Electronic band structure in the solid and its relation to the energy gap of the monomer is all about studying how intermolecular interactions change electronic structure. In experimental studies this results in broader absorption bands and by extension a lowering of the LUMO and raising of HOMO energy to the conduction and valence band edges respectively. This electronic change involves splitting of the molecular energy levels into bands of non-degenerate energies and can be calculated either quantum mechanically (QM) or by classical force field models through the change in ionization potential (IP) and electron affinity (EA), called the apparent polarization energy, and its relation to HOMO and LUMO through Koopman’s and Janak’s theorem. The study of the formation of a ‘band’ like structure is important in regimes and systems where conventional quantum mechanical (QM) methods become infeasible. Specifically, when systems are non-periodic and plane wave approximations fail, such as in amorphous structures, or in regimes between where the plane wave bulk approximation and the gas phase single molecule QM methods where the scaling of conventional gas phase atomic orbital methods becomes exorbitantly costly and the plane wave approximation fails for open systems. Therefore, the objective of this work is to highlight the changing optoelectronic properties of molecular solids within this regime using both density functional theory and molecular mechanics. The scalability of DFT limits it to multimer systems, leaving the larger nanoscale materials to be studied using molecular mechanics. Here we have utilized a variety of dispersion sensitive functionals in order to characterize the intermolecular interactions and splitting energies in small multimers of some of the smallest oligoacene species, benzene and anthracene. Benzene and anthracene nanoclusters from 0.8 to 5.0 nm in radius have had their changes in electronic band energy calculated due to polarization using the AMOEBA force field and bulk values have also been extrapolated. AMOEBA’s explicit polarization terms allow for direct handling of the polarization energy, control of nanocluster size and shape in a regime that QM methods cannot probe efficiently, and the ability to specify the position of charge carriers in order to examine specific electronic surface behavior. Using differing DFT methods the change in the HOMO and LUMO energy from the single molecule state to multimers of the size of 10 and 12 units for anthracene and benzene respectively. The HOMO band of benzene was raised by ~0.3 eV and LUMO lowered by 0.35 eV. In anthracene the HOMO was lowered by ~0.1 eV and the LUMO by ~0.15 eV. These values remain within 0.1 eV across all dispersion functionals. Using Ren’s parameterization procedure and MP2 for the AMOEBA force field he apparent polarization was calculated. The extrapolated values for the change in the HOMO and LUMO of benzene from single molecule to bulk were 1.42 eV and 0.49 eV respectively. For anthracene the crystalline bulk changes the HOMO and LUMO by 1.34 eV and 1.16 eV respectively. The regression for bulk extrapolation also predicts that benzene clusters of 12 units will be 0.77 eV for HOMO and -0.41 eV for LUMO. Similarly for an anthracene cluster made up of 10 molecular units the apparent polarization is predicted through linear regression to be 0.58 eV for HOMO and 0.53 eV for LUMO.

Dans cette thèse, nous présentons quelques analyses théoriques récentes ainsi que des observations expérimentales de l’effet tunnel quantique macroscopique et des tran- sitions de phase classique-quantique dans le taux d’échappement des systèmes de spins élevés. Nous considérons les systèmes de spin biaxial et ferromagnétiques. Grâce à l’approche de l’intégral de chemin utilisant les états cohérents de spin exprimés dans le système de coordonnées, nous calculons l’interférence des phases quantiques et leur distribution énergétique. Nous présentons une exposition claire de l’effet tunnel dans les systèmes antiferromagnétiques en présence d’un couplage d’échange dimère et d’une anisotropie le long de l’axe de magnétisation aisé. Nous obtenons l’énergie et la fonc- tion d’onde de l’état fondamentale ainsi que le premier état excité pour les systèmes de spins entiers et demi-entiers impairs. Nos résultats sont confirmés par un calcul utilisant la théorie des perturbations à grand ordre et avec la méthode de l’intégral de chemin qui est indépendant du système de coordonnées. Nous présentons aussi une explica- tion claire de la méthode du potentiel effectif, qui nous laisse faire une application d’un système de spin quantique vers un problème de mécanique quantique d’une particule. Nous utilisons cette méthode pour analyser nos modèles, mais avec la contrainte d’un champ magnétique externe ajouté. La méthode nous permet de considérer les transitions classiques-quantique dans le taux d’échappement dans ces systèmes. Nous obtenons le diagramme de phases ainsi que les températures critiques du passage entre les deux régimes. Nous étendons notre analyse à une chaine de spins d’Heisenberg antiferro- magnétique avec une anisotropie le long d’un axe pour N sites, prenant des conditions frontière périodiques. Pour N paire, nous montrons que l’état fondamental est non- dégénéré et donné par la superposition des deux états de Néel. Pour N impair, l’état de Néel contient un soliton, et, car la position du soliton est indéterminée, l’état fondamen- tal est N fois dégénéré. Dans la limite perturbative pour l’interaction d’Heisenberg, les fluctuations quantiques lèvent la dégénérescence et les N états se réorganisent dans une bande. Nous montrons qu’à l’ordre 2s, où s est la valeur de chaque spin dans la théorie des perturbations dégénérées, la bande est formée. L’état fondamental est dégénéré pour s entier, mais deux fois dégénéré pour s un demi-entier impair, comme prévu par le théorème de Kramer / This thesis presents recent theoretical analyses together with experimental observa- tions on macroscopic quantum tunneling and quantum-classical phase transitions of the escape rate in large spin systems. We consider biaxial ferromagnetic spin systems. Using the coordinate dependent spin coherent state path integral, we obtain the quantum phase interference and the energy splitting of these systems. We also present a lucid exposition of tunneling in antiferromagnetic exchange-coupled dimer, with easy-axis anisotropy. Indeed, we obtain the ground state, the first excited state, and the energy splitting, for both integer and half-odd integer spins. These results are then corroborated using per- turbation theory and the coordinate independent spin coherent state path integral. We further present a lucid explication of the effective potential method, which enables one to map a spin Hamiltonian onto a particle Hamiltonian; we employ this method to our models, however, in the presence of an applied magnetic field. This method enables us to investigate quantum-classical phase transitions of the escape rate of these systems. We obtain the phase boundaries, as well as the crossover temperatures of these phase transi- tions. Furthermore, we extend our analysis to one-dimensional anisotropic Heisenberg antiferromagnet, with N periodic sites. For even N, we show that the ground state is non-degenerate and given by the coherent superposition of the two Neél states. For odd N, however, the Neél state contains a soliton; as the soliton can be placed anywhere along the ring, the ground state is, indeed, N-fold degenerate. In the perturbative limit (weak exchange interaction), quantum fluctuation stemming from the interaction term lifts this degeneracy and reorganizes the states into a band. We show that this occurs at order 2s in (degenerate) perturbation theory. The ground state is non-degenerate for inte- ger spin, but degenerate for half-odd integer spin, in accordance with Kramers’ theorem