Density function theory processes

Density functional theory study of aqueous-phase rate acceleration and endo/exo selectivity of the butadiene and acrolein Diels-Alder reaction72 shows that approximately 50% of the rate acceleration and endo/exo selectivity is attributed to hydrogen bonding and the remainder to bulk-phase effects, including enforced hydrophobic interactions and cosolvent effects. This appears to be supported by the experimental results of Engberts where a pseudothermodynamic analysis of the rate acceleration in water relative to 1-propanol and 1-propanol-water mixtures indicates that hydrogen-bond stabilization of the polarized activated complex and the decrease of the hydrophobic surface area of the reactants during the activation process are the two main causes of the rate enhancement in water.13... 

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

There are also important features of current implementations of density functional theory which leave some biological processes beyond the scope of the DFT studies ... 

The mechanism of direct oxidation of cyclohexene to cyclohexanone by N20 mediated oxidation was analyzed by density functional theory (DFT) using B3LYP/6-31G approximation. A two-step reaction mechanism was predicted where the substituted 1,2,3-oxadiazoline ring system 5 forms as the first intermediate in the process before subsequent conversion to the cyclohexanone <1999JOC6710, 2003CC42, 2005MI177>. 

Currently, the density functional theory (DFT) method has become the method of choice for the study of reaction mechanism with transition-metals involved. Gradient corrected DFT methods are of particular value for the computational modeling of catalytic cycles. They have been demonstrated in numerous applications for several elementary processes, to be able to provide quantitative information of high accuracy concerning structural and energetic properties of the involved key species and also to be capable of treating large model systems.30... 

Quantum mechanical methods follow a similar path, except that the starting point is the solution of the Schrodinger equation for the system under investigation. The most successful and widely used method is that of Density Functional Theory. Once again, a key point is the development of a realistic model that can serve as the input to the computer investigation. Energy minimization, molecular dynamics, and Monte Carlo methods can all be employed in this process. 

Theoretical considerations leading to a density functional theory (DFT) formulation of the reaction field (RF) approach to solvent effects are discussed. The first model is based upon isolelectronic processes that take place at the nucleus of the host system. The energy variations are derived from the nuclear transition state (ZTS) model. The solvation energy is expressed in terms of the electrostatic potential at the nucleus of a pseudo atom having a fractional nuclear charge. This procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy, since all integrations involved are performed over [O.ooJ The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density functional theory. 

Since the early days of quantum mechanics, the wave function theory has proven to be very successful in describing many different quantum processes and phenomena. However, in many problems of quantum chemistry and solid-state physics, where the dimensionality of the systems studied is relatively high, ab initio calculations of the structure of atoms, molecules, clusters, and crystals, and their interactions are very often prohibitive. Hence, alternative formulations based on the direct use of the probability density, gathered under what is generally known as the density matrix theory [1], were also developed since the very beginning of the new mechanics. The independent electron approximation or Thomas-Fermi model, and the Hartree and Hartree-Fock approaches are former statistical models developed in that direction [2]. These models can be considered direct predecessors of the more recent density functional theory (DFT) [3], whose principles were established by Hohenberg,... 

Notice that since rj > 0, we always have AE < 0, i.e., the charge transfer process is energetically favorable. We proposed the new density functional theory (DFT) reactivity index, electrophilicity index oj as... 

Density functional theory has also been applied successfully to describe the solvent exchange mechanism for aquated Pd(II), Pt(II), and Zn(II) cations (1849 ). Our own work on aquated Zn(II) (19) was stimulated by our interest in the catalytic activity of such metal ions and by the absence of any solvent (water) exchange data for this cation. The optimized transition state structure clearly demonstrated the dissociative nature of the process in no way could a seventh water molecule be forced to enter the coordination sphere without the simultaneous dissociation of one of the six coordinated water molecules. More... 

Model computational studies aimed at understanding structure-reactivity relationships and substituent effects on carbocation stability for aza-PAHs derivatives were performed by density functional theory (DFT). Comparisons were made with the biological activity data when available. Protonation of the epoxides and diol epoxides, and subsequent epoxide ring opening reactions were analyzed for several families of compounds. Bay-region carbocations were formed via the O-protonated epoxides in barrierless processes. Relative carbocation stabilities were determined in the gas phase and in water as solvent (by the PCM method). 

Fig. 5 A proposed mechanism for enhanced emission (or AIEE) in solid-state organic dye nanoparticles. The dye considered here is trans-biphenylethylene (CN-MBE) compound. The geometry is optimized by the density functional theory (DFT) calculation at the B3LYP/6-31G level. Molecular distortion such as twisting and/or subsequent planarization causes prevention of radiationless processes along with specific aggregation such as the /-aggregate in the nanoparticles...

Molecular-level studies of mechanisms of proton and water transport in PEMs require quantum mechanical calculations these mechanisms determine the conductance of water-filled nanosized pathways in PEMs. Also at molecular to nanoscopic scale, elementary steps of molecular adsorption, surface diffusion, charge transfer, recombination, and desorption proceed on the surfaces of nanoscale catalyst particles these fundamental processes control the electrocatalytic activity of the accessible catalyst surface. Studies of stable conformations of supported nanoparticles as well as of the processes on their surface require density functional theory (DFT) calculations, molecular... 

In accordance with these experimental results, Wang et al. employed density functional theory calculations to comprehensively examine the possible reduction pathways for EC molecules in super-molecular structures Li+—(EC) [n = 1—5) and found that, thermodynamically, both one- and two-electron reductive processes are possible.A complete array of the possible reduction products from EC was listed in their paper considering the various competitive pathways, and they concluded that both (CH2OCO2-Li)2 and (CH2CH20C02Li)2 are the leading species in SEI, while minority species such as lithium alkox-ide, lithium carbide, and the inorganic Li2C03 coexist. 

With the aid of density functional theory, the ZnCl2 acceleration of the Simmons-Smith reaction of ethylene and allyl alcohol has been investigated. A pathway involving direct Lewis acid acceleration of the leaving halogen atom (327) was found to be a more facile process than the more popular pathway involving 1,2-chlorine migration (328). 

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