Transfer

• Photoexcitation of diatomic molecules
• Photodissociation of diatomic molecules
• Dissociative electronic energy transfer
• Predissociation of diatomic molecules
• Inelastic atomic collisions

Reactions in non-polar solvents

• Diffusion coefficients
• Unimolecular reactions of neutral molecules
• Bimolecular reactions of neutral molecules
• Fluorescence quenching and excitation transfer

Reactions in polar solvents

• Bimolecular reactions of neutral molecules
• Charge transfer
• Reaction between ions
• Ion recombination

The fundamental models, implemented in frame of Khimera software, allow one to calculate the thermodynamic properties of individual substances in gas phase and transport properties of multi-component reacting gases and plasma from the data on molecular structures and properties.

Thermodynamic properties of pure substances in gas phase

The parameters of substance molecular structure are used to calculate:

• Specific heat
• Enthalpy of formation
• Entropy

The independent sets of models are implemented for:

• Di-atomic molecules
• Poly-atomic molecules, including internal rotations
• Atoms with account for electronically excited states

Multicomponent Reactive Gas Transport Properties

The Chapman-Enskog method is used to calculate transport properties of reactive gas mixture. The choice of model (Lennard-Jones, HFD-B, Stockmayer, Buckingham-Corner, Born-Mayer) or ab initio interaction potentials is available. The following properties are calculated:

• Viscosity of mixture
• Thermal conductivity (translational, internal, reaction, efficient)
• Binary diffusion and thermo-diffusion coefficients

All the properties are calculated as function of temperature, gas pressure, gas composition, electron energy and stored in tabular form. Tabular data are used for:

• Export into Excel and Origin readable text files
• Built-in plots for calculated dependences of properties on temperature, gas pressure, gas composition, electron energy, etc.
• Fitting of the calculated dependences of properties to widely used approximations:
  • NASA and IVTAN polynomials for thermodynamic functions
  • Arrhenius, Lindeman, Troe, SRI approximations for reaction rate constants

To accelerate the collection of input data for running the models, Khimera is integrated with a set of Kitech Lab and third-party software:

• Automatically download molecular properties of species from KintechDB database and fill in corresponding model parameters in Khimera GUI
• Automatically parse results of the quantum-chemical simulations with widely used QC codes (Gaussian, GAMESS, ADF, Jaguar) and fill in corresponding model parameters in Khimera GUI
• Store the calculated approximations of the thermodynamic function and rate constants (NASA and IVTAN polynomials, Arrhenius, Lindeman, Troe, SRI approximations) into KintechDB database and export into Chemical Workbench software

Thermodynamic properties of individual substances are required for any analysis of multielemental multiphase physico-chemical systems. As a rule most of them are retrieved from existing databases. In some cases the data for a substances you need are not available or out-of-date in these databases and should be calculated.

Types of species for which the calculation of thermodynamic properties can be done by Khimera

Statistical mechanics approach is used to calculate partition functions over electronic, vibrational and rotational energy levels for mono, di, and polyatomic gases. The calculations for condensed phases are based on low temperature thermodynamic functions (at some selected temperatures, standard entropy and enthalpy at room temperature) and equations for heat capacity temperature dependence, temperatures and enthalpies of phase transitions.

The realization of direct summation technique requires constructing full set of vibrational-rotational levels for all electronic states taking into account for partition functions calculations. Experimental data as a rule refer to low-lying vibrational and rotational levels. Dissociation energy value and constructing Limiting Curve of Dissociation (LCD) allows extrapolate experimental data to describe all bound and quasibound states.
The result of calculations of the rotational levels for selected vibrational quantum number is presented in the picture. It should be noted that only four vibrational levels of the ground state of AlH molecule are investigated in spectroscopic studies.

Full set of vibrational and rotational levels is constructed for the ground electronic state of AlH molecule.

Example: general case of internal rotation in polyatomic molecules

The usual approximation with one term potential:
V(f)=V0/2[1+cos(nf)]
is not applicable for the general case of internal rotation (IR) with complicated potential. The case of torsional potential for relatively simple methyl n-propyl ether is shown on the picture. The potential was obtained from quantum chemical calculation and is fully unsymmetrical. The most general form of periodic function containing cosine and sine terms should approximate it. The results are presented in the picture. The direct summation over calculated torsional levels using such potential give reliable result of IR contribution calculation into thermal functions.

Potential function of internal rotation and torsional energy levels for methyl n-propyl ether (CH3 – O – CH2CH2CH3).

