Exchange correlation time optimization

As we have seen above, a large number of parameters (proton exchange rate, kex = l/rm rotational correlation time,. electronic relaxation times, 1/TI 2(, Gd - proton distance, rG H hydration number, q) influence the inner sphere proton relaxivity. If the proton exchange is very slow (Tlm < rm), it will be the only limiting factor (Eq. (5)). If it is fast (rm Tlm), proton relaxivity will be determined by the relaxation rate of the coordinated protons, Tlm. which also depends on the rate of proton exchange, as well as on rotation and electronic relaxation. The optimal relationship is ... 

In order to visualize the effects of water exchange, rotation and electronic relaxation as well as of magnetic field on proton relaxivity, we have calculated proton relaxivities as a function of these parameters (Fig. 2). The relaxivity maximum is attained when the correlation time, tc1, equals the inverse proton Lar-mor frequency (l/rcl = l/rR + l/rm + l/Tle = a>j). The most important message of Fig. 2 is that the rotational correlation time, proton exchange and electronic relaxation rates have to be optimized simultaneously in order to attain maximum relaxivities. If one or two of them have already an optimal value, the remaining parameter starts to become more limitative. The marketed contrast agents have relaxivities around 4-5 mM1 s 1 contrary to the theoretically attainable values over 100 mM 1 s1, which is mainly due to their fast rotation and slow water exchange. 

Note that each cycle of the inner loop does not require computing a new Kohn-Sham matrix, with the expensive Coulomb and exchange-correlation contributions, so that the time spent for optimizing is usually not problematic in terms of computational time, especially if an initial guess can be provided. So far, we have not specified the form of the weight function w(r) and its corresponding matrix elements that are used in the cDFT constraint We now turn to this point. 

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