Analytical Derivatives Theory for Molecular Solutes

We shall present here an equilibrium simulation of the transport of a solute across a liquid-liquid interface, which permits to measure the rate constant. This work has been done with the same rationale than other recent molecular dynamics studies of chemical kinetics /5,6/. The idea is to obtain by simulation, at the same time, a computation of the mean potential as a function of the reaction coordinate and a direct measure of the rate constant. The mean potential can then be used as an input for a theoretical expression of the rate constant, using transition state /7/, Kramers /8/ or Grote-Hynes /9/ theories for instance. The comparaison can then be done in order to give a correct description of the kinetics process. A distinct feature of molecular dynamics, with respect to an experimental testing of theoretical results, is that the numerical simulations have both aspects, theoretical and experimental. Indeed, the computation of mean potentials, as functions of the microscopic models used, is simple to obtain here whereas an analytical derivation would be a heavy task. On the other hand, the computation of the kinetics constant is more comparable to an experimental output. 

Several implementations of the PCM-CC theories have been presented. Caricato et al. (2010) have presented an implementation of the PCM-CC analytical gradients for the ground state of molecular solutes within the Gaussian suite of programs (Frisch et al. 2009). Cammi et al. (2010b) have presented an implementation of the PCM-CC and PCM-EOM-CC analytical derivatives methods within the framework of SAC/SACCI methods. We hope that these computational advances can be profitably used to study molecular processes in condensed phase, where both the accuracy of the QM descriptions and the influence of the environment play a critical role, as in photo-ionization processes, electronic transitions, and charge transfer reactions. 

The retention times of analytes are controlled by the concentration(s) of the organic solvent(s) in the mobile phase. If a relatively small entropic contribution to the retention is neglected, theoretical considerations based either on the model of interaction indices [58], on the solubility parameter theory [51,52] or on the molecular statistical theory [57], lead to the derivation of a quadratic equation for the dependence of the logarithm of the retention factor of a solute. A, on the concentration of organic solvent. aqueous-organic mobile phase ... 

While this result confirmed the feasibility of the general approach, it did not precipitate wider exploration of dielectric medium effects. Recently, however, Wiberg et al. have incorporated the Onsager self-consistent reaction-field model into ab initio MO theory in an implementation which provides analytical gradients and second derivatives. The model considers just the dipole of the solute molecules and a spherical cavity whose radius is chosen for a given solute molecule from the molecular volume estimated at the 0.001 eB electron-density contour (B is the Bohr radius), plus an empirical constant 0.5 A to account for the nearest approach of solvent molecules [164]. Cieplak and Wiberg have used this model to probe solvent effects on the transition states for nucleophilic additions to substituted acetaldehydes [165]. For each... 

An attractive virtue of PRISM theory is the ability to derive analytic solutions for many problems if the most idealized Gaussian thread chain model of polymer structure is adopted. The relation between the analytic results and numerical PRISM predictions for more chemically realistic models provides considerable insight into the question of what aspects of molecular structure are important for particular bulk properties and phenomena. Moreover, it is at the Gaussian thread level that connections between liquid-state theory and scaling and field-theoretic approaches are most naturally established. Thus, throughout the chapter analytic thread PRISM results are presented and discussed in conjunction with the corresponding numerical studies of more realistic polymer models. 

In the Gaussian thread limit analytic results have been derived for copolymer fluids using the molecular closures. " The analytic results provide insights to several key questions and behaviors that emerge from the numerical PRISM studies. These Include (1) the role of nonzero monomer hard-core diameter, density fluctuations, and concentration fluctuations on dlblock liquid-phase behavior and structure (2) relationship between phenomenological field-theoretic approachesand the molecular closure-based versions of PRISM theory and (3) the influence of molecular weight, composition, solution density, and chemical and conformational asymmetries of the blocks on copolymer microphase separation temperatures. 

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