Exchange matrix

The exchange matrix, K, is just the rate, k, times the unit matrix. In block fonn, the full matrix for two sites is given in the eigenvalue equation, (B2.4.38). 

Conduction in the raw doped polymer can be improved by devices such as compression and stretching and judicious after-synthesis dopant ion exchange. Matrix-guided electropolymerization also yields superior products. 

Moseley, H. N. B., Curto, E. V., Krishna, N. R. Complete Relaxation and Conformational Exchange Matrix (CORCEMA) analysis of NOESY spectra of interacting systems two-dimensional transferred NOESY. J. Magn. Reson. Sen B 1995, 108, 243-261. 

Challacombe, M., E. Schwegler, and J. Almlof. 1995. Linear scaling computations of the Hartree-Fock exchange matrix. J. Chem. Phys. 105, 2726. 

Anisotropic exchange interaction within the Lines model described above. Dipole-dipole magnetic interaction between centres is calculated fully ah initio and is added to the exchange matrix. 

Terms containing the W intermediates no longer contain a factor of The energy-independent, third-order term, Epp (oo), is a Coulomb-exchange matrix element determined by second-order corrections to the density matrix, where... 

The basic theoretical formulation for the quantitative analysis of the STD-NMR data is similar to the one we developed for the analysis of transferred NOESY data, and is based on a complete relaxation and conformational exchange matrix (CORCEMA) theory [33]. 

Aq is the spectral peak volume of a single proton and n is the number of protons at the spin site i. Obviously, when different spin sites have different populations, i.e., rii rij, neither the product matrix A(rm) A(0) nor the exchange matrix L is symmetric, eq. (11). This also follows from the principle of detailed balance [28, 48],... 

In this respect the dense nonporous ion-exchange material of a membrane may be viewed as a one-phase medium. In contrast to this a porous bulk ion-exchanger (e.g., an ion-exchange bed or a single microporous ion-exchange bead) is a two-phase medium with the possibility for each ion to be in either one of the two phases—in the ion-exchange matrix proper or in the aqueous pore. 

The dependence of the exchange matrix element on the distance i between the donor and the acceptor is discussed in Sect. 3. 

The probability of an electron tunneling reaction is directly proportional to the square of the exchange matrix element (see the following section). Therefore, the dependence of the rate constant of an electron tunneling reaction on the distance between the donor and the acceptor and on their mutual orientation is also determined, to a considerable degree, by the dependence of the exchange matrix element on these parameters. 

In the three-dimensional case, the computation of the exchange matrix element can be carried out by the asymptotic method [15]. Without dwelling upon the details of the calculation, we quote the final result... 

Along with the harmonic approximation, the Franck-Condon approximation is usually also used in calculating the probability of electron tunneling. In accordance with the latter approximation, the exchange matrix element V(q) in eqn. (20) is factorized outside the integral sign... 

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