Step 1: Recalling dipole moment fundamentals.
Dipole moment μ = q · r, contingent upon charge separation magnitude and molecular shape.
Step 2: Impact of molecular geometry.
H₂O possesses a bent configuration, causing bond dipoles to vectorially add rather than cancel, yielding a substantial net dipole moment.
Step 3: Evaluating symmetry.
BeF₂ is linear, so its bond dipoles oppose and negate each other, resulting in μ = 0.
Step 4: Considering NH₃.
NH₃ adopts a trigonal pyramidal shape with a net dipole, though smaller than that of water.
Step 5: Considering CH₄.
CH₄ exhibits tetrahedral symmetry where bond dipoles cancel completely, giving μ = 0.
Step 6: Final deduction.
Hence, among these molecules, H₂O has the highest dipole moment.