We report a conventional ab initio and density functional theory study of the polarizability (alpha(alphabeta)/e(2)a(0)(2)E(h)(-1)) and hyperpolarizability (gamma(alphabetagammadelta)/e(4)a(0)(4)E(h)(-3)) of the sodium dimer. A large [18s14p9d2f1g] basis set is thought to yield near-Hartree-Fock values for both properties: (α) over bar =272.28, Deltaalpha=127.22 and (γ) over bar =2157.6x10(3) at R-e=3.078 87 Angstrom. Electron correlation has a remarkable effect on the Cartesian components of gamma(alphabetagammadelta). Our best value for the mean is (γ) over bar =1460.1x10(3). The (hyper)polarizability shows very strong bond-length dependence. The effect is drastically different for the longitudinal and transverse components of the hyperpolarizability. The following first derivatives were extracted from high-level coupled cluster calculations: (d(α) over bar /dR)(e) = 54.1, (dDeltaalpha/dR)(e)=88.1e(2)a(0)E(h)(-1), and (d(γ) over bar /dR)(e)=210x10(3)e(4)a(0)(3)E(h)(-3). We associate the (hyper)polarizability to bonding effects between the two sodium atoms by introducing the differential property per atom Q(diff)/2equivalent to{Q[Na-2(X (1)Sigma(g)(+))]/2-Q[Na(S-2)]}. The differential (hyper)polarizability per atom is predicted to be strongly negative for the dimer at R-e, as [(α) over bar (Na-2)/2-alpha(Na)]=-33.8 and [(γ) over bar (Na-2)/2-gamma(Na)]=-226.3x10(3). The properties calculated with the widely used B3LYP and B3PW91 density functional methods differ significantly. The B3PW91 results are in reasonable agreement with the conventional ab initio values. Last, we observe that low-level ab initio and density functional theory methods underestimate the dipole polarizability anisotropy. Experimental data on this important property are highly desirable. (C) 2004 American Institute of Physics.