Fully Polarized Interactions

Although complete, fully polarizable QM/MM schemes are computationally demanding, a simplified version of this formalism was arguably the first QM/MM approach to be described (Warshel and Levitt 1976), and the method still sees some use today. The simplification involves replacing explicit, polarizable MM molecules with a three-dimensional grid of fixed, polarizable dipoles - each a so-called Langevin dipole (LD) as it is required to obey 

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Let us consider the spin relaxation of an ensemble of j = 1, N electrons moving with the velocities Vj, v l = v for all electrons assuming that the free path / vt >- /(). We select one representative of the ensemble which starts at a point pi in the fully polarized state with sz)j = 1/2. Its path is then l = vt and the coordinate p f) = pi + Vjt Each electron in the ensemble interacts with the random Rashba field corresponding to its path. The spin precesses randomly and when an electron arrives at time t at the point //. its -component and the mean 2-polarization of the ensemble Sz(l) are given by ... 

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