Spectroscopic-network-assisted Precision Spectroscopy And Its Application To Water: Theoretical Framework

Using the NICE-OHMS (noise-immune-cavity-enhanced optical-heterodyne-molecular spectroscopy) technique, a large number of rovibrational transitions have been observed in the 7000-7350 \wn\ window for \chem{H_2^{16}O} [Nat. Commun. 2020, 11, 1708.] and \chem{H_2^{18}O} [in preparation], at the kHz-accuracy level. This talk focuses on the theoretical methods that were applied in the design of high-precision NICE-OHMS experiments and the extraction of accurate spectroscopic information from the measured lines. In spectroscopic networks (SN), the vertices and edges are the energy levels and the transitions, respectively. We used the SNAPS (spectroscopic-network-assisted precision spectroscopy) method [Nat. Commun. 2020, 11, 1708.] to select the target lines for measurement and provide initial line positions. The internal consistency of the ultraprecise experimental transitions was verified using cycles of the SN, while paths allow to extract high-accuracy energy levels and derive benchmark-quality predicted lines. The SN of \chem{H_2^{16}O} and \chem{H_2^{18}O} consists of four subcomponents, corresponding to the \textit{ortho} and \textit{para} nuclear-spin isomers combined with even and odd parity. For a given nuclear-spin isomer, the levels with even and odd parity are not connected by the vibrational measurements, their connectivity relies on the inclusion of purely rotational transitions. No transitions connecting the \textit{ortho} and \textit{para} states have been observed. Thus, the \textit{ortho} and \textit{para} components of the SNs are not connected, and the energy of the \textit{ortho} states is known only relative to the lowest \textit{ortho} state and not to the \textit{para} ground state. The energy of the lowest \textit{ortho} state was determined in two ways: 1) an effective-Hamiltonian fit to a set of energy differences (taken from the literature and calculated from NICE-OHMS lines) within the ground vibrational band; 2) a network-based approach: paths of NICE-OHMS transitions augmented with diminishing \textit{ortho-para} energy splittings obtained from first-principles quantum-chemical computations. Notably the quantum-chemical computations resulted in highly accurate splittings without the consideration of any experimental data