(4.42) A refinement of the classical transition state theory is the variational transition state theory that attempts to minimize reaction energy by varying the surface between reactants and products [60]. In the classical transition state theory, only the lowest energy conformer for each of the reactants, transition state, and products is considered. This is not appropriate in cases where multiple conformers generated by torsions have similar energy to the lowest energy conformer.
In these situations, the multi-structural variational transition theory that accounts for multiple conformers should be used [165].
4.6 Programs
Various program and software packages have been developed to apply the theoretical methods discussed in this chapter for modeling chemical systems of varying sizes. Some of
them are open source programs while others are commercial.
Available software packages for quantum chemistry calculations include Gaussian 16 [55], GAMESS [64], ORCA [114], CASTEP [36], DMol3 [38], and VASP [94, 93, 91, 92].
Gaussian is used for various types of calculations like molecular mechanics, semi-empirical, DFT, hybrid functionals, among others. Gaussian is coupled with GaussView 6 [40], which is a graphical interface that allows building molecules and visualizing results in a convenient way. GAMESS is also a program for ab initio computations that allows prediction of various molecular properties. ORCA is a flexible and modern electronic structure package with a specific emphasis on spectroscopic properties. It is built in a way that allows its usage in different fields including computational chemistry, physics, and biology. CASTEP is unique in its capability to compute properties on the nano-scale and for different types of materials like ceramics, metals, and semiconductors. DMol3is focused on DFT calculations for chemicals and pharmaceuticals industries and can be applied reliably for different phases. Finally, VASP is a plane-wave code that employs DFT, HF, hybrid functionals, Green’s functions, or the many-body perturbation theory for modeling atomic scale materials.
Output files from quantum chemistry packages contain molecular information like vibrational frequencies and moments of inertia. These files are used in kinetic programs for pre-dicting reaction rates and effects of parameters like temperature on reaction progress. Among the developed kinetic programs are Polyrate [172], Variflex [88], CanTherm [139], MESMER [61], and MultiWell [11, 12, 13]. In Polyrate, reaction rates are calculated based on the vari-ational transition state theory. Conventional transition state theory calculations are also pos-sible. Polyrate is capable of calculating rates of unimolecular and bimolecular reactions of gases, solids, and gas-solid systems. Tunneling approximations are also included and pressure-dependent rate constants can be computed for elementary reactions. Polyrate is used in con-junction with electronic structure method software like Gaussian and GAMESS through specific interface programs. In addition, Polyrate can treat torsional anharmonicity along the reaction pathway by using coupled torsional potentials in the multi-structural method. Nonethelss, only one structure of the transition state is taken into account. MSTor program [173, 175, 174] ac-counts for multiple conformers for calculating accurate partition functions and thermodynamic data as a function of temperature for gas-phase molecules with coupled torsions. MSTor applies the internal-coordinate torsional anharmonicity method for treating torsional anhramonicity. It also includes the multi-structural local harmonic approximation and the multi-structural local quasiharmonic approximation. MSTor includes several utility codes, the purpose of which is
to generate conformational structures, calculate molecular information, and generate input files required for partition function calculations. Results from MSTor can be combined with those from Polyrate to calculate reaction rates while accounting for multi-structural anharmonicity all along the reaction pathway. This combined method is referred to as the full MS-VTST method [176]. In Variflex and CanTherm, reduced moments of inertia are calculated based on the ro-tation and type of atoms on top of the dihedral angle that is rotated. By solving the Master Equation, both software packages are able to estimate rate constants for pressure dependent elementary reactions. CanTherm is developed as part of RMG-Py, which stands for reaction mechanism generator [65, 59]. RMG is an automated open-source program written in Java and Python. It uses literature and chemical knowledge to propose elementary reaction networks and estimate their rates when provided with reactants, temperature, and pressure. It is convenient for large chemical systems like those encountered in combustion models and biofuel produc-tion. In RMG, the highest flux reaction pathways are considered while the lowest flux ones are ignored. In addition, an automated transition state theory calculator (AutoTST) [21] has been developed and integrated with CanTherm and RMG. AutoTST automatically locates reactants, products, and transition states based on distance geometry algorithms and calculates rates of the corresponding reactions. MESMER is also developed for solving the Master Equation for multi-energy well unimolecular reactions to predict rate constants for gas-phase and solution-phase systems. It also offers a web-based graphical user interface that allows constructing input files and interpreting results. In MultiWell, moments of inertia are treated as a function of the dihedral angle being rotated internally and fitted to a cosine function. MultiWell outputs con-centrations and yields of chemical reactions as a function of time, temperature, and pressure. It also solves the Master Equation using the stochastic method. Despite the differences between these program packages, their predictions of rates are found to be in good agreement for some of the reactions that occur during the combustion of alcohols [84].
Reaction rates estimated from the programs discussed in this section are used for un-derstanding and optimizing chemical processes like combustion, production of biofuels, and formation of refrigerant from chlorinated hydrocarbons. Reaction progress is studied in batch, CSTR, and PFR reactors. In addition, effect of temperature and time on yield, selectivity, and distribution of products is estimated. Among the open-source packages used for this purpose is Cantera [63]. Besides kinetic modeling, Cantera allows studying thermodynamic and transport processes.
Computational Methods
5.1 Introduction
In this chapter, the methods used for estimating rates of reactions leading to the forma-tion of nitrogen heterocyclic compounds during HTL of microalgae are discussed. The workflow is shown in Figure 5.1. In the first step, chemical classes in HTL biocrude are identified from experimental results reported in the literature. Chemical constituents of microalgae, i.e. protein, lipid, and carbohydrate undergo hydrolysis to form amino acids, fatty acids, and carbohydrate monomers. Simple compounds from each of the three classes are selected for the current study and a pathway connecting microalgae to biocrude components is proposed (Section 5.2). The identified reactions are updated based on experimentally proposed HTL mechanisms in the lit-erature. When the reaction mechanism is finalized, geometry optimizations, frequency calcula-tions (Section 5.3), and PES scans (Section 5.4) are performed on the species. Transition states are also determined and confirmed by carrying IRC calculations (Section 5.5). Quantum chemi-cal results are then used for estimating thermochemichemi-cal and kinetic parameters for each reaction pathway (Section 5.6). The impact of torsional coupling in some of the considered molecules is studied by performing multi-structural calculations and comparing estimated thermochemical data to the ones from the 1-DHR model (Section 5.7).