2. COMPUTATIONAL METHODOLOGY
The methodology adopted in the present work to compute the rotational
and vibrational data is similar to that utilized for the spectral study
of Glutamic acid in our previous such work.33 The
conformers of biologically significant left-handed isomer
(L )-Leucine and its isomeric species being investigated in this
work are depicted in Figure 1. Note that the global minimum
(lowest-energy conformer) of Leucine (EQ0#) has been
verified through its structure optimization performed at different
levels of quantum-mechanical theory (for details, see Ref. 10). For the
present work, ab-initio Møller-Plesset 2ndorder (MP2) perturbation theory with frozen-core (fc) approximation as
well as density functional theory (DFT) are utilized to compute the
spectroscopic parameters.34-35 The rotational
constants computed for EQ0# at different levels of the
theory are provided in Table 1. These are also compared with the
available experimental gas-phase data from a study by Cocinero et
al.29 The computed rotational constants are found to
be in good agreement with experimental one. In particular, the
MP2/6-31+G(d,p) method using a Gaussian basis set, 6-31+G(d,p), resulted
in a more closer agreement with deviations less than 5 MHz compared to
MP2/6-311++G(d,p) method exhibiting deviations up to 7 MHz, as evident
in Table 1. This observation in the present work, thereby, improves upon
the previously known computational results of Cocinero et
al.,29 in their prediction of rotational parameters
through MP2/6-311++G(d,p) method which was used to assist their
experimental results.
Besides the aforementioned wave-function based MP2 method, the DFT
computations for rotational constants were also carried out. For this, a
conventional hybrid exchange correlational functional, B3LYP, is
employed along with a correlation consistent, cc-pVTZ and aug-cc-pVTZ,
basis set.37,38 Additionally, in view of various
non-covalent (dispersion) interactions in the branched structural
framework of Leucine, Grimme’s D3 dispersion correction has also been
employed along with a Becke-Johnson (BJ) damping function in the
computaions.39,40 It is quite evident from Table 1
that DFT/B3LYP-D3(BJ)/cc-pVTZ method gives more closer values (to the
experimental one) for rotational constants of global conformer, with
deviation of only 5 MHz than that computed using the
DFT/B3LYP-D3(BJ)/aug-cc-pVTZ method. Besides this, a recently proposed
SNSD basis set,41 constituted from the polarized
double-zeta (ζ) N07D basis set including the diffuse s-typefunctions on every atom and diffuse polarized (d-type ) functions
on heavy atoms as well as p-type on hydrogen atoms, is also
tested in besides the B3LYP-D3(BJ) method. However, though SNSD is known
to be quite accurate and cost-effective for spectroscopic calculations
but in the present work, it is observed to be less accurate than
B3LYP-D3(BJ)/cc-pVTZ method. Moreover, in the present work, DFT
calculations were also performed employing a recently recommended double
hybrid functional, B2PLYP-D3(BJ),42 however,
significant deviations of more than 10 MHz are observed using this
method as can be seen in Table 1. Thus, overall, B3LYP-D3(BJ)/cc-pVTZ is
observed to be the best DFT method although it is found to be relatively
less accurate than the wave-function based ab initioMP2/6-31+G(d,p) method as clearly evident in Table 1.
On the basis of aforementioned observations for the global conformer,
the rotational parameters of other isomeric species being investigated
in this work were computed using their optimized geometries at both the
aforementioned quantum-mechanical levels of theory, namely,
MP2/6-31+G(d,p) and DFT/B3LYP-D3(BJ)/cc-pVTZ. The optimized structures
were additionally validated through harmonic vibrational frequency
check. However, anharmonic frequency calculations are also
performed at the specified levels of the theory to accurately estimate
the vibrational frequencies beyond harmonic oscillator approximation,
which further provided other rotational parameters listed in Table 2,
for example, the Ray’s asymmetry parameter, quartic centrifugal
distortion constants, and nuclear quadrupole coupling constants. Note
that for these calculations, a quartic force field (QFF) is deployed for
the inter-nuclear potential in the ‘Watson’ Hamiltonian so as to account
for ro-vibrational interactions.9,21 Further, for the
computation of vibrational frequencies, the anharmonicity is estimated
at the level of the second order vibrational perturbation theory (VPT2)
which is basically rooted in the Rayleigh-Schrödinger perturbation
theory.43,44 Note that the inclusion of anharmonic
effects actually contribute towards an accurate estimation of both
vibrational and rotational parameters,21 by aiding the
evaluation of rotational constants associated with vibrationally
averaged ground state. Besides this, the anharmonic calculations also
provide the centrifugal distortion constants which are estimated
employing Watson’s A-reduced Hamiltonian in irreducible
(Ir) representation.45,46
In the present work, all the aforementioned quantum-mechanical
computations are performed using Gaussian 09
program.47 The rotational parameters computed at
MP2/6-31+G(d,p) level of the theory, as collected in Tables 2 and 3,
were further used for generating the rotational spectral line data and
simulating the rotational spectra through the PGOPHER
program,48 as depicted in Figure 2 as well as listed
in the Supporting Information (SI) Tables S1 and S2. Besides this, the
anharmonic vibrational spectroscopic data computed for the global
minimum conformer EQ0# is further compared in Table 4
with the experimental gas-phase values for Leucine available from
matrix-IR and fast thermal heating experiments.30,31As evident in Table 4, DFT/B3LYP-D3(BJ)/cc-pVTZ exhibits a closer
agreement with the experiment. Thus, this DFT method was employed for
computing the vibrational spectral data for all other species in the
complete IR region (from mid-IR to far-IR). Additionally, a VEDA4
program,49 has also been used to further characterize
each mode of vibration in terms of potential energy distribution (PED)
for all the conformers of Leucine and its isomeric species, as provided
in supporting information SI Table S3. It should be noted that in the
present work, these calculations are performed at a temperature of
298.15K, the effect of temperature on vibrational lines is not attempted
in this work. However, since the rotational intensities considerably
depend on the temperature, therefore, while simulating the rotational
spectra and generating the line-data through PGOPHER
program,45 a low temperature of 10 K is used in order
to assist the search of species in cold molecular clouds as elaborated
in the next section.
Table 1. Computed equilibrium rotational constants
(Ae, Be, Ce) for the
global minimum conformer of Leucine (EQ0#) at various
levels of quantum-mechanical (MP2 and DFT) methods. The respective
absolute deviations relative to the experimental values are listed in
parenthesis. The best estimated values are marked in bold, for details
see the text.