GF Method - Relation With Eckart Conditions

Relation With Eckart Conditions

From the invariance of the internal coordinates St under overall rotation and translation of the molecule, follows the same for the linearized coordinates stA. 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.

See this article for more details.

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