# 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)