Thorpeaycock1245

realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.A weak excitation transit-time resolution limited analytic line shape is derived for a Doppler broadening-free degenerate two-photon transition from a standing wave with a TEM00 transverse profile. This approximation is appropriate when the collisional mean free path is much larger than the transverse width of the TEM00 beam. It is considerably simpler than the two-photon absorption line shape previously published, Bordé, C. R. Hebd. Seances Acad. Sci., Ser. B 282, 341-344 (1976), which was derived for more general experimental conditions. The case of a saturating field, with an intensity-dependent shift of the resonance frequency, is treated and expressed in reduced units. Numerical calculations are presented for the line shape for a range of the reduced intensity and light intensity shifts values.Water has a rich phase diagram with several crystals, as confirmed by experiments. High-pressure and high-temperature water is of interest for Earth's mantle and exoplanetary investigations. It is in this region of the phase diagram of water that new plastic crystal phases of water have been revealed via computer simulations by both classical forcefields and ab initio calculations. U0126 nmr However, these plastic phases still remain elusive in experiments. Here, we present a complete characterization of the structure, dynamics, and thermodynamics of the computational plastic crystal phases of water using molecular dynamics and the two-phase thermodynamic method and uncover the interplay between them. The relaxation times of different reorientational correlation functions are obtained for the hypothetical body-centered-cubic and face-centered-cubic plastic crystal phases of water at T = 440 K and P = 8 GPa. Results are compared to a high pressure liquid and ice VII phases to improve the understanding of the plastic crystal phases. Entropy results indicate that the fcc crystal is more stable compared to the bcc structure under the studied conditions.A dissipative particle dynamics (DPD) model is developed and demonstrated for studying dynamics in colloidal rod suspensions. The solvent is modeled as conventional DPD particles, while individual rods are represented by a rigid linear chain consisting of overlapping solid spheres, which interact with solvent particles through a hard repulsive potential. The boundary condition on the rod surface is controlled using a surface friction between the solid spheres and the solvent particles. In this work, this model is employed to study the diffusion of a single colloid in the DPD solvent and compared with theoretical predictions. Both the translational and rotational diffusion coefficients obtained at a proper surface friction show good agreement with calculations based on the rod size defined by the hard repulsive potential. In addition, the system-size dependence of the diffusion coefficients shows that the Navier-Stokes hydrodynamic interactions are correctly included in this DPD model. Comparing our results with experimental measurements of the diffusion coefficients of gold nanorods, we discuss the ability of the model to correctly describe dynamics in real nanorod suspensions. Our results provide a clear reference point from which the model could be extended to enable the study of colloid dynamics in more complex situations or for other types of particles.Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-π, π]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH4 complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan-Starling and Percus-Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials.Vibrational strong coupling of molecules to optical cavities based on plasmonic resonances has been explored recently because plasmonic near-fields can provide strong coupling in sub-diffraction limited volumes. Such field localization maximizes coupling strength, which is crucial for modifying the vibrational response of molecules and, thereby, manipulating chemical reactions. Here, we demonstrate an angle-independent plasmonic nanodisk substrate that overcomes limitations of traditional Fabry-Pérot optical cavities because the design can strongly couple with all molecules on the surface of the substrate regardless of molecular orientation. We demonstrate that the plasmonic substrate provides strong coupling with the C=O vibrational stretch of deposited films of PMMA. We also show that the large linewidths of the plasmon resonance allow for simultaneous strong coupling to two, orthogonal water symmetric and asymmetric vibrational modes in a thin film of copper sulfate monohydrate deposited on the substrate surface. A three-coupled-oscillator model is developed to analyze the coupling strength of the plasmon resonance with these two water modes. With precise control over the nanodisk diameter, the plasmon resonance is tuned systematically through the modes, with the Rabi splitting from both modes varying as a function of the plasmon frequency and with strong coupling to both modes achieved simultaneously for a range of diameters. This work may aid further studies into manipulation of the ground-state chemical landscape of molecules by perturbing multiple vibrational modes simultaneously and increasing the coupling strength in sub-diffraction limited volumes.The non-adiabatic quantum dynamics of the H + H2 + → H2 + H+ charge transfer reactions, and some isotopic variants, is studied with an accurate wave packet method. A recently developed 3 × 3 diabatic potential model is used, which is based on very accurate ab initio calculations and includes the long-range interactions for ground and excited states. It is found that for initial H2 +(v = 0), the quasi-degenerate H2(v' = 4) non-reactive charge transfer product is enhanced, producing an increase in the reaction probability and cross section. It becomes the dominant channel from collision energies above 0.2 eV, producing a ratio between v' = 4 and the rest of v's, which that increase up to 1 eV. The H + H2 + → H2 + + H exchange reaction channel is nearly negligible, while the reactive and non-reactive charge transfer reaction channels are of the same order, except that corresponding to H2(v' = 4), and the two charge transfer processes compete below 0.2 eV. This enhancement is expected to play an important vibrational and isotopic effect that needs to be evaluated. For the three proton case, the problem of the permutation symmetry is discussed when using reactant Jacobi coordinates.Cavity-mediated light-matter coupling can dramatically alter opto-electronic and physico-chemical properties of a molecule. Ab initio theoretical predictions of these systems need to combine non-perturbative, many-body electronic structure theory-based methods with cavity quantum electrodynamics and theories of open-quantum systems. Here, we generalize quantum-electrodynamical density functional theory to account for dissipative dynamics of the cavity and describe coupled cavity-single molecule interactions in the weak-to-strong-coupling regimes. Specifically, to establish this generalized technique, we study excited-state dynamics and spectral responses of benzene and toluene under weak-to-strong light-matter coupling. By tuning the coupling, we achieve cavity-mediated energy transfer between electronically excited states. This generalized ab initio quantum-electrodynamical density functional theory treatment can be naturally extended to describe cavity-mediated interactions in arbitrary electromagnetic environments, accessing correlated light-matter observables and thereby closing the gap between electronic structure theory, quantum optics, and nanophotonics.The particle mesh Ewald (PME) method has become ubiquitous in the molecular simulation community due to its ability to deliver long range electrostatics accurately with ON  ⁡log(N) complexity. Despite this widespread use, spanning more than two decades, second derivatives (Hessians) have not been available. In this work, we describe the theory and implementation of PME Hessians, which have applications in normal mode analysis, characterization of stationary points, phonon dispersion curve calculation, crystal structure prediction, and efficient geometry optimization. We outline an exact strategy that requires O(1) effort for each Hessian element; after discussing the excessive memory requirements of such an approach, we develop an accurate, efficient approximation that is far more tractable on commodity hardware.Several oil-water separation techniques have been proposed to improve the capacity of cleaning water. With the technological possibility of producing materials with antagonist wetting behavior, for example, a substrate that repels water and absorbs oil, the understanding of the properties that control this selective capacity has increased with the goal of being used as the mechanism to separate mixed liquids. Besides the experimental advance in this field, less is known from the theoretical side. In this work, we propose a theoretical model to predict the wetting properties of a given substrate and introduce simulations with a four-spin cellular Potts model to study its efficiency in separating water from oil. Our results show that the efficiency of the substrates depends both on the interaction between the liquids and on the wetting behavior of the substrates itself. The water behavior of the droplet composed of both liquids is roughly controlled by the hydrophobicity of the substrate. Predicting the oil behavior, however, is more complex because the substrate being oleophilic does not guarantee that the total amount of oil present on the droplet will be absorbed by the substrate.