Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde

Geometric energy
derivatives which rely on core-corrected focal-point
energies extrapolated to the complete basis set (CBS) limit of coupled
cluster theory with iterative and noniterative quadruple excitations,
CCSDTQ and CCSDT­(Q), are used as elements of molecular gradients and,
in the case of CCSDT­(Q), expansion coefficients of an anharmonic force
field. These gradients are used to determine the CCSDTQ/CBS and CCSDT­(Q)/CBS
equilibrium structure of the S0 ground
state of H2CO where excellent agreement is observed with
previous work and experimentally derived results. A fourth-order expansion
about this CCSDT­(Q)/CBS reference geometry using the same level of
theory produces an exceptional level of agreement to spectroscopically
observed vibrational band origins with a MAE of 0.57 cm–1. Second-order vibrational perturbation theory (VPT2) and variational
discrete variable representation (DVR) results are contrasted and
discussed. Vibration–rotation, anharmonicity, and centrifugal
distortion constants from the VPT2 analysis are reported and compared
to previous work. Additionally, an initial application of a sum-over-states
fourth-order vibrational perturbation theory (VPT4) formalism is employed
herein, utilizing quintic and sextic derivatives obtained with a recursive
algorithmic approach for response theory.