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.