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README.md

@@ -151,6 +151,7 @@ where __P<sub>k</sub>__ is the momentum for the __k__ th nuclear degrees of free
 One can always, set __V<sub>0</sub>(\{R<sub>k</sub>})__ = 0, and instead redefine __V<sub>ij</sub>(\{R<sub>k</sub>}) ⟶ V<sub>ij</sub>(\{R<sub>k</sub>}) + V<sub>0</sub>(\{R<sub>k</sub>})δ<sub>ij</sub>__ and they should be equivalent in principle. However, some of the semiclassical approaches (**pldm-sampled**, **sqc-square** and **sqc-triangle**) produce results that depend on how one separates the state-independent and state-dependent parts of the gradient of the electronic Hamiltonian. This is because, this separation provides state dependent and independent gradients : __∇<sub>k</sub>V<sub>0</sub>(\{R<sub>k</sub>})__  and __∇<sub>k</sub>V<sub>ij</sub>(\{R<sub>k</sub>})__ which will provide different forces on nuclear particle for different choices of separations in some of these approximate quantum dynamics approaches. The nuclear forces computed in all of these approaches assumes this general form:
 
 ![Hm](eqns/Force.svg)
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 where Λ<sub>ij</sub> vaguely resembles the electornic density matrix elements. For example, in MFE, Λ<sub>ij</sub> = c<sub>i</sub>*c<sub>j</sub>.  For methods that have ∑<sub>i</sub>Λ<sub>ii</sub> = 1 (like MFE) for individual trajectories this separation of state-dependent and independent does not matter. For other's as I said before, it does. In my experience, the more you can put in the independent part the better. 
 
 When such separation is not aparent, one can separate state-independent and state-dependent parts in the following manner. Consider the following molecular Hamiltonian with no aparent state-independent part of the electronic Hamiltonian: