Damping effects density matrix

Finally, we should mention the possibility of coherent excitation transfer when the donor-acceptor interaction is strong, but the coupling of the system to the thermal bath is weak. The resulting two-level weakly damped system lends itself to the time-dependent density-matrix approach [33], which is essentially identical to the familiar spin-1/2 treatment in magnetic resonance. Under certain circumstances, coherence effects can be important for singlet energy transfer, because the donor states are populated instantaneously by direct photoexcitation. With a sufficient band width of the excitation source (e.g., ultrashort femtosecond pulses), quantum superposition states can be prepared in a coherent fashion even in condensed media at room... 

In NMR-SIM the simulation of an NMR experiment is based on the density matrix approach with relaxation phenomena implemented using a simple model based on the Bloch equations. Spectrometer related difficulties such as magnetic field inhomogenity, acoustic ringing, radiation damping or statistical noise cannot be calculated using the present approach. Similarly neither can some spin system effects such as cross-relaxation and spin diffusion can be simulated. 

There are a number of situations in which additional measures must be taken to speed up or establish convergence. One of the most common problems encountered in peptide systems is the occurrence of asymmetric oscillations in the electron distribution from cycle to cycle. In some cases these oscillations damp out on their own, but more often than not, the energy and density matrix undergoes large fluctuations for an indefinite number of SCF cycles. This particular problem can be dealt with quite effectively in conventional MO calculations using what is commonly known as the level shift technique. ... 

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