  The quartic force field of SO$_3$ was computed fully ab initio using coupled
cluster (CCSD(T)) methods and basis sets of up to $spdfgh$ quality. The effect
of inner-shell correlation was taken into account. The addition of tight $d$
functions is found to be essential for accurate geometries and harmonic
frequencies. The equilibrium geometry and vibrational fundamentals are
reproduced to within 0.0003 \AA and (on average) 1.15 cm^{-1}, respectively. We
recommend the following revised values for the harmonic frequencies: $\omega_1
= 1082.7, \omega_2 = 502.6, \omega_3 = 1415.4, \omega_4 = 534.0 cm^{-1}$. In
addition, we have shown that the addition of inner polarization functions to
second-row elements is highly desirable even with more approximate methods like
B3LYP, and greatly improves the quality of computed geometries and harmonic
frequencies of second-row compounds at negligible extra computational cost. For
larger such molecules, the B3LYP/VTZ+1 level of theory should be a very good
compromise between accuracy and computational cost.
