GF Method - Relation With Eckart Conditions | Relation Eckart Conditions

Relation With Eckart Conditions

From the invariance of the internal coordinates S_t under overall rotation and translation of the molecule, follows the same for the linearized coordinates st_A. It can be shown that this implies that the following 6 conditions are satisfied by the internal coordinates,

$\sum_{A=1}^N \mathbf{s}^t_{A} = 0\quad\mathrm{and}\quad \sum_{A=1}^N \mathbf{R}^0_A\times \mathbf{s}^t_A= 0, \quad t=1,\ldots,3N-6.$

These conditions follow from the Eckart conditions that hold for the displacement vectors,

$\sum_{A=1}^N M_A\; \mathbf{d}_{A} = 0 \quad\mathrm{and}\quad \sum_{A=1}^N M_A\; \mathbf{R}^0_{A} \times \mathbf{d}_{A} = 0.$

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