Density-functional chemical shielding calculations are reported for the alanine dipeptide with a variety of backbone torsion angles and for methane and N-methylacetamide complexes with rare gases, monatomic ions, water, and other amides. These fragment systems model electrostatic, nonbonded, and hydrogen bonding interactions in proteins and have been investigated at a variety of geometries. The results are compared to empirical formulas that relate intermolecular shielding effects to peptide group magnetic anisotropies, electrostatic polarization of the C-H and N-H bonds, magnetic contributions from C-C and C-H bonds, and close contact effects. Close contacts are found to deshielded protons involved in close nonbonded contacts that typically occur in hydrogen bonds. "Lone pair" charges improve the model for electrostatic effects and are important for understanding the angular dependence of shifts for protons involved in hydrogen bonds. C-C and C-H bond anisotropy contributions help to explain the torsional dependence of amide proton shifts in alanine dipeptide. Good agreement is found between the empirical formulas and the quantum chemistry results, allowing a reassessment of empirical formulas that are used in the analysis of chemical shift dispersion in proteins.