Simulations for carbon capture and utilisation

The generation of large amounts of carbon dioxide from fossil fuels presents both significant challenges and opportunities for humanity. Due to the role that carbon dioxide plays in anthropogenic climate change, methods need to be developed to mitigate the release of carbon dioxide from large, fixed point sources. However once this carbon dioxide is captured, a number of opportunities may be found to utilise some of this carbon dioxide in the manufacture of other chemicals. In this work molecular simulation is used to investigate methods for carbon capture and utilization. New methods of simulation are also developed to properly account for the complexity of some systems. In the first section, comprising the first chapter, a summary of the relevant background work is given. In the second section, comprising chapters two to four, standard molecular simulation techniques are applied to the problem of understanding gas adsorption in Metal-Organic Frameworks (MOFs). In the second chapter Grand Canonical Monte Carlo (GCMC) simulations are used to estimate the gas adsorption properties of 9 characteristic MOFs. Both simulations of single gases and gas mixtures typical of different CO2 sources are performed. Here it is found that gas adsorption is determined by a range of factors, including pore size, pore geometry, polarity of potential gas binding sites and also the temperature of adsorption. Factors that lead to a large selectivity of CO2 over other non-polar gases such as N2 or CH4 are also found to lead to increased adsorption of water. In the third chapter a study of the effects of functionalization on the gas adsorption properties of the MOF Cu3(BTC)2 is carried out. Here a range of simulation techniques are used to evaluate properties such as selectivity for CO2 adsorption, gas diffusivity and suitability for use in humid environments. These simulations show that the inclusion of electron withdrawing groups such as nitrile or nitro groups onto the benzene ring can significantly increase CO2 selectivity and low pressure adsorption capacity. Gas diffusivity is shown to have a more complex relationship to functionalization. Here simulations show that larger functional groups have the ability to block pores in the material, leading to a decrease in adsorption capacity. Water stability may also be increased by the inclusion of hydrogen bonding groups such as amines, which provide alternative binding sites for water and protect the metal secondary building units from being hydrolysed. In the fourth chapter, the accuracy of a range of simulation techniques for modelling gas adsorption in MOFs is studied. Here different methods for estimating both the electrostatic and van der Waals interactions are evaluated. It is found that the accuracy of Monte Carlo simulation is largely dependent on the quality of the potentials used to characterise the gas-framework interactions. Using a forcefield with more specific atom types is found to give better results over more generic forcefields. Utilising electrostatic potentials directly from periodic density functional theory (DFT), thereby avoiding charge parameterisation, is also found to give better results compared to charge assignment methods. These simulations highlight the importance of the gas-framework interaction potential in simulations of gas adsorption in a framework with exposed metal cations. Here a novel method is used to parameterise an interaction potential between the gas and the metal based on DFT calculations, giving a much better match between simulation and experiment. Given the challenges of accurate Monte Carlo simulation using generic potentials, in the third section comprising chapters five to nine, new methods of simulation are sought to improve the overall accuracy and efficiency of simulations of MOFs. In chapter five, methods for determining the atomic structure of the framework material are first addressed. Here different algorithms for geometry optimisation were tested. In particular algorithms that scale in both a linear and cubic manner were used. To assess the applicability of both the BFGS and L-BFGS algorithms, the DFT package SIESTA is modified to include these algorithms. Geometry optimisations on a range of frameworks of different sizes were carried out to evaluate both the efficiency of each algorithm and the effects of scaling. Here it is found that in each case the majority of computational time was taken in evaluating the energy and forces of each structure. The BFGS algorithm was found to be overall the most efficient. Given appropriate methods for determining the structure of the material, in chapter 5 six methods for calculating the interaction potential between gases and framework atoms are investigated. Here the general method of Ewald summation is extended to potentials of any reciprocal power, including typical electrostatic, dispersion and repulsion potentials. Expressions for energies, forces, stresses and Hessian elements are all considered, as are estimates for the truncation error of the energy sums. Given these