09-14-2021-0338 - Rotational spectroscopy - The electric dipole moment of the dioxygen molecule, O2 is zero - microwave @ paramagnetic

Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The spectra of polarmolecules can be measured in absorption or emission by microwave spectroscopy^[1] or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as pure rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy (or just vibronic spectroscopy) where rotational, vibrational and electronic energy changes occur simultaneously.

For rotational spectroscopy, molecules are classified according to symmetry into spherical top, linear and symmetric top; analytical expressions can be derived for the rotational energy terms of these molecules. Analytical expressions can be derived for the fourth category, asymmetric top, for rotational levels up to J=3, but higher energy levels need to be determined using numerical methods. The rotational energies are derived theoretically by considering the molecules to be rigid rotors and then applying extra terms to account for centrifugal distortion, fine structure, hyperfine structure and Coriolis coupling. Fitting the spectra to the theoretical expressions gives numerical values of the angular moments of inertia from which very precise values of molecular bond lengths and angles can be derived in favorable cases. In the presence of an electrostatic field there is Stark splitting which allows molecular electric dipole moments to be determined.

An important application of rotational spectroscopy is in exploration of the chemical composition of the interstellar medium using radio telescopes.

Oxygen[edit]

The electric dipole moment of the dioxygen molecule, O2 is zero, but the molecule is paramagnetic with two unpaired electrons so that there are magnetic-dipole allowed transitions which can be observed by microwave spectroscopy. The unit electron spin has three spatial orientations with respect to the given molecular rotational angular momentum vector, K, so that each rotational level is split into three states, J = K + 1, K, and K - 1, each J state of this so-called p-type triplet arising from a different orientation of the spin with respect to the rotational motion of the molecule. The energy difference between successive J terms in any of these triplets is about 2 cm⁻¹ (60 GHz), with the single exception of J = 1←0 difference which is about 4 cm⁻¹. Selection rules for magnetic dipole transitions allow transitions between successive members of the triplet (ΔJ = ±1) so that for each value of the rotational angular momentum quantum number K there are two allowed transitions. The ¹⁶O nucleus has zero nuclear spin angular momentum, so that symmetry considerations demand that K have only odd values.^[22][23]

https://en.wikipedia.org/wiki/Rotational_spectroscopy