Energy embedding algorithm

Based on the RIS Ansatz, the embedding algorithm benefits from a great flexibility in the choice of the input parameters that account for the local chain energy configuration the input for the correlations of torsion angles along the chain backbones can be either calculated with the help of a force field, or extracted from measurements, or even biased in order to study any thinkable structural properties of the macromolecules. 

As a hypothetical case, consider the situation when all the watermarking information are known for the watermark embedding process. Then for each lc-region, some cut-off c is selected in step 2c of Algorithm 1. It is the best to take fc = c for that lc-region. In that case, the energy difference created in that lc-region will be vanished. 

Finally, algorithms have been developed which incorporate electron correlation effects explicitly in wave function based band theory for crystalline solids [16, 17]. These algorithms construct the many-electron Hamiltonian matrix for a periodic system by extracting the matrix elements from calculations on finite embedded clusters. In this way the incorporation of correlation effects leads to many-electron energy bands, not only associated with hole states and added-electron states but also with excited states. More recently, Pisani and co-workers [18] introduced a post-Hartree-Fock program based on periodic local second order Mpller-Plesset perturbation theory. 

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