expressions a method for automatically optimising the Ewald summation based on gas loading is presented. This method is applied to both GCMC and molecular dynamics simulations of CO₂ in the MOF material MOF-5. Both different Ewald based methods and pairwise potentials are compared. These calculations show that the new Ewald method gives superior accuracy to other pair based potentials and also shows favourable scaling properties in Monte Carlo simulations. In molecular dynamics simulations Ewald summation is shown to only be advantageous at low gas loading. With the development of high accuracy methods for evaluating empirical potentials, in chapter seven methods for estimating the electrostatic interactions between gases and the MOF materials are investigated. Here a new charge equilibration method for rapid assignment of atomic partial charges is outlined. This method is based on treating each atom as having an ionised, rather than a neutral electronic configuration. This new charge equilibration method is compared to other rapid charge assignment methods, as well as more detailed DFT calculations of electrostatic interactions. A test set of 24 different MOFs spanning different metals and geometries is used. Comparisons of simulated and experimental CO₂ adsorption show that the new method best replicates the electrostatic potential calculated from DFT methods. The new charge equilibration method also leads to a closer estimate to adsorption compared to other rapid charge assignment methods. These comparisons to experimental adsorption also illustrate some of the limitations of generic van der Waals potentials. To overcome some of the problems associated with generic van der Waals potentials, in chapter eight methods for parameterising van der Waals potentials based on the results of DFT calculations are investigated. In this method the adsorption energy of a randomly generated set of gas positions is determined with DFT simulations, and then van der Waals parameters are assigned with linear least squares fitting. Novel weighting functions are also defined that help to restrain the fitting to chemically realistic values, as well as providing a trade-off between accuracy of the potential and the number of calculated gas positions. This fitting method is applied to three MOF materials, Zn₂(BDC)₂(TED), MIL-47 and Mg-MOF-74. Gas adsorption energies are calculated using three different density functionals, the PBE-D2, PBE-D3 and vdw-DF2 functionals. Of these three functionals the PBE-D3 functional produces potentials that provide a close match to experimental adsorption in the fully coordinated Zn₂(BDC)₂(TED) and MIL-47 materials. In the case of Mg-MOF-74 none of the fitted potentials completely replicates the experimental isotherm. Here the lack of accuracy is caused both by poor representation of the CO₂-metal potential in the DFT calculations as well as limitations in the functional form of the empirical potential. In the last chapter in this section on improvements to gas adsorption simulation, the problem of modelling water adsorption and condensation in MOF materials is investigated in chapter nine. Here transition matrix Monte Carlo methods are applied to the simulation of water. To improve the efficiency of the simulation, biased insertion and deletion moves are outlined and tested using canonical Monte Carlo simulations. These show that at high water densities biasing is essential in gaining reliable statistics. Transition matrix Monte Carlo methods are then applied to the simulation of both bulk water and the adsorption of water in the MOF material Zn₂(BDC)₂(TED). These simulations show that water adsorbs with a pore-condensation mechanism, resulting in free energy barriers between various pore filled states. This mechanism of adsorption is problematic for normal GCMC simulations, which focus on sampling individual free energy minima. Adsorption simulations using these methods typically rely more on the sizes of the barriers between states rather than the true equilibrium of the system. Using both transition matrix Monte Carlo simulations and a water-framework potential fitted to DFT calculations, estimates of water adsorption are made that are in accordance with experimental adsorption isotherms. In the fourth and final section in chapter 10, simulation is applied to the problem of CO₂ utilisation. Here the catalysis and conversion of CO₂ using gold and gold-palladium nanoclusters in investigated. Molecular DFT simulations are used to evaluate the binding energy of a range of gases and radicals relevant to CO₂ catalysis. This is done to evaluate possible reaction mechanisms for the conversion of CO₂. In these calculations it is found that while CO, H₂O and radicals bind to the gold and gold-palladium nanoclusters, CO₂, H₂ and CH₄ all have weak binding interactions. Doping the gold clusters with palladium or adsorbing other molecules onto the cluster is shown to have highly localised effects on the binding energy. While gold nanoclusters are found to be effective for oxygen splitting reactions, they are poor catalysts for CO₂ conversion