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It has recently been argued that atoms and molecules may become good targetsof determining neutrino parameters still undetermined, if atomic/molecularprocess is enhanced by a new kind of coherence. We compute photon energyspectrum rate arising from coherent radiative neutrino pair emission processesof metastable excited states of I$_2$ and its iso-valent molecules, $|Av\rangle \rightarrow |Xv' \rangle + \gamma + \nu_i\nu_j$ and $|A'v \rangle\rightarrow |Xv' \rangle + \gamma + \nu_i\nu_j$ with $\gamma$ an IR photon and$\nu_{i(j)}$ $i(j)-$th neutrino mass eigenstates, and show how fundamentalneutrino parameters may be determined. Energies of electronically excitedstates of I$_2$, including the effect of spin-orbit couplings were calculatedby the multiconfigurational second order perturbation (CASPT2) method.Summation over many vibrational levels of intermediate states is fullyincorporated. Unlike atomic candidate of a much larger energy difference suchas Xe, I$_2$ transitions from a vibrational level $A(v=0)$ to $X(v' = 24)$ givean opportunity of determination of the mass type (Majorana vs Diracdistinction) and determination of Majorana CPV (charge-conjugation parityviolating) phases, although the rate is much smaller.

I$_{2}$ molecule for neutrino mass spectroscopy: ab initio calculation of spectral rate