Nuclear transition state model

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. 

Formulation of the insertion energy within the Nuclear Transition State (ZTS) Model. 

The inner-sphere component of the reorganization energy represents the minimum energy required to change the internal structure of the redox center to its nuclear transition state configuration. Equation (2.3) is derived from the classical harmonic oscillator model and is an expression of the free energy associated with... 

The previous sections summarize and illustrate the detailed successes of a standard transition-state model for the electron transfer reaction coordinate when AGDA nuclear coordinates of the reactants are in facile equilibrium with the medium all across the reaction coordinate, and that the donor-acceptor... 

Based on the empirical results/ X-ray-diffraction data/ and solution-phase NMR experiments/ a transition state model (6) has been advanced to explain the observed enantioselectivity. The presence of an ortho substituent in the A arylmaleimide reactant directs aluminum coordination to occur with the lone pair of electrons anti to the nitrogen atom. A 3,5-dimethylphenyl moiety present on the ethylenediamine framework blocks one face of the dienophile, resulting in approach of the diene from the backside. A considerable amount of spectroscopic evidence, most notably that obtained fromNOE (nuclear Overhauser effect) experiments, has been accumulated to support this model. A -arylmaleimide derivatives that lack an ortho substituent and other dienophiles (e.g., maleic anhydride) can coordinate to the aluminum catalyst in alternative modes such that the reactive olefin is far removed from the chiral environment of the ligand scaffold, thereby resulting in cycloaddition reactions that exhibit little or no enantioselectivity. 

An ab initio MO calculation by Jorgensen revealed enhanced hydrogen bonding of a water molecule to the transition states for the Diels-Alder reactions of cyclopentadiene with methyl vinyl ketone and acrylonitrile, which indicates that the observed rate accelerations for Diels-Alder reactions in aqueous solution arise from the hydrogenbonding effect in addition to a relatively constant hydrophobic term.7,76 Ab initio calculation using a self-consistent reaction field continuum model shows that electronic and nuclear polarization effects in solution are crucial to explain the stereoselectivity of nonsymmetrical... 

Fe ". In the two-state model, the electron transfer is viewed as a quantum transition between two localized states V, - and Pf. In IF,-, the ion with charge <7/ is at equilibrium with the interfacial water molecules, and the electron is in the metal. In the metal has lost one electron, and the ion with charge q/ is at equilibrium with the interfacial water. The total Hamiltonian of the system H, including all nuclear and electronic degrees of freedom, is not diagonal in the basis ( , , Pf), and so if the system is prepared in the state P, it will evolve in time according to ... 

The quantum alternative for the description of the vibrational degrees of freedom has been commented by Westlund et al. (85). The comments indicate that, to get a reasonable description of the field-dependent electron spin relaxation caused by the quantum vibrations, one needs to consider the first as well as the second order coupling between the spin and the vibrational modes in the ZFS interaction, and to take into account the lifetime of a vibrational state, Tw, as well as the time constant,T2V, associated with a width of vibrational transitions. A model of nuclear spin relaxation, including the electron spin subsystem coupled to a quantum vibrational bath, has been proposed (7d5). The contributions of the T2V and Tw vibrational relaxation (associated with the linear and the quadratic term in the Taylor expansion of the ZFS tensor, respectively) to the electron spin relaxation was considered. The description of the electron spin dynamics was included in the calculations of the PRE by the SBM approach, as well as in the framework of the general slow-motion theory, with appropriate modifications. The theoretical predictions were compared once again with the experimental PRE values for the Ni(H20)g complex in aqueous solution. This work can be treated as a quantum-mechanical counterpart of the classical approach presented in the paper by Kruk and Kowalewski (161). 

The energies E [Pn] in Eq. [35] depend on the nuclear solvent polarization that serves as a three-dimensional (3D) nuclear reaction coordinate driving electronic transitions. The two-state model actually sets up two directions the vector of the differential field AS b and the off-diagonal field Sab-Therefore, only two projections of Vn need to be considered the longitudinal field parallel to ASab and the transverse field perpendicular to ASab- In the case when the directions of the differential and off-diagonal fields coincide, one needs to consider only the longitudinal field, and the theory can be formulated in terms of the scalar reaction coordinate... 

There are other measurable physical properties which reflect the change of electronic character as a function of the inter-nuclear distance R in the avoided crossing region. Examples can be found in the measurements of the vibrationally resolved dipole moments of the A E" state of LiH and NaH ( ) to complement earlier X Z results (35). Also, measurements on the lifetimes (36, 37) and the fluorescence intensity patterns (, M) provide information about the transition moment functions. Further experimental measurements when coupled with the theoretical calculations of the dipole moments and the transition moments (25, 26) and the radiative lifetimes (40) will eventually give a more detailed picture of the ionic-covalent interactions, and should also more clearly establish the limitations of a two-state model. 

The electronic coupling matrix element (//ab) reflects the strength of the interaction between reactants and products at the nuclear configuration of the transition state. Square-barrier ET tunneling models predict that the coupling will... 

In chemical dynamics, one can distinguish two qualitatively different types of processes electron transfer and reactions involving bond rearrangement the latter involve heavy-particle (proton or heavier) motion in the formal reaction coordinate. The zero-order model for the electron transfer case is pre-organization of the nuclear coordinates (often predominantly the solvent nuclear coordinates) followed by pure electronic motion corresponding to a transition between diabatic electronic states. The zero-order model for the second type of process is transition state theory (or, preferably, variational transition state theory ) in the lowest adiabatic electronic state (i.e., on the lowest-energy Bom-Oppenheimer potential energy surface). 

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