Example: thermodynamic properties and geometry of FeF3

As a result of thermal functions calculation and selection of enthalpy of formation the full thermodynamic properties table can be calculated. The table consists of thermal functions in a wide temperature range, equilibrium constant for a given reaction (for example, dissociation), basic thermochemical quantities (the enthalpy of formation at 0 K and room temperature, the enthalpy of a given reaction), and equations approximating reduced Gibbs energy function in the same temperature range. It should be noted that the approximation is carried out by several conjugated piecewise functions. The heat capacity values in the points of conjugation and its first temperature derivatives are equal for conjugated functions.
Thermodynamic properties table for FeF3(g)
-----------------------------------P=1 atm---------------------------------
                          IRON TRIFLUORIDE   FeF3(g)                        
-------------------------------------------------------------------------------
FeF3=Fe+3F                     ΔкH(0)= 1383.438 kJ/mol   
-------------------------------------------------------------------------------   
T(K)     :     Cp     :      Φ        :       S      :  H(T)-H(0)  :     lgK
                (J/(K.mol)                        kJ/mol
-------------------------------------------------------------------------------     
100          49.414    208.324    247.919        3.959     -708.7343      
200          59.630    238.319    285.548        9.446     -345.9280      
298.15     67.274    258.226    310.864       15.694    -226.2024      
300          67.393    258.552    311.280       15.819    -224.6962     
5700        83.075    465.758    546.243     458.765         6.3363     
5800        83.077    467.158    547.688     467.072         6.5638     
5900        83.080    468.536    549.109     475.381         6.7840     
6000        83.082    469.890    550.505     483.689         6.9970  
--------------------------------------------------------------------------------                                 
M = 112.84220
ΔfH(0) = -739.957     kJ/mol
ΔfH(298.15) = -742.006     kJ/mol
Snucl   =   20.256     J/(K.mol)
---------------------------------------------------------------------------  
T=  298- 1500K,   X=T/10000 :                                                
Φ   = 4.688608E+02 + 6.786536E+01*ln(X) - 3.604143E-03*X + 8.173496E-01*X+ 1.590141E+02*X - 4.055775E+02*X + 5.362902E+02*X  J/(K.mol)        
---------------------------------------------------------------------------
T= 1500- 6000K,   X=T/10000  :                                             
Φ   = 5.097200E+02 + 8.307927E+01*ln(X) - 1.070131E-02*X + 1.542127E+00*X+1.627659E-01*X - 1.008190E-01*X + 3.264821E-02*X  J/(K.mol)        
---------------------------------------------------------------------------

The importance of quantitative information on transport properties for multicomponent reacting gas mixtures needs no comments. Khimera makes possible calculation of all the necessary mixture transport coefficients.

Set of Transport Coefficients Accessible for Treatment by Khimera

• mixture viscosity μ;
• mixture thermal conductivity (translational λ^tr, internal λ^int, total λ=λ^tr+λ^int );
• thermodiffusion coefficients D_Ti and thermodiffusion ratios k_Ti for all species (i=1,...,N);
• multicomponent diffusion coefficients D_ik and multicomponent resistance coefficients Δ_ik for all pairs of species (i,k=1,...,N).

Here, N is the total number of species.

Calculations of the transport coefficients for a multicomponent gas mixture under thermal and chemical equilibrium (LTE) are performed by the accurate formulas of the Chapman-Enskog method. The calculations are made with account for higher approximations 1<ξ<4, where ξ is the number of approximations, i.e., the number of retained terms in the Sonine polynomial expansions.

The Euken-Hirschfelder formula is used to calculate the contribution to thermal conductivity of polyatomic gases due to the internal degrees of freedom of molecules.

Khimera provides the coefficients for both the traditional form of the Stefan-Maxwell relations (fluxes via forces) following the works by Hirschfelder and Devoto (D_Ti, D_ik) and the new form of Stefan-Maxwell relations (forces via fluxes) following Tirskii-Kolesnikov (k_Ti, Δk_ik).

In the current Kimare version, the interparticle potential function for each pair of species is approximated by the Lennard-Jones (126) potential, so the temperature range should be restricted to 2000-4000 K to provide a reasonable accuracy of transport coefficients. The next version of Khimera (under development now) will provide a possibility to use more accurate model potential functions including Buckingham-Corner exp6f potential for nonpolar gases, Stockmayer potential for polar gases, Born-Mayer potential for high temperature calculations, Aziz HFD potentials for noble gases.

Set of Transport Coefficients Accessible for Treatment by Khimera

Viscosity and thermal conductivity were calculated for the two cases: LTE argon and dissociated air. In both cases calculations were done at a pressure of P=1 atm in the temperature range 300≤T≤4000 K by the accurate formulas of the Chapman-Enskog method with account for higher approximations, e.g., ξ=2 for viscosity and ξ=4 for translational thermal conductivity.

