How Reliable Are Modern Density Functional Approximations to Simulate Vibrational Spectroscopies?

We
show that properties of molecules with low-frequency modes calculated
with density functional approximations (DFAs) suffer from spurious
oscillations along the nuclear displacement coordinate due to numerical
integration errors. Occasionally, the problem can be alleviated using
extensive integration grids that compromise the favorable cost-accuracy
ratio of DFAs. Since spurious oscillations are difficult to predict
or identify, DFAs are exposed to severe performance errors in IR and
Raman intensities and frequencies or vibrational contributions to
any molecular property. Using Fourier spectral analysis and digital
signal processing techniques, we identify and quantify the error due
to these oscillations for 45 widely used DFAs. LC-BLYP and BH&H
are revealed as the only functionals showing robustness against the
spurious oscillations of various energy, dipole moment, and polarizability
derivatives with respect to a nuclear displacement coordinate. Given
the ubiquitous nature of molecules with low-frequency modes, we warrant
caution in using modern DFAs to simulate vibrational spectroscopies.