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Text: Here, we propose a new method for the calculation of the average (scalar) polarizabilities of proteins based on their amino acid compositions, which utilizes the fact that objects with the same volume V and dielectric constant ɛ r have the same average polarizabilities α independent of shape, see also (1). The static dielectric constants are then calculated using the ClausiusÀ Mossotti relation. This method is computationally highly efficient and facilitated the calculations of the average polarizabilities and dielectric constants of all proteins in the protein **data** bank (PDB). [17] The average polarizability of a molecule can be calculated from the sum over hybridization configurations of the atoms in the molecule, [18] 
 a ¼ 4 N ð X A t A Þ 2 (2)
 with the number of electrons in the molecule N and the hybrid component τ A of each atom A, obtained by approximating the zeroth order wavefunction by an antisymmetrized product of molecular orbitals and spin functions. Average polarizabilities predicted by this method showed a very good agreement with experimental polarizabilities for more than 400 relatively small molecules with only~2 % error. Furthermore, since the atomic hybridizations of the atoms within the constituents amino acids do not change in proteins, (2) could be rearranged to obtain the average polarizability of a protein α p by summing over effective amino-acid hybrid components:
 a p ¼ 4 N p ð X aa t aa Þ 2(3)
 Here, N p is the number of electrons in the protein and τ aa are the hybridization components of amino acid aa, which are obtained as
 t aa ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi N aa a aa 2 p 2 (4)
 with the number of electrons N aa in an amino acid aa and its average polarizability α aa . The latter could be obtained from quantum-chemical calculations and, therefore, the values of τ not only include the summation of the atomic hybrid components within the amino acids, but also exchange correlation interactions at the level of quantum-chemistry employed. Furthermore, for (2) to be applicable for very polar compounds, τ A has to be modified to include the effect of the atoms to which A is bonded. However, τ aa already includes this effect since it reproduces the exact polarizabilities calculated from first principles.<|eot_id|><|start_header_id|>assistant<|end_header_id|>

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