The analytic evaluation of energy first derivatives for two-configuration self-consistent-field configuration interaction (TCSCF-CI) wave functions. Application to ozone and ethylene

An efficient formulation for the analytic evaluation of two-configuration self-consistent-field configuration interaction (TCSCF-CI) energy first derivatives is presented. Use is made of the Z-vector approach of Handy and Schaefer. The procedure outlined does not require the transformation of derivative integrals. We have applied the new procedure to the ground states of ozone and ethylene. For ozone, the (DZP) TCSCF-CI procedure yields a structure which is much improved relative to that obtained using a single-reference description. However, the incorrect ordering of the harmonic vibrational frequencies ω1(a1) and ω3(b2), which was first found using a TCSCF description of O3, remains at the TCSCF-CI level of theory. Anharmonic vibrational frequencies (utilizing TCSCF-CI harmonic frequencies and SCF anharmonic corrections) are reported for ethylene. With a DZP basis set, 11 of the 12 TCSCF-CI fundamental frequencies of C2H4 agree very well with experiment, the mean absolute error being 2.4%. However, the infrared inactive ν8=799 cm−1 is 15.0% below the accepted experimental value. The utilization of a TZ2P basis set resolves this discrepancy. The TZ2P TCSCF-CI ν8=922 cm−1 is 1.9% below experiment, and the average absolute error of all of the TZ2P fundamentals is only 2.6%.