Electrochemical Energy Storage Systems are a viable and popular solution to fulfill energy storage requirements for energy generated through sustainable energy resources. With the increasing demand for Electrical Vehicles (EVs), Lithium-ion batteries (LIB) are being widely and getting popular compared to other battery technologies due to their energy storage capacity. However, LIBs suffer from disadvantages such as battery life and the degradation of electrode material with time, that can be improved by understanding these mechanisms using experimental and computational techniques. Further, it has been experimentally observed and numerically determined that lithium-ion intercalation induced stress and thermal loading can cause capacity fading and local fractures in the electrode materials. These fractures are one of the major degradation mechanisms in Lithium-ion batteries. With LixMn2O4 as a cathode material, stress values differ widely especially for intermediate State Of Charge (SOC), and very few attempts have been made to understand the stress distribution as a function of SOC at molecular level. Therefore, the estimates of mechanical properties such as Young’s modulus, diffusion coefficient etc. differ, especially for partially charged states. Further, the effect of temperature, particularly elevated temperatures, have not been taken into the consideration. Studying these parameters at the atomic scale can provide insight information and help in improving these materials lifetime. Hence, molecular/atomic level mathematical modelling has been used to understand capacity fade due to Lithium-ion intercalation/de-intercalation induced stress. Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [1], that is widely used for atomic simulations, has been used for the simulation studies of this dissertation. Thus, the objective of this study is to understand the fracture mechanisms in the Lithium Manganese Oxide (LiMn2O4) electrode at the molecular level by studying mechanical properties of the material at different SOC values using the principles of molecular dynamics (MD). As part of the model validation, the lattice parameter and volume changes of LixMn2O4 as a function of SOC (0 < x < 1) has been studied and validated with respect to the experimental data. This validated model has been used for a parametric study involving the SOC value, strain-rate (charge and discharge rate), and temperature. Based on the validated MD setup, doping and co-doping studies have been undertaken to design and develop new and novel cathode materials with enhanced properties. In the absence of experimental data for the new engineered structures, validation with Quantum Mechanics generated lattice structures has been done. The results suggest that lattice constant values obtained from both MD and QM simulations are in good agreement (∼ 99%) with experimental values. Further, Single Particle Model (SPM) based macro scale Computational Fluid Dynamics findings show that co-doping has improved the material properties especially for Yttrium and Sulfur doped structures which can improve the cycle life anywhere between 600-7000 cycles. Further in order to reduce the required computational time to obtain minimum potential energy ionic configuration out of millions of scenario, Artificial Neural Network (ANN) technique is being used. It improved the processing time by more than 88%. / Thesis / Doctor of Philosophy (PhD)

yes / The properties of quantum probabilities are linked to the geometry of quantum mechanics, described by the Birkhoff-von Neumann lattice. Quantum probabilities violate the additivity property of Kolmogorov probabilities, and they are interpreted as Dempster-Shafer probabilities. Deviations from the additivity property are quantified with the Möbius (or non-additivity) operators which are defined through Möbius transforms, and which are shown to be intimately related to commutators. The lack of distributivity in the Birkhoff-von Neumann lattice Λd, causes deviations from the law of the total probability (which is central in Kolmogorov’s probability theory). Projectors which quantify the lack of distributivity in Λd, and also deviations from the law of the total probability, are introduced. All these operators, are observables and they can be measured experimentally. Constraints for the Möbius operators, which are based on the properties of the Birkhoff-von Neumann lattice (which in the case of finite quantum systems is a modular lattice), are derived. Application of this formalism in the context of coherent states, generalizes coherence to multi-dimensional structures.

The knowledge of the packing behaviour of small organic compounds in crystal lattices is of great importance for industries dealing with solid state materials. The properties of materials depend on how the molecules arrange themselves in a crystalline environment. Crystal structure prediction provides a theoretical approach through the application of computational strategies to seek possible crystal packing arrangements (or polymorphs) a compound may adopt. Based on the chemical diagrams, this thesis investigates polymorphism of several small organic compounds. Plausible crystal packings of those compounds are generated, and their lattice energies are minimised using molecular mechanics and/or quantum mechanics methods. Most of the work presented here is conducted using two software packages commercially available in this field, Polymorph Predictor of Materials Studio 4.0 and GRACE 1.0. In general, the computational techniques implemented in GRACE are very good at reproducing the geometries of the crystal structures corresponding to the experimental observations of the compounds, in addition to describing their solid state energetics correctly. Complementing the CSP results obtained using GRACE with isostructurality offers a route by which new potential polymorphs of the targeted compounds might be crystallised using the existing experimental data. Based on all calculations in this thesis, four new potential polymorphs for four different compounds, which have not yet been determined experimentally, are predicted to exist and may be obtained under the right crystallisation conditions. One polymorph is expected to crystallise under pressure. The remaining three polymorphs might be obtained by using a seeding technique or the utilisation of suitable tailor made additives. / University of Bradford

In this Bachelor thesis project, the Lindblad master equation is derived, both as the most general way of modeling interaction with an environment that lacks memory, and through microscopic derivations focused on assumptions about the way the system interacts with its environment (weak-coupling, Born-Markov and rotating wave approximations). It is then applied to a two-level system (qubit).

Electron-driven processes lie at the core of a large variety of physical, biological, and chemical phenomena. Despite their crucial roles in science and technology, detailed description of these processes remains a significant challenge, and there is a need for the development of accurate and efficient computational tools that enable predictive simulation. This work is focused on the development of novel software tools and methodologies aimed at two classes of electron-mediated processes: (i) electron-molecule scattering, and (ii) charge transfer in proteins. The first major focus of this thesis is the electronic structure of autoionizing electronic resonances. The theoretical description of these metastable states is intractable by means of conventional quantum chemistry techniques, and specialized techniques are required in order to accurately describe their energies and lifetimes. In this work, we have utilized the complex absorbing potential (CAP) method, and describe three developments which have advanced the applicability, efficiency, and accessibility of the CAP methodology for molecular resonances: (1) implementation and investigation of the smooth Voronoi potential (2) implementation of CAP in the projected scheme, and (3) development of the OpenCAP package, which extends the CAP methodology to popular electronic structure packages. The second major focus is the identification of electron and hole transfer (ET) pathways in biomolecules. Both experimental and theoretical inquiries into electron/hole transfer processes in biomolecules generally require targeted approaches, which are complicated by the existence of numerous potential pathways. To this end, we have developed an open-source web platform, eMap, which exploits a coarse-grained model of the protein crystal structure to (1) enable pre-screening of potentially efficient ET pathways, and (2) identify shared pathways/motifs in families of proteins. Following introductory chapters on motivation and theoretical background, we devote a chapter to each new methodology mentioned above. The open-source software tools discussed herein are under active development, and have been utilized in published work by several unaffiliated experimental and theoretical groups across the world. We conclude the dissertation with a summary and discussion of the outlook and future directions of the OpenCAP and eMap software packages.

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Indiana University-Purdue University Indianapolis (IUPUI) / Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points. We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.

no / The finite set of subsystems of a finite quantum system with variables in Z(n), is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently, the quantum probabilities related to commuting projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell inequalities, which contain "Heyting factors," are discussed. The formalism is also applied to the infinite set of all finite quantum systems, which is appropriately enlarged in order to become a complete Heyting algebra.