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The simulations are performed with an interactive computer program package.

The Gaussian 03 program package was used [26].

Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package.

The structures were solved by the SIR97 program [83] incorporated within the WinGX program package [84].

The theoretical dispersion curve was calculated by using the DISPER80 program package (Saito 1988).

All calculations are performed using Gaussian 09 W [21] program package.

We used the TSEIS visualization program package (Tsuruoka 1996) for selection of datasets from the catalogs.

For this purpose, the program package NAMD[35] was employed with Charmm27 force field parameter set[36].

All crystallographic calculations including full-profile Rietveld refinement were performed by using WinCSD program package [14].

All the theoretical calculations were performed using Gaussian 03 program package [21].

a Phylogenetic trees were reconstructed by the neighbor-joining methods with the MEGA 5 program package.

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