Molecular Properties¶
\(n^{th}\) derivative with regard to:
- Change in geometry (\(R\))
- External electric field (\(F\))
- External magnetic field (\(B\))
- Nuclear magnetic field (\(I\))
Gives us:
| \(n_R\) | \(n_F\) | \(n_B\) | \(n_I\) | Property |
|---|---|---|---|---|
| 1 | 0 | 0 | 0 | Energy gradient (\(g\)) |
| 2 | 0 | 0 | 0 | Harmonic vibrational frequencies (\(\omega_i\)) |
| 3 | 0 | 0 | 0 | (Cubic) anharmonic corrections to vibrational frequencies (\(\omega_ix_i\)) |
| 0 | 1 | 0 | 0 | Electric dipole moment (\(\mu\)) |
| 0 | 2 | 0 | 0 | Electric polarisability (\(\alpha\)) |
| 0 | 3 | 0 | 0 | (First electric) hyperpolarisability (\(\beta\)) |
| 0 | 0 | 1 | 0 | Magnetic dipole moment (\(\mu\)) |
| 0 | 0 | 2 | 0 | Magnetic susceptibility (\(\chi\)) |
| 0 | 0 | 0 | 1 | ESR hyperfine coupling constant \(a_i\) |
| 0 | 0 | 0 | 2 | Spin-spin coupling (\(J_{ij}\)) of different nuclei |
| 1 | 1 | 0 | 0 | Intensities of fundamental IR transitions |
| 2 | 1 | 0 | 0 | Intensities of overtones and combination bands in IR spectra |
| 1 | 2 | 0 | 0 | Intensities of fundamental Raman transiitions |
| 2 | 2 | 0 | 0 | Intensities of overtones and combination bands in Raman spectra |
| 0 | 1 | 1 | 0 | Circular dichroism (CD) |
| 0 | 2 | 1 | 0 | Magnetic circular dichroism (MCD) |
| 0 | 0 | 1 | 1 | Nuclear magnetic shielding (chemical shift in NMR) |