Spectroscopic measurements are a foundational tool in chemical research that quantify the interaction between electromagnetic radiation and quantum states of matter. The details of experimental spectra are fundamentally determined by the electronic structure of the system under study, which is the ultimate basis of all its chemical properties. The utility of a spectrum lies in being able to extract detailed information about the way in which nuclei and electrons are organized within the system.

Molecular spectroscopy comprises a set of techniques for obtaining information on the electronic and geometric structure of molecules, both isolated and in different environments, providing information of the systems studied under the measurement conditions in which they have been recorded. Among the most widely used spectroscopic techniques we have ultraviolet-visible (UV-vis) spectroscopy, which interrogates transitions between electronic states of molecules; microwave spectroscopy, which measures the energy required to transition between different rotational quantum states; nuclear magnetic resonance spectroscopy, a technique used mainly in the elucidation of molecular structures, that is based on the absorption of electromagnetic radiation (radio frequency waves) by some atomic nuclei under the influence of a magnetic field; and vibrational spectroscopy, the focus of this study, which directly provides information on transitions between vibrational energy levels, and indirectly reflects the composition, structure and bonding of a system. The most common vibrational spectroscopic techniques are Infrared (IR) spectroscopy and Raman spectroscopy. An overview of the principles behind both of these techniques is provided in Appendix A.

The vibrational spectrum is a unique and characteristic physical property of a molecule or material. Thus, vibrational spectra can be used as a "molecular fingerprint" in the identification of unknown samples by comparison with reference spectra. Some examples of this can be found in the characterization and identification of polymers as well as their structural and surface properties. Also, in the field of biological and medical sciences, the uses of vibrational spectroscopy are widespread in the characterization of lipids, nucleic acids, proteins and peptides, in addition to characterizing disease in animal tissues, recognizing plants and differentiating microbial cells, among others. However, in recent times, new industrial and environmental applications of vibrational spectroscopy have been introduced. Industrial applications include the characterization of pharmaceutical materials for production processes, food quality analysis, identification of the different components of paints, pulp and paper quality control and even potentially quantifying strain in wood. Environmental applications include air, water and soil analysis, as well as measurement of gases and atmospheric compositions, which is crucial for understanding global climate changes and astronomical observations.

However, if reference spectra are unavailable, interpretation of vibrational spectra is much harder. In some cases, vibrations arising from specific functional groups can be assigned using heuristic rules, but in general, computational support is required to ensure vibrational spectra can be thoroughly and meaningfully assigned.

Quantum chemical software packages provide access to a range of electronic structure models that can be used to describe how the energy changes as a function of molecular configuration (i.e. construct potential energy surfaces) and consequently solve the nuclear vibrational Schrödinger equation to predict vibrational spectra. A hierarchy of electronic structure models of different computational cost and accuracy are available, and these may be combined with a range of different models for predicting nuclear vibrational motion, as well, to yield overall predictions of varying accuracy and computational cost. A brief description of all electronic structure and nuclear vibrational models employed in this thesis is provided in the Methods section.

For small molecules, very accurate predictions of vibrational spectra are possible by constructing potential energy surfaces at high levels of ab initio theory and using nuclear vibrational models that account for anharmonicity; the propensity of a molecule to spend more time at longer bond lengths to avoid the repulsive forces that are magnified upon bond compression, and also the way that stretching/compressing a molecule in one way makes it harder/easy to stretch/compress it in a different direction.

Because benchmark results can be generated for small molecules, they provide an ideal testing ground for trialling approximate and less computationally intensive schemes for constructing potential energy surfaces and/or solving the nuclear vibrational Schrodinger equation. In the first results chapter of this thesis (Chapter 3), we address the problem of finding more efficient schemes for constructing potential energy surfaces by taking a “two-level” approach – computing the harmonic part of the potential energy surface that describes symmetric vibrations along normal mode coordinates at a high level of ab initio theory, while constructing the remainder of the potential energy surface (the anharmonic region) at a lower level of theory.

The remainder of this thesis focusses on using more approximate nuclear vibrational models to interpret experimental observations. First, we study the nature of two novel chloride hydrates trapped in cyclopropenium chloride crystal. These chloride-water clusters are of fundamental importance in understanding a broad range of physicochemical processes in nature, particularly in biological and geological systems.29-31 The discreteness of these clusters can be assessed by comparing experimental IR spectra to predicted IR spectra obtained from gas phase calculations. If a cluster is discrete, there will not be any specific interactions stabilizing it, so a gas phase model should provide quite accurate predictions. However, in some cases, specific interactions with the surrounding environment may contribute to forming and/or stabilising a particular chloride hydrate structural motif. In such cases, modelling the IR spectrum is more

complicated because environmental effects need to be taken into account. In Chapters 4 & 5, we investigate the structure and vibrational spectroscopy of two quite different chloride hydrate clusters that form within subtly different cyclopropenium chloride crystal environments.

For very large systems, applying quantum nuclear vibrational models can become impractical. In these cases, it may be appropriate to use classical physics-based approaches to modelling macromolecular structure and dynamics. In Molecular Mechanics (MM), the energy of the system is then calculated as a function of the nuclear coordinates with the use of force fields, in which atoms are simulated as balls, and bonds as springs. To simulate the time-dependent evolution of the system, we can use Molecular Dynamics (MD) simulations. Further details of how force fields are defined and parameterised is provided in the Methods section, along with an explanation of how molecular dynamics simulations work and how key thermodynamic parameters such as temperature, pressure and volume are set and controlled.

Cellulose, the most abundant material in the biosphere, is one such system that is not particularly amenable to quantum nuclear vibrational analysis. The interest in this polymer has grown in the recent years as it has become a potential source of renewable fuel and materials.34-38 The presence of hydrogen bonds play an important role, not only in the physical properties, solubility, hydroxyl reactivity and crystallinity, but also in the mechanical properties of cellulose. The structure and hydrogen bonding patterns within common allotropes of cellulose (I and I) have been studied experimentally and confirmed computationally. Although some quantum harmonic frequency calculations have been performed, they are not accurate enough to allow experimental IR spectra to be fully understood or assigned. Thermal shifts in IR stretching frequencies have also been observed. Paradoxically, these may be easier to understand and explain than the IR frequencies themselves, because thermal effects can be modelled via classical molecular dynamics simulations. In the last results chapter (Chapter 6), we address this problem, using a classical molecular dynamics model to explore how changes in temperature affect O- H stretching vibrations and hydrogen bond lengths, and how this is coupled to and driven by changes along other vibrational modes of crystalline cellulose.