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

The nature of the tetrahedral H 4 2+ 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 [4 s 2 p 1 d ;2 s 1 p ] [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 C 3 H 4 2+ 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‐ p VDZ levels, the C 3 v 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 4 h 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 ,2 p ) basis set]. Not all cases are critical. A survey of examples, also including some boron compounds, provides calibration.