On the performance of four-component relativistic density functional theory: Spectroscopic constants and dipole moments of the diatomics HX and XY (X,Y=F, Cl, Br, and I)

We have tested the performance of four-component relativistic density functional theory (DFT) by calculating spectroscopic constants $(re,$ $ωe,$ and $ωexe)$ and dipole moments $μ0$ in the vibrational ground state for a selected set of 14 molecules: the hydrogen halides HX, the dihalogens $X2,$ as well as the interhalogens XY (X,Y=F, Cl, Br, and I). These molecules have previously been studied by four-component relativistic wave function based methods by Visscher and co-workers [J. Chem. Phys. 108, 5177 (1998); 104, 9040 (1996); 105, 1987 (1996)]. We have used four different nonrelativistic functionals at the DZ and TZ basis set level. What is perhaps the most striking result of our study is the overall good performance of the local density approximation functional SVWN5; at the triple zeta basis set level it predicts bond lengths $re,$ harmonic frequencies $ωe,$ anharmonicities $ωexe,$ and dipole moments $μ0$ with relative errors of 0.46%, 0.39%, −16.3%, and −0.74%, respectively. The corresponding values for the B3LYP hybrid functional are 1.27%, −2.10%, −20.4%, and 4.71%. The two generalized gradient approximation functionals PW86 and BLYP show a less convincing performance, characterized by a systematic overestimation of bond lengths and underestimation of harmonic frequencies. We show that only the constant term is modified in second-order vibrational perturbation theory upon the inclusion of a linear term, corresponding to the choice of a nonstationary reference geometry. Upon shifting the reference geometry from the optimized to the experimental geometry the calculated harmonic frequencies are significantly improved, whereas the anharmonicities are basically unchanged. Dipole moments calculated at the experimental geometry at the B3LYP/TZ level appear to be remarkably accurate with a mean relative error of −1.1% and a standard deviation of less than 4%. Our study reveals that anharmonicities are quite sensitive to the numerical integration scheme employed in the DFT calculations, and for the interhalogens we had to modify the Becke partitioning scheme by using atomic adjustments along the lines of the atom in molecules approach of Bader.