In this project, we examined the reliability of various density functional theory methods for the prediction of spectroscopic properties of several diatomic molecules (BF, CO, N₂, CH⁺, NO⁺, and H₂). The specific spectroscopic constants examined were: bond length (r_e), rotational constant (B_e), harmonic vibrational frequency (w_e), vibrational anharmonicity (w_ex_e), centrifugal distortion constant (D_e), and vibration-rotation interaction constant (alpha_e). This work is the first systematic examination of the reliability of DFT for higher-order (anharmonic) constants of ground states comparing several different density functionals with several different basis sets to experiment and to higher-level (coupled-cluster) theory. Likewise, we also presented the first systematic examination of the reliability of time-dependent density functional theory (TD-DFT) for equilibrium properties of excited electronic states, and the first examination of the reliability of quantum chemistry predictions of anharmonic constants for excited states.

For ground states, density functional theory was found to give reliable predictions of the spectroscopic constants, including those depending on anharmonic terms in the potential energy function. Although not as accurate as highly sophisticated multi-reference configuration interaction methods, DFT predictions are frequently as good or better than the more expensive coupled-cluster singles and doubles (CCSD) results and often are competitive with the more accurate CCSD(T) method. Of the density functionals considered, S-VWN is worst and B3LYP is best. Using anharmonic corrections, DFT is capable of providing very accurate predictions of vibrationally averaged rotational constants (B₀) and fundamental vibrational frequencies (nu) which are more relevant to experimental measurements than the equilibrium constants (B_e) or harmonic frequencies (w_e).

For excited states, we considered the low-lying valence states (usually the lowest excited singlet state) for the molecules above. TD-DFT gives fairly good predictions of adiabatic excitation energies, with most errors within about 0.3 eV for the cases considered. This compares very favorably with about 0.2 eV for the more elaborate EOM-CCSD method. (See fig. 1 for a comparison of methods using the aug-cc-pVTZ basis set).

Predictions of equilibrium properties are not as accurate for excited states as for ground states, as shown in figures 2-4. The errors for equilibrium bond lenghts (fig. 2) and vibration-rotation interaction constants (not shown) are almost twice as large as for ground electronic states with the same theoretical methods.

Errors in predicted harmonic vibrational frequencies (fig. 3) and the centrifugal distortion constants (not shown) are almost the same for both ground and excited states.

Errors in the vibrational anharmonicity (w_ex_e) are about 50% worse than for ground states, as shown in fig. 4. Nevertheless, because the vibrational anharmonicity is so small and because it is predicted so accurately for the ground state, predictions of excited state vibrational anharmonic constants are sufficiently accurate to obtain good estimates of the differences between harmonic and fundamental vibrational frequencies.