Is tetrahedral H42+ a minimum? Anomalous behavior of popular basis sets with the standard p exponents on hydrogen

The nature of the tetrahedral H₄²⁺ stationary point (minimum or triply degenerate saddle) depends remarkably upon the theoretical level employed. Harmonic vibrational analyses with, e.g., the 6-31G** (and 6-31 + +G**) and Dunning's 4s2p1d;2s1p] D95(d,p)] basis sets using the standard p exponent suggest (erroneously) that the T_d geometry is a minimum at both the HF and MP2 levels. This is not the case at definitive higher levels. The C₃H₄²⁺ structure with an apical H is another example of the failure of the calculations with the 6-31G**, 6-311G**, and D95(d,p) basis sets. Even at MP2/6-31G** and MP2/ cc-pVDZ levels, the C_3v structure has no negative eigenvalues of the Hessian. Actually, this form is a second-order saddle point as shown by the MP2/6-31G** calculation with the optimized exponent. The D_4h methane dication structure is also an example of the misleading performance of the 6-31G** basis set. In all these cases, energy-optimized hydrogen p exponents give the correct results, i.e., those found with more extended treatments. Optimized values of the hydrogen polarization function exponents eliminate these defects in 6-31G** calculations. Species with higher coordinate hydrogens may also be calculated reliably by using more than one set of p functions on hydrogen e.g., the 6-31G(d,2p) basis set]. Not all cases are critical. A survey of examples, also including some boron compounds, provides calibration. © 1993 John Wiley & Sons, Inc.