The average OH stretching vibrational frequency for the water molecules in the first hydration shell around a Li+ ion in a dilute aqueous solution was calculated by a hybrid molecular dynamics + quantum-mechanical ("MD + QM") approach. Using geometry configurations from a series of snapshots from an MD simulation, the anharmonic, uncoupled OH stretching frequencies were calculated for 100 first-shell OH oscillators at the B3LYP and HF/6-31G(d,p) levels of theory, explicitly including the first shell and the relevant second shell water molecules into charge-embedded supermolecular QM calculations. Infrared intensity-weighting of the density-of-states (DOS) distributions by means of the squared dipole moment derivatives (which vary by a factor of 20 over the OH stretching frequency band at the B3LYP level), changes the downshift from approximately -205 to -275 cm(-1) at the B3LYP level. Explicit inclusion of relevant third-shell water molecules in the supermolecular cluster leads to a further downshift by approximately -30 cm-1. Our final estimated average downshift is approximately -305 cm-1. The experimental value lies somewhere in the range between - 290 and -420 cm-1. Also, the absolute nu(OH) frequency is well reproduced in our calculations. "In-liquid" instantaneous correlation curves between nu(OH) and various typical H-bond strength parameters such as R((OO)-O-...), R((HO)-O-...), the intramolecular OH bond length, and the IR intensity are presented. Some of these correlations are robust and persist also for the rather distorted instantaneous geometries in the liquid; others are less so.