Automated Fragmentation Polarizable Embedding Density Functional Theory (PE-DFT) Calculations of Nuclear Magnetic Resonance (NMR) Shielding Constants of Proteins with Application to Chemical Shift Predictions

Full-protein nuclear magnetic resonance (NMR) shielding constants based on <i>ab initio</i> calculations are desirable, because they can assist in elucidating protein structures from NMR experiments. In this work, we present NMR shielding constants computed using a new automated fragmentation (<i>J. Phys. Chem. B</i> <b>2009</b>, <i>113</i>, 10380–10388) approach in the framework of polarizable embedding density functional theory. We extend our previous work to give both basis set recommendations and comment on how large the quantum mechanical region should be to successfully compute <sup>13</sup>C NMR shielding constants that are comparable with experiment. The introduction of a probabilistic linear regression model allows us to substantially reduce the number of snapshots that are needed to make comparisons with experiment. This approach is further improved by augmenting snapshot selection with chemical shift predictions by which we can obtain a representative subset of snapshots that gives the smallest predicted error, compared to experiment. Finally, we use this subset of snapshots to calculate the NMR shielding constants at the PE-KT3/pcSseg-2 level of theory for all atoms in the protein GB3.