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.