Higher analytic derivatives. I. A new implementation for the third derivative of the SCF energy

This is the first of a series of papers on the ab initio calculation of the second, third, and fourth derivatives of the energy with respect to nuclear coordinates. The knowledge of these derivatives yields anharmonic spectroscopic constants. Here, we present efficient formulae for the analytic evaluation of these derivatives for closed‐shell SCF wave functions. We discuss our implementation of the third derivative formula, in particular the integral and vectorization procedures. Applications are reported for H 2 S, CHOF, and HCCF.