Dissociated air (78% N₂, 21% O₂, 1% Ar) consists of the 6 components (N₂, O₂, Ar, NO, N, O).

Figures 1-2 present a comparison of the Khimera results (blue line) with available experimental and theoretical data.

Model approaches to evaluating the cross sections and rate constants of processes involving electrons are based on qualitative physical ideas about the mechanisms of interaction between the incident electron and the atomic or molecular target. The elastic scattering, dissociation, and excitation processes are treated within the framework of the Born approximation, corrected by taking into account the set of available experimental data. The processes performed through the formation of a temporary compound are processed within the framework of the Breit–Wigner model using quantum chemical data on the width of the relevant state.

Example: electron impact ionization of Te

The process Te + e → Te⁺ + e + e plays an important role in plasma chemical technology of semiconductor electronics. The cross section of this process is calculated within the frame of Born-Compton approximation, that has manifested itself quite well in evaluation of the ionization cross section for elements with a moderate value of the ionization potential. This approach is distinguished in its simplicity and requires a few data on the atom under investigation.

The window of the Khimera module with the results of calculations of the ionization cross section for Te is presented in the picture along with the available experimental data.

Example: electron impact excitation of Mg (3s¹S_o-3p¹P₁)

Electron impact excitation of optically allowed states of atoms determines the emission and electrical properties of low-temperature plasmas. The cross section of this process is determined within the framework of the modified Born approximation using the similarity function method. This approach requires knowledge of the oscillator strength and the energy of the transition under consideration. The figure below compares the results of calculations of the excitation cross section with the available experimental data. It is seen that the similarity function method provides quantitative agreement with experiment and can be used as a tool of high predictability.

Example: electron impact dissociation of SF molecule

The process of the electron impact dissociation of molecules is one of the main mechanisms of initial chemical transformation in chemically active plasma. Specifically, the dissociation of an SF molecule determines the kinetics of plasma etching in semiconductor production. The cross section of this process is calculated within the framework of the similarity function method using the results of quantum chemical calculations of the potential energy curves for both the ground and excited states of the molecule, as well as the dependence of the transition dipole moment on the internuclear distance. The dissociation process proceeds through the formation of a repulsing state on the molecule.

Quantitative data on the cross sections and rate constants of the processes of generation and relaxation of electronically and vibrationally excited particles are of great importance for kinetic modeling in materials, environmental chemistry, plasma chemistry and plasma processing.

Universal Set of Processes Accessible for Treatment by Khimera

The state of art models of generation and relaxation of electronically and vibrationally excited particles incorporated into Khimera are based on the qualitative physical ideas about the character of electronic potential surfaces of the systems and their dynamics. The main simplification of dynamics underlying all the models is the use of a quasiclassical or classical approximation treating the motion of nuclei.

Example: photodissociation of CH molecule

The cross section of the photodissociation of the CH molecule from the X²Π electronic bound state to the upper 2²Σ unbound state is calculated using the corresponding ab initio potential curves. The electronic dipole moment D(R) of the X²Π–2²Σ electronic transition as a function of the internuclear distance R is obtained from quantum chemical calculations. The Born–Oppenheimer approximation is used for the description of the molecular energy levels. The results of calculations and a comparison of the results of calculation are shown in the figure.

Example: electronic deactivation in atomic collisions O(¹D) + Ar →O(³P) + Ar

Rate constant of the electronic quenching processes O(¹D) + Ar(¹S) →O(³P) + Ar(¹S) was evaluated using Landau-Zener model incorporated to Khimera. The model allows calculating rate constants of electronic energy transfer induced by nonadiabatic transitions at the crossings of electronic potential curves of diatoms. In the case of the process under consideration there exist three such crossings which contribute to the overall rate constant. The parameters of the O-Ar diatom necessary for the application of the Landau-Zener model were calculated using quantum chemistry. It is seen that Landau-Zener model with the parameters obtained from quantum chemical calculations provides quantitative description of electronic quenching in atomic collision.

Example: vibrational energy transfer in collisions of N₂ with He

The rate constant of the vibrational transition from the first excited vibrational state of N₂ to the ground state in collisions with He (N₂(v=1)+He → N₂(v=0)+He) was evaluated in the framework of the Schwartz-Slawsky-Herzfeld (SSH) theory of VT energy exchange in collisions involving diatomic molecules. The parameters of interaction between N2 and He were evaluated ab initio within the framework of DFT using the Gaussian 2003 program package. The results are presented in the picture along with the available experimental data. It is seen from the picture that SSH theory provides a quantitative description of the vibrational relaxation of diatomic molecules.

