Approximate Force Constants from Uncoupled Self-Consistent Field Perturbation Theory Using Nonhybrid Density Functional Theory

Second derivatives of the molecular energy with respect
to the
nuclear coordinates (the nuclear Hessian or force constant matrix)
are important for predicting infrared and Raman spectra, for calculating
thermodynamic properties, for characterizing stationary states, and
for guiding geometry optimization. However, their calculation for
larger systems scales with molecular size one power higher than the
calculation of the energy and the forces. The step responsible for the steep scaling of the nuclear
Hessian is the coupled-perturbed self-consistent field (CP-SCF) iteration.
This is omitted in the uncoupled SCF (UC-SCF) approximation. We have
found that, though UC-SCF performs rather poorly at the Hartree–Fock
and hybrid DFT levels, its performance for “pure” (non-hybrid)
DFT is remarkably good. This is valid also for imaginary frequencies
that characterize transition states. UC-SCF vibrational frequencies
and normal modes are compared with coupled calculations for various
exchange–correlation functionals including Hartree–Fock,
and with basis sets ranging from simple to large for a variety of
organic and some organometallic molecules. Their unexpectedly good
performance makes them good candidates for calculating thermodynamic
properties and for guiding difficult geometry optimizations, including
the determination of transition states.