Table 2. First and Second Derivatives of the Dipole and Polarizability Computed at Zero-Field for the Totally Symmetric Stretching and Bending Modes of the Molecules Investigated in this Worka.
| molecule | ν̅k (cm–1) | ωk (au) | fkkk (au) | ∂μx/∂qk (au) | ∂2μx/∂q2k (au) | ∂αxx/∂qk (au) | ∂2αxx/∂q2k (au) |
|---|---|---|---|---|---|---|---|
| H2O | 3853 | 1.755 × 10–2 | –1.910 × 10–5 | –1.605 × 10–3 | 6.151 × 10–5 | 0.117 | 1.150 × 10–3 |
| NH3 | 3497 | 1.593 × 10–2 | –1.189 × 10–5 | 1.505 × 10–3 | 3.793 × 10–5 | 0.104 | 0.137 × 10–3 |
| H2S | 2733 | 1.245 × 10–2 | –0.721 × 10–5 | 0.341 × 10–3 | 3.138 × 10–5 | 0.178 | 1.598 × 10–3 |
| HF | 4170 | 1.900 × 10–2 | –3.286 × 10–5 | –7.868 × 10–3 | 0.774 × 10–5 | 0.136 | 3.624 × 10–3 |
| H2O | 1659 | 7.561 × 10–3 | –7.778 × 10–7 | 6.423 × 10–3 | 6.859 × 10–5 | –2.150 × 10–2 | 1.658 × 10–3 |
| NH3 | 1067 | 4.862 × 10–3 | –9.755 × 10–7 | 8.739 × 10–3 | 15.62 × 10–5 | 2.120 × 10–2 | 1.599 × 10–3 |
| H2S | 1221 | 5.565 × 10–3 | –0.808 × 10–7 | –0.683 × 10–3 | –1.820 × 10–5 | –3.496 × 10–2 | 1.760 × 10–3 |
a
Results are from CCSD/aug-cc-pVTZ calculations and are reported in atomic units80 to ease the numerical evaluation of eq 2. The x-axis is oriented along the molecular dipole. The stretching modes are the first four lines; the bending modes are the last three lines. Since all the reported modes belong to the totally symmetric irreducible representation, the dipole derivatives are oriented along the symmetry axis of the molecules, which corresponds to the x-axis, i.e., (∂2μy/∂q2k)0 = (∂2μz/∂q2k)0 = 0. Further details about the calculation of these quantities are reported in the Supplementary Information.