The ribose and deoxyribose molecules of RNA and DNA nucleosides are substituted with simple model compounds 1-methoxy-2-ethanol and 1-methoxypropane to mimic the effect of binding to sugars on the vertical excitation energies of purine and pyrimidine bases. The (R)-1-methoxy-2-ethanol, CH3OC*HCH2OH, for model ribose nucleosides and (R)-1-methoxypropane, CH3OC*HC2H5, for model deoxyribose nucleosides have minimal structural characteristics of ribose and deoxyribose molecules when attached to nucleic acid purine and pyrimidine bases. The bases are attached to the C1 carbon atom designated by the asterisk. The vertical excitation energies of these model nucleosides are calculated with the time-dependent density functional theory method at the B3LYP level with 6-311++G(d,p) and aug-cc-pVDZ basis sets. The attachment of the ether molecules qualitatively and quantitatively modifies the excited state energy levels of the model nucleosides when compared to the free bases. These changes can affect the deexcitation mechanisms for photoexcited nucleosides.