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Self-consistency based Kohn-Sham density functional theory (KS-DFT)electronic structure calculations with Gaussian basis sets are reported for aset of 17 protein-like molecules with geometries obtained from the protein databank. It is found that in many cases such calculations do not converge due tovanishing HOMO-LUMO gaps. A sequence of polyproline I helix molecules is alsostudied, and it is found that self-consistency calculations using purefunctionals fail to converge for helices longer than six proline units. Sincethe computed gap is strongly correlated to the fraction of Hartree-Fockexchange, test calculations using both pure and hybrid density functionals arereported. The tested methods include the pure functionals BLYP, PBE, and LDA,as well as Hartree-Fock and the hybrid functionals BHandHLYP, B3LYP, and PBE0.The effect of including solvent molecules in the calculations is studied, andit is found that the inclusion of explicit solvent molecules around the proteinfragment in many cases gives a larger gap, but that convergence problems due tovanishing gaps still occur in calculations with pure functionals. In order toachieve converged results, some modeling of the charge distribution of solventwater molecules outside the electronic structure calculation is needed.Representing solvent water molecules by a simple point charge distribution isfound to give non-vanishing HOMO-LUMO gaps for the tested protein-like systemsalso for pure functionals.

Difficulties in applying pure Kohn-Sham density functional theory electronic structure methods to protein molecules