Quantitative data on the rate constants of equilibrium chemical reactions are of great importance for kinetic modeling in combustion, materials, environmental chemistry, plasma chemistry and plasma processing.

Universal Set of Processes Accessible for Treating by Khimera

State of art models of thermal chemical reactions incorporated into Khimera are based on qualitative physical ideas about the character of electronic potential surfaces of the interacting systems. The dynamics is treated within well approved variants of statistical approach.

Example: chain branching reaction O+H₂ → OH+H

The reaction O+H₂ → OH+H is one of the chainbranching reactions in the practically important process of hydrogen combustion. The rate constant of this reaction was evaluated using the transition state theory. This theory is applicable if only one potential barrier exists on the reaction path from reagents to products and there are no deep potential wells.

The window of the Khimera module with the results of calculations of the rate constant using the Khimera module is shown in the figure along with the available experimental data. It is seen that the transition state theory with the parameters obtained from quantum chemical calculations provides a quantitative description of the direct bimolecular reaction.

Example: chain initiation reaction O₂ +C₂H₆ → HO₂ + C₂H₅

The reaction O₂ +C₂H₆ → HO₂ + C₂H₅ is one of the chain initiation reactions in the practically important process of hydrocarbon low temperature combustion. The rate constant of this reaction was evaluated using the transition state theory. The parameters of the potential surface were evaluated ab initio within the framework of DFT using the Gaussian 98 program package.

The window of the Khimera module with the results of calculations of the rate constant using the Khimera module is shown in the figure along with the available experimental data. It is seen that the transition state theory with the parameters obtained from quantum chemical calculations provides a quantitative description of a bimolecular reaction involving a polyatomic molecule.

Example: soot growth reaction C₂H₂ + C₂H₂→C₄H₃ + H

The reaction C₂H₂ + C₂H₂→C₄H₃ + H is of importance in the process of soot formation at high temperatures.

The rate constant of this reaction was evaluated using the statistical theory of bimolecular reactions through an intermediate complex. The parameters of the potential surface of the system were evaluated ab initio using the Complete Active Space Self-Consistent Field method and the second order Multi-Reference Moeller-Plesset Perturbation Theory using PC GAMESS/Firefly program package.

The window of the Khimera module with the results of calculations of the rate constant is shown in the picture along with the experimental data. In the present case of strongly discordant experimental results, it can be supposed that theoretical results are more reliable.

Quantitative information about surface diffusion of adsorbed particles and its chemical reactions is of crucial importance for kinetic modeling in heterogeneous catalysis, nanotechnology, and plasma chemistry.

Universal Set of Processes Accessible for Treating by Khimera

State of art models of surface processes incorporated into Khimera are based on qualitative physical ideas about the potential energy surfaces of the adsorbed particles and their dynamical interaction with phonons of the solid. Two approaches are used in the diffusion processes. One is based on the kinetic FokkerPlank equation and another is used the stochastic Langevin approach. Model of surface reaction in kinetic regime is based on wellapproved variant of statistical approach.

Example: surface diffusion Na/Cu(100)

The diffusion of sodium on copper is a practically important process in nanotechnology and has been studied in detail both experimentally and theoretically. The diffusion coefficient of this process was evaluated using the stochastic model of surface diffusion. This theory is applicable if the characteristic frequency of adatom vibration is lower than the Debye frequency.

The window of the Khimera module with the results of calculations of the diffusion coefficient using the Khimera module is presented in the figure along with the available experimental data.

Example: oxidization of CO on Pt

The reaction O+CO → CO₂ on platinum is the limiting stage of heterogeneous oxidization of carbon monoxide. The rate constant of this reaction was evaluated using the transition state theory. In this case, the reaction activation energy should be lower than the diffusion activation energy.

The window of the Khimera module with the results of calculations of the rate constant using the Khimera module is presented in the figure along with the available experimental data. It is seen that the transition state theory with the parameters obtained from quantum chemical calculations provides a quantitative description of the direct bimolecular reaction.

Example: annealing of tungsten

The surface annealing is controlled by the trapping of diffusing adatoms by vacancies. The rate constant of this process for the tungsten surface was evaluated using the statistical model of surface diffusioncontrolled reactions. The results were obtained using the Khimera module and are presented in the figure along with the available experimental data. It is seen from the figure that the theory provides a quantitative description of the surface diffusioncontrolled reactions in a wide range of temperatures.