Note on the Calculation of Analytical Hessians in the Zeroth-Order Regular Approximation (ZORA)

The previously proposed atomic zeroth-order regular approximation (ZORA) approch, which was shown to eliminate the gauge dependent effect on gradients and to be remarkably accurate for geometry optimization, is tested for the calculation of analytical second derivatives. It is shown that the resulting analytic second derivatives are indeed exact within this approximation. The method proves to yield frequencies that are remarkably close to the experimental frequency for uranium hexafluoride but less satisfactory for the gold dimer.