Coordinate coupling

Although Eqs. (4-1) and (4-2) have identical expressions as that of the classical rate constant, there is no variational upper bound in the QTST rate constant because the quantum transmission coefficient Yq may be either greater than or less than one. There is no practical procedure to compute the quantum transmission coefficient Yq- For a model reaction with a parabolic barrier along the reaction coordinate coupled to a bath of harmonic oscillators, the quantum transmission... 

Rao and Singh32 calculated relative solvation free energies for alkyl- and tetra-alkylammonium ions using same conditions as described before for neutral molecules (except, atomic partial charges were not scaled for ions). The values obtained with coordinate coupling were in better agreement with... 

Reaction Free Energy Profiles Using Free Energy Perturbation and Coordinate Coupling Methodologies Analysis of the Dihydrofolate Reductase Catalytic Mechanism... 

The energy Ea is a quantum term associated with the proton reaction coordinate coupling to the Q vibration, Ea = h1 /2m. and Co is the tunneling matrix element for the transfer from the 0th vibrational level in the reactant state to the 0th vibrational level in the product state. The term AQe is the shift in the oscillator equilibrium position and F L(Eq, Ea, Laguerre polynomial. For a thorough discussion of Eq. (8), see [13],... 

Interestingly Gokel has demonstrated the existence of a direct coordination coupling pathway between this ferrocene cryptand and a silver cation. Complexation studies were carried out with [24] and [25] (as well as other ferrocene cryptand-type species) by X-ray crystallography, FAB mass spectral analysis, nmr and UV/Vis spectroscopy. 

Scheme 7 A direct coordination coupling pathway is not possible between the redox centre of [49] and the binding site.

Direct coordination between the redox centre and guest leads to generally large perturbations in the electrochemical behaviour of the host. A particularly elegant example of this type redox/coordination coupling is given by the quinone crown ether species synthesized by Cooper and co-workers (Wolf and Cooper, 1984 Delgado et al., 1992) (Fig. 24). 

The energy E is a quantum term associated with the proton reaction coordinate coupling to the Q vibration, E = 12m and Q is the tunneling matrix ele-... 

Niunerical algorithms for solving the GLE are readily available. Only recently, Hershkovitz has developed a fast and efficient 4th order Runge-Kutta algorithm. Memory friction does not present any special problem, especially when expanded in terms of exponentials, since then the GLE can be represented as a finite set of memoiy-less coupled Langevin equations. " Alternatively (see also the next subsection), one can represent the GLE in terms of its Hamiltonian equivalent and use a suitable discretization such that the problem becomes equivalent to that of motion of the reaction coordinate coupled to a finite discrete bath of harmonic oscillators. ... 

Many drugs of abuse make the individual feel excited, aroused, and strong. Others result in drowsiness and poor coordination. Coupled with these feelings, however, may be an impairment of cognitive functions such as judgment, perception, and attentiveness. When these effects are combined, the individual may make rash decisions and take risks that otherwise would not be undertaken, which can lead to motor vehicle accidents and criminal activities such as robbery and homicide. 

The coordinates, coupling parameter C and frequency fl in (4.29), are dimensionless, and time is measured in dimensionless units o>0t, where 0 is the frequency of small vibrations in the well for the adiabatic potential... 

The metal-to-ligand coordination coupling chosen for the construction of a family of giant amphiphiles was that of a metal-terpyridine complex, which is known to form stable bis-complexes with a variety of transition-metal ions.275 The versatility of this metal-to-ligand system has been recently demonstrated in the construction of a series of coordination polymers and block copolymers.276... 

Makri, N. and Miller, W.H. (1987). Time-dependent self-consistent field (TDSCF) approximation for a reaction coordinate coupled to a harmonic bath Single and multiple configuration treatments, J. Chem. Phys. 87, 5781-5787. 

We consider a model Hamiltonian that consists of a one-degree-of-freedom reaction coordinate coupled with n degrees of freedom that are vibrational modes. Thus, the total number, N, of the degrees of freedom is n + 1. The reaction coordinate is a degree of freedom that has an unstable fixed point. The position of the fixed point corresponds to a saddle with index 1 of the whole system— that is, a transition state in the conventional sense. The n-degrees-of-freedom vibrational modes are, in general, nonlinear. Moreover, when the... 

---