3.1 Rotational Analysis
There are basically two approaches to analyse the rotational spectra: ‘Bottom Up’ and ‘Top Down’. The first approach utilizes the computed rotational parameters to simulate the spectra whereas the other approach involves the estimation of rotational parameters from the observed rotational spectra. Quantum-mechanical calculations for computing rotational spectroscopic parameters had already manifested their proficiency in assisting the experimental investigations.50 In case of astronomical detection of molecular species, the quantum-mechanically computed rotational parameters are being utilized through different working strategies.51
A ‘Bottom Up’ approach is generally used if an experimental laboratory based rotational study on the molecular species is either not available or cannot be carried out. In such a case, the simulated rotational spectrum computed quantum-mechanically can be directly compared with the astronomical observations. This strategy becomes extremely important particularly in the case of charged and radical species because such species are difficult to detect due to their tendency to form stable terrestrial molecules by reacting with the similar reactive species. In fact, the astrophysical detection of C5N ion and C4H radical was entirely based on the quantum mechanical computations.52–54
On the contrary, in the ‘Top Down’ approach, a laboratory based experimental rotational study is an essential pre-requisite so as to fit the rotational spectra obtained from experiments with the simulated rotational spectrum from quantum calculations. The fitting will thus provide the experimental rotational parameters which can be used to assist the astronomical observations. This is the most conventional approach to detect cosmic species in a definitive manner. The recent detection of first disilicon molecule, SiCSi, in the ISM is the outcome of this kind of synergic working module between astronomical observatories, laboratory experiments, and quantum mechanical computations.55,56
However, the present study employs an additional strategy for improving the computed rotational parameters. In this approach, the computed rotational parameters, particularly the rotational constants, are appropriately scaled for the species for which no experimental data is available. For this, a scaling factor is determined using the experimentally known rotational parameters of a similar reference species studied in the literature.57 This strategy is in fact parallel to the ‘Bottom Up’ approach but employing scaled and more accurate rotational parameters. In the present work, the gas-phase experimental rotational data is available for global minimum conformer EQ0# of Leucine, thereby acting as the reference molecular species. The experimental rotational constants of this reference species was then used to determine a suitable scaling factor to evaluate the rotational constants of other conformers of Leucine and isomeric species for which no experimental rotational data is available. The scaled rotational constants so obtained were further used to simulate the rotational spectra in rotational frequency region of interest as discussed below.
As analysed in the previous section, MP2/6-31+G(d,p) was found to be the optimal method for rotational calculations. For the global conformer EQ0#, the spectrum simulated using the computed rotational constants is compared with that simulated using experimental rotational constants in Figure 2. Note that only ‘R’ branch transitions (following the selection rule ΔJ = +1, in terms of principal rotational quantum number J ) are considered because of their much higher intensity compared to ‘Q’ branch (ΔJ = 0) and ‘P’ branch (ΔJ = −1) transitions. For simplicity, the spectrum has been simulated in the lower frequency range of 4000 MHz to 20000 MHz, as applicable to the laboratory observations,29 while limiting the value of principal rotational number to J = 5. A detailed comparison of rotational line data predicted from the computed parameters with those from the experimental parameters29 is further provided in SI Table S1. Nevertheless, from Figure 2, it is apparent that both the spectra follow the same pattern of rotational transitions. A closer observation, however, indicates some deviation in the position of rotational lines which can be as small as 8 MHz involving lower rotational states, for example, J (2 1) transition. The deviation, however, continuously increases with higher rotational states. Further, the transitions corresponding to the lower value of rotational quantum numbers correspond to the low frequency region. However, the telescopic observations of rotational transitions are generally studied in higher frequency region than the frequency range involved in laboratory studies.13 The deviation in the rotational line location may increase even more for higher frequency regions as can be observed from SI Table S1. Moreover, a notable difference of 65 MHz (as evident in SI Table S1) is not acceptable if a direct comparison with the telescopic observations is required. Therefore, in the present work, a scaling factor becomes inevitable. The procedure adopted for obtaining the scaling factors is similar to the one employed in our previous study on Glutamic acid.33 In the present work, the ratio of experimental (exp) and computed rotational constants of global conformer EQ0# act as scaling factors, thus, 0.999 (Aexp/Ae), 0.996 (Bexp/Be), 0.994 (Cexp/Ce) are the scaling factor used for the rotational constants A, B and C, respectively. The scaled rotational constants calculated for all the species are further listed in Table 3.