Optimization solvated electrons

Sprik, M. and Klein, M.L. (1988) Optimization ofa Distributed Gaussian Basis Set using Simulated Annealing Application to the Adiabatic Dynamics of the Solvated Electron,. /. Chem. Phys. 89, 1592—1607. 

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

Solvatochromic shifts are rationalized with the aid of the Franck-Condon principle, which states that during the electronic transition the nuclei are essentially immobile because of their relatively great masses. The solvation shell about the solute molecule minimizes the total energy of the ground state by means of dipole-dipole, dipole-induced dipole, and dispersion forces. Upon transition to the excited state, the solute has a different electronic configuration, yet it is still surrounded by a solvation shell optimized for the ground state. There are two possibilities to consider ... 

Charged interphases may also be exploited to create high local concentrations of electron acceptors which affect the rate of electron transfer reactions confined within these restricted reaction volumes and diminish considerably the efficiency of the corresponding back-transfer [24], These results have been primarily applied in photochemical conversion projects [22,25], but technically more interesting applications may be found in their use for the development of new specific analytical procedures (e.g., optical or photoelectrochemical probes). High local concentrations are also of considerable interest in the optimization of photochemical dimerization reactions [22], as the rate of bimolecular reactions between excited and ground state molecules confined in an extremely restricted reaction volume (microreactor) will be considerably enhanced. In addition, spatial gradients of polarity may lead to preferential structures of the solvated substrate and, hence, to the synthesis of specific isomers [24, 22, 26], Similar selectivities have been found when monomolecular photochemical or photoinduced reactions [2,3] are made via inclusion complexes [27,28]. 

Inspecting the table, we observe that some experimental trends are reproduced by the calculations (for instance, the small increase in the chemical shift of cis-UF4CI2 as compared to UFCI5). However, other experimental trends are not reproduced by either theoretical method. The reasons for this somewhat disappointing result are not clear in the moment. However, solvation effects are expected to have a non-negligible influence on the electronic structure, and hence on the calculated chemical shifts, and probably also on the optimized geometries. Note that some of the molecules in the... 

Alternatively, suppose you want to determine which heteroatom in a molecule is protonated first as pH is lowered. Or conversely, you may want to know which is the most acidic proton in a compound (even if it is a hydrocarbon, for example). In such cases, you can obtain optimized geometries for the parent molecule Z and its conjugate acid ZH+ (or conjugate base Z ) for each site of proton attachment or removal. Simply take the differences in total energy (obtained quantum mechanically), E(ZH+)-E(Z) [or E(Z ) E(Z)], and you have a theoretical assessment of the relative gas-phase acidity (basicity). (The electronic energy of a proton is zero because it has no electron.) Of course, these energy differences do not account for solvation, but if the two protonation (or deprotonation) sites are very similar, the vacuum results may suffice. Alternatively, you can turn on implicit (continuum) solvation in your calculation and obtain energies of the simulated solution species. 

Most of these extensions have involved electron correlation methods based on variational approaches (DFT, MCSCF, CI,VB). These methods can be easily formulated by optimizing the free energy functional (1.117), expressed as a function of the appropriate variational parameters, as in the case of the HF approximation. In contrast, for nonva-riational methods such as the Moller-Plesset theory or Coupled-Cluster, the parallel extension to solvation model is less straightforward. 

A further issue arises in the Cl solvation models, because Cl wavefunction is not completely variational (the orbital variational parameter have a fixed value during the Cl coefficient optimization). In contrast with completely variational methods (HF/MFSCF), the Cl approach presents two nonequivalent ways of evaluating the value of a first-order observable, such as the electronic density of the nonlinear term of the effective Hamiltonian (Equation 1.107). The first approach (the so called unrelaxed density method) evaluates the electronic density as an expectation value using the Cl wavefunction coefficients. In contrast, the second approach, the so-called relaxed density method, evaluates the electronic density as a derivative of the free-energy functional [18], As a consequence, there should be two nonequivalent approaches to the calculation of the solvent reaction field induced by the molecular solute. The unrelaxed density approach is by far the simplest to implement and all the Cl solvation models described above have been based on this method. 

QMSTAT has to date been applied in a number of studies since its original formulation [19,20,21,85,120,121,122,139,161,162,163,164,165,166], These involve studies of ground state solvation, with geometry optimizations in a water solvent and solvation of ions also, solvent shift distributions have been computed for a number of different one-photon absorption and fluorescence transitions. We will not review all these studies, instead three noteworthy applications of QMSTAT are highlighted below. We start with a study of the solvation of the monatomic ions Li+, Na+, F and Cr, with special focus on the coupling between repulsion and the electronic degrees... 

The most well-known member of this class is the polyether, polyethylene oxide, whose complexes with lithium perchlorate have been used commercially in lithium batteries.60-62 The good solvating power of polyethylene oxide is attributed to an optimal spacing of the electron-donating ether oxygens along a flexible backbone that allows multiple contacts between the polymer backbone and cations. When this distance is decreased, as in polymethylene oxide, chain flexibility is greatly reduced when it is increased, as in 1,3-polypropylene oxide, the distance between... 

Figure 4. Backbone structures of salt-solvating polymers. The figure shows the similarity of backbone structure, with optimal spacing between electron-donating oxygens, of polymers that form ion-conducting salt complexes. PPL-poly-3-propiolac-tone PEO polyethylene oxide PPO 1,2- polypropylene oxide.18...

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